Optimal State Estimators for a Class of Discrete-time Linear Systems with Colored Observation Noise Using Improved Recursive Formula

Abstract

This paper describes an optimal state estimator for a class of discrete-time linear stochastic systems subject to both colored observation noise and unknown inputs. The authors have already proposed an optimal filter in our previous paper for such systems based on the idea of Chen and Patton's ODDO (Optimal Disturbance Decoupling Observer). On the other hand, we have proposed a modification of the ODDO by showing a correction to the estimation error covariance matrix. In this paper, we combine those results and propose a new optimal state estimator for the system with colored observation noise and the unknown inputs.