A Finite-Step Injection Problem of Discrete-Time Kalman Filter into the Stationary-State with the Optimal Observation Gain Matrix

Abstract

In this paper, we are concerned with a problem of finding the series of the observation gain matrices by which, in the assigned number of steps, the Kalman filter goes into the stationary state, and which minimizes a quadratic criterion with the same form as the stationary problem. The condition of optimality of the observation gain matrices is obtained in the same form as the corresponding stationary problem. The results of numerical experiments are provided to show the efficiency of the algorithm.