On the selection of measurements in least-squares estimation

The problem of selecting measurements to enhance the performance of a Kalman estimator is considered. It is assumed that all the states of the random process model used by the estimator are accessible so that any linear combinations of them can be formed and used as measurements, but that their number is to be limited. Solutions are provided for two situations: when the measurement noise is zero, and when the noise covariance matrix is positive definite. The solutions are optimal in the sense that the measurements at any particular time instant minimize the trace of the a posteriori error covariance matrix at the same instant. An example of application of the above solutions to a speech coding scheme is given. Some of the limitations of the solutions are point out.<>