On Low Order Optimal Filters for Linear Discrete-Time Systems with Measurement Noise Whose Covariance Matrix is Singular
Tsuneo Yoshikawa · Transactions of the Society of Instrument and Control Engineers · 1971
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.