Hybrid Algorithm for Indoor Positioning Using Wireless LAN

Transcription

1 Hybrid Algorithm for Indoor Positioning Using Wireless LAN Jaimyoung Kwon Institute of Transportation Studies University of California, Berkeley and Department of Statistics California State University Hayward, CA Baris Dundar and Pravin Varaiya Department of Electrical Engineering and Computer Science University of California Berkeley, CA, Abstract Locating an indoor mobile station based on wireless communication infrastructure, has practical applications. The most widely employed methods today use a RF propagation loss (PL) model or location fingerprinting (LF). The PL method is known to perform poorly compared to LF. But LF requires an extensive training dataset and cannot adapt well to configuration changes or receiver breakdown. In the current paper, we develop a hybrid method that combines the strength of these two methods. It first formulates the RF propagation loss in a nonlinear, censored regression model and adjusts the regression function to the observed signal strength in the fingerprint dataset. In the absence of a training dataset, the hybrid method coincides with the PL method and as the spatial granularity of training dataset increases, the result of the algorithm approaches the result of the LF method. It balances flexibility and accuracy of the two traditional methods, makes intelligent use of missing values, produces error bounds, and can be made dynamic. We evaluate the performance of the algorithm by applying it to a real site and observe satisfactory positioning accuracy. I. INTRODUCTION Positioning the location of a mobile station has various practical applications. It can be achieved either by special infrastructure like the Global Positioning System (GPS), but it is also desirable to use existing infrastructures. Such infrastructures include cell phone antennas for locating mobile phone users and access points (APs) for locating wireless LAN users. The current paper studies indoor positioning based on IEEE 802.b wireless communication infrastructure. The problem can be summarized as follows. We have a transmitter (mobile user) with unknown coordinate A R 2 and receivers (access points) with known coordinates B j, where j =,...,M indexes receivers. Both A and B resides either in R 2 (more common) or in R 3. At some time, the receivers report the strength of the wireless signal they receive from the transmitter. Call Y j the received signal strength (RSS) reported from receiver j. The problem is to estimate the location A from the data {Y j,b j }. Currently two approaches are commonly employed: RF propagation loss model method and location fingerprinting. See [2], [3], [] and [5], among others, for a brief survey of the field and alternative approaches. A. RF propagation Loss Model Method From the RSS vector Y = (Y,...,Y N ), the scheme searches for the location A that is likely to generate the observed vector assuming the observed RSS follows a radio frequency (RF) propagation loss model. For example, one could model the RSS at receiver j at B j when the transmitter with power P 0 is at A by Y j g j (Θ,A) () = P 0 0 δ log 0 d(a, B j ) wallloss, where P 0 is the power of transmitter, δ (so called the clutter density ) is a number (default 3) which represents the clutter, d(a, B j ) is the Euclidean distance between A and B j, and wallloss is the sum of the losses introduced by each wall on the line segment drawn between A and B j. The regression function g j (Θ,A) is specific to the receiver j, and Θ is the general site characteristic parameter vector. In the simplest setting, we estimate d(a, B j ) for at least three j and use triangulation to find the coordinate A. B. Location fingerprinting Location fingerprinting method requires a training dataset, which is the collection of data {(Y i,c i ),i =,...,N}, for N locations in the site, where C i is the known location of the i th measurement and Y i =(Y i,...,y in ) is the RSS vector when the transmitter is at C i. The vector Y i is the fingerprint of the location C i. Based on this training dataset, when a new fingerprint Y is observed from a transmitter with unknown location A, one searches for the fingerprint Y i that is closest to Y in say L p distance for certain p (typically p= or 2) and estimate A with the corresponding C i. C. Comparison of the two methods Due to the difficulty of correctly modeling multipath environment in indoor areas, RF propagation loss model based methods perform poorly compared with location fingerprinting. On the other hand, to perform well, location fingerprinting requires a large training dataset covering locations on very fine

2 grids (large N). This requires an extensive initial deployment effort. Also, if the configuration changes, the training dataset needs to be constructed again. Finally, fingerprinting is not very robust aginst the breakdown of some receivers. We develop a new method with these characteristics: ) It is a hybrid method that combines the strengths of the RF propagation loss model and fingerprinting methods. The idea is to achieve accuracy comparable with fingerprinting, but requiring a much smaller data collection effort. 2) The method produces an error bound of the location estimate. In many applications, the user can benefit by having a measure of accuracy. 3) The method makes intelligent use of missing values to increase positioning accuracy. Ambiguity in positioning can arise when fewer than three receivers hear the transmitter, and one can resolve the resulting ambiguity in many cases from the knowledge that certain receivers do not hear the transmitter. ) The method can be easily extended to dynamic positioning via Kalman filtering to estimate the trajectory of a moving transmitter. Details of the algorithm are presented in Section 2. In Section 3, we apply the algorithm to a test site and investigate its performance. Section concludes the paper. II. METHODS We first formulate the RF propagation loss in the following probabilistic model: Y j = g j (Θ,A)+e j,j =,..., M, (2) where the error terms e j are assumed to be independent and follow the common normal distribution N(0,σ 2 ). Also, if the signal strength is weaker than some threshold Y 0, the receiver j does not hear the transmitter, resulting in a missing value. Such observation is said to be censored in statistics literature. A. Nonlinear Censored Regression Model and Maximum Likelihood Estimation Considering A as the unknown parameter, the likelihood and the log-likelihood functions of this model are M L(A) = Φ(Y 0 g j (Θ,A)) (Yj<Y0) (3) l(a) = φ(y j g j (Θ,A)) (Yj Y0), and M (Y j <Y 0 ) log Φ(Y 0 g j (Θ,A)) () +(Y j Y 0 ) log φ(y j g j (Θ,A)), respectively. Here Φ and φ denote the cumulative distribution and probability density function of the normal distribution N(0,σ 2 ), respectively. In effect, we formulate the positioning based on RF propagation loss model as a nonlinear censored regression model [7]. Once the model is represented in this way, we can apply standard likelihood theory to this model to obtain the maximum likelihood estimate (MLE) Â of A and the error bound with certain confidence level. See [] for details on the properties of MLEs. B. Hybrid Algorithm To improve positioning accuracy, we combine the method with fingerprinting in the following way. As in fingerprinting, we obtain a training dataset (Y i,c i ) at several locations C i,i =,...,N. With this information, we adjust the regression function g j (Θ,A) in (2) as h j (Θ,A)=g j (Θ,A)+ g j (Θ,A), j =,..., M, (5) where g j (Θ, ) is the surface over the domain R 2 or R 3 that is estimated from the residuals Y ij g j (Θ,C j ),i=,..., N viewed as a marked point process on the domain. Various methods exist for estimating such a surface, from simple interpolation to more complicated spatial statistics techniques. In this paper, we use the trend surface ([6] and [8]) with degree 2 polynomial surface. Given the corrected regression function h j (Θ, ), the rest of the positioning algorithm is identical to the censored nonlinear regression method given above. If there is no training dataset, the hybrid method coincides with RF propagation loss model method. As the spatial granularity of training dataset increases, the regression function h j approaches the one (implicitly) used by fingerprinting and the result of the algorithm become close to that of the fingerprinting method. But even in this case, unlike in fingerprinting, the hybrid method retains characteristics 2-, i.e., it makes intelligent use of missing values, produces an error bound, and can be made dynamic. C. Computation of the Error Bound From the MLE theory, for MLE Â of A, M( Â A) N(0,I (A)) (6) approximately for large M, where the Fisher information matrix I(A) is given by [ ] I(A) =E A 2 log f(x, A). (7) A2 Here f(x, A) is the probability density function of X with parameter A, whose log appears as the summand in (). We approximate I(A) by replacing A with Â, the expectation with the average, and differentiation with the finite difference. This can be done without much cost especially when one maximizes l(a) directly over grid in R 2. To summarize, 2 Î(Â) = l(â)/m, (8) A2 where / A denotes the finite difference operator.

3 Fig.. Test Site at the 3rd Floor of Cory Hall, UC Berkeley Fig. 2. Measurement (White Circle) and AP Locations (Black Dots) D. Dynamic Positioning Using one of the above strategies, one can estimate A t by Ât with the accompanying error estimate ˆΣ t over time t =, 2,... We present extension of the algorihm to a dynamic positioning algorithm by the Kalman filtering formulation [9]. We assume the linear stochastic difference equation with the measurement x t = Dx t + w t z t = Hx t + v t. One obvious way of embedding our static scheme to this dynamic setup is by letting D = H = I (identity), so the mobile user moves as a random walk (the distribution of w t needs to be supplied) and setting x t = A t = true location of the mobile user at time t z t = Ât = estimated location of the mobile user at time t Naturally, v t N(0, Σ t ) (9) with Σ t estimated by Î(Ât) above. Then the usual Kalman filter algorithm can be applied to produce dynamic tracking of the location. See [9]. III. EXPERIMENT We evaluate the performance of the algorithm by applying it to a real site with 802.b wireless LAN infrastructure. The data are collected from the 3rd Floor of Cory Hall of UC Berkeley. Figure shows the floor plan of the 7 58 meter site. For the study, we divide the site into 7 58 grid points, each grid corresponding to one square meter. We took RSS measurements at 23 locations in the site (shown in Figure 2) using our site survey software. At each measurement location, four active scans were performed and at each scan, the APs that are heard, identified by their MAC addresses, and corresponding RSS (in dbm), are recorded. A Fig. 3. AP Deployment Level (Circle = 23; Triangle = 0; and Cross = 5) total of 38 APs are heard in at least one scan, but no AP is heard at all locations. Each location hears 7.9 APs on the average, with the number of APs heard at any location ranging from 9 to 2. Thus there is a lot of censoring due to weak RSS. Wireless signal gets unstable when RSS reaches -75 to -80 dbm and wireless devices typically cannot hear signal weaker then -0 db or -96 dbm. For the current dataset, the RSS ranges between -9 and - dbm with the mean and median of and -78, respectively. We use -9 dbm as the censoring point Y 0, below which wireless device can t hear. Note that we can compute standard deviation (SD) of RSSI from the same AP from the multiple scans. For those APs that are heard in all four scans at each location, we compute the SD; the mean of all SDs is.37 (dbm). We set this to be the parameter σ in the Gaussian error distribution. Among the 38 APs heard in the training data, we consider only the APs that are located on the same floor, i.e., we restrict ourselves to 2-dimensional, not 3-dimensional, positioning. The true location of those APs are also shown in the Figure 2. Heuristically, there are high chances of getting

4 very weak signals due to the adverse direction of the receiver, passing obstacles, interference, etc., while the chances of getting a very strong signal is small. Reflecting this heuristics as well as to speed up computation, for each measurement location and AP pair, we use the largest RSS as the observed Y j. The original problem is positioning a mobile user/transmitter with unknown location from RSS received at multiple receiver/aps with known locations. Since the relationship between a transmitter and a receiver is symmetric under the reasonable assumption that all transmitters (APs in this case) have same output power P 0, we apply the algorithm to locate APs with RSS received at various measurement locations. The reason for this is to evaluate the effect of decreasing number of APs in the positioning accuracy more easily. (There are more measurement locations than APs in our data.) Thus, from now on, we refer to the original APs and receiver as (mobile user) location and APs. So M = 23 and we have unknown mobile locations to estimate in our data. Note that 23 AP locations in 7 58 meter site is unusually dense in practice. To simulate more realistic AP deployment situations, we reduce these to 0 and 5 AP locations. They are selected to be distributed in a balanced and nested manner. Figure 3 shows the original and reduced AP deployment levels. At each level of deployment, we apply the following methods to position the receiver: ) Closest AP method: Estimate A by the location Bj with the strongest RSS j = max,...,m Y j. 2) Naive MLE: Estimate A by maximizing the observed Y j -only log-likelihood l (A) l (A) = M (Y j Y 0 ) log φ(y j g j (Θ,A)), (0) instead of (). 3) Proper MLE: Estimate A by maximizing the loglikelihood l(a). ) Corrected MLE: Proper MLE with corrected regression function (5). Table I and Figure show the median positioning error of each method at each deployment level. As expected, the closest AP method performs increasingly poorly as the number of APs decreases. The naive MLE performs better than the closes AP method except at M = 5. The proper MLE improves upon both the closest AP method and the naive MLE. The improvement is negligible at very dense deployment M =23 but the benefit is visible at both M =0and 5. Still, at M = 5, the method performs nearly as poorly as the closest AP method. The corrected MLE, on the other hand, improves over all other competitors at all deployment levels, exhibiting 2%, 2% and % reduction in median positioning error compared to the next best method, the proper MLE. Quite interestingly, it doesn t suffer much from the sparse deployment of APs. As one moves from 23 APs to 0 APs and then to 5 APs, the median positioning error increases at the moderate rate of % (meter) Median Positioning Error Deployment Level Fig.. Median Positioning Error of the Four Methods at Various Deployment Levels (=Closest AP; 2=Naive MLE; 3=Proper MLE; and =Corrected MLE) TABLE I MEDIAN POSITIONING ERROR OF THE ALGORITHMS (IN METERS) Deployment Level M Closest AP Naive MLE Proper MLE Corrected MLE and 27%. Even when only 5 APs are deployed, the median positioning error is less than 7 meters, which is acceptable. Figure 5 illustrate the behavior of the Naive MLE, Proper MLE and Corrected MLE algorithms. Note that the pure white area in the contour plots signifies the lowest likelihood value. It is clear from the likelihood contour of the proper MLE that as one starts to handle missing values correctly, the high likelihood region reduces to the area around the true location, excluding a lot more area as highly unlikely (white area) compared to the likelihood contour for the naive MLE. As one starts to use the corrected regression function (the third contour plot), the white patch expands even further and the likelihood zooms in to the true value and the proper MLE estimates the true location with a very small error. Figure 6 illustrate the error bound estimated by the normal approximation (6) for the corrected MLE for the same example. Such error bound provides the helpful information to the end user by providing a quantitative measure of how reliable the positioning is. Also, regarded as Σ t of (9) at the current time, it can be used for dynamic positioning by Kalman filtering as presented above. IV. CONCLUSION We presented a hybrid algorithm for indoor positioning using wireless LAN that aims to combine the benefits of the RF propagation loss model and fingerprinting method. It relies on the probabilistic formulation of the wireless positioning 2 3

5 60 70 Naive MLE Corrected MLE Proper MLE Fig , 95, 99% Confidence Ellipses (From the Smallest to the Largest) for Corrected MLE In an application to a real site, the proposed algorithm exhibits 20 to 0% improvement in positioning accuracy compared to competing methods at all deployment levels. Also, it maintains reasonable positioning accuracy of about 5 to 7 meter even for a very sparse deployment of APs. Corrected MLE Fig. 5. Likelihood Contour for Naive, Proper and Corrected MLE Methods with the MLE Estimate (White Circle) and the True Location (Black Square) for a Location with M =0 problem as a nonlinear censored regression problem and nonparametric correction of the RF propagation loss model function using empirical RSS. It handles missing values in a correct manner and produces a likelihood-theory based error bound, which is useful as a reliability measure as well as an input for the dynamic extension of the algorithm based on Kalman filtering. The algorihtm requires less initial deployment effort than LF method and is robust against the breakdown of some receivers. The algorithm is also substantially more accurate than unmodified RF propagation loss model. ACKNOWLEDGMENT Research supported by California Department of Transportation. REFERENCES [] P. J. Bickel and K. A. Doksum, Mathematical Statistics:Basic Ideas and Selected Topics, Vol I, 3nd ed. Prentice Hall, [2] T. Kitasuka, T. Nakanishi, and A. Fukuda, Wireless LAN based Indoor Positioning System WiPS and Its Simulation. Proc IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM 03), pp , August, [3] Kotanen, A., Hannikainen, M., Leppakoski, H., and T. D. Hamalainen, Positioning with IEEE 802.b wireless LAN, th IEEE Proceedings on Personal, Indoor and Mobile Radio Communications, 2003., Vol. 3, (September 2003): [] Ladd, A. M., Bekris, K. E., Rudys, A., Kavraki, L. E., and D. S. Wallach, On the Feasibility of Using Wireless Ethernet for Indoor Localization. IEEE Transactions on Robotics and Automation, 20(3):In Press, June 200. [5] T. Liu, P. Bahl and I. Chlamtac, Mobility Modeling, Location Tracking, and Trajectory Prediction in Cellular Networks. IEEE Journal on Special Areas in Communications, Special Issue on Wireless Access Broadband Networks, Vol. 6, No. 6, (August 998): [6] Ripley, B. D., Spatial Statistics. Wiley, 98. [7] Stute, W., Nonlinear censored regression. Statistica Sinica, Vol. 9, (999): [8] Venables, W. N. and Ripley, B. D., Modern Applied Statistics with S. Fourth edition. Springer, [9] Welch, G. and Bishop, G., An Introduction to the Kalman Filter. TR 95-0, Department of Computer Science, University of North Carolina at Chapel Hill. April 5, 200.