Frequency domain analysis of robust signal estimators

The author addresses the problem of robust linear estimations when the noise follows a wide-sense stationary process with its spectral density known to be in the neighborhood of some specified spectral density (i.e., white noise). The robust estimators for time series proposed so far in the literature are based mainly on heuristic ideas, for instance, on aging or forgetting factor. The author considers a generalized least-squares estimator which optimally robustifies the least-squares estimator against serial correlation. The author analyzes the estimator in the frequency domain. It turns out to be easier to analyze the robust estimator if the observed data are Fourier transformed. The optimal robust estimators minimize the asymptotic variance under a constraint on the upper bound of the serial correlation spectrum