Convergence analysis of the filtered-U LMS algorithm for active noise control in case perfect cancellation is not possible

Authors:
Rufus Fraanje;Michel Verhaegen;Niek Doelman
Affiliations:
Delft University of Technology, Faculty of Information Technology and Systems, Control Systems Engineering Laboratory, P.O. Box 5031, 2600 GA Delft, The Netherlands;Delft University of Technology, Faculty of Information Technology and Systems, Control Systems Engineering Laboratory, P.O. Box 5031, 2600 GA Delft, The Netherlands;TNO Institute of Applied Physics, Department of Active Noise and Vibration Control, P.O. Box 155, 2600 AD Delft, The Netherlands
Venue:
Signal Processing
Year:
2003

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Abstract

The Filtered-U LMS algorithm, proposed by Eriksson for active noise control applications, adapts the coefficients of an infinite-impulse response controller. Conditions for global convergence of the Filtered-U LMS algorithm were presented by Wang and Ren (Signal Processing, 73 (1999) 3) and Mosquera and Pérez-González (Signal Processing, 80 (2000) 5) for the case where perfect noise cancellation is achievable, which means only measurement noise remains. This, paper shows that the assumption of perfect cancellation is not necessary. In real situations perfect cancellation is often not achievable due to delays and non-minimum phase zeros. The conclusion is derived by analysis of the structure of the Wiener optimal solution. This also leads to the suggestion of preconditioning filters in the Filtered-U LMS updating. The preconditioning has shown considerable increase of the convergence rate in a realistic simulation study.