Robust Limits of Risk Sensitive Nonlinear Filters

Abstract.

Deterministic filter models are considered, and a criterion for a deterministic filter to be robust is introduced. Among the candidates for robust deterministic filters are so-called minimax estimators. In the second part of the paper, a risk sensitive stochastic approach to nonlinear filtering is considered, in which the traditional expected mean squared error criterion is replaced by an expected exponential-of-mean squared error. Minimax filters are obtained as totally risk averse limits of risk sensitive filters.