Minimax estimation of unknown deterministic signals in colored noise

The estimation of a deterministic signal corrupted by random noise is considered. The strategy is to find a linear noncausal estimator which minimizes the maximum mean square error over an a priori set of signals. This signal set is specified in terms of frequency/energy constraints via the discrete Fourier transform. Exact filter expressions are given for the case of additive white noise. For the case of additive colored noise possessing a continuous power spectral density, a suboptimal filter is derived whose asymptotic performance is optimal. Asymptotic expressions for the minimax estimator error are developed for both cases. The minimax filter is applied to random data and is shown to solve asymptotically a certain worst-case Wiener filter problem