RSS-based WLAN Indoor Positioning and Tracking System Using Compressive Sensing and Its Implementation on Mobile Devices.

Transcription

1 RSS-based WLAN Indoor Positioning and Tracking System Using Compressive Sensing and Its Implementation on Mobile Devices by Anthea Wain Sy Au A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto Copyright c 2010 by Anthea Wain Sy Au

2 Abstract RSS-based WLAN Indoor Positioning and Tracking System Using Compressive Sensing and Its Implementation on Mobile Devices Anthea Wain Sy Au Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto 2010 As the demand of indoor Location-Based Services (LBSs) increases, there is a growing interest in developing an accurate indoor positioning and tracking system on mobile devices. The core location determination problem can be reformulated as a sparse natured problem and thus can be solved by applying the Compressive Sensing (CS) theory. This thesis proposes a compact received signal strength (RSS) based real-time indoor positioning and tracking systems using CS theory that can be implemented on personal digital assistants (PDAs) and smartphones, which are both limited in processing power and memory compared to laptops. The proposed tracking system, together with a simple navigation module is implemented on Windows Mobile-operated smart devices and their performance in different experimental sites are evaluated. Experimental results show that the proposed system is a lightweight real-time algorithm that performs better than other traditional fingerprinting methods in terms of accuracy under constraints of limited processing and memory resources. ii

3 Acknowledgements I would like to express my sincere gratitude to my supervisor, Professor Shahrokh Valaee, whose knowledge, guidance and support have make this work possible. I would also like to thank Professor Moshe Eizenman, who gives valuable opinions to improve this work. I owe my special thanks to Chen Feng, whom I have been working with regarding to this project. In addition, I would like to thank my colleagues at the Wireless and Internet Research Laboratory (WirLab). I am grateful for the Natural Sciences and Engineering Research Council of Canada (NSERC) for its generous financial support. Finally, I would give my regard to my parents and my sister for their strong moral supports and encouragement. iii

4 Contents 1 Introduction Motivation RSS-based WLAN Positioning Systems Location-Sensing Techniques Existing Positioning Systems Problem Statement and Objectives Technical Challenges Scope Contributions Background and Related Works Indoor RSS-based WLAN Positioning Techniques Signal Propagation Modeling Location Fingerprinting Fingerprinting-Based Positioning Methods K-Nearest Neighbour Method (KNN) Probabilistic Approach Region of Interest and Access Points Selections Indoor Tracking Kalman filter iv

5 2.3.2 Particle filter Other Methods Pedestrian Navigation Affinity Propagation Algorithm For Clustering Compressive Sensing Theory Chapter Summary Compressive Sensing Based Positioning System Indoor Positioning System Overview Offline Phase Fingerprint Collections Clusters Generation by Affinity Propagation Interaction between the database server and the mobile device during offline phase Online Phase Coarse Localization Stage: Cluster Matching Fine Localization Stage: Compressive Sensing Recovery Interaction between the database server and the mobile device during online phase Chapter Summary Indoor Tracking System General Bayesian Tracking Model Kalman Filter Overview of Proposed Indoor Tracking System Modified Coarse Localization Stage Map-Adaptive Kalman Filter Chapter Summary v

6 5 Simple Navigation System Overview of Navigation System Map Database Generation at Initial Setup Layout Definition Map Features Definition Path Routing Module Path Analysis Tracking Update Analysis Module Analysis Process Voice Generation Chapter Summary Software Implementation on Mobile Devices Software Platform Devices in Testing Software Design Software s Functionalities Resources Folder Libraries Definitions Chapter Summary Experimental Results Experimental Setup Experimental Sites Performance Benchmarks Figure of Merit Positioning Results on Bahen Fourth Floor RSS Distributions vi

7 7.2.2 Offline Phase: Clustering Results by Affinity Propagation Online Phase: Coarse Localization Analysis Online Phase: Fine Localization Analysis Performance Comparison Tracking Results on CNIB Second Floor RSS Distributions CS-based Positioning Results Modified Coarse Localization Analysis Map Adaptive Kalman Filter Analysis Performance Comparison Navigation and Real Time Implementations Subject Testing Chapter Summary Conclusion Future Works Bibliography 113 vii

8 List of Tables 1.1 Existing RSS-based WLAN Position Systems [1] Comparison of a PDA and a laptop Devices Specifications Comparison of experimental sites Traces Summary Actual parameters γ (o) used for experiments on Bahen fourth floor A set of optimal parameters for the CS-based position system applied on Bahen fourth floor Position error statistics for different methods on Bahen fourth floor. (For validation set) Position error statistics for different methods on Bahen fourth floor. (For stationary user testing set) A set of optimal parameters for the CS-based position system applied on CNIB second floor Positioning error statistics for different positioning methods on CNIB second floor. (For mobile user testing set) A set of optimal parameters for the proposed tracking system applied on CNIB second floor viii

9 7.10 Position error statistics for the CS-based positioning system and the two tracking systems on CNIB second floor. (For mobile user testing set) Summary of the three traces tested by the subjects Subjects testing results on CNIB second floor ix

10 List of Figures 1.1 The problem setup Kernel-based method [2] Block diagram of the proposed indoor localization system Interaction between the database server and the mobile device during offline phase Interaction between the database server and the mobile device during online phase Block diagram of the proposed indoor tracking system Coarse localization stage for the proposed tracking system Map-Adoptive Kalman Filter Navigation System Overview Dijkstra Algorithm Tracking update analysis A point in close range to a line segment Determining the direction of turn based on the two line segments l i and l i The overview of the software design. Arrows shows the dependency of the libraries and blue colored boxes are the developed modules for the software An example screenshot of Detect AP operation x

11 7.1 Example histograms of RSS distributions of the same access point over 50 time samples for different devices pointing North at the same reference point on Bahen fourth floor An example of RSS measurements over time and their averages with respect to the number of time samples of the same access point for different devices at the same reference point on Bahen fourth floor An example of averaged RSS of the same access point in spatial domain for different orientations and different devices on Bahen fourth floor Number of clusters generated by the affinity propagation algorithm depending on the value of parameter γ (o) for four orientations on Bahen fourth floor The clustering results on the four fingerprint databases collected by PDA1 on Bahen fourth floor. Each circle is a RP collected in the database and each color represents one cluster The ARMSE versus number of used APs, when different number of generated clusters are used for the coarse localization on Bahen fourth floor The cumulative error distributions using different number of clusters for the coarse localization on Bahen fourth floor. (8 APs are used) The cumulative error distributions using different cluster matching schemes on Bahen fourth floor. (8 APs are used) The ARMSE versus number of used APs, using different AP schemes for fine localization on Bahen fourth floor Effect of the threshold λ 1 on ARMSE on Bahen fourth floor. (8 APs are used) The cumulative error distributions using different positioning systems on Bahen fourth floor. (8 APs are used) xi

12 7.12 Comparison of mean computation time using different positioning systems in Bahen fourth floor. (8 APs are used) Example histograms of RSS distributions of the same access point over 50 time samples (40 time samples for Smartphone) for different devices at the same reference point in CNIB second floor An example of RSS distributions across time and their averages with respect to the number of time samples of the same access point for different devices at the same reference point in CNIB second floor An example of RSS distributions of the same access point in spatial domain for different orientations and different devices in CNIB second floor. (only a part of the fingerprints are shown) The clustering results on the four fingerprint databases collected by PDA2 on CNIB second floor The cumulative error distributions for different positioning systems on CNIB second floor. (10 APs are used) Effect of the walking distance β on ARMSE in CNIB second floor. (10 APs are used) The cumulative error distributions using different Kalman filter parameters in CNIB second floor. (10 APs are used) The cumulative error distributions for different Kalman filter update schemes in CNIB second floor. (10 APs are used) The cumulative error distributions using the CS-based positioning system and the three tracking systems in CNIB second floor. (10 APs are used) Example trace results. The black line is the actual trace, the green dots are the CS-based positioning results and the purple line is the results of the proposed tracking system xii

13 7.23 The definition of the connected graph and the map features on CNIB second floor. The blue lines and blue circles represent the edges and nodes of the connected graph. The red squares represents the destinations. The diamonds represents the map features and the pink circles represents the locations of the 15 deployed access points Example screenshot of the software that shows the actual track that the user is walking. The line shows the routed path generated by the navigation module. The squares denote the user s locations and the circle denotes the destination xiii

14 Chapter 1 Introduction 1.1 Motivation With the wide deployment of the mobile wireless systems and networks, the locationbased services (LBSs) are made possible on mobile devices, such as laptops, smartphones and personal digital assistants (PDAs). There are a lot of applications that rely on the locations of these mobile devices, such as navigation, people and assets tracking, locationbased security and coordination of emergency and maintenance responses to accidents, interruptions of essential services and disasters, etc [3 5]. In order to deliver reliable LBSs, real-time and accurate user s locations must be obtained. Hence, there is a growing interest in developing effective positioning and tracking systems. For the outdoor environment, Global Positioning System (GPS) and cellular network based systems [3,6,7] are commonly used as the techniques to provide navigation services. However, these techniques cannot be used directly in indoors, as the signals are usually too weak to be used for localization purposes. Thus, wireless indoor positioning has become an increasingly popular research topic in recent years. There are several methods that are built on top of the GPS-capable phones to provide indoor localization [8]. One example is the Assisted GPS (A-GPS), which requires a 1

15 Chapter 1. Introduction 2 connection to a network location server in order to obtain the estimated location with an average of 5-50m accuracy [8]. Another one is the Calibree proposed in [9], which utilizes the detected signal strength from GSM cell towers to determine relative positions of mobile phones and their absolute locations can be determined if some of the phones are equipped with GPS receivers. In addition, indoor localization can also be implemented on GSM mobile phones [10] and CDMA mobile phones [11] through the use of wide signal-strength fingerprints. The median errors of these cellular-based system are around 4-5m. Although these methods are able to provide moderately accurate position estimate in indoors, their accuracies may not be enough to provide reliable LBSs and also they are only applicable to mobile phones. Besides the use of GPS and cellular network, different types of wireless technologies and sensors are also employed for the indoor positioning. In particular, positioning systems using ultra-wide band (UWB) signals, infrared, radio frequency (RF), proximity sensors and ultrasound systems [1, 8, 12] are able to localize users with high accuracies. However, these systems require the installation of additional infrastructures and sensors, which lead to high budget and labour cost and preventing them from having large-scale deployments. Due to the wide deployment of wireless local area network (WLAN), which is specifically referred to as the IEEE b/g standard in this thesis, there are many indoor positioning systems that make use of WLAN for estimating user s position. Time of arrival (TOA) [13] and time difference of arrival (TDOA) [1,14] are two techniques that can be used for localization, but they require extra configuration and setup to provide valid measurements. Thus, received signal strength (RSS) is the feature metric used for the WLAN positioning systems, as it can be obtained directly from existing WLAN access points (APs) by any device that is equipped with a WLAN network adapter. This thesis presents an accurate RSS-based WLAN positioning and tracking system that can be implemented on mobile devices with limited resources. The affinity propa-

16 Chapter 1. Introduction 3 gation algorithm for clustering data points [15] and the compressive sensing theory for recovery of the sparse and incoherently sampled signals [16] are two concepts applied on the proposed system. 1.2 RSS-based WLAN Positioning Systems The WLAN IEEE b/g is a standard used for providing wireless internet access for indoor areas. It is operated at 2.4 GHz Industrial, Scientific and Medical (ISM) band within a range of m. As mentioned earlier, the RSS can be easily obtained by using any WLAN-integrated device, thus it is used by most of the WLAN positioning systems Location-Sensing Techniques There are three major techniques to obtain the location estimate from the RSS [8, 17]. They are listed as follows: 1. Triangulation: The RSS can be translated into distance from the particular AP according to a theoretical or empirical signal propagation model. Then, with distance measurements from at least 3 APs with known positions, lateration can be performed to estimate the locations. This approach does not give accurate estimate, as the indoor radio propagation channel is highly unpredictable and thus the use of the propagation model is not reliable. 2. Proximity: This method finds the strongest RSS from a specific AP and determines the location to be the region covered by this AP. This method only gives a very rough position estimate but it is easy to be implemented. 3. Scene Analysis: This method first collects RSS readings at known positions, which are referred to as fingerprints, in the area of interest. Then, it estimates the loca-

17 Chapter 1. Introduction 4 tions by comparing the online measurements with the fingerprints through pattern recognition techniques. This method is used by most WLAN positioning systems, as it is able to compute accurate location estimates. This is the approach used by the positioning and tracking system proposed in this thesis Existing Positioning Systems Table 1.1 summarizes some of the existing WLAN positioning systems that can be accessible to the public. It shows that the use of fingerprinting achieves the best accuracy in indoor areas. Although the Ekahau [18] attains the best accuracy, it uses the the probabilistic method to compute the estimated positions and thus requires a more comprehensive survey of RSS readings in the region of interest. In addition, its position calculation is computed at the server as the complexity of the probabilistic method is too high to be performed on the mobile devices. This raises additional issues when using this systems. First, the devices must be connected to the same network as the server to obtain position estimates. Second, positions obtained from the server must be encrypted before it is transmitted to the mobile devices, in order to protect the privacy of the users. The aim of this thesis is to design an indoor positioning and tracking system that can provide accurate position estimate with relatively low computational complexity, so that it can be computed on mobile devices. This solution may have a database server to keep track of the fingerprints database collected, but once downloaded to the devices, they are no longer required to be connected to the server to obtain position estimates. This system is more flexible and has no privacy concerns to the users. 1.3 Problem Statement and Objectives A typical WLAN indoor tracking scenario as illustrated in Fig. 1.1 consists of 1) a mobile device equipped with a WLAN adapter, which is carried by a user and collects

18 Chapter 1. Introduction 5 Microsoft Research Ekahau [18] Inter Place Lab and RADAR [19, 20] Skyhook s WPS [21] Range Building/local area Building/local area Metropolitan area Position Mobile device Server (Ekahau Posi- Mobile device Calculation tioning Engine) Position Fingerprinting + Fingerprinting + Map-based pinpoint- Method KNN + Viterbi-like probabilistic ing (obtain APs data algorithm by war driving) and triangulation Accuracy 3-5 m 1-3 m 20+ m Table 1.1: Existing RSS-based WLAN Position Systems [1] RSS from detectable access points for localization; 2) access points (APs), which can be commonly found in most buildings and their exact positions are not necessarily known to the localization systems, as they may belong to different network groups and possibly 3) a database server, which stores the fingerprints collected by the mobile device. The WLAN-enabled device can extract information, such as MAC address, SSID and received signal strength (RSS) about these APs by receiving messages broadcasted from them. This thesis focuses on the WLAN localization and tracking problem using RSS as the measurement metric. The mobile device carried by the user collects the RSS from L different APs whose unique MAC addresses are used for identification. Then, the system determines the current position based on this RSS measurements and previously collected fingerprint database. The goal of this thesis is to propose a real-time WLAN positioning and tracking system that can give accurate position estimate and can be implemented on mobile devices, so that LBSs can be applied. In the context of this thesis, the mobile devices refer to the handheld devices, such as personal digital assistants (PDAs) and smartphones, which

19 Chapter 1. Introduction 6 Reference Point WLAN Access Point User equipped with mobile device Database Server Figure 1.1: The problem setup have degraded WLAN antennas, limited power, memory and computation capabilities, thus a light-weight algorithm is required to allow these devices to have real-time and accurate performance. The localization problem is defined as follow. First, the device collects online RSS readings from available APs periodically at a time interval t, which is limited by the device s network card and hardware performances. These online RSS readings can be denoted as r(t) = [r 1 (t), r 2 (t),..., r L (t)], t = 0, 1, 2,..., where r l (t) refer to the RSS reading collected from AP l at time t. Then, the proposed positioning and tracking system uses r(t) to compute the position estimate, denoted as ˆp(t) = [ˆx(t), ŷ(t)] T, where (ˆx(t), ŷ(t)) are the Cartesian coordinates of the estimated position at time t. 1.4 Technical Challenges The unpredictable variation of RSS in the indoor environment is the major technical challenge for the RSS-based WLAN positioning systems. There are four main reasons that lead to the variation of RSS. First, due to the structures of the indoor environment and the presence of different obstacles, such as walls and doors, etc, the WLAN signals experience severe multi-path and fading and the RSS varies over time even at the same location. Secondly, since the WLAN uses the licensed-free frequency band of 2.4GHz, the interference on this band can be very large. Example sources of interference are the

20 Chapter 1. Introduction 7 cordless phones, BlueTooth devices and microwave. Moreover, the presence of human bodies also affects the RSS by absorbing the signals [22], as human bodies contain large amount of water, which has the same resonance frequency as the WLAN. Finally, the orientation of the measuring devices also affects the RSS, as orientation of antenna affects the antenna gain and the signal is not isotropic in real indoor environment. All of the above reasons make it infeasible to find a good radio propagation model to describe the RSS-position relationship. Thus, a fingerprinting method is often used instead to characterize the RSS-position relationship. This method computes the position estimate by matching the online RSS readings to the fingerprints collected during training phase. This pattern matching process is a non-trivial problem as there are derivations between the online RSS readings to the fingerprint RSS readings due to the time-varying characteristics of the indoor radio propagation channel. In addition, the movement of objects, including the movement of the user who carries the mobile device, also affects the RSS readings. This type of variation of RSS is needed to be addressed by the fingerprinting-based positioning systems, in order to provide accurate position estimate. Another challenge relates to the computational capabilities of the mobile devices. Table 1.2 compares the processor speed and memory equipped by a PDA, which is used in this thesis to evaluate the performance of the proposed positioning system and a labtop with average performance. It shows that the PDA has very limited computation speed and memory when comparing to the labtop. Thus, some of the positioning systems that can be implemented on the laptop may not be able to be used by the PDA. The computational complexity and the use of memory must be taken into consideration when designing the positioning and tracking systems in this thesis.

21 Chapter 1. Introduction 8 Devices Processor Speed RAM HP ipaq hx MHz 64 MB Dell Inspiron 15 Laptop 2.2 GHz 4 GB Table 1.2: Comparison of a PDA and a laptop 1.5 Scope In this thesis, a two stage indoor RSS-based WLAN positioning and tracking system is proposed and implemented on two mobile devices. Such system is able to address the challenges mentioned in the previous section. The structure of this thesis is organized as follows. First, Chapter 2 reviews the existing RSS-based WLAN positioning techniques. It also describes two fingerprinting based methods: K-nearest neighbour (KNN) and kernelbased probabilistic methods which are used in later chapter as performance benchmarks to the proposed positioning system. In addition, it presents different ways to improve these positioning methods, such as the determination of region of interest, selection of APs and the use of filters with inputs of previous estimate and pedestrian motion models. Some overview of navigation systems design is also included. Finally, the two concepts used in this thesis for developing the proposed system are presented. It describes how the affinity propagation algorithm is operated to generate clusters. Then, the compressive sensing theory is briefly summarized. The compressive sensing based positioning system is introduced in Chapter 3. This chapter presents how such system is operated to estimate the user s position. It first describes how the clustering process is done on the collected fingerprint database by applying the affinity propagation algorithm during offline phase. Then, it discusses the two stage online phase where the actual positioning is operated. First, the coarse localization stage reduces the area of interest by choosing a few clusters of RPs, whose RSS readings

22 Chapter 1. Introduction 9 from the database are best-matched to the online RSS readings. Then, the fine localization stage converts the localization problem into sparse signal recovery problem, so that CS theory can be applied. The interactions between the mobile device and the server are also explained in the chapter. In Chapter 4, the CS-based positioning system is extended into a tracking system. The proposed tracking system has a modified coarse localization stage, which the previous estimate is used to select the nearby RPs, in addition to the clusters of RPs selected according to the online RSS readings. The tracking system uses the Kalman filter to smooth the estimate update. Since the user is more likely to make turns at intersection regions and hence may violate the liner motion model, the Kalman filter is reset at these regions to enhance the performance of such tracking system. Chapter 5 describes a simple navigation system, which consists of a path routing module to generate the path that leads the user to the destination and a tracking update analysis module that checks whether the user follows the path and gives appropriate guidance accordingly. It also explains how the map information is extracted to be used by the navigation system. This navigation system, together with the proposed positioning and tracking system are implemented as a software that can be installed on any smartphone or PDA that uses the Windows Mobile platform. The design of the software is presented in Chapter 6. Chapter 7 includes all the experimental results conducted in two experimental sites. The experiments done on the fourth floor of Bahen Centre focused on the evaluation of the proposed positioning system, whereas the performance of the proposed tracking system was evaluated using the data collected on the second floor of Canadian Nation Institute for the Blind (CNIB). work. Finally, Chapter 8 presents the concluding remarks and gives directions for the future

23 Chapter 1. Introduction Contributions This thesis proposes and implements a two stages indoor RSS-based WLAN positioning, tracking and navigation system using compressive sensing, clustering and filtering techniques. Here are the list of contribution, including the chapters presenting them and publications referring to them: 1. Compressive sensing based positioning system: This positioning system applies the affinity propagation algorithm on the collected fingerprint database to generate clusters of RPs, which have similar RSS values and are geographically close to each other. Then, such system uses the coarse localization stage to choose the relevant clusters of RPs, based on the online RSS measurement. Finally, the localization problem is translated into a sparse signal problem, so that the estimated position can be computed by solving a l 1 norm minimization problem according to the compressive sensing theory. (Chapter 3 and [23, 24]) 2. Tracking system: The CS-based positioning system can be easily extended to include the previous position estimate and the map information to improve its performance. The tracking system has a modified coarse localization stage. In addition to the clusters of RPs selected based on the online RSS measurements, RPs which are physically close to the previous position estimate are also chosen and the common RPs found in both sets are used in the fine localization stage. The computed estimate is then post-processed by the Kalman filter. This filter is reset when the estimate is at the intersection regions, as the user may make turns and violate the liner motion model used by the Kalman filter. (Chapter 4) 3. Navigation system: A simple navigation system, which uses the map database to generate path to destination using Dijkstra algorithm and gives guidance, is developed. It also determines whether the user follows the path and gives appropriate instructions at proper times. (Chapter 5).

24 Chapter 1. Introduction Software implementation and performance evaluation: A software is developed to implement the proposed positioning and tracking system, as well as a simple navigation system. It is written in C# and can be installed on any smartphone or PDA that uses Windows Mobile as its operating system. This software can give real-time position updates and also navigation guidance to the user. The performance evaluations of the proposed positioning and tracking system are done for two different experimental sites: Bahen centre and CNIB. Experimental results show that these systems are able to provide good position estimate of the user and can be implemented on the PDAs with limited resources, to give real-time performance. (Chapter 6 and 7 and [23, 24]). This project is a joint work with Chen Feng, a visiting PhD student from the Beijing Jiaotong University, at the Wireless and Internet Research Laboratory (WirLab), supervised by Professor Shahrokh Valaee. We work closely together to implement the indoor tracking and navigation system on the handheld devices. Chen focuses more on the compressive sensing based positioning system, while I focus more on the tracking and navigation system, as well as the software implementation.

25 Chapter 2 Background and Related Works In this section, a brief overview of RSS-based WLAN positioning and tracking techniques is given. The two fingerprinting-based methods, namely KNN and Kernel-based are summarized in Sections and 2.2.2, as they are implemented in Chapter 7 to compare the performance of the proposed positioning system. In addition, some works about pedestrian navigation are summarized. There are two additional concepts used by this thesis to develop the proposed positioning and tracking system using the fingerprinting approach. Section 2.5 describes the operation of the affinity propagation algorithm, which generates clusters of similar data points. Section 2.6 summarizes the compressive sensing theory which can be applied on the localization problem to estimate the user s location. 2.1 Indoor RSS-based WLAN Positioning Techniques The key problem for the indoor RSS-based positioning systems is to identify the RSSposition relationship, so that the user s location can be estimated based on the RSS collected at that location. There are two approaches in dealing with this relationship [25]: the uses of signal propagation models [26, 27] and the location fingerprinting methods [2, 19, 28]. 12

26 Chapter 2. Background and Related Works Signal Propagation Modeling This technique uses the RSS readings collected by the mobile device to estimate the distances of the device from at least three APs, whose locations are known, based on a signal radio propagation model. Then triangulation is used to obtain the device s position [8]. The accuracy of this technique depends heavily on finding a good model that can best describe the behavior of the radio propagation channel. However, the indoor radio propagation channel is highly unpredictable and time-varying, due to severe multipath in indoor environment; shadowing effect arising from reflection, refraction and scattering caused by obstacles and walls; and interference with other devices operated at the same frequency (2.4GHz) as the IEEE b/g WLAN standard, such as cordless phones, microwaves and BlueTooth devices. There are two models that are often used for the indoor radio propagation channel: Combined model of path loss and shadowing [29] This model combines the simplified path-loss model with the effect of shadowing, which is assumed to be a log-normal random process. The received power p r which is d meters away from a specific AP is given by: p r [dbm] = p 0 [dbm] + 10 log 10 K 10γ log 10 d d 0 η db (2.1) where K is a constant depending on the antenna characteristics and channel attenuation, p 0 is the signal power at a reference distance d 0 for the antenna far field, γ is the path-loss exponent, which varies for different surrounding environments (2 γ 6 for indoor environment) and η db N (0, σ 2 η) is a Gaussian random variable. Wall Attenuation Factor model [19] This model includes the effects of obstacles or walls between the transmitter and

27 Chapter 2. Background and Related Works 14 receiver. The received power can be obtained by: d p r [dbm] = p 0 [dbm] 10γ log 10 d 0 n W W AF C W AF n W < C n W C (2.2) where n W is the number of obstacles or walls between the transmitter and receiver, C is a threshold up to which no significant attenuation can be observed and W AF is the wall attenuation factor. The two empirical models require the calibration of the parameters, such as the path loss exponent, which vary depending on different environments. This often requires a comprehensive survey of the RSS distributions over the environment, which is a time consuming process. In addition, the models assume the RSS is distributed isotropically from the transmitter. This is often not the case for indoor environments due to the presence of obstacles. The orientation of the antenna of the mobile device also affects the RSS [22], but it is not reflected in the two models. Finally, the locations of the APs may not be known in the real scenario, as these APs may be installed and owned by different vendors. All of these make the models inadequate to describe the RSS-position relationship in real situation and lead to errors in estimating the user s location Location Fingerprinting A location fingerprinting method is often used instead of the radio propagation model, as it can give better estimates of the user s locations for indoor environments. This method is divided into two phases: offline and online phases. During the offline phase, which is also referred to as the training phase, the RSS readings from different APs are collected by the WLAN-integrated mobile device at known positions, which are referred to as the reference points (RPs) to create a fingerprint database, also known as the radio map. Since the orientation of the device s antenna affects the RSS readings, a more comprehensive fingerprint database can be built by collecting RSS readings for different

28 Chapter 2. Background and Related Works 15 orientations at the same RP. The actual positioning takes place in the online phase. The mobile device, which is carried by the user collects RSS readings from different APs at an unknown position. Then, these RSS online measurements are compared to the fingerprint database to estimate the user s location by using different methods described in the next section. The accuracy of the estimated position of the user depends highly on the number of RPs collected in the fingerprint database. If there are more RPs, then the radio map has a finer resolution and thus allows a better estimation [28]. In addition, since the RSS varies over time, collecting more time samples of RSS readings at the same RP also improves the position estimation. Thus, this fingerprint database collection is a time consuming and labour-intensive process. [30] uses the spatial correlation of adjacent RPs to generate the database by interpolation from a small number of RPs and this method is able to reduce the labour effort and time required for the offline phase. Another disadvantage of this fingerprinting approach is the maintenance of such databases. Since the RSS propagation environment varies with time, the accuracy of using the database degenerates over time, as the current RSS readings slowly deviate from the readings in the database. The database may even be rendered useless, if the environment changes significantly. This requires the fingerprint database to be rebuilt periodically, in order to ensure the accuracy of the positioning system. [31] presents a novel method to update the radio map using the online RSS readings, which can efficiently update the fingerprint database without the labour and time overhead cost as required by rebuilding such database from scratch. As shown in [32], the RSS readings collected by different network cards are different, which can vary up to -25dBm. This indicates that the same fingerprint database cannot be used by different mobile devices, which are equipped with different WLAN network cards. That means that the fingerprint collection process must be done on each device and lead to very high labour and time costs. Another method is to use the signal strength

29 Chapter 2. Background and Related Works 16 difference (SSD) between APs instead of the RSS as the fingerprint [33]. Although there are limitations to the location fingerprinting, it is a simple and effective method to be used by indoor positioning systems. This thesis also uses this approach to estimate the user s location. 2.2 Fingerprinting-Based Positioning Methods There are two approaches to estimate the user s location based on the online RSS measurements and the fingerprint database [34, 35]. The deterministic approach only uses the average of the RSS time samples from each RP to estimate the location, whereas the probabilistic approach incorporates all the RSS time samples for the computation. For the following section, assume the collected fingerprint database is denoted as a set {(p i, ψ i (1),..., ψ i (T )) i = 1,..., N}, where p i is the Cartesian coordinates for RP i, ψ i (t) = [ψ i,1 (t),..., ψ i,l (t)] T is the RSS readings vector for RP i at time t with ψ i,j (t) denoted as the RSS reading from AP j for RP i at time t. T is the total number of collected time samples, N is the total number of RPs and L is the total number of APs. The online RSS measurement vector can be denoted as r = [r 1,...r L ] T K-Nearest Neighbour Method (KNN) The K-nearest neighbour (KNN) method is a deterministic approach that uses the average of the RSS time samples of RPs from the fingerprint database to estimate the user s location [19]. It first examines the Euclidean distance of the online RSS measurement vector to the RPs in the database, namely: D i = r ψ i (2.3) where ψ i = 1 T T τ=1 ψ i,1(τ) is the average RSS vector for RP i. Then, the distances are sorted in ascending order and the first K RPs that have the smallest distances are

30 Chapter 2. Background and Related Works 17 obtained to estimate the location ˆp: ˆp = 1 K K p i (2.4) The calculated distances can be used as weights to estimate the location and it is referred to as the weighted-knn. The estimated location can be found by i=1 ˆp = K 1 i=1 D i p i K i=1 (2.5) 1 D i Probabilistic Approach The location estimation problem can be solved by using probabilistic models [2, 36, 37, 37, 38]. The core concept is to find the posterior distribution of the location, which is the conditional probability p(p i r) [37]. This conditional probability can be estimated by using the Maximum A Posteriori (MAP) estimator, which is derived from Bayes rule. That is: f(r p ˆp MAP = arg max f(p i r) = arg max i )f(p i ) p i p i N f(r p i )f(p i ) i=1 (2.6) where f(p i r) and f(r p i ) are the conditional probability density functions. Note that the denominator of (2.6) can be safely ignored as it remains the same regardless of the choice of p i. In general, there is no prior knowledge of the device s location and thus the prior density f(p i ) is assumed to be uniform, which transforms this MAP estimation into a Maximum Likelihood (ML) estimation: ˆp ML = arg max f(r p i ) (2.7) p i The estimation can be further improved by including the likelihood densities as the weight for the K RPs with the highest likelihood densities, namely: ˆp ML+weight = w i = K w i p i (2.8) i=1 f(r p i ) K j=1 f(r p i) (2.9)

31 Chapter 2. Background and Related Works 18 There are several methods to estimate the likelihood density functions f(r p i ), i = 1,..., N from the fingerprint database. Two of the common methods are reviewed here. Both of them assume that the RSS from different APs are uncorrelated and independent, so that the density function can be simplified to f(r p i ) = L k=1 f(r k p i ). Histogram The likelihood density functions can be estimated by the histogram method. This method requires two parameters to generate a histogram for the RSS time samples collected for each of the AP at each of the RP [37]. The first parameter is the number of bins, which are a set of non-overlapping intervals that cover the whole possible range of the RSS values. The second is the origin of the bins, which is necessary to determine the boundaries of the bins. Then, the likelihood density estimate for a particular RSS value can be obtained as the relative frequency of the bin, which contains that particular RSS value [37]. There are several drawbacks for this method. First, the likelihood density estimate depends heavily on the choice of the origin and the bin width and thus careful experimental calibration of these parameters is required [37]. Second, a large amount of RSS samples for each RP is required to generate a reliable histogram that produces good location estimate. Kernel-Based Instead of using the histogram, the kernel-based method uses the kernel density estimator to estimate the density functions [2,37]. The density function can be estimated as follows: ˆf(r p i ) = 1 T T K(r; ψ i ) (2.10) t=1 where K(r; ψ i ) denotes the kernel function. A common choice of the kernel function is the Gaussian kernel. By assuming that the RSS from different APs are uncorrelated and

32 Chapter 2. Background and Related Works 19 independent, the Gaussian kernel function is defined as: K(r; ψ i ) = 1 ( exp ( r ψ ) i(t) 2 2πσi )L 2(σi )2 (2.11) where σ i is the kernel bandwidth. The determination of this kernel bandwidth is evaluated in [2]. Since this method takes all the RSS time samples collected at each RP into account for estimating the likelihood densities, the computation time is much larger than the KNN method. In this thesis, the kernel-based method is also implemented to compare its performance to the proposed positioning system. The operation of the method using the Gaussian kernel is summarized in Fig. 2.1 [38] Region of Interest and Access Points Selections Before applying the above methods on the whole fingerprint database to estimate the user s location, two pre-processing steps can be introduced to confine the localization problem into a subset of relevant RPs and a subset of APs, which can distinguish the RPs easily. The region of interest determination step is able to mitigate the effect of the deviations between the online readings and the radio map due to the time-varying characteristic of the indoor radio channel [39]. In addition, the purpose of AP selection step is to remove extra APs that may lead to biased estimations and redundant computations, which is often the case as APs are widely deployed in indoor buildings [38]. Both steps are often carried out together as the reliability of the APs varies for different RPs [36, 38, 39]. The joint clustering technique proposed in [39] selects the strongest m APs to generate the probability distribution for each RPs and groups the RPs, which have the same q strongest APs list, as a cluster during offline phase. The argument of using strongest APs is that they provide the highest probability of coverage over time [39]. However, they may not be a good choice, as the variation of the APs may also lead to error in estimation [28]. [40] presents another AP selection criterion that is

33 Chapter 2. Background and Related Works 20 Given: Radio Map: {(p i, ψ i (1),..., ψ i (T )) i = 1,..., N} Number of APs: L Number of time samples: T Inputs: Online RSS measurement vector: r Outputs: Position estimate: ˆp Kernel-based Method: Optimal bandwidth: σi σi = ( ) 1 4 L+4 ˆσ L+2 i T 1 L+4 where, ˆσ 2 i = 1 L L l=1 (ˆσl i) 2 (ˆσ l i) 2 = 1 T 1 T t=1 (ψ i,l(t) ψ i,l ) 2, ψi,l = 1 T T t=1 ψ i,j(t) Weight calculation: ( ) 1 w i = T T ( 2πσi )L t=1 exp r ψ i (t) 2 2(σi )2 Estimation: ˆp = N i=1 w ip i N i=1 w i Figure 2.1: Kernel-based method [2]. based on AP s discrimination power in terms of entropy calculations. Several more AP selection schemes and the use of spatial filtering for region of interest determination can be found in [2]. This thesis uses the affinity propagation algorithm to generate cluster of RPs with similar RSS readings during offline phase. Then, a coarse localization stage is introduced in online phase to identify in which cluster of RPs should the user be located. In addition,

34 Chapter 2. Background and Related Works 21 different AP selection schemes are also explored for the proposed positioning system. 2.3 Indoor Tracking Most of the indoor tracking methods use past position estimates and pedestrian motion dynamics to refine the current position estimate determined by the above positioning methods. In addition, the dynamic motion model can also be used in conjunction with the current position estimate to predict the future possible locations. The pedestrian motion dynamics can be modeled by a general Bayesian tracking model and a filter is then derived to refine the position estimates [41]. There are two filters that are used commonly to improve the accuracy of positioning systems [41]: Kalman filter and Particle filter Kalman filter By assuming the Gaussian tracking noise model and linear motion dynamics, the general filter becomes a Kalman filter, whose optimal solution is a minimum mean square error (MMSE) estimate. Although the assumption of Gaussian RSS-position relationship is not often the case [22], the application of the Kalman filter as the post-processing step is able to improve the accuracy of the positioning systems [41 44]. The parameters of the Kalman filter are needed to be found experimentally. [45] provides some guidelines on how to set the parameters for each update steps based on the map information Particle filter The particle filter is a sequential Monte Carlo method that generates random samples, known as particles, according to a motion models and estimates their probability densities [46, 47]. Unlike the Kalman filter, the particle filter can be applied on non-gaussian and non-linear models. In addition, map information can be used to further improve the

35 Chapter 2. Background and Related Works 22 performance of the particle filter by assigning zero weights to the invalid particles, such as those across the wall [48,49]. Backtracking based on the map information is also proposed in [50]. Moreover, information obtained from accelerometers and inertial measurement units (IMU) can also be used to refine the motion models and let the filter to generate particles that are more relevant and hence improve the tracking accuracy [51, 52]. However, the major drawback of the particle filter is its high computation complexity. For example, 1600 particles are needed for each filter update for a 40m 40m experimental area to achieve the best performance [49]. This large computation workload can not be handled by the mobile devices to give real-time updates to the user. Hence, this thesis chooses the Kalman filter to post-process the estimates instead of the particle filter, which may severely hinder the operations of the mobile devices Other Methods Besides the use of the above filters, several other methods are also used for the indoor tracking. The Horus positioning system [36] smooths out the resulting location estimate by simply averaging the last W location estimates obtained by the discrete-space estimator. Liao et al. proposed a method to predict the user s orientation, which is then used for the next position estimate to improve the accuracy, from the previously computed location estimates [53]. A Viterbi-like algorithm, which is developed to enhance the RADAR system [20] and is also implemented by [54], makes use of historical data based on the KNN method to determine the location estimates. Finally, a nonparametric information filter based on the kernel-based probabilistic method is proposed in [55]. This filter, whose computational complexity is lower than particle filter, is able to deal with tracking scenarios where Kalman filter is inapplicable.

36 Chapter 2. Background and Related Works Pedestrian Navigation Indoor navigation for pedestrian is different from the vehicular navigation using GPS, which becomes an essential tool to the driver. Gillièron and Merminod [56] describes how to implement the personal navigation system for indoor applications. It is crucial to extract information from the indoor maps as topological models and node/link models, so that they can be used for implementation of route guidance. They also implement map matching algorithms, so that the system can self-correct the user s locations due to bad estimates based on the topological elements from the map databases, traveled distances and direction changes. [48] also describes how the map information can be used for indoor location-aware systems. There are different ways to present the guidance information graphically to the users based on different output devices and they are explored in [57]. The experience of using the indoor navigation systems can be enhanced in a smart environment, which is equipped with different kinds of sensors that can convey additional information to users [58]. There are more restrictions for the navigation systems when they are targeted to visually impaired users. [59] describes the path planning and following algorithms specifically designed for visually impaired. In summary, such systems generate obstacle-free paths; provide more detailed information about the surrounding area and give the guidance in relation to special objects, such as walls, doors and rails, etc. In addition to the commonly used Dijkstra algorithm to generate the routes [56], a cactus tree-based algorithm is also used to generate a high-level guidance. A more detailed development of an indoor routing algorithm for the blind and its comparison to the one for the sighted can be found in [60]. This thesis develops a simple navigation system, which uses the proposed tracking system to provide updates of user s locations. Such system is implemented as a software on PDAs and smartphones and is given to the visually impaired people to test its usefulness in helping them to get familiar with the indoor environment.

37 Chapter 2. Background and Related Works Affinity Propagation Algorithm For Clustering In this thesis, the affinity propagation algorithm described in [15] is used to cluster the RPs with similar RSS readings, so that the proposed positioning and tracking system is able to confine the localization problem into a smaller region. Unlike the traditional K-means clustering method, which may lead to bad clustering results due to bad choice of randomly selected K initial exemplars [61], the affinity propagation algorithm is able to generate good clustering results without predetermining the initial exemplars. This algorithm allows all the data points to have equal chance to become exemplars and is easy to be implemented, thus it is chosen in this thesis to cluster the RPs. The affinity propagation algorithm generates a set of exemplars and corresponding clusters by recursively transmitting real-valued messages between data points with an input measure of similarity between pairs of data points [15]. The pairwise similarity s(i, j) indicates the suitability of data point j to be the exemplar of data point i. Another input measure is the preference, which is also the self similarity for data point k, p(k) = s(k, k). This value defines the a priori possibility that data point k to become an exemplar. If all the data points are equally possible to be exemplars, then their preferences can be set to a common value. High preference values will lead to large number of clusters generated by the algorithm. In practice, the preference values are commonly assigned as the minimum or median similarity to generate moderate number of clusters. The core operations of the algorithm is the transmission of two kinds of real-valued messages: responsibility message, r(i, j) and availability message, a(i, j). The responsibility message, r(i, j), is sent from data point i to candidate exemplar j to reflect the suitability of data point j to serve as the exemplar for data point i taking into considerations the other potential exemplars. It is updated according to r(i, j) = s(i, j) max {a(i, j s.t.j j j ) + s(i, j )} (2.12)

38 Chapter 2. Background and Related Works 25 The availability message, a(i, j) is sent from candidate exemplar j to data point i to reflect how appropriate that data point i should choose data point j as its exemplar, taking into account the responsibility messages from other data points that data point j should be an exemplar. Its update rule is: a(i, j) = min 0, r(j, j) + i s.t.i {i,j} max{0, r(i, j)} (2.13) Two additional messages: self-responsibility, r(i, i) and self-availability, a(i, i) are also calculated for each data point i. These messages reflect accumulated evidence that i is an exemplar. The formulas to update these two messages are stated below: i, find r(i, i) = p(i) a(j, j) = i s.t.i j max {a(i, j s.t.j j j ) + s(i, j )} (2.14) max{0, r(i, j)} (2.15) The exemplars can then be identified by combining the two messages. For data point If j j = arg max{a(i, j) + r(i, j)} (2.16) j = i, then data point i is an exemplar; otherwise, data point j is the exemplar for data point i. The messages are passed recursively between pairs of data points by following the above updating rules (2.12) to (2.15) until a good set of exemplars and corresponding clusters gradually emerges. 2.6 Compressive Sensing Theory This thesis describes how the localization problem can be re-formulated into a sparse signal recovery problem, so that the compressive sensing theory discussed in [16, 62, 63] can be applied to estimate the user s location. Compressive sensing theory allows compressible signals to be recovered by fewer samples than traditional methods, which according to the Nyquist sampling theory requires

39 Chapter 2. Background and Related Works 26 the sampling rate to be at least twice the maximum bandwidth. This is possible when signals of interest are sparse and are sampled incoherently. The compressive sensing problem can be formulated as follow [16, 63]: Consider a discrete-time signal x as a N 1 vector in R N. Such signal can be represented as a linear combination of a set of basis {ψ i } N i=1. Constructing a N N basis matrix Ψ = [ψ 1, ψ 2,...ψ N ], the signal x can be expressed as x = N s i ψ i = Ψs (2.17) i=1 where s is a N 1 vector and is an equivalent representation of x in the different basis Ψ. A signal is K-sparse when it can be represented as a linear combination of K N basis vectors. This means that there is only K nonzero entries for vector s. The overall compressive sensing problem can be expressed as y = Φx = ΦΨs = Θs (2.18) where Φ is a M N, M < N measurement sensing matrix for sensing the signal x, Θ = ΦΨ is an M N matrix, and y is a M 1 observation vector collected as a result of this sensing process. This problem can be referred to as incoherent sampling if the largest correlation between the sensing matrix Φ and the representation basis Ψ, µ(φ, Ψ) = N max 1 i,j N < ϕ i, ψ j > is small. Compressive sensing theory requires both the sparsity and incoherent sampling, so that the signal can be recovered exactly with high probability. If M cklog(n/k) N, where c is a small constant, the signal can be reconstructed by solving the following l 1 norm minimization problem: ŝ = arg min s 1 such that Θs = y (2.19) s R N This is a convex optimization problem that can be easily converted into a linear program, known as basis pursuit, through primal-dual method [62, 64]. Additional algorithms

40 Chapter 2. Background and Related Works 27 to solve this optimization problem can also be found in [64]. In this thesis, the l 1 - minimization problem is solved by using the basis pursuit linear program provided in the matlab toolbox, l 1 -MAGIC, developed by Candès [65]. 2.7 Chapter Summary This chapter gives a brief overview of different methods developed for the RSS-based WLAN indoor positioning systems. It also discusses how the reduction of the region of interest and selection of access points can enhance the accuracy of these systems. Two fingerprinting methods, KNN and kernel-based probabilistic techniques are described in details, as they are served as the performance benchmarks for the proposed positioning system. Moreover, several indoor tracking techniques that are able to improve the accuracy through the use of previous estimates and pedestrian motion models are also discussed. The developments of indoor navigation systems are also included to provide some insight on how the location information produced by the positioning and tracking systems can be used. Finally, the affinity propagation algorithm for clustering data points and the compressive sensing theory for sparse and incoherent sampled signals are discussed, these concepts are used by the proposed positioning and tracking systems.

41 Chapter 3 Compressive Sensing Based Positioning System Due to the unpredictable nature of the RSS distribution at indoor environment, most of the indoor RSS-based WLAN positioning systems use the fingerprinting approach to acquire the explicit RSS and position relationship, in order to compute a more accurate estimation of user s position. The compressive sensing based positioning system proposed in this chapter is also a fingerprinting method. Unlike the traditional fingerprinting systems, the proposed system reformulates the localization problem into a sparse-natured problem and thus the compressive sensing concept can be applied to find the estimated positions. A coarse localization stage is also introduced to constraint the region of interest into smaller relevant area, which effectively reduces the computation time and minimizes the maximum errors attained. 3.1 Indoor Positioning System Overview As depicted in Fig. 3.1, the compressive sensing based positioning system consists of two phases: offline phase where the training is done to generate the fingerprint database and the affinity propagation algorithm is applied to generate clusters; online phase where 28

42 Chapter 3. Compressive Sensing Based Positioning System 29 RSS readings are obtained for the actual localization to take place. The online phase consists of two stages. First, the coarse localization stage is carried out to reduce the area of interest into a smaller region by choosing clusters of RPs based on online RSS readings. Then, in fine localization stage, the localization problem is reformulated into a sparse signal recovery problem, which allows the application of compressive sensing theory to estimate the device s position. The following sections describe the individual blocks as shown in Fig. 3.1 in details. Offline Phase Fingerprinting RSS Collections in 4 orientations Clustering Affinity Propagation Online Phase online RSS readings Coarse Localization cluster matching Fine Localization Compressive Sensing AP selection Orthogonalization L1-norm minimization Estimated Location Figure 3.1: Block diagram of the proposed indoor localization system. 3.2 Offline Phase Offline phase is the training period that allows the positioning system to collect RSS data at the area of interest and preprocess them to enable the system to estimate the mobile device s position in the online phase. This training must be done wherever the positioning system is first deployed. The time required for the training depends on the

43 Chapter 3. Compressive Sensing Based Positioning System 30 size of the survey site. Moreover, the database may need to be rebuilt if the surrounding environment of the area of interest changes significantly. According to Fig. 3.1, two operations are performed in the offline phase for the proposed system and they are described in the following subsections Fingerprint Collections The first operation of the offline phase is the fingerprinting. During fingerprinting, RSS readings from different APs are collected by a WLAN-enabled mobile device at desired known positions, referred to as the reference points (RPs), which are often the grid points pre-defined on the map. RSS readings are sampled at a regular time interval, in order to obtain their distributions over time. Since the orientation of the antenna inside the device affects the RSS readings, the device is pointed to a specific orientation when collecting RSS readings at each RP. In this thesis, RSS readings are collected at four common directions, namely North, East, South and West as represented mathematically by the set O = {0, 90, 180, 270 }. The raw set of RSS time samples collected from AP i at RP j and orientation o is denoted as {ψ (o) i,j (τ), τ = 1,..., q, q > 1}, where q is the total number of time samples collected. Then, the average of these raw time samples are computed and stored in a database, known as the radio map on the server. Such radio map database gives the spatial and RSS relationship in the given environment and can be represented as Ψ (o) : ψ (o) 1,1 ψ (o) 1,2 ψ (o) 1,N Ψ (o) ψ (o) 2,1 ψ (o) 2,2 ψ (o) 2,N = (3.1) ψ (o) L,1 ψ (o) L,2 ψ (o) L,N where o O = {0, 90, 180, 270 } and ψ (o) q i,j τ=1 ψ(o) i,j (τ) is the average of RSS readings over time from AP i at RP j at a specific orientation o, for i = 1, 2,..., L and j = 1, 2,..., N. L is the total number of APs detected throughout the whole region of = 1 q

44 Chapter 3. Compressive Sensing Based Positioning System 31 interest and N is the total number of RPs. The columns of Ψ (o) represent the average RSS readings at each RP, which can be referred to as the radio map vector and is denoted as ψ (o) j = [ψ (o) 1,j ψ (o) 2,j ψ (o) L,j ]T, j = 1, 2,..., N (3.2) Besides the average RSS reading matrix Ψ (o), the database server also stores the variance of these time samples, which are useful in determining which APs should be selected for localization. The variance vector for each RP is defined as (o) j = [ (o) 1,j (o) 2,j (o) L,j ]T, j = 1, 2,..., N (3.3) where (o) i,j = 1 q 1 AP i at RP j for orientation o. q τ=1 (ψ(o) i,j (τ) ψ(o) i,j )2 is the unbiased variance of RSS readings from For each RP j, its position represented as Cartesian coordinates (x j, y j ), together with its average and variance of the RSS readings from different APs at different orientations form a set of (x j, y j ; ψ (o) j ; (o) ), o O, which is stored in the fingerprint database. The j database is then preprocessed as described in the next subsection before being used for the computation of position estimation during online phase. Note that if there is no RSS readings collected from an AP at a RP and an orientation, the corresponding value in the fingerprint database is set to a small value to imply its invalidity Clusters Generation by Affinity Propagation Due to the time varying characteristics of the indoor propagation channel, RSS readings collected during online phase may deviate from those stored in the radio map database. As a result, these deviation may lead to error estimation of position. In addition, the computation time for finding position updates increases proportionally to the number of RPs. Therefore, a coarse localization stage is introduced at the online phase to confine the localization problem into a smaller region, namely a subset of RPs that have similar RSS readings to the online measurement, before the fine localization is performed. This

45 Chapter 3. Compressive Sensing Based Positioning System 32 stage can effectively reduce the computation time due to the reduction of number of relevant RPs, as well as the errors introduced by the potential outliers. The RPs collected in the offline phase are required to be divided into subsets, so that a coarse localization stage can take place during the online phase. The RPs whose RSS readings are similar and physically close to each other should belong to the same group. This group division process, which is referred to as the clustering process in the proposed system is done during the offline phase after the fingerprints collection is finished. Since the RSS readings for the same RP vary for the four orientations, the clustering process is performed on each of the four radio map databases separately. The affinity propagation algorithm described in Section 2.5 is used to generate the desirable clusters, as this algorithm allows all the RPs to have equal chances to be exemplars and is easily to be implemented. It requires two input parameters, namely the similarity between pairs of RPs and the preference values. At orientation o, the similarity between RP i and RP j is defined as s(i, j) (o) = ψ (o) i ψ (o) j 2, i, j i {1, 2,..., N}, o O (3.4) Since all of the RPs are equally desirable to be exemplars, their preferences are set to a common value. In order to generate a moderate number of clusters, the common preference for orientation o is defined as p (o) = γ (o) median{s(i, j) (o), i, j i {1, 2,..., N}}, o O (3.5) where γ (o) is a real number which is experimentally determined, such that a desired number of clusters is generated. For each orientation, o O, the affinity propagation algorithm takes the above definitions of similarity (3.4) and preference (3.5) as inputs and then it recursively updates the responsibility messages and availability messages according to (2.12) to (2.15) until a good set of exemplars and the corresponding clusters emerges [15]. This set of generated exemplars is denoted as H (o) and the corresponding cluster member set with RP

46 Chapter 3. Compressive Sensing Based Positioning System 33 j as the exemplar is represented as C (o) j, j H (o). In general, the RPs that are within the same cluster should be physically in close proximity, as the neighboring RPs should attain similar RSS readings. However, due to the varying characteristics of RSS readings (such as the shadowing effects), there exist RPs that are physically far away from their assigned clusters. These RPs, referred to as outliers, are manually assigned back to the clusters that are physically closeby to reduce the potential errors in position estimations Interaction between the database server and the mobile device during offline phase Fig. 3.2 illustrates how the proposed positioning system is set up on the mobile device and the server during offline phase to obtain and process the training data required for the localization. The mobile device collects RSS time samples from detectable APs at specific positions (RPs) and transmits these data to the server. After the fingerprint collection is done by the device, the server creates the radio map database and generates clusters for each orientation by applying the affinity propagation algorithm. This algorithm is run on the server as it is an iterative process that consumes a large amount of memory and processing power that may not be supported by the mobile device. At the end of the offline phase, the server obtains the coordinates of the RPs, radio map matrices, variance of RSS readings and also clusters information for each orientation. These data are then used in the online phase for the computation of position estimations. 3.3 Online Phase During the online phase, the device, carried by a mobile user and pointed to an unknown orientation, collects online RSS readings from detectable APs, which are then used together with the fingerprint database to estimate the device s location. The online RSS

47 Chapter 3. Compressive Sensing Based Positioning System 34 Mobile Device Server Collect RSS time samples from APs at RP j for 4 orientations Compute the average and variance of RSS readings over time, ψ_j (o), _j (o) Send RP j s information: ψ_j (o), _j (o) & coordinates (x_j, y_j) SEND Collect fingerprint for RP j in 4 orientations Use the device to collect N RPs Create overall radio map matrix: Ψ (o) = [ψ_1 (o),ψ_2 (o),,ψ_n (o) ] Apply affinity propagation on each radio map to generate sets of exemplars H (o) and their corresponding members C_j (o) Outlier adjustment for each radio map Figure 3.2: Interaction between the database server and the mobile device during offline phase. measurement vector at time t is denoted as r(t) = [r 1 (t), r 2 (t),, r L (t)] T (3.6) where {r k (t), k = 1,..., L} is the online RSS readings from AP k at time t. Since the positioning system does not take into account the previous estimate, the time dependency notation (t) is dropped in this chapter for simplicity purpose, i.e. the online RSS reading is denoted as r instead of r(t). As shown in Fig. 3.1, the collected measurement vector is the input to the proposed positioning system. First, it is used in the coarse localization stage to reduce the area of interest. Then it is also used in the fine localization stage to obtain the final estimated position. The details of these two stages are described in the following sections.

48 Chapter 3. Compressive Sensing Based Positioning System Coarse Localization Stage: Cluster Matching As mentioned earlier, the goal of the coarse localization stage is to reduce the region of interest from the whole fingerprint database to a subset of it. Thus, it can reduce the computation time for the fine localization stage, as fewer RPs are considered. It can also confine the maximum localization error to be the size of this subset, whereas this error can be much larger when no coarse localization stage is implemented. The coarse localization is done by selecting the clusters, as defined in the offline phase, whose RSS radio map vectors best-match with the online RSS measurement vector r. Since the target device can be physically located at the boundaries of the defined clusters, a few best-matched clusters, instead of only one cluster, are selected to eliminate the inaccuracy due to the edge problem. The cluster matching process can be interpreted as finding a set of best-matched exemplars S RSS with their corresponding cluster members set C RSS, such that they have the highest similarities with the online reading. It is crucial to have a good similarity function between the online reading r and an exemplar j H (o), o O, denoted as S Match (r, j) (o), so that the clusters for which the online measurement vector r should belong to can be correctly identified. The worst case scenario, where wrong sets of clusters are chosen for the online measurement vector r, should be avoided, as this results in a wrong localization region and thus introduces large localization error. This may happen, as the online RSS readings may deviate from the fingerprint database due to the time varying indoor radio propagation channel. In order to reduce the occurrences of such scenarios, several matching schemes are considered in this thesis. These schemes provide different ways to define the appropriate similarity function S Match (r, j) (o). 1. Exemplar based cluster matching This is the most basic scheme, which uses the same definition as (3.4) for the clustering in offline phase. The similarity computes the Euclidean distance of the

49 Chapter 3. Compressive Sensing Based Positioning System 36 online measurement vector r to the individual exemplar s RSS radio map vector from each cluster: S Match (r, j) (o) = r ψ (o) j 2, j H (o), o O (3.7) 2. Average based cluster matching Instead of using the exemplar RSS radio map vector, the average of the RSS radio map vectors of all the cluster members, which gives a more comprehensive and representative readings of the whole cluster, is used to compute the Euclidean distance against the online measurement vector r: S Match (r, j) (o) = r 1 C (o) j k C (o) j ψ (o) k 2, j H (o), o O (3.8) 3. Weighted Average cluster matching This scheme takes into account the stability of the RSS readings from a specific AP at different RPs. Different weights are added to the similarity function for each AP of each cluster at each orientation, so that it gives more weight to the stable RSS readings. The stability of an AP at a RP can be determined as the inverse of the variance of the RSS readings collected from that AP at that RP calculated in the offline phase, thus APs with smaller variances are more reliable and have larger weights. The similarity function is defined as: S Match (r, j) (o) = W (o) j (r 1 C (o) W (o) j = w (o) j k C (o) j 1,j w (o) 2,j ψ (o) k ) 2, j H (o), o O (3.9) w (o) L,j (3.10)

50 Chapter 3. Compressive Sensing Based Positioning System 37 where W (o) j is the diagonal weight matrix and w (o) l,j, l = 1, 2,..., L is the weight of AP l for cluster j at orientation o. This weight is proportional to the inverse of the variance of the AP for the specific cluster, namely w (o) l,j 1 (o) l,j (o) l,j = 1 C (o) j k C (o) j Then these weights are normalized, so that L k=1 w(o) l,j = 1. (3.11) (o) l,k (3.12) 4. Strongest APs matching In this scheme, the online measurement vector is first pre-filtered to determine L APs that have the strongest RSS readings. Then, the similarity can be calculated using any of the above schemes by only considering the RSS readings from these selected APs. Since the APs that have stronger RSS readings tend to be more stable as the device is with high probability within their coverage area, whereas the APs with weaker signals tend to vary in time, the scheme is able to provide good matching similarity definition by only considering the reliable APs. All the above cluster matching schemes attempt to reduce the possibility of choosing the wrong clusters used by the fine localization and thus improving the system s stability and accuracy. The performances of these schemes are evaluated in details in Chapter 7. By evaluating the similarity function described above, the set of best matched exemplars S RSS with their corresponding cluster members set C RSS can be found as: S RSS = {(j, o) S Match (r, j) (o) > α, j H (o), o O} (3.13) C RSS = {(k, o) k C (o) j, (j, o) S RSS } (3.14) where α is a predefined threshold value to determine whether a cluster should be included into S RSS. Since only a few set of clusters are desired to be included in S RSS, α is set to

51 Chapter 3. Compressive Sensing Based Positioning System 38 be a high percentage, α 1, of the maximum similarity difference, that is α = α 1 max { SMatch (r, j) (o)} + (1 α 1 ) min { SMatch (r, j) (o)} (3.15) j H (o),o O j H (o),o O Finally, the region of interest of the localization problem can be reduced to the set of C RSS. The modified radio map matrix Ψ L Ñ, Ñ = C RSS can be obtained as Ψ = [ψ (o) j, (k, o) C RSS ]. (3.16) This matrix will then be used by the following fine localization stage. Note it is possible that this matrix may contain the radio map vectors from the same RP but at different orientations, as all clusters from different orientations are considered for cluster matching Fine Localization Stage: Compressive Sensing Recovery The fingerprint-based localization problem can be reformulated as a sparse signal recovery problem, as the position of the mobile user is unique in the discrete spatial domain. By assuming that the mobile user is located exactly at RP j and facing at orientation o, such that (j, o) C RSS, the user s location can be represented relative to these RPs instead of the actual location. The mathematical representation is a 1-sparse vector, denoted as θñ 1, whose elements are all equal to zero except the n-th element, so that θ(n) = 1, where n is the corresponding index of the RP at which the mobile user is located, that is as: θ = [0,..., 0, }{{} 1, 0,..., 0] T (3.17) nth element Then, the online RSS measurement r obtained by the mobile device can be expressed y = Φr = Φ Ψθ + ε (3.18) where Ψ is the modified radio map matrix as defined in (3.16) and ϵ is an unknown measurement noise. The matrix Φ M L is an AP selection operator applied on the online

52 Chapter 3. Compressive Sensing Based Positioning System 39 RSS measurement vector r to obtain vector y, where M < L is the desired number of APs to be selected. Based on this sparse signal recovery formulation, the following parts explain how the location of the mobile user can be recovered by using the compressive sensing theory. A. Access Points Selection Since most modern buildings are equipped with a large number of APs to ensure good quality of wireless services, the total number of detectable APs in these buildings, L is often much greater than that required for positioning. These extra APs lead to excessive computations and possibly biased estimations if some of the APs are not reliable. Inclusion of RSS readings from unstable APs may introduce error to the estimations, as online RSS values may deviate from the readings in the offline database. Therefore, an access point selection step is introduced to select a subset of reliable and stable APs from the available ones to be used for the actual positioning, in order to eliminate the errors due to large number of APs. Denote the set of all available APs found within all the RPs by L with L = L. Then the AP selection step is to determine a subset of APs, M L, such that M = M L. The AP selection process is carried out by applying the AP selection operator Φ on the online measurement vector r as defined in (3.18). Each row of Φ, is a 1 L vector that selects the desired lm th AP, where l m M, by assigning ϕ(l m ) = 1 and zero to the rest of the elements, namely: ϕ m = [0,..., 0, }{{} 1, 0,..., 0], l m M, m = 1, 2,..., M (3.19) l m th element In this thesis, three AP selection schemes are used based on APs stabilities and differentiability in spatial domain. Their performances are evaluated in a later chapter. 1. Strongest APs [39]

53 Chapter 3. Compressive Sensing Based Positioning System 40 This scheme selects the set of M APs with the strongest RSS readings from the online RSS measurement vector. These APs with strong RSS readings are more reliable than the ones with weak RSS readings, as they provide a high probability of coverage over time. The set of APs can be obtained by sorting the elements of the online measurement vector r in descending order and selecting indices of the first M values that correspond to the APs with highest RSS readings. Since the online RSS readings are different for each run, the AP selection operator Φ is created dynamically on the device for each update during the online phase. 2. Fisher Criterion [38, 66] This scheme selects the APs which discriminate themselves the best within RPs. The discrimination ability for each AP i, i {1, 2,..., L} can be quantified through the Fisher criterion. The metric for AP i, denoted as ξ i is defined as ξ i = (j,o) C RSS (ψ (o) i,j ψ i ) 2 (j,o) C RSS (o) i,j (3.20) where ψ i = 1 Ñ (j,o) C RSS ψ (o) i,j. The APs with highest ξ i are chosen to construct the AP selection operator Φ for the actual localization. This metric accounts for two factors: the denominator ensures that RSS values should not vary too much over time, thus implies that the offline and online values are similar and the numerator evaluates the discrimination ability of each AP by considering the strength of variations of mean RSS across RPs. Since this metric calculations are done across the RPs j at orientation o chosen in the coarse localization stage, (j, o) C RSS, the AP selection operator Φ is created dynamically on the device for each update during the online phase. 3. Random Combination Unlike the above two schemes, which select the appropriate APs based on different criteria and create the AP selection operator Φ dynamically for each update, the

54 Chapter 3. Compressive Sensing Based Positioning System 41 random combination scheme does not take into account the performance of the APs and thus have less computation complexity during online phase and also does not require large number of RSS time samples for the variance calculation in the offline phase as required by the Fisher criterion. The AP selection operator Φ is defined as a randomly generated i.i.d. Gaussian M L matrix. Thus, according to (3.18), y = Φr, y is a set of M linear combinations of online RSS values from L APs. Since the same matrix can be reused for each update, it can be generated and stored first during the training period and retrieved for use directly in the online phase, saving the time to dynamically generate the matrix as required by the other two schemes. B. Orthogonalization and Signal Recovery using l 1 -minimization Compressive sensing theory requires both sparsity and incoherence of the signal, so that it can be recovered accurately. Although the localization problem as defined in (3.18) satisfies the sparsity requirement, Φ and Ψ are in general coherent in the spatial domain. Thus, an orthogonalization procedure is applied to induce the incoherence property as required by the CS theory [67, 68]. The orthogonalization process is done by applying an orthogonalization operator, T, on the vector y, such that z = Ty. The operator is defined as T = QR (3.21) where R = Φ Ψ, and Q = orth(r T ) T, where R is a pseudo-inverse of matrix R and orth(r) is an orthogonal basis for the range of R. By applying this operator on y, (3.18) becomes: z = Ty = QR y = QR Rθ + QR ε (3.22) = Qθ + ε

55 Chapter 3. Compressive Sensing Based Positioning System 42 where ε = Tε. If M is in the order of log Ñ, the minimum bound required by the CS theory, θ can be well-recovered from z with very high probability, by solving the following l 1 -minimization problem [67, 68]. ˆθ = arg min θ 1, s.t. z = Qθ + ε. (3.23) θ RÑ The computation complexity of the l 1 -minimization algorithm grows proportional to the dimension of vector θ, which is the number of potential RPs. Therefore, the coarse localization stage, which reduces the area of interest from all the N RPs into a subset of Ñ < N RPs, reduces the computational time and resources required for solving the l 1 -minimization problem, and thus allows this procedure to be carried out by resourcelimited mobile devices. C. Interpretation of Actual Position The above procedure is able to recover the exact position, if the mobile user is located at one of the RPs facing one of the orientations in the set of O, which is the assumption made earlier in order to formulate the localization problem into a 1-sparse natured problem. However, in real situation, the mobile user may not be located at an RP facing a certain orientation. Thus, in actual implementation, the recovered position vector ˆθ is not a 1-sparse vector, rather a vector with a few non-zero coefficients. A post-processing step is conducted to interpret this recovered location vector ˆθ into an actual location and compensate the error induced by the grid assumption. The procedure chooses the set of all indices of the dominant elements in ˆθ, which are above a certain threshold λ, denoted as R R = {n ˆθ(n) > λ} (3.24) λ = λ 1 max(ˆθ) (3.25) where λ 1 is a parameter within a range (0, 1) and is adjusted experimentally. Then, the estimated location of the mobile user can be calculated as a weighted average of these

56 Chapter 3. Compressive Sensing Based Positioning System 43 potential candidate points, using the normalized value in ˆθ as the corresponding weight for each potential RP, that is ˆp = (ˆx, ŷ) = n R η n (x n, y n ) (3.26) where η n = ˆθ(n)/ n R ˆθ(i) and (x n, y n ) is the cartesian coordinates of RP n Interaction between the database server and the mobile device during online phase The roles of the mobile device and the server during the online phase are illustrated in Fig First, the device collects the online RSS readings from all the detectable APs, namely r. Then the device requests the map and the representative RSS readings for each cluster from the server, in order to perform coarse localization. After the best-matched clusters are found, the device communicates with the server to obtain the relevant radio map matrix Ψ for the following fine localization. The device carries out steps of AP selection, orthogonalization and l 1 -minimization to obtain the recovered location vector ˆθ. Finally, the device asks the server for the potential candidate RP s coordinates and computes the estimated position according to ˆθ. 3.4 Chapter Summary In this chapter, the proposed compressive sensing based positioning system is described in details. The system involves two phases. The offline phase is the training period that collects RSS values from detectable access points at reference points to create the fingerprint database. It also runs the affinity propagation algorithm to create different clusters of RPs with similar RSS reading patterns and within physical proximity. The actual localization takes place in the online phase, which consists of two stages. First, the mobile device collects the online RSS readings, which are used to find the subset of

57 Chapter 3. Compressive Sensing Based Positioning System 44 Mobile Device Server Collect online RSS readings, r It contains: Ψ (o), _j (o), H (o), C_j (o) - list of RPs coordinates - map Coarse Localization (cluster matching) Request and obtain map and RSS values of exemplars. REQUEST SEND Retrieve map and RSS readings of exemplars Find best matched cluster exemplars, S SEND S Use the received matched cluster exemplars S to obtain the matched cluster members C and generate a smaller radio map matrix Ψ Obtain Ψ, _j (o) SEND Send Ψ, _j (o) AP selection Fine Localization (CS-theory) Orthogonalization l1-norm minimization Interpret device s location using relevant RPs coordinates. REQUEST RPs coordinates SEND RPs coordinates Retrieve relevant RPs coordinates Figure 3.3: Interaction between the database server and the mobile device during online phase. relevant RPs by the coarse localization stage through cluster matching process. Several cluster matching schemes are discussed in an attempt to reduce the effect of outliers and derivations in RSS readings between offline and online phases. This stage reduces the area of interest from the whole database into a smaller region, thus reducing the computation time for the latter stage, and also minimizes the effect of outliers and RSS time varying derivations. Then, a fine localization stage is applied on this reduced area to find the estimated position. It is done by formulating the localization problem into a sparsenatured signal recovery problem, such that the compressive sensing theory can be applied to recover the desired signal. There are several steps to compute the estimated position: access point selection, orthogonalization, l 1 -minimization problem and interpretation of recovered location vector into actual location, which are described in the chapter. The chapter also explains different roles of the mobile device and the server in the

58 Chapter 3. Compressive Sensing Based Positioning System 45 proposed system. The server is mainly served as a database storage, which when requested by the device, sends required information, such as map and RSS readings to the device. It is also responsible for running the affinity propagation algorithm to form clusters during offline phase, as the device does not have enough computation resources to run such clustering scheme. The mobile device collects the RSS readings and obtains information from the server, in order to estimate its location locally.

59 Chapter 4 Indoor Tracking System The previous chapter describes a positioning system that can accurately estimate a stationary user s position. This positioning system is modified in this chapter in order to track the dynamic mobile user. The proposed indoor tracking system uses the Kalman filter with map information to smooth out the location estimate and also uses previous position estimate to choose the relevant region of interest in the coarse localization stage. This chapter first describes the Kalman filter and then the proposed indoor tracking system. In this chapter, the tracking problem is defined as follows. The device carried by the mobile user periodically collects the online RSS readings from each APs at a time interval t, which is limited by the device s network card and hardware performances. The online RSS readings vector is denoted as r(t) = [r 1 (t), r 2 (t),..., r L (t)], t = 0, 1, 2,..., where r l (t) corresponds to the RSS from AP l at time t. Then, the indoor tracking system uses these RSS readings to estimate the user s location at time t, which is denoted as ˆp(t) = [ˆx(t), ŷ(t)] T. 46

60 Chapter 4. Indoor Tracking System General Bayesian Tracking Model The tracking problem of a mobile user can be modeled by a general Bayesian tracking model as follows [41] and [47]: x(t) = f t (x(t 1), w(t)) (4.1) z(t) = h t (x(t), v(t)) (4.2) where x(t) = [x(t), y(t), v x (t), v y (t)] is the state of the user at time t with (x(t), y(t)) as the Cartesian coordinates of the user s location and v x (t) and v y (t) as the velocities in x and y directions, respectively. Assuming the tracking is a Markov process of order one, the state evolves as a function f t of previous state and w(t), i.i.d. process noise vector only. In addition, the measurement z(t) depends on the current state and the i.i.d. measurement noise vector v(t) through the function h t. The current location of the mobile user, x(t) can then be estimated recursively from the set of measurements up to time t, i.e. z(1 : t) = {z(i), i = 1,..., t}, in terms of the probability distributive function (pdf), denoted as p(x(t) z(1 : t)). Assuming that the initial pdf p(x 0 z 0 ) p(z 0 ) and p(x(t 1) z(1 : t 1)) are known, the pdf p(x(t) z(1 : t)) can be obtained by the following prediction and update stages: 1. Prediction Stage: The prior pdf p(x(t) z(1 : t 1)) can be predicted based on p((x(t) x(t 1)), which is defined by the state process equation (4.1) and the previous state pdf. p(x(t) z(1 : t 1)) = p((x(t) x(t 1))p(x(t 1) z(1 : t 1))dx(t 1) (4.3) 2. Update Stage: Then, the prior pdf can be updated by the measurement z(t) obtained at time t

61 Chapter 4. Indoor Tracking System 48 using the Bayes rule, p(z(t) x(t))p(x(t) z(1 : t 1)) p(x(t) z(1 : t)) = (4.4) p(z(t) z(1 : t 1)) p(z(t) z(1 : t 1)) = p(x(t) z(1 : t 1))dx(t) (4.5) where p(z(t) x(t)) is defined by the measurement model (4.2). 4.2 Kalman Filter If the process and measurement noises are assumed to be Gaussian and the motion dynamic model is linear, i.e. the process and measurement functions f t and h t are linear in equations (4.1) and (4.2), then the general Bayesian tracking model is reduced to a Kalman filter. The optimal solution can be obtained for this Kalman filter as the minimum mean square estimates (MMSE). The process and measurement equations of the Kalman tracking model can be formulated as x(t) = Fx(t 1) + w(t) (4.6) z(t) = Hx(t) + v(t) (4.7) where x(t) = [x(t), y(t), v x (t), v y (t)] T is the state vector and z(t) is the measurement vector. The process noise w(t) N (0, S) and the measurement noise v(t) N (0, U) are assumed to be independent with the corresponding covariance matrices S and U. The matrices F and H in (4.6) define the linear motion model. For the tracking problem, they are assigned as follows: 1 0 t t F = H = (4.8) That means the current location of the mobile user is assumed to be the previous location of the user plus distance traveled, which is computed as the time interval t times the

62 Chapter 4. Indoor Tracking System 49 current velocity, and is corrupted with Gaussian noise. The current measurement should be the current location subject to Gaussian noise. By assigning the initial conditions of ˆx(0) and P(0), the steps to obtain the final estimates of state vector ˆx(t) and the error covariance P(t) are computed as follows: 1. Prediction Stage ˆx (t) = Fˆx(t 1) (4.9) P (t) = FP(t 1)F T + S (4.10) 2. Update Stage K(t) = P (t)h T (HP (t)h T + U) 1 (4.11) ˆx(t) = ˆx (t) + K(t)(z(t) Hˆx (t)) (4.12) P(t) = (I K(t)H)P (t) (4.13) For each time step t, the measurement vector z(t) in (4.12) is the current user s estimated location computed by the positioning system. After the state vector is estimated, the final filtered estimate of the user s location can be found as: ˆp(t) = Hˆx(t) (4.14) 4.3 Overview of Proposed Indoor Tracking System The Kalman filter can be applied on the CS-based positioning system described in the previous chapter to improve the accuracy in estimating the dynamic user s trajectory. Fig. 4.1 shows the proposed indoor tracking system that is built on top of the CS-based positioning system. As compared to Fig. 3.1, there are two major modifications for the tracking system. Besides the introduction of the Kalman filter stage after the end of the fine localization stage, the tracking system also has a different coarse localization

63 Chapter 4. Indoor Tracking System 50 stage that uses the previous user s position estimate in aiding the selection of relevant area of interest. The offline phase and the fine localization stage in the online phase remain unchanged for the tracking system. The following subsections describe these two modifications of the tracking system. Offline Phase Fingerprinting RSS Collections in 4 orientations Clustering Affinity Propagation Online Phase online RSS readings r(t) Coarse Localization cluster matchingbased on 1) RSS readings 2) Physical proximity within previous position Fine Localization Compressive Sensing AP selection Orthogonalization L1-norm minimization pˆ( t 1) Computed Location p ( t) Delay Tracking Kalman Filter with Map Information pˆ( t) Final Estimated Location Navigation 1) Location analysis with routed path 2) Generation of voice commands Voice Command Figure 4.1: Block diagram of the proposed indoor tracking system Modified Coarse Localization Stage During the online phase, the device periodically collects the online RSS readings. The online measurement vector collected at time t, denoted as r(t) is first evaluated at coarse

64 Chapter 4. Indoor Tracking System 51 localization stage to reduce the area of interest by selecting the relevant RPs in the database for the fine localization stage. In addition to using the online RSS readings to find the relevant RPs, the tracking system also uses the previous user s position estimate to select the appropriate RPs. Fig. 4.2 depicts the coarse localization stage employed by the tracking system. The modified coarse localization stage chooses the relevant RPs based on two criteria: Group I) online RSS readings, and Group II) physical proximity of previous estimate. Fingerprint Database r(t) pˆ( t 1) Group I Choose clusters of RPs with similar RSS Group II Choose RPs within physical proximity C RSS C Dist O Find Common RPs C Figure 4.2: Coarse localization stage for the proposed tracking system. Group I: RPs with similar online RSS readings The system first selects the clusters of RPs defined in the offline stage that have similar RSS reading patterns to the online RSS vector r(t). This cluster matching process is the same as that described in Section In summary, the system uses one of the cluster matching schemes to evaluate the cluster matching similarities to the online RSS vector, i.e. {S Match (r(t), j) (o), j H (o), o O} and then selects the best-matched clusters C RSS according to (3.13).

65 Chapter 4. Indoor Tracking System 52 Group II: RPs within physical proximity Besides the use of the online RSS readings to choose the relevant RPs, they can be chosen by finding the possible range of the device s current location based on the previous estimated location, ˆp(t 1) = (ˆx(t 1), ŷ(t 1)). Since a person cannot walk far away within a short period of time, it is reasonable that the system can limit the region of interest into the possible walking range based on the previous estimated position, if it is known and reliable. There are two schemes to choose this possible walking range and are discussed as follows. 1. Unpredicted - Based only on previous estimation This scheme selects a set of RPs that are within walking distance during the specified update time interval to the previous estimated location, that is C Dist = {j (x j ˆx(t 1)) 2 + (y j ŷ(t 1)) 2 < β, j {1,..., N}} (4.15) where (x j, y j ) is the location of RP j and β is the walking distance within the specified update time interval t. 2. Predicted - Based on previous estimation and prediction using linear motion model This scheme uses the previous estimated location to predict the current possible location based on a linear motion model and then chooses the RPs which are within the walking range of this predicted position. The same linear model used by the Kalman filter defined in (4.8) and (4.6) without the addition of Gaussian noise can be used to predict the user s current locations, denoted as p(t): p(t) = HF x(t 1) (4.16) where x(t 1) = [ˆx(t 1), ŷ(t 1), v x (t 1), v y (t 1)] T is the state vector with (ˆx(t 1), ŷ(t 1)) = ˆp(t 1) as the previous user s estimated position computed by the tracking system. The velocities in x and y directions, represented as v x (t 1)

66 Chapter 4. Indoor Tracking System 53 and v y (t 1), respectively, can be defined in several ways. First, if both of them are set to zeros, then the predicted location is the same as the previous estimate, p(t) = ˆp(t 1). This is equivalent to the previous described scheme. Second, if the user is known to be walking at a constant speed, these values can be assigned accordingly. However, for real applications, a user may walk to a random direction at a random speed. Thus, it is necessary to find a way to predict the user s velocity at each time interval, in order to have a good estimation for the current location. The estimation of these velocities can be obtained from the output of the Kalman filter, which is implemented after the fine localization stage and will be described in Section Then, the state vector for (4.16) can be assigned directly as the final estimate of the state vector for the Kalman filter, i.e. x(t 1) = ˆx(t 1). The system then selects a set of RPs which are in close proximity to this predicted current location p(t) = [ p 1 (t), p 2 (t)] T, that is: C Dist = {j (x j p 1 (t)) 2 + (y j p 2 (t)) 2 < β, j 1,..., N} (4.17) After the selection of these two groups of relevant RPs based on RSS readings similarities and physical proximities, the system then includes the common RPs that appear in both groups as the set of reduced region, where the final localization stage is applied. The common RPs is obtained as a set C, C = C RSS {(j, o) j CDist and o O} (4.18) This set contains RPs that satisfy both conditions of similar RSS readings to the online RSS measurement and within close range to the user s previous location. Thus, they are very likely to be the possible locations that the current user is located. By introducing the constraint of physical range, the system is able to identify the instants when the online RSS readings collected is not useful to find the user s position. In normal operation, the user must be within a range around his previous location. If the selected

67 Chapter 4. Indoor Tracking System 54 clusters of RPs in C RSS are far away from the previous location, then the online RSS readings can be regarded as invalid, as there are large deviations between the online readings and offline database, so that the cluster matching based on similarities of RSS readings fails to find the correct clusters of RPs. This scenario leads to an empty set of C and halts the fine localization stage. If such thing occurs, the system discards this online RSS measurement vector and obtains a new one to restart the localization process. There may be a possibility that all the consecutive online RSS measurement vectors lead to empty sets of C. This makes the system continuously collect a new online RSS measurement, which is then discarded, preventing it from computing the true estimate of the user s location. This happens as the previous position estimate is not accurate and hence the selection of RPs based on such estimate does not match with the RPs selected based on the online RSS measurement vector. Thus, the system is reset to use only the online RSS measurement vector to select the RPs, when N empty consecutive online RSS measurement vectors are discarded, arguing that the previous position estimate is no longer valid to reduce the localization problem into a smaller relevant region. After a successful computation of finding the non-empty set of C, the modified radio map matrix Ψ L Ñ, Ñ = C can be obtained as Ψ = [ψ (o) j, (j, o) C]. (4.19) This matrix will then be used by the fine localization stage. The fine localization stage for the tracking system remains the same as the one in the CS-based positioning system, which is already described in Section Since the estimated user s position computed by the fine localization stage is then fed into the Kalman filter to obtain the final estimate in the tracking system, such temporal solution is referred to as p(t) in this chapter, which indicates that it is not the final solution.

68 Chapter 4. Indoor Tracking System Map-Adaptive Kalman Filter After the computation of the location estimate, p(t) at the end of the fine localization stage, the Kalman filter described in Section 4.2 is applied to enhance the tracking performance. By substituting z(t) = p(t) into the Kalman filter updating equations (4.9) to (4.14), the final estimated position ˆp(t) can be obtained from the estimated state ˆx(t) according to (4.14). In real situation, the Kalman filter is able to enhance the tracking performance when the user is walking along a corridor inside a building, as the linear motion assumed by the filter is sufficient to model the user s trajectory. However, when the user is making a turn at an intersection, the linear model does not apply on this behavior which involves abrupt change in direction and hence the Kalman filter requires several more updates to reflect the user s true trajectory and thus leads to more errors in position estimate. This issue can be addressed by updating the Kalman filter according to the map information. Since the Kalman filter behaves the best when the user is walking straight along a corridor but performs poorly around the intersections, the Kalman filter is reset when the user is in the region of intersection. Prior to the actual tracking, the map of region of interest is studied to extract a list of intersections which are represented as nonrotated bounding boxes, denoted as a set R intersection = {(x i min, ymin), i (x i max, ymax) i i = 1,..., B}, where (x i min, ymin) i and (x i max, ymax) i are the lower-left and upper-right corners respectively of intersection i and B is the number of intersections found on the map. Thus, the user is within the intersection region i at time t turn if the below two conditions are satisfied: x i min ˆx(t turn ) x i max (4.20) y i min ŷ(t turn ) y i max When the user is within any of the intersection regions, the Kalman filter is reset by reassigning the state vector and covariance matrix at time t turn, which are the initial

69 Chapter 4. Indoor Tracking System 56 conditions for this new Kalman filter. Namely, ˆx(t turn ) = [ˆp(t turn ), 0, 0] T P(t turn ) = P(0) (4.21) Then, the Kalman filter is updated as normal according to (4.9) to (4.13) for the next estimate at time (t turn + 1) using z(t turn + 1) = p(t turn + 1). This removes the inaccurate estimation by the Kalman filter when the user is making a turn. Fig. 4.3 summarizes how the Kalman filter is applied on the proposed tracking system. 4.4 Chapter Summary This chapter modifies the CS-based positioning system described in the previous chapter into a tracking system, which is able to improve the accuracy in estimating the mobile user s locations. By using the user s previous estimated locations, the tracking system is able to refine the current estimate in two ways: 1) to select appropriate RPs in the coarse localization stage and 2) to apply Kalman filter for better location estimate. First, during the coarse localization stage, a set of RPs that are within walking range to the i) previous estimated location ˆp(t 1) or ii) the predicted current location p(t) based on the previous estimated location, are selected as the potential region of interest, arguing that a user cannot be physically far away within a short period of time in the indoor environment. The RPs appeared in both set of C Dist, found based on previous estimated location and the set of C RSS, determined by the original cluster matching scheme for the CS-based positioning system, are then used to generate a modified radio map matrix Ψ that is required for the fine localization stage. This modified coarse localization stage ensures that the reduced region of interest are within the walking range of the user and provides a way to reject the invalid online RSS readings when no common RPs are found in both sets. The tracking system also introduces the Kalman filter stage, which uses the temporal

70 Chapter 4. Indoor Tracking System 57 Given: Intersections Set: R intersection = {(x i min, ymin), i (x i max, ymax) i i = 1,..., B} Inputs: Computed estimate from fine localization stage: p(t) Final estimate of previous update: ˆp(t 1) = (ˆx(t 1), ŷ(t 1)) Outputs: Final estimate of current update: ˆp(t) = (ˆx(t), ŷ(t)) Kalman Filter: Initial conditions ˆx(0) = [ˆp(0), 0, 0] T, P(0) Check if user is already at intersection for i = 1,... B if (x i min ˆx(t 1) x i max and ymin i ŷ(t 1) ymax) i then At intersection, reset Kalman filter ˆx(t 1) = [ˆp(t 1), 0, 0] T P(t 1) = P(0) break for loop endif endif Update set z(t) = p(t) to update the Kalman filter through (4.9) to (4.13) compute for ˆp(t) according to (4.14) Figure 4.3: Map-Adoptive Kalman Filter

71 Chapter 4. Indoor Tracking System 58 position estimation, p(t), computed at the end of the fine localization stage as the input to update the previous estimated location ˆp(t 1) into the current final estimation ˆp(t). Since the Kalman filter performs poorly when the user makes turns and thus does not follow the linear model, the proposed tracking system is designed to reset the Kalman filter whenever the user is in an region of intersection, which is a possible place for the user to make turns.

72 Chapter 5 Simple Navigation System The proposed indoor tracking system can be implemented on mobile devices to provide reliable and accurate real-time location estimates of the mobile user and thus is adequate to provide location based services to the user. As an illustration and a way to evaluate the performance of the tracking system, a simple navigation system is designed and implemented on top of the tracking system to provide real-time guidance to the user to reach the desired destination. The design and the implementation of such navigation system is described in details in this chapter. 5.1 Overview of Navigation System The goal of the navigation system is to decide a path between the user s current location and his desired destination and then provide guidance, which can be in the form of voice instructions to let the user follow this planned path. In addition, the location updates, {ˆp(t), t = 1,...}, generated periodically by the tracking system are fed into the navigation system to generate adequate instructions that are helpful to the user to get familiar with the surrounding area. All of these operations require a detail map database that stores all the map-related data for path routing and guidance. Fig. 5.1 illustrates the navigation system. It consists of a map database, which is generated at the initial set up to provide 59

73 Chapter 5. Simple Navigation System 60 the required map information for the navigation system; a path routing module, which generates the path that leads the user to reach the destination and a tracking update analysis module, which generates appropriate voice instructions according to the user s locations. Initial Setup Map Database Generation - represent the layout as a connected graph - define coordinates of special map features - create audio files for all possible voice commands During Real-Time Navigation Indoor Tracking System User-defined destination pˆ(0) pˆ( t) Path Routing Module Routed path Tracking Update Analysis Module pˆ( t) Yes Require reroute? No Voice Instructions Figure 5.1: Navigation System Overview 5.2 Map Database Generation at Initial Setup The navigation system relies heavily on the map of the region of interest, which illustrates the layout of different features such as rooms, corridors, elevators, etc. For the initial setup, different map features are extracted from the map, which allow the system to generate a feasible path and descriptive instructions about the surrounding to the user during the actual navigation process. The map database generation can be divided into two operations: i) to represent the map layout as a connected path and ii) to define locations of the map features.

74 Chapter 5. Simple Navigation System Layout Definition The layout of the map is interpreted as a connected graph, so that the path routing problem can be transformed into a graph problem [56], which is solved by the path routing module described in the later section. The nodes of this graph are a set of Cartesian coordinates of the possible passage points along the corridors or destinations. Two nodes are connected together with an edge, if both nodes can reach each other physically without obstacles in their ways. A non-negative weight is assigned to each edge and is defined as the Euclidean distance between the connected nodes. In order to ensure that at least one feasible path can be generated for all the destinations defined on the map, the graph must be connected meaning that there must be a path, which is a set of edges that connect any pairs of nodes defined in this graph. This connected graph can be represented as G = (E, V ), where E is a set of edges and V is a set of nodes. The weight of the edges can be represented as a matrix D G = [d Gij ] V V, where d th Gij entry corresponds to the Euclidean distance between node i and node j if they are connected by an edge, otherwise the value is set to infinity which implies the two nodes are not connected to each other Map Features Definition In order to provide more information about the surrounding environment, which will be useful to help user to get familiar with the area, a list of map features can be extracted from the map to generate a more comprehensive map database for the navigation system. This list of the map features can include general facilities and accesses and can be expanded as needed depending on user s preferences. Washrooms, elevators and stairs are some examples of map features that are of interest to users. The list of the features can be stored as a set F map = {(p j f, Feature j), j = 1,..., n F }, where p j f = (xj f, yj f ) is the location of feature j and Feature j is the feature s name and n F is the total number of

75 Chapter 5. Simple Navigation System 62 map features defined on the map. 5.3 Path Routing Module At the beginning of the actual navigation, the device first obtains the user s input of the desired destination and user s current location, which can be either specified by the user or estimated by the device using the proposed tracking system. Then, the system identifies the source node, v source and the target node, v target on the connected graph predefined in the setup stage, that are closest to the user s current location and the destination, respectively. The path routing problem is interpreted as finding the shortest path between these two nodes on the connected graph [56]. This problem can be easily solved by applying the Dijkstra algorithm, which is described in [69] and is summarized in Fig Path Analysis After a set of nodes sequence, P, which constitutes the shortest path from the user s current position to the destination, is generated, the path is then analyzed to produce necessary navigation information to the user. The generated path is first divided into series of line segments, such that consecutive line segments are pointing at different directions and the connected point between the two segments becomes the turning point. This set of line segments extracted for the path P can be denoted as P l = {l 1, l 2,...l S }, where S is the total number of line segments and each segment is denoted as l i = {p i s, p i e}, where p i s = (x i s, ys) i and p i e = (x i e, ye) i are the starting and ending points of the ith line segment, respectively. The turning points are identified as the ending points between line segments, that is T = {p i e i = 1,..., S 1}. Based on these generated line segments, the system is able to determine the turning points, the direction of turns and the distance traveled at each line segment

76 Chapter 5. Simple Navigation System 63 Given: Connected graph of the map layout with weight: G(E, V ), D G = [d Gij ] V V Inputs: User s current location: ˆp(t) Source node: v source Destination location Target node: v target Outputs: A list of nodes of the shortest path from target node to source node: P Dijkstra: Initializations: d = [d(1),..., d( V )]; {d(v i ) =, v i v source V }, d(v Source ) = 0 e = [e(1),..., e( V )]; {e(v i ) = 1, v i V } V unvisited := V Actual operations: while V unvisited is not empty u = arg min V unvisisted d, remove u from V unvisited exit while loop if d(u) = or u == v target for each v in V unvisited exit foreach loop ifd Guv == a = d(u) + d Guv ; if a < d(v) then d(v) = a; e(v) = u Determine path sequence: u := v target, P = {} insert u at beginning of P and u := e(u) while e(u) 1 Figure 5.2: Dijkstra Algorithm

77 Chapter 5. Simple Navigation System 64 which facilitate the analysis of the user s current locations in the tracking update analysis module. In addition, the system also finds out a list of relevant map features that appeared along this generated path. For each line segment i, the system chooses the map features from the set F map that are within β f meters from the line segment i and form a set Fpath i F map. These sets {Fpath i, i = 1,..., S} are useful for the system to effectively determine if the user is close to these map features when he is following the path correctly, and thus save the system from searching the full map feature set F map for each tracking update. 5.4 Tracking Update Analysis Module Tracking Module (periodic update ) pˆ( t) Reach destination? No Yes Match to one of line No segments in path? For N offpath consecutive Yes updates Routing Module (5) (7) (1) Voice Generation Engine (1) Please wait for rerouting (2) Go straight (3) Prepare to turn left /right (4) Turn left/right (5) Wrong direction (6) <map feature> is on your left/right (7) You have arrived at <destination> (2) (3), (4) (6) Is walking in wrong direction? No Yes For N wrong direction consecutive updates Determine if user turn left or right Yes Yes Near end of the line segment? No Are there any nearby map feature? No Figure 5.3: Tracking update analysis After the generation of the path that can lead the user to his targets, the device

78 Chapter 5. Simple Navigation System 65 starts the tracking system to keep track of user s position. For each tracking update, the analysis module compares the location estimate to the routed path to check if the user follows the path properly and then generate voice instructions when necessary. The analysis process is illustrated in Fig Analysis Process The analysis module first determines if the user already reaches the destination by checking the Euclidean distance between the user s current position and the target being within a range of β destination. If the user is at the destination, the module generates the voice instruction stating that the destination is reached and stops tracking system and navigation module automatically. pˆ ( t) = ( xˆ ( t), yˆ ( t)) p i e = (x i e, y i e ) p i p i s = (x i s, y i s ) Figure 5.4: A point in close range to a line segment Otherwise, the module attempts to match the user s current position ˆp(t) to one of the line segments in the generated path set P l. If this tracking update is close to line segment l i as illustrated in Fig. 5.4, then we can find the projection and the minimum distance of the tracking update point ˆp(t) to the line segment l i by solving the two equations [70]: p i = p i s + µ i (p i e p i s) (5.1) (ˆp(t) p i ) (p i e p i s) = 0 (5.2) where p i is the projected point which is collinear with p i s and p i e, and µ is the ratio in terms of the distance between p i s and p i e indicating how far the point p i is away from p i s.

79 Chapter 5. Simple Navigation System 66 By substituting (5.1) into (5.2), the solution to µ i is µ i = (ˆp(t) pi s) (p i e p i s) p i s p i e 2 (5.3) If the computed µ i is within the range [0, 1], then the projected point falls onto the line segment, which implies that the update estimate is within the range of this line segment. By substituting (5.3) back into (5.1), the projected point p i can be computed and the shortest distance of the tracking update point to the line segment can be obtained as d i min = ˆp(t) p i. The system determines that the tracking estimate ˆp(t) follows the line segment l i if i) µ i [0, 1] and ii) d i min < β path. If there are consecutively N offpath tracking estimates failing to match with any of the line segments in P l, the analysis module assumes that the user does not follow the path properly. Thus, the analysis module will ask the user to stop walking and inputs the user s current position as the starting point to the path routing module to reroute an alternate path for the user to reach the destination. The value of µ i is also a good indicator to tell if the user is walking along the path properly. In normal situation, where the user follows the path correctly, the value of µ i should increase from zero to one along the same line segment l i for consecutive tracking updates and then eventually move to the next segment l i+1, where the value of µ i is no longer valid and the value of µ i+1 is then computed. Thus, when µ i, i < S is close to one, this indicates that the user is close to the end of the line segment l i, where a turn is required for the user to move to the next line segment l i+1. The direction of turn can be determined by finding the positive angle difference, ρ i between the two vectors that are formed by joining the starting and ending points of the current and next line segments as illustrated in Fig For simplicity, the module only identifies either a left or right turn. The module assumes a very simple scheme to determine the orientation of the mobile user. For each tracking update, a direction vector is computed between the current update and the previous one and then is compared with the currently matched line segment

80 Chapter 5. Simple Navigation System 67 p i e = (x i e, y i e ) = P i+1 s = (x i+1 s, y i+1 s ) i ρ ρ + i 1 i i+ 1 i 1) ρ = ρ ρ i i i 2) if ρ < 0, then ρ = ρ i 3) if ρ 90, then it is a right turn i else if ρ 180, then it is a left turn p i s = (x i s, y i s ) P i+1 e = (x i+1 e, y i+1 e ) Figure 5.5: Determining the direction of turn based on the two line segments l i and l i+1 direction. If consecutive N wrong direction tracking updates are in opposite direction of the line segment, then a voice command of wrong direction is issued to the user. Finally, the analysis module computes the Euclidean distance between the user s current estimate ˆp(t) to the map features in Fpath i, where i corresponds to the line segment i that the user is currently following. If the distance is smaller than β f, then the module will generate the corresponding voice command regarding this specific map features to the user Voice Generation The voice instructions of the analysis module can be generated on-the-fly by using textto-speech (TTS) engine. However, TTS engines are not readily available for free to be used on smart devices and render delays in giving real-time instructions to the user. Thus, the navigation system uses an alternate method to obtain the voice commands. Since the navigation system only has a small library of instructions, all of these commands are first created and saved as audio files during initial setup. The audio can be generated from text by using the online AT&T Natural Voices R Text-to-Speech Demo [71]. Then, the analysis module determines which instructions are needed and plays the corresponding audio files. Although these audio files occupy extra amount of memory spaces on the smart devices, the system is able to generate reliable voice instructions in real time, which

81 Chapter 5. Simple Navigation System 68 may not be achievable by using the TTS engines. 5.5 Chapter Summary This chapter describes the navigation system that is built on top of the tracking system to provide guidance to the user. The navigation system requires an initial setup to extract information from the map and generates pre-determined voice instructions that are used by the actual navigation process. The navigation system is then divided into two modules. One is the path routing module, which takes in the user s current location and desired destination as inputs to generate a feasible path based on the connected path defined according to the layout of the map and identifies the turning points and map features found along this path. Then, the tracking update analysis module uses the path information along with the current user s estimated position to determine the appropriate voice instructions to be given to the users. This navigation system is implemented on the smartphone and its details are found in the next chapter.

82 Chapter 6 Software Implementation on Mobile Devices This chapter describes how the indoor CS-based positioning and tracking system, along with the navigation application described in Chapters 3 to 5 are implemented as a software on the PDAs and smartphones. 6.1 Software Platform The software is developed on PDAs and smartphone that are installed with Windows Mobile operating systems to implement the proposed indoor tracking and navigation system. Unlike Android platform [72], which has become popular just recently and only available on android-powered smartphones, the Windows Mobile platform has been developed maturely and in addition to Window Mobile-powered smartphones, such platforms have also been used on PDAs. The development of software application for the iphone is also ruled out as the wifi scanning functionality, which is the core requirement for the indoor tracking system, is not provided by the Apple s official software development kit (SDK). Although there are private libraries available online to provide that function, they require the jailbreaking of the iphone and thus violate the Apple s development license [73], [74]. 69

83 Chapter 6. Software Implementation on Mobile Devices 70 The software is written in C# using Microsoft.Net Compact Framework version 3.5 in Visual Studio It utilizes two open source libraries available on the internet to relieve the burden on developing the application on this platform. They are the OpenNetCF library [75] and the DotNetMatrix library [76], which provide the WiFi RSS scanning functions and basic matrix operations respectively. 6.2 Devices in Testing The developed software has been deployed onto three different devices and their specifications in comparison to a standard laptop of the same price level (around $ 600) are shown in Table 6.1 [77 80]. Devices Processor RAM Window Mobile WLAN WiFi Scan- Speed Version ning Rate PDA1: HP ipaq 624 MHz 64 MB Pocket PC b 1 sam- hx4700 2nd ple/second PDA2: HP ipaq 624 MHz 128 MB Pocket PC b 1 sam- hx2750 2nd ple/second Smartphone: Samsung Omnia II Dell Inspiron GHz 4 GB Windows g 800 MHz 256 MB Professional b/g 0.67 sample/second Laptop Table 6.1: Devices Specifications It is obvious that the PDAs and smartphone have much more restricted resources in processing power and memory than a standard laptop. Thus, indoor tracking systems that use probabilistic approach [38] and particle filters [47, 51, 81] that require large computation power may not be realizable on these devices. The proposed indoor tracking

84 Chapter 6. Software Implementation on Mobile Devices 71 system is implemented on these devices to illustrate that such system is a compact algorithm that is able to provide real-time and accurate estimate of user s location. The performances of these devices are evaluated in Chapter 7. Note that the Samsung smartphone is equipped with an accelerometer and a digital compass. By using the Samsung Mobile SDK [82], the software is able to access these two sensors. The maximum sampling interval that can be set by the SDK for these sensors is 200 milliseconds. Attempts have been made to let the system utilize both sensors in aiding to determine the user s travel distances and orientations. However, the phone is incompetent to handle both sampling of the sensors data and scanning the WiFi RSS from APs at the same time and thus the program becomes unstable and often crashes unexpectedly. Besides, the sampling rate and the response are too slow for both sensors to let the system obtain useful real-time data within a short time interval for the tracking updates. Thus, these sensors are not incorporated into the proposed tracking system in this thesis. Both of the PDAs use the WiFi network adaptor as the basic wireless connection method, unlike the smartphone, which cellular reception precedes the WiFi reception. Thus, the signal strength level and the refresh rate of the WiFi antenna of the smartphone are inferior to the ones in PDAs. By using the OpenNetCF library, the software is able to detect the WiFi adaptor on the devices and then scan the detectable APs with their unique media access control (MAC) address as their identifications and their RSS readings. All the three devices require a duration of one second to accomplish this operation. However, tests have shown that the smartphone is required to wait for 500 milliseconds between each scanning operations, rather than 100 milliseconds for both PDAs, in order to detect valid RSS readings, thus proved that the refresh rate for smartphone is slower. Since the PDAs have a faster refresh rate, the performance evaluations in the next chapter are focused on these PDAs.

85 Chapter 6. Software Implementation on Mobile Devices Software Design Samsung Mobile SDK IndoorLocalizerProg OpenNetCF OpenNetCF.Net LocalizerBasicLibrary IndoorLocResources DotNetMatrixCF MathAlgorithm Localization Tracking Config.txt Fingerprint Database with clustered information Map Database Log files Navigation Figure 6.1: The overview of the software design. Arrows shows the dependency of the libraries and blue colored boxes are the developed modules for the software. The overall design of the software is illustrated in Fig The screenshot of the PDA shows the menu of the software, which has five major operations. The flowchart on the left of the screenshot shows the dependencies of the libraries of the software design structure. The resources, such as the fingerprint and map databases, which are needed by the software are stored in a folder on the PDA and represented as the cylindrical shape on this figure Software s Functionalities As depicted in Fig. 6.1, the software has five major operations. They are: 1. Detect APs, which run the WiFi scanning function provided by the OpenNetCF library and displays the MAC address and RSS for each detectable APs in table format as depicted in Fig. 6.2

86 Chapter 6. Software Implementation on Mobile Devices 73 Figure 6.2: An example screenshot of Detect AP operation. 2. Collect Fingerprints, which let the user to properly setup the tracking system by collecting fingerprints and defining the map features on the screen; 3. Localize Yourself, which runs the CS-based position system described in Chapter 3 and displays the user s position on the screen; 4. Tracking, which periodically collects RSS readings and runs the tracking system described in Chapter 4 and displays the user s position on the screen; 5. Navigation, which asks the user s input of destination and implements the navigation system described in Chapter Resources Folder There is a folder on the device that contains all the required resources to run the tracking and navigation system properly and is accessible by the software. This folder, Indoor- LocResources, also contains a configuration setting file, namely Config.txt, which defines the device in test, the map scale ratios and also all the parameters that can be adjusted for the tracking and navigation system. In addition, an image file, which displays the

87 Chapter 6. Software Implementation on Mobile Devices 74 map of the region of interest, is included to allow the software to use it to collect fingerprints and displays user s location properly on the screen. This image map is stored as a bitmap format and is scaled, so that it can be showed properly on the screen of smart devices. The same image map file is used by all the three devices and their image pixel to actual distance meter scale is included in the Config.txt to allow the system to estimate the actual distance according to the map. During the initial setup, the user uses the Collect Fingerprint functions to collect fingerprint database and map features which are all stored in this folder. The raw fingerprint database is then transferred to a computer to generate clusters based on Section using affinity propagation algorithm and put this cluster information back to the PDA s resources folder. Then, the online operations: localization, tracking and navigation obtain the fingerprint database and the map database from this folder to achieve their purposes Libraries Definitions Fig. 6.1 shows that the software is divided into six blocks of libraries. These libraries are organized so that each individual block deals with one specific task and allows the developer to modify these codes easily. These libraries are: MathAlgorithm This library contains the math algorithms that are required by the proposed system. It uses the open source library DotNetMatrix to perform the standard matrix operations. The four algorithms defined in this library are i) affinity propagation algorithm, which is converted from matlab code found in [15]; ii) l 1 -minimization by using primal-dual interior point method, known as basis pursit, which is also converted from matlab code found in CS-solver l 1 -Magic [65]; iii) Dijkstra algorithm as depicted in Fig. 5.2 and iv) the Kalman Filter as defined in Section 4.2. Although the affinity propagation algorithm is implemented, the software can only handle the computation for a small number of collected RPs. It complains for the lack of memory and crashes when the number of collected

88 Chapter 6. Software Implementation on Mobile Devices 75 fingerprints exceeds 15. Thus, the clustering process is done by a computer instead. LocalizerBasicLibrary This library provides the basic functions that are used by the rest of the program. It uses the open source libraries OpenNetCF to obtain the WiFi scanning function and the Samsung Mobile SDK to control the sensors of the Samsung smartphone. In addition, the config file is read by this library to set up the software to run properly with user s defined parameters. The behavior of the software during its launch is recorded in log files produced by this library for later observation. Moreover, it contains the functions to collect and write the fingerprint and map database into the IndoorLocResources folder. Localization This library implements the CS-based positioning system described in Chapter 3. It refers to MathAlgorithm to solve the l 1 -minimization problem. Tracking This library implements the CS-based tracking system described in Chapter 4. It is built based on the Localization and MathAlgorithm libraries. Navigation This library implements the navigation system described in Chapter 5. It refers to the MathAlgorithm library to run the Dijkstra algorithm for the path routing module. In addition, it also includes functions to load and play the voice instructions audio properly. IndoorLocalizerProg This is the main program of the software which defines the user interface and connects all the libraries together to the desirable functionalities. 6.4 Chapter Summary This chapter describes the software developed on the PDAs and smartphones for the proposed indoor tracking and navigation system. The software is developed in C# using Microsoft.Net Compact Framework version 3.5 for Windows Mobile-powered smartdevices. Besides the online operations that localize, track or navigate the user, the software

89 Chapter 6. Software Implementation on Mobile Devices 76 also includes the functions to collect offline fingerprint and map databases. In this thesis, the software is deployed on three devices: two HP PDAs and one Samsung smartphone to evaluate the performance of the proposed tracking and navigation system.

90 Chapter 7 Experimental Results In this chapter, the proposed CS-based positioning and tracking system is evaluated in different experimental sites using the devices mentioned in the previous chapter. Due to the dynamic and unpredictable nature of the radio channel in indoor environment, the RSS varies over time and cannot be modeled accurately by a propagation model. Thus, RSS readings are collected in real indoor environments to evaluate the performance of the proposed system. The results obtained by using different parameters for proposed systems are also examined to illustrate the effect of these parameters. In addition, the proposed systems are also compared with other positioning and tracking algorithms. Finally, the implementation of the navigation system for the actual sites is also included. 7.1 Experimental Setup Experimental Sites The experiments took place at two different sites: i) Bahen Centre for Information Technology of the University of Toronto and ii) Canadian National Institute for the Blind (CNIB). Their general information is summarized in Table 7.1. The proposed positioning and tracking system can be directly used in the buildings 77

91 Chapter 7. Experimental Results 78 Sites in Study Dimensions # of additional Total # Device # of deployed APs of APs in Test RPs Bahen 4th Floor 30 m 31 m 8 26 PDA1 72 CNIB 2nd Floor 35 m 71 m PDA2 128 Table 7.1: Comparison of experimental sites that are already equipped with access points (APs), whose settings and positions are unknown. Besides the original access points, several additional access points are deployed in the experimental sites to ensure that the sites have enough reliable RSS readings to estimate the locations accurately. The additional deployed APs denoted in Table 7.1 are the off-the-shelf access points, Cisco Linksys Wireless-G Router WRT54G2, which are set to have maximum transmission power 18dBm and set to transmit signals at channel 1. Note that all RSS readings collected by the devices are in dbm scale. Bahen Center: Positioning Analysis The first experimental site is a part of the fourth floor of the eight storey building, Bahen centre at the University of Toronto [83]. The main focus of this site is to analyze the performance of the CS-based positioning system as described in Chapter 3. The region of interest is a office area with a L-shaped corridor with a dimension of 30 m 31 m, which is comparable to those experimented in [19, 28, 38, 49]. Including the 8 additional deployed access points, which are spread across the whole area, a total of 26 access points can be detected. Both the PDA1 and Smartphone as defined in Table 6.1 are used for the fingerprint collection, but the analysis of the positioning system is mainly based on the PDA1 device, as it can obtain a better RSS fingerprint database due to better antenna and faster WiFi scanning rate than the Smartphone.

92 Chapter 7. Experimental Results 79 Fingerprint Collections For this experimental site, the PDA1 and Smartphone, each carried by an individual, are used to collect the fingerprints during the offline phase. At each RP, 50 RSS time samples from 26 APs were collected for each of the four orientations: North, East, South and West, by PDA1 and Smartphone with the sampling rates of 1 sample/second and 0.67 sample/second respectively. If the devices cannot detect the RSS from a particular AP, a small default value of -110dBm is assigned to that particular reading. A total of 72 RPs, which were evenly distributed along the corridors of the site with an average grid spacing of 1.5m were collected on both devices over a period of 5 days and 8 days for PDA1 and Smartphone respectively. These raw sets of RSS readings are then processed to generate the required fingerprint database for the positioning systems. Note that, the samples of default readings (-110dBm) are excluded when calculating the average and variance of the RSS readings. The positioning system is then evaluated by the following two RSS sets as the online RSS measurement vectors. Validation Data The positioning system is first tested by a validation set, which is extracted from the raw RSS readings of the fingerprint database. That is, at each of the RPs, choose one of the 50 RSS time samples at one of the four orientations collected by the device as the online RSS measurement vector to estimate the desired location, which should be the location of the corresponding RP. This set is used to evaluate the performance of the system under zero noise interference situation. Stationary User Testing Data Another set of online RSS readings were collected by the PDA1 on a different day to evaluate the performance of the system under timevarying environment. In order to obtain the actual locations of the user, the device let the stationary user orientated at an arbitrary orientation to click on the map, which was shown on the device s touchscreen, where he was standing and then the device started the WiFi scanning process. Each online observation was an average of 2 RSS time samples which was taken over a period of 2 seconds. In total, 3 online observations of 48 locations

93 Chapter 7. Experimental Results 80 spread across the area of interest were collected as the stationary user set. CNIB: Tracking and Navigation Analysis The evaluation of the performance of the proposed tracking and navigation systems described in Chapter 4 and 5 took place on the second floor of CNIB, located in midtown Toronto. Subject testings were also conducted at this site to evaluate the usefulness of the navigation system to the visually impaired people. This building is designed to provide easy accessibility to anyone, especially the visually impaired people [84]. The area of dimensions 35 m 71 m, which is larger than the experimental site at Bahen Centre, consists of a main straight central hallway connected to a C-shaped small corridor that leads to different conference rooms. Unlike the campus areas, such as the Bahen centre, which are densely populated with access points, there are only a few APs detectable in the CNIB. Thus, 15 additional APs are deployed throughout the whole area, creating a total of 23 APs that can be used in the experiments. All the three devices described in Table 6.1 are used to collect the fingerprint database, but the analysis of the tracking and navigation systems is mainly focused on the PDA2 device, as it has the best fingerprint database in terms of the number of real RSS readings from detectable APs, whereas the other two devices often cannot obtain the RSS readings from APs during the sampling periods. Fingerprint Collections Similar to the fingerprint collection process at the Bahen Centre, 50 RSS time samples were collected for each orientation at each RP by all the devices, except the Smartphone, which only 40 RSS time samples were collected instead. A total of 128 RPs, which were evenly distributed along the hallway and corridors with an average grid spacing of 1.5m were collected by PDA2. The number of RPs collected by the PDA1 (120 RPs) and Smartphone (126 RPs) varied slightly as they were operated by different individuals. It took about 10 days to finish this offline phase.

94 Chapter 7. Experimental Results 81 Mobile User Testing Data In order to evaluate the performance of the tracking system, several traces were collected on a different day by PDA2. The user carried the PDA2 device, which obtained RSS samples at every second, and walked at a constant speed along 4 different traces, as summarized in Table 7.2. The actual locations of the user for each step can be deduced based on the user s speed and elapsed time. Trace # # of turns # Repetitions Distance Average Duration m 156.3s m 89.2s m 84.6s m 279.5s Table 7.2: Traces Summary Performance Benchmarks The performance of the proposed positioning system is compared to two methods. The first one is the KNN method [19], described in Section 2.2.1, which is a simple technique that can be easily implemented on the mobile devices. In the following experiments, three neighbors (k = 3) are used to estimate the user s location. Another one is the kernelbased method [38], which is summarized in Fig The computation of this probabilistic approach technique involves all the RSS time samples collected during the offline phase and thus requires more processing time and resources. It may not be realizable by the mobile devices, as they have limited processing power and memory. As for the proposed tracking system, two performance benchmarks are used for comparison. They are the original proposed positioning system and the direct application of the Kalman filter on the original proposed positioning system.

95 Chapter 7. Experimental Results Figure of Merit The performance of the positioning and tracking systems can be evaluated in terms of the position error, which is defined as the Euclidean distance between the actual location and its estimation. The average root mean square error (ARMSE) is used as a metric for the performance evaluations and it is defined below: Average Root Mean Square Error (ARMSE) The ARMSE for the stationary user is defined as: ARMSE 1 N p 1 T i p N p T i ˆp i (t) 2 (7.1) i i=1 where p i is the actual location for test point i and ˆp i (t) is the estimated location for test point i using test sample t. N p and T i are the number of test points and number of test samples for test point i respectively. Similarly, the ARMSE for the mobile user is defined as: ARMSE 1 N trace 1 N i p N trace N i (t) ˆp i (t) 2 (7.2) i i=1 where p i (t) and ˆp i (t) are the actual and estimated locations for a particular trace i at step t. N trace is the number of traces and N i is the number of steps of trace i. t=1 t=1 7.2 Positioning Results on Bahen Fourth Floor This section focuses on the evaluation of the implementation of proposed CS-based positioning system using the PDA1 device on the fourth floor of Bahen Centre RSS Distributions RSS readings in an indoor environment vary due to several factors. The radio channel impediments such as shadowing and multi-path propagation due to walls and obstacles,

96 Chapter 7. Experimental Results 83 the orientation of the antennas of the wireless devices, the movements of human bodies are some of the causes that induce the time varying characteristics of the RSS, which cannot be easily predicted by a radio propagation model. In this section, the RSS distributions collected by PDA1 and Smartphone on the Bahen fourth floor are examined to illustrate these variations of RSS in indoor environment. RSS Distribution Over Time Fig. 7.1 depicts the histograms of RSS time samples from the same access points collected by both devices at the same reference point. Both histograms show that the RSS varies around the average values with certain variances. In this example, the mean and variance of the RSS collected by PDA1 are -48dBm and 23dBm, whereas for Smartphone (excluding the invalid -110dBm instances) are -68dBm and 18dBm respectively. The RSS readings collected by Smartphone are much lower than the ones collected by PDA1. This illustrates that the antenna gain for Smartphone is smaller than the one for PDA1. In addition, there are several instances that Smartphone is not able to detect any RSS (which is then assigned to a default value of -110dBm). This may be due to the hardware limitation of the antenna of the Smartphone. The low quality antenna of Smartphone makes it not as reliable as the PDA1 to be a WiFi-scanning device. The actual RSS readings across time are shown in Fig. 7.2a. This figure further illustrates that the RSS collected by PDA1 is much more stable and higher than the one collected by Smartphone, thus the RSS data collected by the PDA1 is used for the analysis of the CS-based positioning system applied on the Bahen fourth floor. Since the average RSS values are used by the proposed positioning and tracking system to estimate the user s location, it is important to obtain a reliable average value. Fig. 7.2b depicts the average RSS values against the number of RSS samples used. The average RSS for PDA1 converges to -48dBm after 30 samples are used, thus the fingerprint database that is generated from 50 time samples should be enough for the system.

97 Chapter 7. Experimental Results Frequency 4 3 Frequency RSS Readings [dbm] (a) RSS collected by PDA RSS Readings [dbm] (b) RSS collected by Smartphone Figure 7.1: Example histograms of RSS distributions of the same access point over 50 time samples for different devices pointing North at the same reference point on Bahen fourth floor PDA1 North Smartphone North PDA1 North Smartphone North RSS readings [dbm] RSS Average [dbm] Time [s] Number of RSS time samples (a) RSS measurements over time (b) RSS averages across time samples Figure 7.2: An example of RSS measurements over time and their averages with respect to the number of time samples of the same access point for different devices at the same reference point on Bahen fourth floor. RSS Distribution Across Reference Points The RSS distributions in spatial domain are shown in Fig Several observations are made from these figures. First, the orientation of the antenna of the same device affects the RSS variations slightly as illustrated in Fig. 7.3a. Second, the variations of RSS are much larger when different devices are used as shown in Fig. 7.3b. However, the trends

98 Chapter 7. Experimental Results 85 of the RSS distributions across the spatial domain are similar for all these cases. This particular access point is located close to the 20 th RP, thus the RSS at this RP is the strongest and decreases as the RPs are moving away from the access point. Note that there is a second peak of the RSS value at the 6 th RP, as this RP is in the same corridor where the AP is located. 20 PDA1 North PDA1 South 20 PDA1 North Smartphone North RSS Readings [dbm] 50 RSS Readings [dbm] Reference Points Indices Reference Points Indices (a) Different Orientations (b) Different Devices Figure 7.3: An example of averaged RSS of the same access point in spatial domain for different orientations and different devices on Bahen fourth floor Offline Phase: Clustering Results by Affinity Propagation The fingerprint database collected by the PDA1 are used for the analysis of the CS-based positioning system. As described in Chapter 3, the fingerprints are first pre-processed during the offline phase to generate clusters that are required for the later coarse location stage. Effect of Preferences on the Number of Clusters Generated According to (3.5), γ (o) is determined experimentally to obtain desirable number of clusters for the fingerprints. The number of clusters generated by affinity propagation using different values of γ (o) is shown in Fig Since the medians of the similarities defined in (3.4) are negative, smaller values of γ (o) result in larger values of preferences and hence

99 Chapter 7. Experimental Results 86 more clusters; this is a property for the affinity propagation algorithm [15]. The number of clusters generated for different orientations are very similar for the same value of γ (o) as RSS only varies slightly for different orientations North γ (0 ) East γ (90 ) South γ (180 ) West γ (270 ) 30 Number of Clusters γ (o) Figure 7.4: Number of clusters generated by the affinity propagation algorithm depending on the value of parameter γ (o) for four orientations on Bahen fourth floor. Generated Clusters Result The number of desirable clusters required by the CS-based positioning system is determined based on two criteria. First, most of the RPs from the same generated cluster should be geographically close to each other to minimize the number of distant outliers. This can be done by observing the clustering results generated in the above section using different values of γ (o). Second, the number of clusters should reasonably divide the fingerprints into smaller regions. If there are too few clusters, it leads to more RPs to be included for the fine localization stage and thus increases the computation cost in solving the l 1 minimization problem, whereas too many clusters are undesirable as well, as the fine localization stage within a small set of RPs becomes insignificant. The clustering results used by the CS-based positioning system for the following experiments are obtained by first setting the parameters γ (o) for the affinity propagation algorithm as in Table 7.3 and then reassigning the outliers that are physically far away from their own clusters to their geographically surrounding clusters. A total of 56 clusters

100 Chapter 7. Experimental Results 87 are generated in four orientations and the clustering results on the map are illustrated in Fig 7.5. North East South West γ (o) Number of clusters Table 7.3: Actual parameters γ (o) used for experiments on Bahen fourth floor Online Phase: Coarse Localization Analysis By using the validation set and the stationary user testing set collected by the PDA1, the performance of the CS-based positioning system is evaluated. This section examines the different settings and schemes used by the coarse localization stage as described in Section In order to ensure that only a few set of best-matched clusters are selected for the fine localization stage, the value of α 1 defined in (3.15) is set to In addition, the settings for the fine localization stage remain the same in this section, which are i) the random combination is used for the AP selection scheme and ii) the threshold defined in (3.24) is set to λ 1 = 0.4. Effect of the Number of Generated Clusters As shown in Fig. 7.6, the number of generated clusters affects the ARMSE of the positioning system when the same cluster matching scheme, namely the average-based plus strongest APs matching scheme as described in Section is applied. The same trend is observed for both the validation and stationary user testing data. When the system skips the coarse localization stage, which corresponds to the No clustering curve in the figure, the system has the highest ARMSE. This proves that the coarse localization stage is able to reduce the errors in estimating the user s position by reducing the area of

101 88 Chapter 7. Experimental Results (a) North (b) East (c) South (d) West Figure 7.5: The clustering results on the four fingerprint databases collected by PDA1 on Bahen fourth floor. Each circle is a RP collected in the database and each color represents one cluster. interest into a smaller region and hence minimizing the effect of outliers. Furthermore, increasing the number of clusters also reduces the ARMSE, as the system is able to confine the problem into a much smaller region in the coarse localization stage. The ARMSE remains fairly the same when eight or higher number of APs are used. Fig. 7.7 depicts the cumulative error distributions of the system using different number of generated clusters when eight APs are selected. The figure shows that the 58 clusters

102 Chapter 7. Experimental Results 89 used by the system achieve the best performance and attain the smallest maximum error. Note that the error obtained from the stationary user testing set is slightly higher. This is justified, as this set of data is collected on a different day and thus their RSS readings are varied from the fingerprint database, introducing errors in estimations No clustering 29 clusters; γ (o) =1 43 clusters; γ (o) = clusters; actual clusters used by system No clustering 29 clusters; γ (o) =1 43 clusters; γ (o) = clusters; actual clusters used by system 7 7 ARMSE [m] ARMSE [m] Number of APs Used Number of APs Used (a) Validation Data (b) Stationary User Testing Data Figure 7.6: The ARMSE versus number of used APs, when different number of generated clusters are used for the coarse localization on Bahen fourth floor Cumulative Error Probability No clustering 29 clusters; γ (o) = clusters; γ (o) = clusters; actual clusters used by system Distance Error [m] Cumulative Error Probability No clustering 29 clusters; γ (o) = clusters; γ (o) = clusters; actual clusters used by system Distance Error [m] (a) Validation Data (b) Stationary User Testing Data Figure 7.7: The cumulative error distributions using different number of clusters for the coarse localization on Bahen fourth floor. (8 APs are used)

103 Chapter 7. Experimental Results 90 Different Matching Schemes Section describes several cluster matching schemes that can be used to select the clusters, which best matched to the online RSS measurement vector r. Fig. 7.8 shows the comparison of using different matching schemes. It is obvious that in the validation set, the schemes that are applied on the strongest APs set have better accuracies and they have similar performances, except that the exemplar-based scheme has a higher maximum error. However, this trend is not as obvious as in the stationary user testing set, as the gap between the schemes with and without the use of strongest APs set is very small. In fact, the weighted average applied on the strongest APs set attains the highest maximum error. According to both sets of data, the average based strongest APs cluster matching scheme is a good choice for the system and is selected as the default operation for the coarse localization stage as it gives reliable results in both sets Cumulative Error Probability Exemplar based Average based Weighted Average Exemplar based + Strongest APs Average based + Strongest APs Weighted Average + Strongest APs Cumulative Error Probability Exemplar based Average based Weighted Average Exemplar based + Strongest APs Average based + Strongest APs Weighted Average + Strongest APs Distance Error [m] Distance Error [m] (a) Validation Data (b) Stationary User Testing Data Figure 7.8: The cumulative error distributions using different cluster matching schemes on Bahen fourth floor. (8 APs are used) Online Phase: Fine Localization Analysis This section focuses on the evaluation of using different settings for the fine localization stage.

104 Chapter 7. Experimental Results 91 AP Selection Schemes There are three access point selection schemes for the fine localization stage as described in Section The performances of using these schemes are compared in Fig For the random combination AP selection scheme, the x-axis refers to the number of linear random combinations of online RSS values from L APs according to (3.18). When the number of used APs is less than 14, both the Fisher criterion and the random combination AP selection schemes have similar results and achieve slightly better than the strongest APs scheme. However, when the number used APs is higher than 14, the strongest APs and Fisher criterion schemes achieve the same ARMSE in both sets of data, whereas, the random combination results in a slightly higher ARMSE. Although the random combination may sometime leads to slightly higher ARMSE than the other two schemes, it is chosen to be the default operation of the CS-based position system, as i) it does not require large samples of RSS data for the calculations of variance as required by the Fisher criterion; ii) it achieves better results when a small number of APs is used and iii) the same random matrix Φ can be reused, unlike the other two online RSS schemes that require on-the-fly generation of the AP selection matrix Φ and thus reduce the online update time. Sensitivity to Threshold λ 1 Another parameter that is required to be determined experimentally is the threshold λ 1 defined in (3.24), as it determines how many non-zero entries of the ˆθ should be used to interpret the actual location of the user. Fig illustrates the effect of λ 1 on the ARMSE results. It shows that the ARMSE can vary for a range of 0.4m, which is not very significant when comparing to the magnitude of the ARMSE, just by setting a different value of λ 1. Although the value of λ 1 does not have a linear relationship to the ARMSE, the figures show that the λ 1 should not be set to a high value, which implies that the system only obtains a few entries with highest value for the location

105 Chapter 7. Experimental Results Strongs APs Fisher Criterion Random Combination Strongs APs Fisher Criterion Random Combination ARMSE [m] ARMSE [m] Number of APs Used Number of APs Used (a) Validation Data (b) Stationary User Testing Data Figure 7.9: The ARMSE versus number of used APs, using different AP schemes for fine localization on Bahen fourth floor. interpretation. According to this experiments, this threshold should be set to λ 1 = 0.4 to let the system have the best performance ARMSE [m] ARMSE [m] λ 1 λ 1 (a) Validation Data (b) Stationary User Testing Data Figure 7.10: Effect of the threshold λ 1 on ARMSE on Bahen fourth floor. (8 APs are used) Performance Comparison Throughout the above experimentations, a set of optimal parameters that gives the best performance of the CS-based positioning system can be determined and is given in Table

106 Chapter 7. Experimental Results The performance of this positioning system is then compared to the KNN and kernel-based techniques in terms of the position error and computation time. Total number of generated clusters 58 Coarse Localization - cluster matching scheme Average-based + Strongest APs Coarse Localization - α Fine Localization - AP selection scheme Random combination Fine Localization - λ Number of APs used 8 Table 7.4: A set of optimal parameters for the CS-based position system applied on Bahen fourth floor. Position Error The position errors of the three methods are compared in Fig in terms of their cumulative error distributions. Table 7.5 and 7.6 summarize the statistics of their position errors. For validation set, the performance of the CS-based positioning system outperforms the other two methods. It reduces the ARMSE by 0.45m (22%) and 0.30m (16%) over the KNN and Kernel-based methods. In addition, the system also improves significantly in terms of maximum error (46%) and variance (62%). The position error is slightly higher for the stationary user testing set, as these RSSs are collected on a different day. Although the improvement of the CS-based positioning system is not significant in terms of ARMSE (4% for KNN and 12% for Kernel-based), the system still outperforms the other two methods in terms of maximum errors and variances.

107 Chapter 7. Experimental Results Cumulative Error Probability KNN 0.3 Kernel based CS based Positioning Distance Error [m] Cumulative Error Probability KNN 0.3 Kernel based CS based Positioning Distance Error [m] (a) Validation Data (b) Stationary User Testing Data Figure 7.11: The cumulative error distributions using different positioning systems on Bahen fourth floor. (8 APs are used) Method ARMSE [m] Mean [m] 90 th Percentile [m] Max[m] Variance [m 2 ] KNN Kernel-based CS-based Table 7.5: Position error statistics for different methods on Bahen fourth floor. (For validation set) Method ARMSE [m] Mean [m] 90 th Percentile [m] Max[m] Variance [m 2 ] KNN Kernel-based CS-based Table 7.6: Position error statistics for different methods on Bahen fourth floor. (For stationary user testing set) Computation Time Fig shows the computation time required for each step on a 2.50GHz Intel R Core TM 2 Quad processor with 4GB RAM using the three different localization techniques. Since

108 Chapter 7. Experimental Results 95 the Kernel-based method is a probabilistic approach that incorporates all RSS time samples from the fingerprint database for computation, it requires much more time to obtain the estimated position than the other two methods. Its computation time also increases as the number of used APs increases. Due to its high-volume computation cost, it is not desirable to implement on the resource-limited mobile devices as a real-time positioning system. Although the CS-based system requires a little more computation time than the KNN method, its simplicity and accuracy makes it a good method to be implemented on any mobile device Mean Computation Time [s] KNN Kernel based CS based Positioning Mean Computation Time [s] KNN Kernel based CS based Positioning Number of APs Used Number of APs Used (a) Validation Data (b) Stationary User Testing Data Figure 7.12: Comparison of mean computation time using different positioning systems in Bahen fourth floor. (8 APs are used) 7.3 Tracking Results on CNIB Second Floor In this section, the performance of the proposed tracking system described in Chapter 4 is evaluated based on the RSS data collected by the PDA2 device on the second floor of CNIB.

109 Chapter 7. Experimental Results RSS Distributions The RSS distributions based on the three sets of fingerprint databases collected by PDA1, PDA2 and Smartphone are examined briefly in this section. Fig. 7.13, 7.14 and 7.15 show the RSS distributions in terms of different parameters for all the three devices. Several observations can be made from these figures: There are some instances during the RSS sampling period that PDA1 and Smartphone are not able to detect the RSS from certain APs, thus their fingerprint databases are degraded. Although the RSS collected by PDA1 is the strongest, its RSS distribution in spatial domain fluctuates significantly when comparing to the other two devices as shown in Fig. 7.15b. This large fluctuation is undesirable as it introduces error to the positioning system. The RSS collected by Smartphone is significantly lower than the other two methods, as the device s antenna is of poor quality. The fingerprint database collected by PDA2 is the most stable over all the three devices and thus is used by the proposed tracking analysis for the following sections CS-based Positioning Results Before the analysis of the tracking system, the original CS-based positioning system is first compared to the KNN and Kernel-based methods. The generated cluster results after the modification of outliers are shown in 7.16 and the optimal set of parameters used by the system is summarized in Table 7.7. Fig and Table 7.8 compare the performances of the three localization methods on the mobile user testing set. The CS-based method behaves slightly worse than the KNN method unlike the results obtained for the Bahen fourth floor. This happens as a

110 Chapter 7. Experimental Results Frequency 5 Frequency 6 Frequency RSS Readings [dbm] RSS Readings [dbm] RSS Readings [dbm] (a) RSS collected by PDA1 (b) RSS collected by PDA2 (c) RSS collected by Smartphone Figure 7.13: Example histograms of RSS distributions of the same access point over 50 time samples (40 time samples for Smartphone) for different devices at the same reference point in CNIB second floor PDA1 North PDA2 North Smartphone North RSS readings [dbm] RSS Average [dbm] PDA1 North PDA2 North Smartphone North Time [s] (a) RSS distributions across time Number of RSS time samples (b) RSS averages across time samples Figure 7.14: An example of RSS distributions across time and their averages with respect to the number of time samples of the same access point for different devices at the same reference point in CNIB second floor. part of the CNIB second floor does not have a good coverage of the APs, which leads to poor clustering results around that region and makes the system hard to identify the correct clusters during the coarse localization stage. This also explains why the system attains very high maximum error, as it selects the wrong regions for localization. This effect is less prominent for the KNN method, as it compares the online RSS measurement

111 98 Chapter 7. Experimental Results PDA1 North PDA2 North Smartphone North RSS Readings [dbm] RSS Readings [dbm] PDA2 North PDA2 South Reference Points Indices (a) Different Orientations Reference Points Indices (b) Different Devices Figure 7.15: An example of RSS distributions of the same access point in spatial domain for different orientations and different devices in CNIB second floor. (only a part of the fingerprints are shown) (a) North (11 Generated Clusters) (b) East (17 Generated Clusters) (c) South (15 Generated Clusters) (d) West (16 Generated Clusters) Figure 7.16: The clustering results on the four fingerprint databases collected by PDA2 on CNIB second floor readings to each of the RP s RSS values instead of a subset of them. The proposed tracking system described in Chapter 4 is able to improve the CS-

112 Chapter 7. Experimental Results 99 Total number of generated clusters 59 Coarse Localization - cluster matching scheme Average-based + Strongest APs Coarse Localization - α Fine Localization - AP selection scheme Random combination Fine Localization - λ Number of APs used 10 Table 7.7: A set of optimal parameters for the CS-based position system applied on CNIB second floor. based positioning system by using previous history to ensure it chooses the correct relevant region during the coarse localization stage and smooths out the trajectory by the application of the Kalman filter. Their analysis are in the following sections Cumulative Error Probability KNN 0.1 Kernel based CS based Distance Error [m] Figure 7.17: The cumulative error distributions for different positioning systems on CNIB second floor. (10 APs are used) Modified Coarse Localization Analysis In this section, the use of different schemes to choose the RPs which are in physical proximity to the previous estimate, described in Section 4.3.1, are examined. The covariances

113 Chapter 7. Experimental Results 100 Method ARMSE [m] Mean [m] 90 th Percentile [m] Max[m] Variance [m 2 ] KNN Kernel-based CS-based Table 7.8: Positioning error statistics for different positioning methods on CNIB second floor. (For mobile user testing set) of the process and measurement noises of the Kalman filter are set to S = diag(1) and U = diag(80), where diag(d) refers to a diagonal matrix with the diagonal entries set to the scalar value d. According to Section 4.3.1, there are two parameters to be set for choosing the relevant RPs depending on their geographical locations to the previous user s location. The first parameter is to decide whether the previous estimated location (Unpredicted) should be used for the distance calculations to the RPs or the predicted location using the Kalman filter estimated state vector (Predicted) should be used. The second parameter is the walking distance range β defined in (4.15) and (4.17). Fig shows the ARMSE versus the walking distance range β when different schemes are used. Both schemes work the best when β = 4. In addition, the Unpredicted one works better than the Predicted one. This happens as the Predicted scheme may not be able to predict the correct user s current location and thus introduce errors when including non-relevant RPs for the fine localization stage Map Adaptive Kalman Filter Analysis In this section, the unpredicted user s location and β = 0.4 are used for the coarse localization stage and different parameters for the Kalman filter are examined.

114 Chapter 7. Experimental Results Unpredicted Predicted 2.6 ARMSE [m] β [m] Figure 7.18: Effect of the walking distance β on ARMSE in CNIB second floor. (10 APs are used) Sensitivity to the Covariances of Process and Measurement Noises. Fig illustrates the performances of the proposed tracking system using different combinations of covariances of process and measurement noises, S = diag(ds) and U = diag(du), respectively. The performances are very similar for most of the combinations, except for the case when ds = 10 and du = 80. It shows that the performance of the proposed tracking system is not affected significantly by changing the parameters of the Kalman filter Cumulative Error Probability ds = 1, du = ds = 1, du = 100 ds = 1, du = ds = 10, du = 80 ds = 0.5, du = Distance Error [m] Figure 7.19: The cumulative error distributions using different Kalman filter parameters in CNIB second floor. (10 APs are used)

115 Chapter 7. Experimental Results 102 Resetting Kalman Filter at Intersections Section mentions that the Kalman filter should be reset at the intersections, where there are a higher chance for the user to make turns and thus violate the linear motion model assumed by the Kalman filter. Fig compares the performance with and without resetting the Kalman filter at the intersections. Resetting the Kalman filter at intersections improves the system s accuracy. For the ARMSE, the resetting scheme improves from 2.20m to 2.07m (6%) and at the 90th percentile, it improves from 3.76m to 3.33m (11%) Cumulative Error Probability No reset Kalman filter at corner Reset Kalman filter at corner Distance Error [m] Figure 7.20: The cumulative error distributions for different Kalman filter update schemes in CNIB second floor. (10 APs are used) Performance Comparison From the above analysis, a set of optimal parameters that gives the best performance for the proposed tracking system is shown in Table 7.9. This tracking system is compared with the original CS-based positioning system and the direct applications of the Kalman filter on both the KNN method and the CS-based positioning system. Fig shows the comparison results in terms of cumulative error distributions and Table 7.10 shows the position error statistics for these four systems. The proposed tracking system outperforms

116 Chapter 7. Experimental Results 103 the other three methods. It reduces the ARMSE by 1.27m (39%), 0.64m (27%) and 0.53m (21%) over the CS-based positioning system, the KNN method with the Kalman filter and the CS-based position system with the Kalman filter, respectively. In addition, the proposed tracking system also has the smallest 90 th percentile error and variance when compared to the other systems. Modified Coarse Localization - Comparison schemes Modified Coarse Localization - β Non-Prediction scheme 4m Kalman Filter Covariances S = diag(1) U = diag(80) Table 7.9: A set of optimal parameters for the proposed tracking system applied on CNIB second floor Cumulative Error Probability CS based 0.1 KNN + Kalman Filter CS based + Kalman Filter Proposed Tracking Distance Error [m] Figure 7.21: The cumulative error distributions using the CS-based positioning system and the three tracking systems in CNIB second floor. (10 APs are used) Some of the example trace results are shown in Fig The estimated traces by the proposed tracking system are able to follow the actual traces walked by the user. These traces certainly improve the locations estimated by the CS-based positioning system shown as green dots on the figures.

117 Chapter 7. Experimental Results 104 Method ARMSE [m] Mean [m] 90 th Percentile [m] Max [m] Var [m 2 ] CS-based Positioning KNN Kalman Filter CS-based Kalman Filter Proposed Tracking Table 7.10: Position error statistics for the CS-based positioning system and the two tracking systems on CNIB second floor. (For mobile user testing set) (a) Trace #1 (b) Trace #2 (c) Trace #3 (d) Trace #4 Figure 7.22: Example trace results. The black line is the actual trace, the green dots are the CS-based positioning results and the purple line is the results of the proposed tracking system Navigation and Real Time Implementations Using the PDA2, which is installed with the developed software that implemented the proposed positioning and tracking system as described in Chapter 6, the user is able to

118 Chapter 7. Experimental Results 105 obtain the real-time estimated position updates periodically from the device. In addition, the user is able to use the navigation function provided by the software. The navigation module of the software requires the input of the map database, which helps the module to generate useful guidance to the user according to his locations. Fig depicts the definition of the connected graph and the map features on CNIB second floor, which are obtained according to Section 5.2. Figure 7.23: The definition of the connected graph and the map features on CNIB second floor. The blue lines and blue circles represent the edges and nodes of the connected graph. The red squares represents the destinations. The diamonds represents the map features and the pink circles represents the locations of the 15 deployed access points At the beginning of the navigation, the device asks the user to enter the desired target and then the module will route the path and play appropriate audio files to ask the user to follow the path. The actual operations of the navigation can be found in Chapter 5. Fig shows an example screenshot that is obtained from the device at the end of the real experiment carried on the CNIB second floor. The device is able to track the user s trajectory and give appropriate commands accordingly. Several video files can be found online in [85] to show the actual experiments conducted on CNIB second floor.

119 Chapter 7. Experimental Results 106 Figure 7.24: Example screenshot of the software that shows the actual track that the user is walking. The line shows the routed path generated by the navigation module. The squares denote the user s locations and the circle denotes the destination Subject Testing A preliminary research study was conducted over two months (in July and August 2010) at this site in collaboration with the CNIB research unit to evaluate if such navigation software developed on the smart device is useful in providing guidance to people with low vision, as defined according to [86]. Before the actual testing, the subject s visual acuity was first examined by a doctor for low vision. A total of 16 visually impaired subjects with an average age of 55 took part in this study and they were randomly assigned into two groups, each group contains 8 subjects: i) subjects in the Control group were only given instructions at the beginning of the test to reach the target by themselves; whereas ii) subjects in the Testing group were given the PDA2, which provided real-time navigation to guide them to the target. Each subject carried either a mobility cane or a guide dog and was required to walk three pre-determined paths, which are the same as the first three testing traces in the mobile user testing data. Table 7.11 gives a summary about these traces. The results of this study are summarized in Table Successful trial means that the subject is able to reach the destination at the end of the test. Several observations can be made according to the results in Table 7.12: The Testing group has a higher successful rate than the Control group. Since the