Spline Prioritization Optimization Lncosh Adaptive Filter for Heavy-Tailed Non-Gaussian Noise

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.