Robust matched filters for noise uncertainty within two alternating capacity classes

The problem of designing matched filters that are robust against uncertainty in the statistics of a noise process modeled by two alternating Choquet capacities is addressed. The robust design is based on the maximum signal-to-noise ratio. The problem is formulated and solved for both discrete-time and continuous-time matched filters with uncertainty in either the autocorrelation function or the spectral measure of the noise. Explicit solutions that are characterized by the Hyber-Strassen derivative of the capacity generating the class with respect to a Lebesgue-like measure on a suitable interval are obtained