A parallel linearly constrained fast RLS-algorithm based on inverse QR-decomposition without square root operations
DOI:
https://doi.org/10.3103/S0735272705120101Abstract
A parallel version of the fast RLS-algorithm of multichannel adaptive filtering with a sliding window and linear constraints is considered. The parallel computations in this algorithm are related to the possibility of independent processing of data flows dictated by modification of the correlation matrix of the adaptive filter due to sliding window and dynamic regularization. The algorithm is derived based on the generalized lemma about matrix inversion and on inverse QR-decomposition without square root operations.References
BENESTY, J.; HUANG, Y. (eds.). Adaptive Signal Processing: Applications to Real-World Problems. Berlin, Heidelberg, N.Y.: Springer-Verlag, 2003.
DZHIGAN, V.I. Mnogokanalnye RLS- i bystrye RLS-algoritmy adaptivnoi filtratcii. Uspekhi Sovremennoy Radioelektroniki, n.11, p.48-77, 2004.
PAPAODYSSEUS, C. A robust, parallelizable, O(m), a posteriori recursive least squares algorithm for efficient adaptive filtering. IEEE Trans. Signal Process., v.47, n.9, p.2552-2558, 1999. DOI: https://doi.org/10.1109/78.782203.
DZHIGAN, V.I. Parallelnye reguliarizirovannye RLS-algoritmy mnogokanalnoi adaptivnoi filtratcii. Tsifrovaya Obrabotka Signalov, n.2, p.7-13, 2004.
GAY, S.L. Dynamically regularized fast RLS with application to echo cancellation. Proc. of Int. Conf. on Acoustic, Speech, and Signal Processing, ICASSP-96, 7–9 May 1996, Atlanta, USA. IEEE, 1996, p.957-960. DOI: https://doi.org/10.1109/ICASSP.1996.543281.
DJIGAN, V.I. A fast RLS-algorithm for linearly constrained adaptive filtering of nonstationary signals. Radioelectron. Commun. Syst., v.48, n.2, p.51-56, 2005. URI: http://radioelektronika.org/article/view/S073527270502010X.
PAN, C.-T.; PLEMMONS, R.J. Least squares modifications with inverse factorizations: parallel implications. J. Comput. Appl. Math., v.27, n.1-2, p.109-127, 1989. DOI: https://doi.org/10.1016/0377-0427(89)90363-4.
DJIGAN, V.I. Algoritm lineino-ogranichennoi adaptivnoi filtratcii nestatcionarnykh signalov. Radioelectron. Commun. Syst., v.47, n.8, p.29-38, 2004.
RESENDE, L.S.; ROMANO, J.M.T.; BELLANGER, M.G. A fast least-squares algorithm for linearly constrained adaptive filtering. IEEE Trans. Signal Process., v.44, n.5, p.1168-1174, 1996. DOI: https://doi.org/10.1109/78.502329.
GIORDANO, A.A.; HSU, F.M. Least Square Estimation with Application to Digital Signal Processing. Toronto: John Wiley and Sons, Inc., 1985.
HSIEH, S.F.; LIU, K.J.R.; YAO, K. A unified square-root-free approach for QRD-based recursive-least-squares estimation. IEEE Trans. Signal Process., v.41, n.3, p.1405-1409, 1993. DOI: https://doi.org/10.1109/78.205742.
GLENTIS, G.-O. On the duality between the fast transversal and the fast QRD adaptive least squares algorithms. IEEE Trans. Signal Process., v.47, n.8, p.2317-2321, 1999. DOI: https://doi.org/10.1109/78.774777.
PROUDLER, I.K. Fast time-series adaptive-filtering algorithm based on the QRD inverse-updates method. IEE Proc. - Vision, Image and Signal Processing, v.141, n.5, p.325-333, 1994. DOI: https://doi.org/10.1049/ip-vis:19941426.
GLENTIS, G.-O.A.; KALOUPTSIDIS, N. Fast adaptive algorithms for multichannel filtering and system identification. IEEE Trans. Signal Process., v.40, n.10, p.2433-2458, 1992. DOI: https://doi.org/10.1109/78.157288.
