Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers (1994)
Pacific Grove, CA, USA
Oct. 31, 1994 to Nov. 2, 1994
P. Park , Inf. Syst. Lab., Stanford Univ., CA, USA
T. Kailath , Inf. Syst. Lab., Stanford Univ., CA, USA
This paper presents a modified form of the conventional QR algorithm for adaptive filtering. By exploiting the displacement structure of the correlation matrix of the data, the paper suggests a fast method of constructing a unitary rotation that can be used to propagate an estimate in the QR algorithm. As a result, the paper provides a numerically better version of the so-called "hybrid QR/LLS" adaptive filtering algorithm discovered by Regalia and Bellanger (see IEEE Transactions on Signal Processing, vol.39, p.879-891, April 1991); in their original version, a so-called likelihood variable computed by using variance-normalized backwards a posteriori prediction errors may not be positive semi-definite because of round-off errors. In our approach, this variable is guaranteed to be positive semi-definite.<
adaptive filters, adaptive signal processing, filtering theory, correlation methods, matrix algebra, lattice filters, circuit feedback, least squares approximations, error analysis, roundoff errors
P. Park and T. Kailath, "A modified QR adaptive filtering algorithm-elementary approach," Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers(ACSSC), Pacific Grove, CA, USA, 1995, pp. 597-601.