Optimization of Linear Observations for the Stationary Kalman-Bucy Filter

抄録

In this paper, we are concerned with a problem of optimization of the linear observations that are used in the stationary Kalman-Bucy filter. Especially, we consider the optimization of the gain matrix in the observation. In the previous works of the author, the corresponding problem for discrete-time systems was already considered and the condition of optimality was obtained. This paper is concerned with the case of the continuous-time systems and it is shown that the condition of optimality is given by the same form as the discrete-time case except for the accompanying Lyapunov equation, which is continuous-type whereas it was discrete-type in the discrete-time problem. We propose a method of solving the set of equations of the Riccati equation for the error covariance and the condition of optimality by a simple recursive algorithm. The results of numerical experiments show the efficiency of the proposed algorithm.