Abstract
This paper treats the linear discrete-time filtering problem where the measurement signals contain some elements free of 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 estimator is made clear.
(iii) Applying the result (i) to the filtering problem with colored measurement noise, BrysonHenrikson's result is obtained without using their measurement differencing method.
