THE HIERARCHICAL RECURSIVE LEAST SQUARES IN THE PRESENCE OF SPARSE OUTLIERS
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One of the major challenges in the field of adaptive signal processing and onlinelearning is encountered when the input signal is contaminated with outliers.Recursive Least Squares which is widely used for online processing of signals failto perform well when such outliers are present in the input data. Many techniquesto achieve robustness to these outliers have been put forward over the years. Mostof these techniques fail when the assumption made for the nominal backgroundnoise is not white in nature.  was the first work to suggest a robust recursiveleast squares algorithm that managed to estimate outliers along with the wantedregression coefficients in the presence of colored noise.As an extension to the outlierestimation problem suggested in , this thesis implements a novel method,therobust Hierarchical Recursive Least Squares which is shown to perform betterthan it’s robust RLS counterparts. Both convex and non convex penalties havebeen implemented to exploit the sparsity of outliers contaminating the data.