Compressive Sensing Based Probabilistic Sensor Management for Target Tracking in Wireless Sensor Networks

In this paper, we consider the problem of sensor management for target tracking in a wireless sensor network (WSN). To determine the set of sensors with the most informative data, we develop a probabilistic sensor management scheme based on the concepts developed in compressive sensing. In the proposed scheme where each sensor transmits its observation with a certain probability via a coherent multiple access channel (MAC), the observation vector received at the fusion center becomes a compressed version of the original observations. In this framework, the sensor management problem can be cast as the problem of finding the probability of transmission at each node so that a given performance metric is optimized. Our goal is to determine the optimal values of the probabilities of transmission so that the trace of the Fisher information matrix (FIM) is maximized at any given time instant with a constraint on the available energy. We consider two cases, where the fusion center has i) complete information and ii) only partial information, regarding the sensor transmissions. The expression for FIM is derived for both cases and the optimal values of the probabilities of transmission are found accordingly. With nonidentical probabilities, we obtain the results numerically while under the assumption that each sensor transmits with equal probability, we obtain the optimal values analytically. We provide numerical results to illustrate the performance of the proposed probabilistic sensor management scheme.