Image Filtering of Colored Noise Based on Kalman Filter

Transcription

1 ECHI International Journal of Computing Science and Communication echnologies, VOL.5 O. 2, Jan (ISS ) Image Filtering of Colored oise Based on Kalman Filter 1 Kamal Upreti, 2 Sushil Kumar Gangwar, 3 Shitiz Upreti, 4 hirunavuarasu K. 1, 2, 4 Galgotias University, Greater oida 3 Galgotia College of Engineering, Greater oida 1 [email protected], [email protected] bstract - his paper presents a core approach to design and develop a real-time based Vehicle racing System using Kalman filter. It is used to determine the current location of a target device in terms of UC time, Data status, latitude, longitude, UC date, Speed over ground in nots, Magnetic variation,mode indicators and Checsum information by utilizing the sms features of GSM technology. n attempt is made to improve the accuracy in locating GPS receiver by filtering out the irregularities using Kalman filter. linear recursive filtering technique, Kalman filter is used for estimating noise co-variance at current state (Q) and measurement error (R) from sensor noise measurement. he result of this proposed adaptive Kalman filter technique gives better accuracy with more consistency and provides better performance level as compared to the standard one. noise, mostly assumed as white noise. o improve the estimated state the Kalman filter uses measurements that are related to the state but disturbed as well. In tracing system, two problems must be considered: prediction and correction. Keywords: GSM, GPS, noise co-variance, Kalman filter, measurement error. I. IRODUCIO here are number of monitoring technologies used. raffic cameras are used for detecting and tracing current position of a vehicle. hese cameras not only used for simple applications such as counting cars,checing car lane but also for more complex applications lie tracing and analysis position of a vehicle. Multiple object tracing is an important research topic in computer vision. It has the ability to deal with the single object difficulties such as changing latitudes, longitudes, magnetic variations, mode indicators, checsum and speed over ground in nots, velocity, time and bacground appearance. In [19] tracing fix number of objects. In [21] an efficient algorithm to trac multiple people is presented. [16] Proposed a Bayesian tracer for tracing multiple blobs. Various tracing algorithms have been proposed in the literature, including approaches templates and local features [22] Kalman filters [14][24] and contours [20][23]. he mean-shift algorithm was first adopted as an efficient tracing technique in [15]. Prediction problem: predicts location of an object being traced in the next frame i.e identifying a region in which probability of finding region is very high. Correction problem: identify predicted frame in the designated region. well-nown solution is Kalman filter, recursive predicts that is based on the use of state space techniques and recursive algorithms. It estimates the state of a dynamic system. his dynamic system can be disturbed by some Figure 1: Diagram of Kalman filter he correction problem is based on symmetric metric to compare current and previous frame of an object. Matching metrics in correction problem is important[1].racing system is based on data association,clustering, finding exact position of moving object when there are more than one valid sample. II. SYSEM OVERVIEW In this research, it is proposed to design an embedded system which is used for tracing and positioning of any vehicle by using GPS and GSM. he current design is an embedded application, which will continuously monitor a moving vehicle and report the status of the vehicle on demand.. In this system, an 89S52 microcontroller is interfaced serially to a GSM modem and GPS receiver. GSM modem is used to send the position of the vehicle from a remote place[1]. he GPS modem will continuously give the data i.e the latitude and longitude indicating the position of the vehicle. he GPS modem gives many parameters as the output, but only the ME data coming out is read and displayed on the LCD. he same data is sent to the mobile at the other end from where the position of the vehicle is demanded. n EEPROM is used to store the mobile number. he hardware interfaces to microcontroller are GSM modem and GPS receiver. he design uses RS-232 protocol for 860

2 ECHI International Journal of Computing Science and Communication echnologies, VOL.5 O. 2, Jan (ISS ) serial communication between the modem and the microcontroller[2]. serial driver IC is used for converting L voltage levels to RS -232 voltage levels. When request by user is sent to the number at the modem, the system automatically sends a return reply to that mobile indicating the position of the vehicle in terms of latitude and longitude. E E Figure 2: Overview of tracing system III. KLM FILER he alman filter, also nown as linear quadratic estimation (LQE), is an algorithm which uses a series of measurement observed over time, containing noise ( random variations) and other inaccuracies and produces estimates of unnown variables that tends to be more precise than those that would be based on a single measurement alone. More formally, the Kalman filter operates recursively on streams of noisy input data to produce a statistically optimal estimate of the underlying system state. he advantages of including alman filter in the tracing process rate are: I. It provides the best optimal location to search for next frame and to improve the error detection rate. II. III. IV. GSM MODEM GPS RECEIVER IERF CE RESE SWICH SWICH IERFCE 8051 MIC ROC O ROL LER CRYSL OSCILLOR (89 S52) POWER SUPPLY LCD DRIVER LCD DISPLY It reduces searching time of next frame, thus shortens the processing time. he variance of the alman filter innovations is smaller than variance of the deterministic innovations. It reduces phantom detection since image does not contain area of frame that exclude from the search. For example, in a radar application, where one is interested in tracing a target, information about the location, speed and acceleration of the target is measured with a great deal of distorted signal by noise at any instance.he alman filter exploits the dynamics of the target, which governs its time evolution, to remove the effects of the noise and get a good estimate of the location of the target at the present time ( filtering ), at a future time (prediction ),or at a time in the past ( interpolation or smoothing ). he filter processes measurements to reduce a minimum error estimate of the system by utilizing the nowledge of the system, measurement dynamics and statistics of the system, noise measurement errors and initial condition information. In addition, smoothing effect of the alman filter will refine the tracing result from uncertainty of the noise [6]. It also helps to get exact location of the vehicle position where vehicles are missed detected. IV. MHEMICL FORMULIO OF KLM FILERS he Kalman filter addresses the general problem of trying to estimate the state x Rn of a discrete time controlled process that is governed by the linear stochastic difference equation as in equation.1. X K = X K -1 + B U K + W K -1 (1) With a measurement x R n that is (as stated in equation 2) Z K = H X K + V K (2) he random variables W K and V K represent the process and measurement noise (respectively). hey are assumed to be independent (of each other), white with normal probability Distribution. P (W) - (0, Q) (3) P (V) - (0, R) (4) he process noise covariance Q and measurement noise covariance R matrices as in equations 3 & 4 might change with each other step or measurement, however here we assume they are constant. (Peter S My bec (2001)). he n n matrix in the difference equation (1) relates the state at the current step K, in the absence of either a driving function or process noise. ote that in practice might change with each time step, but here we assume it is constant. he n 1 matrix B relates the optional control input x R1 to the state x.he m n matrix H in the measurement Equation (2) relates the state to the measurement ZK. In practice, H might change with each time step or measurement, but here we assume it is constant. he Kalman filter estimates a process by using a form of feedbac control: the filter estimates the process state at some time and then obtains feedbac in the form of (noisy) measurements. s such, the equations for the alman filter into two groups: time update equations and measurement update equations as shown equations as in figure 3.Discrete alman filter time update equations (5 & 6) are given as X - = x -1 + B u (5) P = P -1 + Q (6) ime update equations project the state and covariance estimates forward from time step -1 to step. and B are equations (1), while Q is from equation (3). Initial conditions for the filter are discussed in the earlier references. Discrete alman filter measurement update equations (7, 8& 9) are given below. K = P H (H P K H + R) -1 (7) X = X - + K ( Z H X - ) (8) P = (I K H) P (9) 861

3 ECHI International Journal of Computing Science and Communication echnologies, VOL.5 O. 2, Jan (ISS ) he time update equations are responsible for projecting forward (in time) the current state and error covariance estimates to obtain a priori estimates for the next time step. he measurement update equations are responsible for the feedbac i.e for incorporating a new measurement into a priori estimate to obtain an improved a posteriori estimate[3]. he time update equations, while the measurement update equations can be thought of as corrector equations. Indeed the final estimation algorithm for solving numerical problems. he first tas during the measurement update is to compute the alman gain, K. he next step is to measure the process to obtain Z and then to generate a posteriori state estimate by incorporating the measurement as in equation (8). he final step is to obtain a posteriori error covariance estimate via equation (9). fter each time and measurement updates pair, the process repeated with the previous a posteriori estimates used to project or predicts the new a priori estimates. his recursive nature is one of the very appealing features of the Kalman filter it maes practical implementation s much requires the non linear functions f(x -1,-1) and h(x, ) both be twice continuously differentiable. If the errors between the estimated state vector and the true state vector remain small, the linearization assumption is accurate. Higher order approximations have been derived but they typically involve significantly greater complexity while not maredly outperforming the recursive alman filter.[jazwinsi,1970] [Grewal and ndrews, 1993] [Gelb, 1974]. V. FILER PRMEERS D UIG he Kalman filter algorithm comprises of main four steps: Gain computation, state estimate update, covariance update and prediction.matrix K is the gain that minimized a posteriori error covariance. he equation that need to be minimized: xˆ e xˆ K( z x xˆ P E{ e e } Hxˆ ) ime Update ( Predict ) (1) Project the state ahead X = X -1 + B u (2) Project the error covariance ahead P = P -1 + Q Measurement Update ( correct ) (1) Compute the Kalman gain K = P H (H P H + R) -1 (2) Update estimate with measurement X = X + K (Z H X ) (3) Update the error covariance P = (I K H) P Initial estimates for X-1 and P-1 Figure 3: Parameters of alman filter more feasible than ( for example ) an implementation of a Wiener filter (Brown and Hwang 1992) which is designed to operate on all of the data directly for each estimate. he alman filter instead recursively conditions the estimate on all of the past measurements. Figure 3, offers a complete picture of the operation of the filter, combining the high level equations 5 & 6. his method shows linearization So, a posteriori estimate error covariance (P ) So, a posteriori estimate error covariance ( P ) P E{ e e d ( P dk One form of the result is } ) 0, solve for K K P H ( HP H R) 1 862

4 ECHI International Journal of Computing Science and Communication echnologies, VOL.5 O. 2, Jan (ISS ) When the error covariance R approaches 0, the actual measurement Z is trusted more, while the predicted measurement X is trusted less. When a priori estimate error covariance approaches 0, the actual measurement Z, is trusted less, while the predicted measurement X is trusted more. In closing we note that under conditions where Q and R are constant, both the estimation error covariance P and the Kalman gain K will stabilize quicly and then remain constant [5]. he tuning is usually performed off-line, frequently with the help of another (distinct) Kalman filter in a process generally referred to as system identification, which is clearly stated in (Bozic, 1999). For example, in case of tracing the head of a user of a 3D virtual environment we might reduce the magnitude of Q if the user seems to be moving slowly, and increase the magnitude if the dynamics start changing rapidly. In such cases Q might be chosen to account for both uncertainties about the user s intentions and uncertainty in the model. In that study using both synthetic and full-scale experimental data, we showed that the tuning improved the fitting of the data, and that more reliable predictions were obtained. Here we both present results from a study on the robustness of the methodology, using synthetic data, as well as some more results with full scale experimental data. n alternative of using the ensemble Kalman filter to tune the model parameters is to use a least square approach. his technique was exploited in Lorentzen et al. (2001b). he least square approach is, however, more computationally demanding, and seems therefore not to be suitable to online tuning (Lorentzen, 2002). VI. RESULS D DISCUSSIO Using single frequency ML 300 GPS hand held Receiver: data is collected at different locations around Delhi, oida and Meerut. Fig 4- shows that comparative analysis of data collected at different locations on the basis of Longitude, Latitude and ltitude with and without using Kalman filter. In addition, we have implemented a linear recursive filtering technique Kalman filter which improves the system performance by filtering out irregularities such as noise and distortion level. his technique increases the performance level with more consistency as compared to the conventional vehicle tracing system. It is shown in figure-4, that latitude mean error is , longitude mean error is and altitude mean error is which is reduced by using Kalman filter. VI. COCLUSIO In this paper, we have implemented Kalman filtering techniques, with real time based vehicle tracing system for predicting accurately the current location of the vehicle to yield better results. On the basis of this technique, we prepared a comparative analysis to plot a data for different locations that show larger amount of variations in the signals due to noise co-variance which can be smoothened by using alman filtering technique. However the recursive application of this methodology i.e. of smoothening the image or signal, but it has limitation that evaluating data in a robust domain creates some loss in the form of light, heat, white noise and redundancy of record by applying alman filter. Figure 4: Comparative analysis with and without using Kalman filter 863

5 ECHI International Journal of Computing Science and Communication echnologies, VOL.5 O. 2, Jan (ISS ) REFERECES [1] Salarpour and. Salarpur, 2011, Vehicle racing using alman filter and features, International Journal (SIPIJ), Vol. 2. [2] S. eoh and. Braunl,2010, Symmetry based monocular vehicle detection system, Machine Vision and pplications, pp [3]. K Kishore,. S Vardhan and. L arayana, 2010, Vehicle racing Using a Reliable Embedded Data cquistion System with GPS and GSM, Int. Journal of Computer Science and etwor Security,Vol.10 no.2, pp [4] J. Xiao and H. Feng, 2009, Low-Cost Extendable Framewor for Embedded Smart Car Security System, Int. Conf. on etworing, Sensing and Control, Oayama, pp [5] B.L. Malleswari and I.V. MuraliKrishna, 2009, he role of alman filter in the modeling of GPS errors, Journal of heoretical and pplied Information echnology. [6] M.. l-aee, O. B. Khader and.. l-saber, 2007, Remote monitoring of utomobile diagnostics and location using a smart box with Global Positioning System and General Pacet Radio Services,,in Proc. IEEE/CS ICCS,pp [7] B. L. Malleswari, I. V. Mural Krishna and K. L. Kishore, 2007, Kalman filter for GPS Datum Conversion, Mapworld Forum, Hyderabad. [8] W.C.M. Hsiao and S. K. J. Chang, 2006, he optimal location update strategy of cellular networ based traffic information system, Intelligent ransportation Systems conference, volume 4, pp [9] O. Rostamianfar, F. Janabi-Shatifi and I. Hassanzadeh. 2006, Visual racing System for Dense raffic Intersections, Proceeding of the Canadian Conference on Electrical and Computer Engineering CCECE, pp [10] K. Milton, 2006, Method and apparatus for eliminating ionospheric delay error in global positioning system signals. [11] R.K. Kumar, 2005, Improving ccuracy of Wireless L based Location Determination System using Kalman filter and multiple observers, Master hesis, Department of Computer Science and Engineering, II, Mumbai, India. [12] S.J Julier, J. K Uhlmann, 2004, Unscented filtering and nonlinear estimation, Proceedings of the IEEE, vol.92, pp [13] R. V. Merwe, 2004, Sigma-point alman filters for probalistic inference in dynamics state- space models, PhD. dissertation, OGI School of science and Engineering at Oregon Health & Science University (OHSU). [14] J. Lou, H. Yang, W. M. Hu and. an, 2002, Visual vehicle racing using an improved ef, sian Conference on Computer Vision. [15] D. Comaniciu, V. Ramesh and P. Meer, 2002, Real ime racing of non rigid objects using mean shift, IEEE Conference on Computer Vision and Pattern Recognition, vol.2, pp , Hilton Head Island, South Carolina. [16] C.Hue, J.P Le Cadre and P.Perez, 2002, racing multiple objects with particle filtering, IEEE ransactions on eroplane and Electronic System, [17] R. Ewan and V. Merwe, 2001, Kalman Filtering and eutral etwors, First Edition John Wiley & sons, ch-7, pp [18] E..Wan and R. Vander Merwe,2000, he unscented alman filter for non linear estimation, in proceeding of Symposium 2000 on daptive System for signal processing, communication and control (S-SPCC). [19] J. P. MacCormic and. Blae, 1999, probabilistic exclusion principle for tracing multiple objects, in ICC V99, [20] E. B. Meier and F. de, 1999, Using the condensation algorithm to implement tracing for mobile robots, hird European Worshop on dvanced Mobile Robots, pp , Zurich, witzerland. [21] H. ao, H.S. Sawhney and R. Kumar, 1999, sampling algorithm for tracing multiple objects in Vision lgorithms. 864