観測雑音の共分散行列が正則でない場合の線形離散時間系に対する低次元最適フィルタ

抄録

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.