Abstract
This paper studies an optimal filtering problem for discrete-time linear stochastic systems with unknown disturbances. We explicitly compute the covariance matrix of the output estimation error for the optimal disturbance decoupling observer (ODDO) introduced by Chen and Patton, and determine the gain matrices of the optimal filter. Our new result is slightly different from theirs since we used a corrected recursive formula for the error covariance matrix. The output estimation error with both disturbance decoupling and minimum variance properties is used for a residual signal to diagnose faults.
