Distributed Estimation Using Particles Intersection

A technique is presented for combining arbitrary empirical probability density estimates whose interdependencies are unspecified. The underlying estimates may be, for example, the particle approximations of a pair of particle filters. In this respect, our approach, named hereafter particles intersection, provides a way to obtain a new particle approximation, which is better in a precise information-theoretic sense than that of any of the particle filters alone. Particles intersection is applicable in networks with potentially many particle filters. We demonstrate both theoretically and through numerical simulations that depending on the communication topology this technique leads to consensus in the underlying network where all particle filters agree on their estimates. The viability of the proposed approach is demonstrated through examples in which it is applied for multiple object tracking and distributed estimation in networks.