On the effects of modeling errors on distributed continuous-time filtering

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.