Average State Kalman Filters for Large-scale Stochastic Networked Linear Systems

Abstract

In this paper, we propose a design method of average state Kalman filters for networked linear systems with stochastic noises. The average state Kalman filter is a low-dimensional estimator capturing the average behavior of systems from a macroscopic point of view. In general, it is nontrivial to find a set of states that captures the average behavior of systems. To overcome this difficulty, we devise a systematic design procedure of average state Kalman filters based on the notion of network clustering and a tractable representation of the estimation error system. Furthermore, we derive an estimation error bound for the proposed method in a theoretical way. The efficiency of the proposed method is shown by a power system example for smart grid applications.