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

This 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 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