Optimal discrete-time Kalman Consensus Filter

Following recent advances in networked communication technologies, sensor networks have been employed in a broad range of applications at a lower cost than centrally supervised systems. Their major functionality is to track and monitor targets using various distributed estimation techniques. Specifically, the distributed Kalman Consensus Filter (KCF) fuses data from different sensor agents by achieving two objectives for each sensor: 1) locally estimating the state of the target; and 2) reaching a consensus of the state estimate between neighboring agents through communication. Although the KCF has been proven to have superior performance in terms of stability and scalability, it relies on approximated suboptimal consensus gain to avoid algorithmic complexity. Specifically, we seek to address this problem of suboptimality, and analytically derive the closed form solution to the globally optimal consensus gain, which is characterized by the minimum mean square error for the estimation process. Illustrative simulation results are presented to demonstrate that the optimal consensus gain outperforms the suboptimal solution.