Least Squares Problem for Adaptive Filtering

Abstract: We discus and demonstrate ways of deriving solutions to least squares problem in adaptive filtering without forming the conventional triangular system of equation, thus, generalized inverse techniques is used to obtain the tap weight coefficient vector when the autocorrelation matrix is singular, this approach is further extended using matrix inversion lemma to derive normal equation incorporating autocorrelation matrix and cross correlation vector

A new family of approximate QR-LS algorithms for adaptive filtering

The 13th IEEE / S P Workshop on Statistical Signal Processing, Bordeaux, France, 17-20 July 2005This paper proposes a new family of approximate QR-based least squares (LS) adaptive filtering algorithms called p-TA-QR-LS algorithms. It extends the TA-QR-LS algorithm [6] by retaining different number of diagonal plus off-diagonals (denoted by an integer p) of the triangular factor of the augmented data matrix. For p=1 and N, it reduces respectively to the TA-QR-LS and the QR-RLS algorithms. It not only provides a link between the QR-LMS-type and the QR-RLS algorithms through a well-structured family of algorithms, but also offers flexible complexity-performance tradeoffs in practical implementation. These results are verified by computer simulation and the mean convergence of the algorithms is also analyzed. © 2005 IEEE.published_or_final_versio