Robust Adaptive Filtering for Heavy-Tailed Noise and Colored Noise Via Lncosh-Generalized Hyperbolic Secant

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.