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In order to reduce the computational complexity for nonlinear Active Noise Control (ANC) systems, we propose a filtered-x set membership with a time-varying error bound (Fx-SM-VEB) algorithm based on the adaptive approximation principle and data-selective update strategy. By introducing the time-varying error bound (VEB) to replace a pre-specified threshold when nonlinearity exists in the components of the ANC system, the performance of the proposed algorithm is significantly improved. Moreover, the VEB is also easily expanded against the impulsive noise that is normally encountered in actual ANC systems. Based on the impulsive-free estimation, we develop a robust Fx-SM-VEB (RFx-SM-VEB) algorithm for the ANC system which is corrupted by impulsive noise in the reference input signal. Besides, we provide analyses of the steady-state behavior, stability conditions, and computational complexity of the proposed algorithms. Many simulation results in different scenarios of the ANC system have shown that the proposed algorithms are efficient under the nonlinear environment and impulsive noise.

Filtered-x Set Membership Algorithm With Time-Varying Error Bound for Nonlinear Active Noise Control