Robust Distributed Kalman Consensus Filter for Sensor Networks under Parametric Uncertainties

Distributed estimation over sensor networks is one of the fundamental cooperative tasks involving multi-agent systems. Combining the Kalman filter with a consensus protocol is among the most successful strategies to address this problem. However, the availability of exact models is usually assumed. In practice, the models are often subject to parametric uncertainties. In this paper, we propose a robust distributed Kalman consensus filter. We consider that both the target system and sensing models have norm-bounded uncertainties in all parameter matrices. As a benchmark, we first introduce a centralized filter obtained from a robust regularized least-squares estimation problem. Then, we apply the hybrid consensus on measurements and information approach to derive a fully distributed version of this filter. We further establish steady-state stability conditions for both estimators. We also show that, for quadratically stable systems, the filters have bounded estimation error variance. Through an illustrative example, we assess the performance of the proposed estimators and provide comparisons with other robust distributed strategies.