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An algorithm for linearly constrained adaptive filtering of nonstationary signals

Victor I. Djigan


A new multichannel RLS-algorithm of adaptive filtering with a sliding window and linear constraints is considered. The algorithm is based on the inverse QR-decomposition of the matrix of input signals of an adaptive filter. A peculiar feature of the algorithm is absence of square root operations in it. The algorithm’s effectiveness is demonstrated by simulation. The simulation concerns a problem of identification of a three-channel linear adaptive filter, whose input signals represent speech signals. The ERLE parameter value obtained by the new algorithm for this problem is roughly by 20 dB larger compared to the linearly constrained RLS-algorithm with an infinite window.

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HAYKIN, S. Adaptive Filter Theory, 4th ed. Prentice Hall, 2001.

FROST, O. L. "An algorithm for linearly constrained adaptive array processing," Proc. IEEE, v.60, n.8, p.926-935, Aug. 1972. DOI:

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:

ALEXANDER, S.T.; GHIMIKAR, A.L. "A method for recursive least squares filtering based upon an inverse QR decomposition," IEEE Trans. Signal Process., v.41, n.1, p.20-30, 1993. DOI:

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:

GAY, S.L. "Dynamically regularized fast RLS with application to echo cancellation," Proc. of Int. Conf. on Acoustics, Speech, and Signal Processing, ICASSP’96, 9 May 1996, Atlanta, GA, USA. IEEE, 1996, p.957-960. DOI:

DZHIGAN, V.I. "Bystryi mnogokanalnyi RLS-algoritm s reguliarizatciei i stabilizatciei," Izv. VUZ. Elektronika, n.1, p.83-90, 2004.

SLOCK, D.T.M.; KAILATH, T. "Numerically stable fast transversal filters for recursive least squares adaptive filtering," IEEE Trans. Signal Process., v.39, n.1, p.92-114, 1991. DOI:

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