Low Order Optimal Filters for Linear Discrete-Time Systems

Abstract

This paper treats of the linear discrete-time filtering problem where some elements of the measurement signal are free from noise. The main results are as follows : (i) A low order optimal filter is obtained by modifying the ordinary Kalman filter. (ii) Based upon the result (i), the structure of Tse-Athans' optimal minimal-order filter is made clear. (iii) Utilizing the result (i), the filtering problem with colored measurement noise is solved. This solution contains Bryson-Henrikson's result as a special case.