The paper presents a family of the sliding window RLS adaptive filtering algorithms with the regularization of adaptive filter correlation matrix. The algorithms are developed in forms, fitted to the implementation by means of parallel computations. The family includes RLS and fast RLS algorithms based on generalized matrix inversion lemma, fast RLS algorithms based on square root free inverse QR decomposition and linearly constrained RLS algorithms. The considered algorithms are mathematically identical to the appropriate algorithms with sequential computations. The computation procedures of the developed algorithms are presented. The results of the algorithm simulation are presented as well.
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