An Information Theoretic Approach to Optimization of Linear Observations for the Kalman-Bucy Filter
Yoshiki TAKEUCHI, Shinji ESAKI · Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications · 2005
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.