Modified Filtered-X Hierarchical LMS Algorithm with Sequential Partial Updates for Active Noise Control

• Published in: Applied sciences Vol. 11; no. 1; p. 344
• Main Authors: Ramos Lorente, Pedro, Martín Ferrer, Raúl, Arranz Martínez, Fernando, Palacios-Navarro, Guillermo
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.01.2021
• Subjects: Acoustics; active control of periodic noise; adaptive signal processing; Control algorithms; hierarchical filter; modified filtered-x LMS; Noise control; sequential partial updates
• ISSN: 2076-3417; 2076-3417
• DOI: 10.3390/app11010344

In the field of active noise control (ANC), a popular method is the modified filtered-x LMS algorithm. However, it has two drawbacks: its computational complexity higher than that of the conventional FxLMS, and its convergence rate that could still be improved. Therefore, we propose an adaptive strategy which aims at speeding up the convergence rate of an ANC system dealing with periodic disturbances. This algorithm consists in combining the organization of the filter weights in a hierarchy of subfilters of shorter length and their sequential partial updates (PU). Our contribution is threefold: (1) we provide the theoretical basis of the existence of a frequency-dependent parameter, called gain in step-size. (2) The theoretical upper bound of the step-size is compared with the limit obtained from simulations. (3) Additional experiments show that this strategy results in a fast algorithm with a computational complexity close to that of the conventional FxLMS.