This paper proposes a novel spline adaptive filtering (SAF) algorithm for nonlinear system identification under impulsive noise environments. This algorithm combines the logarithmic hyperbolic cosine (LHC) cost function and the modified Nesterov accelerated gradient (MNAG) learning method, which is called the SAF-LHC-MNAG algorithm. The LHC cost function can reduce the sensitivity of SAF to large outliers and improve the robustness to impulsive noises. Additionally, the MNAG method can further accelerate the convergence under the premise of low steady-state error. Performance analysis of this algorithm is carried out and supported by simulations. Numerical results show that the SAF-LHC-MNAG algorithm has better convergence performance than some existing SAF algorithms. Besides, experimental results confirm the effectiveness of SAF-LHC-MNAG for the accurate identification of nonlinear hysteresis system.

提出了一种新颖的样条自适应滤波算法，用于脉冲噪声环境下的非线性系统辨识。该算法结合了对数双曲余弦（LHC）成本函数和改进的Nesterov加速梯度（MNAG）学习方法，称为SAF-LHC-MNAG算法。LHC成本函数可以降低SAF对较大异常值的敏感性，并提高对脉冲噪声的鲁棒性。另外，MNAG方法可以在低稳态误差的前提下进一步加速收敛。对该算法进行性能分析并得到仿真的支持。数值结果表明，与现有的一些SAF算法相比，SAF-LHC-MNAG算法具有更好的收敛性能。除了，