Optimal Information-Weighted Kalman Consensus Filter

2020-04-30T03:15:09Z (GMT) by Shiraz Khan
Distributed estimation algorithms have received considerable attention lately, owing to the advancements in computing, communication and battery technologies. They offer increased scalability, robustness and efficiency. In applications such as formation flight, where any discrepancies between sensor estimates has severe consequences, it becomes crucial to require consensus of estimates amongst all sensors. The Kalman Consensus Filter (KCF) is a seminal work in the field of distributed consensus-based estimation, which accomplishes this.

However, the KCF algorithm is mathematically sub-optimal, and does not account for the cross-correlation between the estimates of sensors. Other popular algorithms, such as the Information weighted Consensus Filter (ICF) rely on ad-hoc definitions and approximations, rendering them sub-optimal as well. Another major drawback of KCF is that it utilizes unweighted consensus, i.e., each sensor assigns equal weightage to the estimates of its neighbors. This fact has been shown to cause severely degraded performance of KCF when some sensors cannot observe the target, and can even cause the algorithm to be unstable.

In this work, we develop a novel algorithm, which we call Optimal Kalman Consensus Filter for Weighted Directed Graphs (OKCF-WDG), which addresses both of these limitations of existing algorithms. OKCF-WDG integrates the KCF formulation with that of matrix-weighted consensus. The algorithm achieves consensus on a weighted digraph, enabling a directed flow of information within the network. This aspect of the algorithm is shown to offer significant performance improvements over KCF, as the information may be directed from well-performing sensors to other sensors which have high estimation error due to environmental factors or sensor limitations. We validate the algorithm through simulations and compare it to existing algorithms. It is shown that the proposed algorithm outperforms existing algorithms by a considerable margin, especially in the case where some sensors are naive (i.e., cannot observe the target).