Exponential Inverse Square Root Recursive Spline Adaptive Filter for Nonlinear System Identification

The article delves into the challenges of nonlinear system identification, particularly in real-time applications with complex nonlinear characteristics. It highlights the limitations of traditional methods like Volterra series and linear-in-the-parameters (LIP) nonlinear filters, which struggle with high-dimensional data and moderate nonlinearity. The proposed solution, an Exponential Inverse Square Root Recursive Spline Adaptive Filter (EISSAF), addresses these issues by incorporating a recursive spline structure and a novel cost function designed to handle non-Gaussian noise interference. The EISSAF algorithm is thoroughly analyzed, including its weight adaptation method, stability criteria, and computational complexity. Simulation results across various nonlinear systems demonstrate the superior performance of EISSAF in maintaining low mean square error (MSE) and robust convergence, even in the presence of impulsive noise. The article also explores the impact of different parameters, such as interval sampling and scaling, on the algorithm's performance, providing insights into its practical implementation. The detailed analysis and comprehensive evaluation make this article a significant contribution to the field of adaptive filtering and nonlinear system identification.