Abstract
In this paper, we are concerned with a problem of optimization of the linear observations which are used in the stationary Kalman filter. Especially, we consider the optimization of the gain matrix in the observation. In the previous works one of the authors, an information theoretic criterion, based on a generalized Water Filling Theorem, was introduced to obtain a gain matrix which minimizes the stationary error variance. The merit of this approach is that both analytical and numerical solutions are rather easily obtained compared with the case of the performance criterion which is quadratic in 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 condition for the existence of the solution of this equation is somewhat stronger than that of the usual Riccati equation. This paper is concerned with the case of the quadratic performance criterion. We propose a new method of numerical optimization by introducing the gradient method and a new rule of updating the angular parameters which are brought by the polar-coordinate representation of an orthogonal matrix. The results of numerical experiments show the efficiency of the algorithm.
