Optimal filtering of discrete-time linear stationary processes under high signal-to-noise ratio conditions

Expressions in closed form are obtained for the minimum error covariance matrix of the a priori filtered estimate of a discrete-time stationary process under high signal-to-noise ratio (SNR) conditions and for its corresponding constant Kalman gain matrix. These expressions are derived explicitly in terms of the process state-space description matrices. They are composed of the simple terms that have been obtained recently for the corresponding completely noise free measurement case and of correction terms that are all of the order of magnitude of the SNR.