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

‍ ‍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 steady-state EMSE findings.