Performance Analysis of Distributed Filtering under Mismatched Noise Covariances

TL;DR

This paper analyzes how mismatched noise covariances affect the performance of consensus-based distributed filtering, providing theoretical bounds, convergence conditions, and numerical validation.

Contribution

It introduces new performance indices, derives relations among them under mismatched noise, and establishes convergence and bounding conditions for distributed filtering.

Findings

Performance indices are related through difference and recursive relations.

Convergence of indices is guaranteed under collective observability.

Estimation error covariance can be bounded by noise deviations and performance indices.

Abstract

This paper systematically investigates the performance of consensus-based distributed filtering under mismatched noise covariances. First, we introduce three performance evaluation indices for such filtering problems,namely the standard performance evaluation index, the nominal performance evaluation index, and the estimation error covariance. We derive difference expressions among these indices and establish one-step relations among them under various mismatched noise covariance scenarios. We particularly reveal the effect of the consensus fusion on these relations. Furthermore, the recursive relations are introduced by extending the results of the one-step relations. Subsequently, we demonstrate the convergence of these indices under the collective observability condition, and show this convergence condition of the nominal performance evaluation index can guarantee the convergence of the estimation error covariance. Additionally, we prove that the estimation error covariance of the consensus-based distributed filter under mismatched noise covariances can be bounded by the Frobenius norms of the noise covariance deviations and the trace of the nominal performance evaluation index. Finally, the effectiveness of the theoretical results is verified by numerical simulations.