  We present the Bayesian consensus filter (BCF) for tracking a moving target
using a networked group of sensing agents and achieving consensus on the best
estimate of the probability distributions of the target's states. Our BCF
framework can incorporate nonlinear target dynamic models, heterogeneous
nonlinear measurement models, non-Gaussian uncertainties, and higher-order
moments of the locally estimated posterior probability distribution of the
target's states obtained using Bayesian filters. If the agents combine their
estimated posterior probability distributions using a logarithmic opinion pool,
then the sum of Kullback--Leibler divergences between the consensual
probability distribution and the local posterior probability distributions is
minimized. Rigorous stability and convergence results for the proposed BCF
algorithm with single or multiple consensus loops are presented. Communication
of probability distributions and computational methods for implementing the BCF
algorithm are discussed along with a numerical example.
