The increasing demand for a better quality of service in radar and wireless communication has attracted research on interference suppression. Nonlinear filtering methods based on spline architecture have been widely utilized in signal processing due to their effectiveness against alpha-stable interference. How- ever, existing nonlinear spline adaptive filter algorithms suffer from high steady-state misalignment. To achieve lower steady- state misalignment along with having comparable computational complexity, we propose a nonlinear spline Versoria prioritiza- tion optimization adaptive filter (SPOAF-MVC) for alpha-stable clutter in this paper. Further, we study the bound on learning rate and computational complexity for the proposed algorithm. Numerical simulations confirm the effectiveness and efficiency of the proposed SPOAF-MVC algorithm for alpha-stable clutter under Wiener system identification.

A filtering algorithm based on frequency domain spline type, frequency domain spline adaptive filters (FDSAF), effectively reducing the computational complexity of the filter. However, the FDSAF algorithm is unable to suppress non-Gaussian impulsive noises. To suppression non-Gaussian impulsive noises along with having comparable operation time, a maximum correntropy criterion (MCC) based frequency domain spline adaptive filter called frequency domain maximum correntropy criterion spline adaptive filter (FDSAF-MCC) is developed in this paper. Further, the bound on learning rate for convergence of the proposed algorithm is also studied. And through experimental simulations verify the effectiveness of the proposed algorithm in suppressing non-Gaussian impulsive noises. Compared with the existing frequency domain spline adaptive filter, the proposed algorithm has better performance.

In signal processing applications such as navigation, radar, and communications, systems often operate in complex environments characterized by strong correlations and the presence of outliers. Such compound noise conditions pose significant challenges to spline-architecture-based adaptive filtering algorithms, limiting their performance in nonlinear system identification. To mitigate the interference of colored noise and heavy-tailed non- Gaussian noise on spline adaptive filtering process for nonlinear system identification, a spline prioritization optimization lncosh- GHS adaptive filtering (SPOAF-lncosh-GHS) is proposed. The proposed algorithm adopts the lncosh function as the cost function for the linear part to optimize the adaptive weights, while employing the generalized hyperbolic secant (GHS) function for the nonlinear part to optimize the control points. These two cost functions exhibit complementary characteristics, enabling an effective trade-off balance between convergence speed and steadystate error. This design significantly enhances the robustness of the spline filtering algorithm under colored noise and heavytailed non-Gaussian noise conditions. Moreover, the convergence of the SPOAF-lncosh-GHS algorithm is theoretically analyzed. Furthermore, to overcome the issue of extended filtering time caused by a large number of filter taps, a frequency domain spline prioritization optimization lncosh-GHS adaptive filtering (FDSPOAF-lncosh-GHS) algorithm is developed. Numerical simulations demonstrate that the proposed SPOAF-lncosh-GHS algorithm and its frequency domain counterpart both exhibit superior performance.

Spline adaptive filters (SAFs) have been extensively investigated in identification systems for their real-time online processing capability. Nevertheless, their performance is often suboptimal in practical environments characterized by extreme values resulting from heavy-tailed non-Gaussian distributions. To enhance robustness against heavy-tailed non-Gaussian noise while ensuring high estimation accuracy, this paper proposes a spline prioritization optimization adaptive filter algorithm based on the lncosh algorithm, termed SPOAF-lncosh. Furthermore, to provide a theoretical basis for the proposed SPOAF-lncosh, a detailed learning rate range analysis based on statistical characteristics is performed. Moreover, simulations are compared with other similar algorithms, and it is verified that the convergence performance of the SPOAF-lncosh algorithm is better with or without heavy-tailed non-Gaussian noise, while maintaining a relatively short computation time. Specifically, under the alpha-stable noise (α = 1.2) in Experiment 2, the steady-state error of the SPOAF-lncosh algorithm reaches –20.00 dB, representing an improvement of about 1.1 dB compared to traditional SAF-type algorithms. In the Cauchy noise with a sudden change of Experiment 3, the maximum difference in steady-state error among the algorithms based on the SPOAF architecture is 0.3049 dB, with the SPOAF-lncosh algorithm achieving a steady-state error of -29.0661 dB. In addition, the SPOAF-lncosh algorithm has a runtime comparable to that of stochastic gradient-based filters and is approximately twice as fast as improved stochastic gradient algorithms, such as SAF-ARC-MMSGD and SAF-LHC-MNAG. The application of the second-order electro-hydraulic servo system in aeroengines under alpha heavy-tailed non-Gaussian noise also proves the feasibility of SPOAF-lncosh.