Optimal sample-based fusion for distributed state estimation

In this paper, we present a novel approach to optimally fuse estimates in distributed state estimation for linear and nonlinear systems. An optimal fusion requires the knowledge of the correct correlations between locally obtained estimates. The naive and intractable way of calculating the correct correlations would be to exchange information about every processed measurement between all nodes. Instead, we propose to obtain the correct correlations by keeping and processing a small set of deterministic samples on each node in parallel to the actual local state estimation. Sending these samples in addition to the local state estimate to the fusion center allows for correctly reconstructing the desired correlations between all estimates. In doing so, each node does not need any information about measurements processed on other nodes. We show the optimality of the proposed method by means of tracking an extended object in a multi-camera network.