Distributed Kalman Filtering: When to Share Measurements

This paper considers the problem of designing distributed Kalman filters (DKFs) when the sensor measurement noise is correlated. To this end, we analyze several existing methods in terms of their Bayesian Cramer-Rao bounds (BCRB), and insights from the analysis motivates a departure from the conventional estimate-sharing frameworks in favor of measurement-sharing. We demonstrate that if the communication bandwidth and computational resources permit, the minimum mean-square error (MMSE) estimator is implementable under measurement-sharing protocols. Furthermore, such approaches may use less communication bandwidth than standard consensus methods for smaller estimation problems. The developments are verified in several numerical examples, including comparisons against previously reported methods.