Abstract
In this paper, we are concerned with a problem of optimization of the linear observations which 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 condition of optimality was already shown by introducing a symmetric matrix called SSNRM which is a quadratic function of the gain matrix weighted by the inverse of the noise covariance matrix. In this paper, a new numerical algorithm to compute the solution is proposed which is applicable to the observations with lesser dimensions than the signal. Most part of numerical computations of this algorithm consists of that of the solutions of Riccati and Lyapunov equations which are easily implemented. The value of SSNRM is updated by a simple scheme based on the condition of optimality. The results of numerical experiments are provided to show the efficiency of the algorithm.
