Minimax robust matched filters for noise uncertainty within 2-alternating capacity classes

In this paper, we address the problem of designing matched filters which are robust against uncertainty in the statistics of the noise process. The design is based on a game-theoretic approach in which a filter is sought that has the maximum worst-case output signal-to-noise ratio possible over the class of allowable statistics, that is the design is maximin signal-to-noise ratio. The problem is formulated and solved for both discrete-time and continoustime matched filters with uncertainty in either the autocorrelation function or the spectral measure of the noise. For uncertainty models determined by 2-alternating Choquet capacities explicit solutions are obtained which are characterized by the Huber-Strassen derivative of the capacity generating the class with respect to a Lebesgue-like measure on a suitable interval.