Minimax Identification of Linear Systems by Probability Criterion

The problem of linear estimation of states and parameters of the multidimensional statistically indeterminate system by minimax probability criterion is considered. A priori information about the distribution law of the model random parameters and disturbances is defined by certain constraints on the first-and second-order moments. The explicit form of the minimax probability estimator and the sharp guaranteed bound for the probability functional are provided. The analytic expression of the "worst-case" distribution of the random model parameters is presented.