Robustness Analysis of Distributed Kalman Filter for Estimation in Sensor Networks

Motivated by the guaranteed stability margins of linear quadratic regulators (LQRs) and standard Kalman filter (KF) in the frequency domain, this article extends these results to the distributed Kalman-consensus filter (DKCF) for distributed estimation in sensor networks. In particular, we study the robustness margins of DKCF in two cases, one of which is based on the direct target observation while the other uses estimates from neighbor sensors in the network. The loop transfer functions of the two cases are established, and gain and phase margin robustness results are derived for both. The robustness margins of DKCF are improved compared to the single-agent KF. Furthermore, as communication topology varies in sensor networks, graph overall coupling strengths change. We also analyze the correlation between overall coupling strengths and the robustness margins of DKCF.