Active noise control without secondary path modelling — Varying-delay LMS approach

The Filtered-Reference LMS, also known as FxLMS algorithm, is one of the most commonly used adaptive algorithms for noise control systems. It is appreciated due to its simplicity, low computational complexity, and performance efficiency. For its convergence, responses of the acousto-electric secondary path and its model should not differ by more than pi/2 for any frequency contributing to the noise being controlled. Good amplitude matching is, in turn, responsible for convergence rate. Thus, without an acceptable model, the FXLMS algorithm is vulnerable to high excess mean square error or even divergence due to updating control filter parameters in improper direction. The literature presents several recipes, of heuristic or theoretic origin, to cope in circumstances of inaccurate secondary path modeling, or when the path is subject to change during control system operation and thus differs from the model. They usually require additional wideband random excitation to allow for on-line modeling during control system operation. Such excitation deteriorates, however, overall noise reduction results, and the acoustic impression perceived by the user is poor. This paper focuses on an active noise control approach, which requires no secondary path modelling. The convergence is guaranteed by switching sign of the algorithm step size and, in this way, the sign of the parameter update term. It is combined with on-line tunable delay of the reference signal to significantly improve convergence properties of the algorithm. Theoretical justification for this approach is shown for a tonal noise. Then, the method is extended for the case of a narrowband noise. Theoretical consideration is validated by simulations based on data acquired from a real application.