Abstract
we are concerned with a problem of the optimal selection of the gain matrix of a linear observation mechanism for the Kalman-Bucy filter. By introducing an information theoretic constraint, we obtain a gain matrix which maximizes the reduction speed of an weighted estimation error. In this paper, we are especially concerned with the case where the weighting matrix is not positive but nonnegative definite. By this condition, we can treat an observation with any dimension. This result is more general than the one obtained by one of the authors using a formulation in the optimal transmission framework.
