Abstract
State estimation procedures of stochastic approximation type are applicable to a considerably wide class of nonlinear systems and noise distributions. They assure the convergence of the estimate to the true state variable in some stochastic sense. We propose, in this paper, an estimation procedure of stochastic approximation type with a nonlinear transformation of residuals to improve the convergence property. The transformation is chosen to minimize the maximum bound of the asymptotic variance of estimation errors over the class of noise distribution, to which the true noise distribution belongs. Hence, the proposed estimation procedure is optimal in minimax sense and robust (insensitive) to the variations of noise distribution. And it is applicable without the knowledge of exact form of noise distribution. Numerical examples are presented to illustrate the usefulness of the proposed approach.
