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Robust estimators that provide accurate parameter estimates even under the condition that classical assumptions like outlier-free additive Gaussian measurement noise do not hold exactly are of great practical importance in signal processing and measurement science in general. Lots of methods for deriving robust estimators exist. In this paper, the authors derive novel algorithms for robust estimation by modeling the outliers as a sparse additive vector of unknown deterministic or random parameters. By exploiting the separability of the estimation problem and applying recently developed sparse estimation techniques, algorithms that remove the effect of the outlying observations can be developed.
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