Performance Analysis of Distributed Filtering Under Misspecified Noise Covariances

This article systematically investigates the performance of the consensus-based distributed filter under misspecified noise covariances. First, we introduce four quantities: the nominal filter parameter, the nominal estimation error covariance, the ideal filter parameter, and the ideal estimation error covariance. We derive the difference expressions among these quantities and establish the corresponding one-step relations. These relations reveal how performance deteriorates when noise covariances are misspecified, and demonstrate how to evaluate the estimation error covariance using the available nominal filter parameter. We particularly highlight the effect of the information fusion step number on these relations. Furthermore, recursive relations are introduced by extending the results of the one-step relations. Subsequently, we demonstrate the convergence of these quantities under the collective observability condition and show that the convergence condition of the nominal filter parameter can guarantee the convergence of the estimation error covariance. In addition, we provide bounds on the estimation error covariance under misspecified noise covariances by utilizing the Frobenius norms of the noise covariance deviations and the trace of the nominal filter parameter. Finally, the effectiveness of the theoretical results is verified through numerical simulations.