Nearly singular filtering for uniform and non-uniform rank linear continuous systems

Abstract

The problem of the minimum variance stationary estimation of linear, time-invariant, continuous systems is considered in the case where the norm of tho measurement white noise intensity approaches zero. Solutions in closed form are obtained for the Kalman gain and the corresponding minimum error covariance matrix of the filtered estimate in terms of the noise intensity norm and the system transfer function matrix. Both uniform and non-uniform rank systems are considered and for the first time a solution is obtained for the case where the infinite zeros of the system tond to infinity with multiple rates.