Abstract
In a stochastic linear composite system, which is composed of several subsystems, it may be desired to obtain an estimate of the state of only one particular subsystem. A usual approach to this problem will be to construct a Kalman-Bucy filter for the total system, and to obtain the required partial state estimate as a part of the total one. That is, a dynamical filter of the same dimension as that of the total system is necessary for only the partial state estimation. From the computational view point, it is preferable to obtain a partial estimate by a suitable dynamical filter, which is not necessarily optimal, of the dimension of that subsystem. In this paper, we consider a class of composite systems in which two subsystems are coupled and their time responses are widely different. And we propose a method to synthesize an approximate filter for the “slower” subsystem. It is also shown that the approximation error vanishes as the ratio of the maximum eigenvalue of the “slower” subsystem to the minimum eigenvalue of the “faster” subsystem approaches to zero.
