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QR-based TLS and mixed LS-TLS algorithms with applications to adaptive IIR filtering

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2 Author(s)
B. E. Dunne ; Dept. of Electr. & Comput. Eng., Illinois Inst. of Technol., Chicago, IL, USA ; G. A. Williamson

The least squares (LS), total least squares (TLS), and mixed LS-TLS approaches are compared as to their properties and performance on several classical filtering problems. Mixed LS-TLS is introduced as a QR-decomposition-based algorithm for unbiased, equation error adaptive infinite impulse response (IIR) filtering. The algorithm is based on casting adaptive IIR filtering into a mixed LS-TLS framework. This formulation is shown to be equivalent to the minimization of the mean-square equation error subject to a unit norm constraint on the denominator parameter vector. An efficient implementation of the mixed LS-TLS solution is achieved through the use of back substitution and inverse iteration. Unbiasedness of the system parameter estimates is established for the mixed LS-TLS solution in the case of uncorrelated output noise, and the algorithm is shown to converge to this solution. LS, TLS, and mixed LS-TLS performance is then compared for the problems of echo cancellation, noise reduction, and frequency equalization.

Published in:

IEEE Transactions on Signal Processing  (Volume:51 ,  Issue: 2 )