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.