Energy efficient distributed filtering with wireless sensor networks

We consider a wireless sensor network (WSN) that monitors a physical field and communicates pertinent data to a distant fusion center (FC). We study the case of a binary valued hidden natural field observed in a significant amount of Gaussian clutter, which is relevant to applications like detection of plumes or oil slicks. The considerable spatio-temporal dependencies found in natural fields can be exploited to improve the reliability of the detection/estimation of hidden phenomena. While this problem has been previously treated using kernel-regression techniques, we formulate it as a task of delay-free filtering on a process observed by the sensors. We propose a distributed scalable implementation of the filter within the network. This is achieved by i) exploiting the localized spatio-temporal dependencies to define a hidden Markov model (HMM) in terms of an exponential family with O(N) parameters, where N is the size of the WSN, ii) using a reduced-state approximation of the propagated probability mass function, and iii) making a tractable approximation of model marginals by using iterated decoding algorithms like the Gibbs sampler (GS), mean field decoding (MFD), iterated conditional modes (ICM), and broadcast belief propagation (BBP). We compare the marginalization algorithms in terms of their information geometry, performance, complexity and communication load. Finally, we analyze the energy efficiency of the proposed distributed filter relative to brute force data fusion. It is demonstrated that when the FC is sufficiently far away from the sensor array, distributed filtering is Significantly more energy efficient and can increase the lifetime of the WSN by one to two orders of magnitude.