A New Online Secondary Path Modeling Method with An Auxiliary Noise Power Scheduling Strategy for Narrowband Active Noise Control Systems  
[PERSON]  
Department of Automatic Testing and Control, Harbin Institute of Technology, Harbin 150080, China; [EMAIL_ADDRESS] (Y.L.); [EMAIL_ADDRESS] (Z.B.)  
[PERSON]  
Department of Automatic Testing and Control, Harbin Institute of Technology, Harbin 150080, China; [EMAIL_ADDRESS] (Y.L.); [EMAIL_ADDRESS] (Z.  
and the acoustics transfer function of the secondary path may be time-varying. Under these situations, online secondary path modeling (SPM) is essential for ensuring the stability of the ANC system.  
Several contributions to the research on online SPM methods have been made by many researchers. The use of auxiliary noise power injection with fixed power was originally proposed by [PERSON] [14]. The original idea of [PERSON]'s method was later modified and extended in [15; 16; 17; 18; 19], which used fixed power auxiliary noise in all operating situations. Nevertheless, the fixed power auxiliary noise contributes to the residual error, which we want to minimize, and leads to the performance degradation of the ANC system in the steady state. To remedy this problem, various auxiliary noise power scheduling strategies have been proposed [20; 21; 22; 23; 24; 25]. However, it should be noted that most of the above mentioned strategies were designed for broadband active noise control (BANC). These strategies cannot be directly applied to an NANC system because the primary noise signal, which is used in the strategies and can be obtained for a BANC system, cannot be obtained for an NANC system. The detailed performance analysis of the NANC system with online SPM using [PERSON]'s method was provided by [PERSON] [26]. In [27], the method of scaling auxiliary noise by one-delayed residual noise signal was proposed for NANC system equipped with an online SPM subsystem and the detailed performance analysis is also given.  
In this study, we are mainly concerned with NANC with an online SPM system and propose a new online SPM method with an auxiliary noise power scheduling strategy. The method we proposed is a further extension of previous works by the authors of [12; 28]. First, a variable forgetting factor filtered-x weighted accumulated least mean square (FXWALMS) algorithm [28] is introduced into the control filter in order to improve the convergence and tracking performance of the system. Second, according to the range of the forgetting factor, the new auxiliary noise power is scheduled based on the convergence status of the forgetting factor to accurately track the change in the NANC system. As a result, the proposed method not only achieves better modeling accuracy but also considerably reduces the residual noise. Extensive simulations are conducted to demonstrate that the proposed system can improve the overall performance of the system effectively.  
The rest of the paper is organized as follows. In Section 2, the existing online SPM method for NANC systems is briefly introduced. Section 3 presents the proposed method in detail. In Section 4, simulation results are given to verify the effectiveness of the proposed method under various scenarios. Finally, conclusions are given in Section 5.  
Existing Online Secondary Path Modeling (SPM) Method for Narrowband Active Noise Control (NANC) Systems