Distributed Particle Filtering of $\alpha$ -Stable Signals

Abstract

In order to present an inclusive framework for distributed estimation/tracking of $\alpha$ -stable signals, a novel distributed particle filtering algorithm is developed. This is achieved through the reformulation of the particle filtering operations from the point of view of the characteristic function and is based on the decomposition of the operations of the particle filter so that they can be distributed among the agents of a sensor network while allowing each agent to retain an estimate of the state vector. In contrast to current distributed particle filtering techniques that approximate distributions with Gaussian mixtures through empirical estimates of the second-order statics and are, thus, limited to signals with finite variance, the developed distributed particle filtering approach is suitable for the generality of $\alpha$ -stable signals, allowing the proposed algorithm to be used in a multitude of applications. Finally, the so introduced distributed particle filtering approach is validated through a simulation example.