An information theoretic scheme for sensor allocation of linear least-squares estimation

We consider a sensor allocation problem for the Kalman-Bucy filter within an information theoretic framework. For the signal and the observation of Kalman-Bucy filter, the mutual information between them is determined by the power of the signal component in the innovations process, and we cannot nuke the mutual information larger without increasing the power of this term in the innovations process. Under a constraint that the mean square power of the term takes a preassigned value, we consider the problem of finding the optimal gain matrix for the sensors that minimizes the least-squares estimation error. A set of equations which were derived in our previous paper is applied to obtain a recursive algorithm by which we can compute the optimal gain matrix. Numerical examples are given to illustrate the applicability of the proposed algorithm.