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This paper considers the problem of linear signal estimation when the time-discrete data consists of signal plus additive independent noise. The signal probability distributions are completely unknown but the noise mean and covariance properties are known. The paper considers two main problems. The first is the definition of an adaptive procedure for filtering. The second is the analysis of the procedure for the special case of stationary Gaussian data with zero mean and square integrable spectral density. It is believed that the procedure defined has a wider applicability than other methods and that the analytical approach is entirely new.