%0 Book Section
%B Filtering from Undersampled Data with an Introduction to Compressed Sensing
%D 2016
%T Distributed approximation and tracking using selective gossip
%A Deniz Üstebay
%A Rui Castro
%A Mark J. Coates
%A Michael G. Rabbat
%E A. Carmi
%E L. Mihaylova
%E S. Godsill
%I Springer-Verlag
%P 325-355
%X Many applications of wireless sensor networks require collection and processing of large amounts of data. The main challenge in fulfilling these tasks is preserving network resources such as lifetime and bandwidth. One approach to fuse and process large amounts of data without draining network resources is to reduce the data dimensionality. We present an algorithm called selective gossip to approximate high dimensional vectors of network data in an efficient manner. Our method is based on gossip algorithms which are decentralized methods studied extensively for scalar network data. In essence, gossip algorithms utilize iterative information exchange between pairs of nodes, and asymptotically all nodes reach consensus on a network aggregate. Selective gossip applies the idea of iterative information exchange to vectors of data. Instead of communicating the entire vector and wasting network resources, our method adaptively focuses communication on the most significant entries of the vector. We prove that nodes running selective gossip asymptotically reach consensus on these significant entries, and they simultaneously reach an agreement on the indices of entries which are insignificant. Selective gossip can be taken as a building block and used in various distributed signal processing algorithms. Here we study the distributed target tracking problem where the nodes of a sensor network collaboratively track a moving object. For problems involving nonlinear dynamics, nonlinear measurements, and non-Gaussian noise, particle filtering is the current state-of-the-art-estimation method. We propose a distributed particle filter implementation using selective gossip. In this setting, nodes maintain a shared particle filter to sequentially estimate the state of the target. The measurements taken by sensors are fused by reaching a consensus on the likelihood associated with the each particle. Selective gossip efficiently identifies particles with large weights and focuses communication resources on computing these important weights. Through a simulation study we demonstrate that selective gossip requires lower communication overhead while achieving similar accuracy as compared to the state-of-the-art distributed particle filtering approaches on a scenario involving bearings-only measurements of a maneuvering target.