抄録
In this paper, we are concerned with a problem of optimal selection of the gain matrix of a linear observation for the stationary Kalman filter. In the previous works of the author, we introduced an information theoretic criterion based on a generalized Water Filling Theorem to obtain a gain matrix which minimizes the stationary error variance. The merit of this approach is that analytical and numerical solutions are rather easily obtained compared with the case of quadratic cost functions on the estimation error and the gain matrix. In this solution process, however, the Riccati equation of the error covariance matrix reduces to a quasi linear equation, and the property of the solution is somewhat different from that of the usual Riccati equation. This paper is concerned with the case of a quadratic cost function, and we obtain an expression of the condition of optimality. Also, a method of numerical solution is proposed
