Adaptive estimation algorithms: convergence, optimality, stability

Adaptive estimation algorithms for computing recurrence estimates in a standard regression problem are discussed. Their convergence is proven and the rate of convergence studied. Ways are indicated to determine the nonlinear transformation of the misalignment and to choose the gain matrix in the adaptive algorithm for insuring its asymptotic optimality. This asymptotically optimal algorithm is equivalent to the recurrent version of the maximal likelihood method. With incomplete a priori data on noise asymptotically optimal, in the minimax sense, algorithms are found and the relation with stable (robust) estimation is demonstrated.