Least Mean p-Power Hammerstein Spline Adaptive Filtering Algorithm: Formulation and Analysis
Haiquan Zhao, Yuan Gao, Rui Zhu · IEEE Transactions on Aerospace and Electronic Systems · 2024
Nonlinear systems play a pivotal role in real-world modeling and identification, extending beyond the capabilities of their linear counterparts. Traditional Spine Adaptive Filters (SAF) have exhibited limitations in adaptability and effectiveness, necessitating alternative solutions. Within this context, this paper advocates for a shift towards the Hammerstein Spline Adaptive Filter (H-SAF) to enhance practical applicability. Addressing the deficiencies of H-SAF associated with the mean square criterion in terms of convergence rate and steady-state error, this paper introduces the Least Mean p-Power Hammerstein SAF algorithm (HSAF-LMP). Additionally, a Variable Step-Size Scheme (HSAF-VSSLMP) is proposed to overcome the limitations of fixed step-sizes, thereby further enhancing convergence performance. Furthermore, to comprehensively analyze and assess all aspects of the algorithms' performance, this paper discusses computational complexity, establishes upper and lower bounds on the stabilization step-size in a theoretical manner, and evaluates steady-state performance. Finally, simulations for nonlinear system identification are conducted, confirming the exceptional performance of both presented algorithms.