1. TARGET DETECTION AND TRACKING IN A WIRELESS SENSOR NETWORK Clement Kam, William Hodgkiss, Dept. of Electrical and Computer Engineering, University of California, San Diego Abstract Target detection and tracking in a wireless sensor network is studied. A Kalman filtering approach is applied both to mitigate false alarm as well as to smooth noisy target position estimates. Simulations illustrating the tracking results are presented. Introduction The emergence of wireless sensor network technology has led to applications in many areas, including industrial, military, and health care fields. Some of the major issues with setting up and running wireless sensor networks in these areas are power conservation, distributed processing, and goal-oriented, on-demand processing. In the detection and tracking system presented in this work, a first-step approach to a tracking system is presented. A Kalman filter algorithm is used to track a target passing through a field of sensors, and the system can predict what area the target is expected to lie in with high probability. This is used to ensure that the detection made by a sensor fits with the targets motion profile, thus minimizing false detections. This approach is taken from the paper by McErlean and Narayanan [1]. Basic Kalman Filter Equations Future Work For the wireless sensor network scenario shown, only a few samples have been processed in a single simulation. It would be desirable to run the same simulation for a longer time in a larger sensor field to obtain more samples, and be able to study the tracking ability of the Kalman filter more closely. Another modification would be to have smarter sensors that can detect where inside the sensing range the target is for comparison with the results shown here. Another issue that concerns wireless sensor networks is power management, since the sensing motes tend to have a limited battery life. The Kalman filter prediction is used here to prevent false alarms, but it can also be used to select a subset of the sensors to be turned on, and for the others to be asleep. Corrector Equations Predictor Equations Given a linear model for target motion, the prediction step in the Kalman filter can be exploited to predict, with high probability, an area where the target is expected to be in the future. The Kalman equations are given as below: Generic Two Dimensional Tracking Problem A two dimensional tracking scenario using Kalman filtering was simulated. Here, observations are available at every time step. Sparsely Sampled Two Dimensional Tracking Problem To study the effect of sparsely sampled data, the Kalman filter tracker was applied to a case where a section of data is missing. Linear Model for Target Motion This is the model for target motion that will be used for all of the simulations. w(n) is zero-mean Gaussian white noise with covariance matrix T is the time step, which in this case was chosen to be 0.1 seconds, and q is some constant. Qk=Qk= where Reference [1] D. McErlean, S. Narayanan, Distributed Detection and Tracking in Sensor Networks, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002. Volume: 2, 3-6, pp. 1174 - 1178 vol.2, Nov. 2002. Figure 1. The above shows a tracking simulation for a target starting at (5,5) plus noise. In this system, data is available at every time step.The red circles show where the Kalman filter predicts the target should be within a 3σ radius. The circles shrink in size asymptotically as time progresses, since there is greater confidence in where the target should be. Figure 2. The variance shown here is the predicted variance P k+1 - in the x- (or equivalently, the y-) coordinate. The variance corresponds to the red circles in Figure 1. Figure 3. The above shows the tracking simulation when data is missing for 10 samples. As a result, the prediction for where the target is after 10 samples is less certain, hence the large circle. Although the target cannot be tracked for those 10 samples, the prediction is still able to enclose the targets location, which is indicated by the square. Figure 4. The variance of the prediction decreases when data is available but grows sharply in the absence of data. Less information about the target location leads to less certainty in the predicted location. Wireless Sensor Network Target Tracking The wireless sensor network version of the tracking simulation reports data only when the target enters into a sensors sensing range. The data reported is the assumed location of the sensor which is randomly perturbed from the true location to model uncertainty in the location of the sensors. Figure 5. The sensors have a sensing range of 4 and are indicated by the dotted lines. Their true locations are indicated by the crosses, and the squares are the data reported. The assumed location is perturbed from the true location with a standard deviation of σ k =2. The red circles are the 3σ prediction circles, and in this case, have not failed to predict the region where the target is located at the moment of detection. As a mitigator of false detection, the Kalman filter prediction has confirmed that all of the events are caused by the target. The small circles are the Kalman filtered data. Their performance is difficult to analyze in a quantitative fashion for such a small number of samples. Figure 6. The prediction variance (size of the red circles in Figure 5) increases with the number of samples that occur between target detections (i.e., no data). The connected line shows the prediction variance at the times of detection, and the crosses show the prediction variance in between detections. It can be seen that following a detection (new data), there is a sharp drop in the variance, because there is greater certainty in the location. As time passes and no new data is available, there is a steep increase in prediction variance, as the prediction grows more uncertain with no observations.