一种改进的变步长LMS算法及在车内降噪中的应用

An Improved Variable-step-size LMS Algorithm and Its Application for Reducing Noise in Vehicles

为了提高传统最小均方(LMS)算法的收敛速度,减小稳态误差,基于Sigmoid函数,提出一种改进步长因子μ的方法。该方法通过建立步长因子μ和误差信号e之间的非线性函数关系,并利用指数函数表示误差信号e和可控参数,实现对步长因子μ进行调整。算法收敛初期步长因子μ相对较大,实现加快算法收敛速度的目的;算法收敛后期适度减小稳态阶段步长因子μ,以达到减小算法稳态误差的目的。将该算法应用于车内噪声的有源控制,并与LMS算法进行仿真比较分析。仿真结果表明,相对于传统LMS算法,该算法有效地加快了收敛速度,同时提高了系统的稳定性。

In order to improve the convergence speed and reduce the steady-state error of the traditional least mean square （LMS） algorithm, a method is proposed to improve the step factor μ based on the Sigmoid function.In the algorithm, a nonlinear relationship is established between the step factor μ and the error signal e .The error signal e and controllable parameters are expressed in exponential form to adjust the step size factor μ .The step factor μ is relatively large in the initial convergence stage to speed up convergence of the algorithm.In the later convergence stage, the step factor μ is moderately reduced to achieve the purpose of reducing the steady-state error.The proposed algorithm is applied to the active control of vehicle interior noise.The control effect of the algorithm is compared with that of the LMS algorithm.The simulation results show that the proposed algorithm accelerates the convergence rate and improves the stability of the system.