Further results in robust Wiener filtering

Some aspects of a previously established minimax formulation of the robust Wiener filtering problem are considered. Existence results are obtained for least-favorable spectral pairs for general spectral-density uncertainty classes in the cases of general noncausal filtering and causal filtering in wide-sense Markov noise. Further, a general type of spectral-measure uncertainty class based on the notion of capacities is proposed. Existence results and a minimax theorem for robust filtering are established within this proposed framework, and a previously noted relationship between robust hypothesis testing and robust filtering is strengthened. Some possible extensions of earlier work on robust causal filtering are also discussed.