Design of Discrete Estimators Using Minimax Techniques.
Paul L. Bongiovanni, Hutchinson,Charles E. · Defense Technical Information Center (DTIC) · 1971
The problem of designing discrete Kalman-type estimators in the presence of uncertainties in the noise covariance matrices and system matrix is considered. One approach to this problem is to design an adaptive filter, but because of their complexity the practical use of adaptive filters is somewhat limited. An alternative is to design a filter on the basis of a minimax criterion where the objective is to construct the best possible design under the worst possible circumstances. The structure of the discrete minimax filter is identical in form to the Kalman filter, and only steady-state design is considered so the gain matrix is constant. Minimax design of time-invariant systems with constant but uncertain input and measurement noise covariances is investigated with respect to the performance indices of total mean square estimation error, and the absolute and relative deviation of this error from the optimum estimation error. In each case the various properties of the filter are derived and as a consequence an algorithm is proposed to find the minimax gain. The nature of these filters is intimately related to the range of the uncertain parameters since the minimax values of the performance indices are generally found on the extreme points of the range. (Author)