Optimal filter based on mutual information

The paper considers an optimal filtering problem based on the maximization of the mutual information between the state vectors and the estimated vectors for a continuous-time linear stochastic system. Attention is given to the relationship between the optimal filter and the Kalman filter with minimum estimated variance and to the relationship between the rate distortion function and the filter which maximizes the mutual information. It is shown that the mutual information does not depend on the average value of the estimated error vectors, and that the Kalman filter can be realized when the filter has the unbiased property of the estimated vector.