Abstract
Nonlinear active control is very important in many practical applications. Many well-known nonlinear active noise control algorithms may suffer from high computational complexity and low convergence speed, especially in the nonlinear secondary path case. Thus, it is still an actively researched topic for reducing complexity and improving the convergence rate. This paper presents a low-complexity Volterra filtered-error least mean square algorithm when taking a decomposable Volterra model into account for active control of nonlinear noise processes, which is referred as DVMFELMS. The computational complexity analysis shows that the proposed DVMFELMS algorithm can significantly reduce the nonlinear active noise control system’s complexity. The simulation results further show that the proposed algorithm can achieve promising performance compared with the Volterra-based FELMS algorithm and other state-of-the-art nonlinear filters, while the decomposable error of the Volterra kernel may be introduced inevitably. Moreover, the proposed DVMFELMS algorithm shows a better convergence rate in the broadband primary noise case due to fewer parameters used in each sub-filter.
Highlights
Active noise control has developed rapidly in the last few decades [1,2], and it has been successfully applied in many fields, such as heating, ventilating and air-conditioning systems [3], motor systems [4], and active headrests [5,6]
The FXLMS algorithm has already been successfully applied in active noise control systems, its performance may degrade in controlling nonlinear noise processes [11]
By utilizing a decomposable Volterra structure and filtered-error structure, the proposed DVMFELMS algorithm can significantly reduce the computational complexity of the algorithm, which is promising in nonlinear active noise control (NANC) systems, especially for the nonlinear secondary path (NSP) case
Summary
Active noise control has developed rapidly in the last few decades [1,2], and it has been successfully applied in many fields, such as heating, ventilating and air-conditioning systems [3], motor systems [4], and active headrests [5,6]. The transfer function of the secondary path may have a non-minimum phase, so that the causality constraint will be violated [11] In all of these situations, the traditional linear structure cannot model the nonlinear part of the system accurately enough. Most artificial neural network-based algorithms are too computationally consuming for real applications of active noise control systems, which is out of the scope of this paper. It is demonstrated that the decomposable Volterra model outperforms the simplified structure in [36] Motivated by these latest works, this paper proposes an adaptive Volterra-filtered error least mean square algorithm (DVMFELMS) that takes a decomposable Volterra model and filtered-error structure into account for the nonlinear active control problem. All transfer functions and control filters are assumed to be linear, which may be violated in many circumstances, as mentioned above
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