A Quantized Minimum Kernel Risk Hyperbolic Secant Adaptive Filtering Algorithm

Abstract The proposed algorithm in this paper is the Quantized Minimum Kernel Risk Hyperbolic Secant Adaptive Filtering Algorithm, which offers a simplified approach to enhancing the performance and stability of kernel adaptive filtering in non-Gaussian noise environments. The algorithm features a newly developed Minimum Kernel Risk Hyperbolic Secant Cost Function, which harnesses the hyperbolic secant function’s strengths to diminish outlier impacts and expedite convergence. In addition, its convex kernel risk-sensitive loss surface facilitates swift and accurate filtering via gradient-based methods , thus ensuring outlier robustness. This method could effectively manage network size and reduce computational complexity by incorporating vector quantization for inputting spatial data. Simulation tests in Mackey-Glass time series prediction and nonlinear system identification have indicated that the Minimum Kernel Hyperbolic Secant Adaptive Filtering Algorithm and its quantized variant excel in terms of convergence speed, robustness, and computational efficiency.