Efficient Adaptive Nonlinear Filters for Nonlinear Active Noise Control

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 54; no. 3; pp. 669 - 681
• Main Authors: Dayong Zhou, DeBrunner, V.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Acoustic noise; Active noise control; Active noise control (ANC); Active noise reduction; Adaptive control; Adaptive filters; Algorithms; Automatic voltage control; Complexity; Computation; Computational complexity; Control systems; Mathematical models; Noise cancellation; Noise control; Nonlinear filters; nonlinear systems; Nonlinearity; Programmable control; Robustness; Studies
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2006.887636

In this paper, we treat nonlinear active noise control (NANC) with a linear secondary path (LSP) and with a nonlinear secondary path (NSP) in a unified structure by introducing a new virtual secondary path filter concept and using a general function expansion nonlinear filter. We discover that using the filtered-error structure results in greatly reducing the computational complexity of NANC. As a result, we extend the available filtered-error-based algorithms to solve NANC/LSP problems and, furthermore, develop our adjoint filtered-error-based algorithms for NANC/NSP. This family of algorithms is computationally efficient and possesses a simple structure. We also find that the computational complexity of NANC/NSP can be reduced even more using block-oriented nonlinear models, such as the Wiener, Hammerstein, or linear-nonlinear-linear (LNL) models for the NSP. Finally, we use the statistical properties of the virtual secondary path and the robustness of our proposed methods to further reduce the computational complexity and simplify the implementation structure of NANC/NSP when the NSP satisfies certain conditions. Computational complexity and simulation results are given to confirm the efficiency and effectiveness of all of our proposed methods