  Motivated by non-linear, non-Gaussian, distributed multi-sensor/agent
navigation and tracking applications, we propose a multi-rate consensus/fusion
based framework for distributed implementation of the particle filter (CF/DPF).
The CF/DPF framework is based on running localized particle filters to estimate
the overall state vector at each observation node. Separate fusion filters are
designed to consistently assimilate the local filtering distributions into the
global posterior by compensating for the common past information between
neighbouring nodes. The CF/DPF offers two distinct advantages over its
counterparts. First, the CF/DPF framework is suitable for scenarios where
network connectivity is intermittent and consensus can not be reached between
two consecutive observations. Second, the CF/DPF is not limited to the Gaussian
approximation for the global posterior density. A third contribution of the
paper is the derivation of the exact expression for computing the posterior
Cramer-Rao lower bound (PCRLB) for the distributed architecture based on a
recursive procedure involving the local Fisher information matrices (FIM) of
the distributed estimators. The performance of the CF/DPF algorithm closely
follows the centralized particle filter approaching the PCRLB at the signal to
noise ratios that we tested.
