Optimal Estimator Design and Properties Analysis for Interconnected Systems with Asymmetric Information Structure

TL;DR

This paper develops an optimal state estimator for interconnected systems with random communication delays, analyzing error covariance properties and identifying a critical delay probability affecting estimator stability.

Contribution

It introduces a new, easily verifiable condition for bounded error covariance and explores how delay probability influences estimator performance.

Findings

Existence of a critical delay probability for bounded error covariance

Derived bounds for the critical delay probability

Validated methods through power system simulations

Abstract

This paper studies the optimal state estimation problem for interconnected systems. Each subsystem can obtain its own measurement in real time, while, the measurements transmitted between the subsystems suffer from random delay. The optimal estimator is analytically designed for minimizing the conditional error covariance. The boundedness of the expected error covariance (EEC) is analyzed. In particular, a new condition that is easy to verify is established for the boundedness of EEC. Further, the properties of EEC with respect to the delay probability are studied. We found that there exists a critical probability such that the EEC is bounded if the delay probability is below the critical probability. Also, a lower and upper bound of the critical probability is derived. Finally, the proposed results are applied to a power system, and the effectiveness of the designed methods is illustrated by simulations.