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

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