KALMAN TYPE FILTER FOR SYSTEMS WITH DELAY IN OBSERVATION NOISE

Abstract

In this paper, we consider a filtering problem for linear systems with delay in observation noise. Approximating delayed white noise by wide band noises, we derive a complete set of equations for the Kalman type optimal filter in this problem. It is shown that the derived Kalman type filter reduces to the classic Kalman filter if the delay is neglected. A comparison of the newly derived Kalman type filter with the classic Kalman filter and predictor is given. On the base of the mean square difference of the respective estimates, it is observed that the newly derived Kalman filter has some medium position between the classic Kalman filter and predictor, being closer to the first one.