鲁棒频域样条优先自适应滤波算法及性能分析

Robust Frequency Domain Spline Prioritization Adaptive Filtering Algorithm and Its Performance Analysis

样条自适应滤波结构由线性滤波器和样条插值机制级联组成,是解决Wiener-Hammerstein模型系统辨识的一类有效方案。在非线性系统辨识问题中,随着滤波器阶数增加,将增大时域样条自适应滤波算法的计算复杂度,造成计算效率的降低,且系统附加的非Gaussian噪声会对最小均方算法的样条自适应滤波器性能造成不良影响,导致算法的性能恶化甚至失效。为处理非Gaussian噪声干扰和提高长脉冲响应系统辨识的计算效率,本文结合最大熵准则和频域策略应用于样条自适应滤波器中,并在样条自适应滤波结构中分别采用不同的误差信号对线性部分和非线性部分进行优化,提出了一种鲁棒频域样条优先自适应滤波算法。该算法在滤波前利用非线性系统辨识的不变性原理对未知系统进行优先的有限脉冲响应辨识,可提高非线性系统辨识的精度;通过最大熵准则使算法在非Gaussian噪声环境下具有稳健性,以降低更新过程对大异常值的敏感性;并将线性卷积和线性相关运算通过重叠存储的快速Fourier变换方式进行计算,显著提升了算法的计算效率。此外,本文对所提出的自适应算法进行了收敛性和稳态性能分析,并推导出该算法的理论稳态额外均方误差。最后,通过数值实验表明所提算法具有抗非Gaussian噪声性能和高效的计算效率,并验证了算法理论稳态分析结果的正确性。

Spline adaptive filter belongs to a class of block-oriented nonlinear filtering structures,which is simple to implement and owns the efficient learning capability,so it has recently attracted tremendous interest in the area of signal processing.The structure of spline adaptive filter is a cascade of the linear filter and the nonlinear spline interpolation mechanism,which is an efficiently adaptive filtering scheme for the Wiener-Hammerstein model-based system identification.In the issue of nonlinear system identification,the computational cost will dramatically increase with the order growth of spline adaptive filter in the time domain,causing the reduction of computational efficiency.The performance of spline adaptive filter based on the least mean-square approach will degenerate seriously,or even be invalid under non-Gaussian noises interference.In order to deal with non-Gaussian noises interference and to improve the computational efficiency for long finite impulse response(FIR)system identification,a novel robust frequency domain spline prioritization adaptive filtering(FDSPAF)algorithm,called the FDSPAF-MCC algorithm in this paper,is proposed based on the maximum correntropy criterion(MCC)and the fast Fourier transform(FFT)strategy,in which both the linear and nonlinear parts of the spline adaptive filtering structure are respectively optimized based on different errors.According to the invariance property in nonlinear system identification,we prioritize optimization and use the FIR filter to identify the unknown system before filtering,which improves the accuracy of system identification.We utilize the robust cost function based on MCC against non-Gaussian noises,leading to reduce the sensitivity to large outliers.The convolution and correlation procedures of linear filtering and adaptation are executed in the frequency domain by using FFT strategy via overlap-save method,which significantly improve the computational efficiency for large length FIR systems.Furthermore,the convergence and the steady-state performance of the FDSPAF-MCC algorithm are rigorously analyzed.The ranges of step sizes for both the weights and spline control points are given,and the steady-state performance analysis of the FDSPAF-MCC algorithm is carried out,whose closed-form expression of the theoretical steady-state excess mean-square error(EMSE)is also derived.Finally,numerical experiments verify the validity of the proposed FDSPAF-MCC algorithm under non-Gaussian noises circumstances in computationally efficient methods,and numerical results also corroborate the theoretical steadystate EMSE findings.