A parallel resampling scheme and its application to distributed particle filtering in wireless networks

We address the design of a particle filter (PF) that can be implemented in a distributed manner over a network of wireless sensor nodes, each of them collecting their own local data. This is a problem that has received considerable attention lately and several methods based on consensus, the transmission of likelihood information, the truncation and/or the quantization of data have been proposed. However, all existing schemes suffer from limitations related either to the amount of required communications among the nodes or the accuracy of the filter outputs. In this work we propose a novel distributed PF that is built around the distributed resampling with non-proportional allocation (DRNA) algorithm. This scheme guarantees the properness of the particle approximations produced by the filter and has been shown to be both efficient and accurate when compared with centralized PFs. The standard DRNA technique, however, places stringent demands on the communications among nodes that turn out impractical for a typical wireless sensor network (WSN). In this paper we investigate how to reduce this communication load by using (i) a random model for the spread of data over the WSN and (ii) methods that enable the out-of-sequence processing of sensor observations. A simple numerical illustration of the performance of the new algorithm compared with a centralized PF is provided.