Low-Complexity Adaptive Algorithms for Robust Subspace Tracking

Abstract

This paper introduces new, low-complexity, adaptive algorithms for robust subspace tracking in certain adverse scenarios of noisy data. First, an adequate weighted least-squares criterion is considered for the design of a robust subspace tracker that is most efficient in the burst noise case. Second, by using data pre-processing and robust statistics estimate, we introduce a second method that is shown to be the most efficient for subspace tracking in the case of impulsive noise (e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula> -stable noise). Finally, a “detect-and-skip” approach is adopted, where the corrupted measurements are detected and treated as “missing” data. The resulting algorithm is particularly effective in the case where the data are affected by sparse “outliers.” All these approaches were analyzed, and their convergence properties were investigated. Moreover, the proposed subspace tracking algorithms were compared by simulated experiments to some state-of-the-art methods in different noise/outliers contexts.