Identification of optimum filter steady-state gain for systems with unknown noise covariances

A discrete linear stationary system is considered for which the input noise covariance Q and the output noise covariance R are unknown. A stable filter with a suboptimal gain is assumed. An identification scheme is presented which uses the autocorrelation functions of the innovations sequence of the suboptimal filter to determine the optimum filter steady state gain directly without the intermediate determination of the unknown covariances Q and R. The approach used is to identify an output equivalent representation of the original system which does not involve the unknown covariances directly.