Optimal Kalman Filter With Information-Weighted Consensus

The use of wireless sensor networks for distributed state estimation has been a popular research topic in the signal processing community. However, there is a distinct lack of emphasis on formal derivation and optimality of distributed state estimation algorithms in the literature. Furthermore, many existing algorithms utilize unweighted average consensus filtering, which has been shown to lead to poor estimation performance in the presence of sensor agents that cannot make measurements due to environmental obstructions or sensor limitations. In this article, a novel distributed minimum mean-squared error estimator is developed by generalizing the Kalman consensus filter to incorporate consensus on a weighted directed graph. By employing weighted consensus, the algorithm is able to achieve a directional flow of information in heterogeneous sensor networks, leading to improved performance in the presence of sensors that have low observability. Unlike several existing algorithms, the proposed algorithm does not rely on approximations or ad hoc parameter tuning and achieves optimal performance in a fully distributed setting. Through numerical simulations, it is demonstrated that the proposed algorithm has a smaller mean-squared estimation error and is robust in the aforementioned scenarios.