On the Effects of Modeling Errors on Distributed Continuous-time Filtering

TL;DR

This paper analyzes how modeling errors affect distributed continuous-time filtering performance, deriving bounds for estimation error covariance and demonstrating the impact of consensus parameters and incorrect noise covariances through theoretical analysis and simulations.

Contribution

It introduces performance indices and bounds for distributed filtering under modeling errors, revealing the influence of consensus parameters and noise covariance inaccuracies.

Findings

Incorrect process noise covariance can cause divergence of estimation error.

Consensus parameter significantly affects bounds of estimation performance.

Numerical simulations validate the theoretical bounds and effects.

Abstract

This paper offers a comprehensive performance analysis of the distributed continuous-time filtering in the presence of modeling errors. First, we introduce two performance indices, namely the nominal performance index and the estimation error covariance. By leveraging the nominal performance index and the Frobenius norm of the modeling deviations, we derive the bounds of the estimation error covariance and the lower bound of the nominal performance index. Specifically, we reveal the effect of the consensus parameter on both bounds. We demonstrate that, under specific conditions, an incorrect process noise covariance can lead to the divergence of the estimation error covariance. Moreover, we investigate the properties of the eigenvalues of the error dynamical matrix. Furthermore, we explore the magnitude relations between the nominal performance index and the estimation error covariance. Finally, we present some numerical simulations to validate the effectiveness of the theoretical results.