抄録
We are concerned with a problem of the optimal selection of the gain matrix of a linear observation for the Kalman filter. The innovations process included in the Kalman filter has the same structure as the model of a set of parallel transmission channels with the optimal output feedback. In the linear coding problem for this set of channels, it is well-known that the optimal output feedback which minimizes the power of the encoded signal is given by the least-squares estimate of the linear term and that the channel output becomes the innovations process. By applying a solution of the optimal transmission problem for this model, we obtain a set of gains which maximizes the mutual information between the observation and the signal under a constraint on the power of the innovations process.
