On robust Wiener signal estimation

A minimax formulation is considered for the problem of designing robust linear causal estimators of continuous-time signals in noise. It is shown that the minimax estimation problem can generally be reduced to finding a least favorable pair of spectra. In particular, robust predictors, filters, and finite-lag smoothers are shown to be just the optimal predictors, filters, and smoothers, respectively, for a least favorable pair. This result can often greatly simplify the design of robust estimators.