Enhanced FIR system identification: Empirical copula delay estimation method and variable stacking length multi-gradient algorithm

This study offers an improved strategy for identifying finite impulse response (FIR) systems. To begin with, a modified time delay estimation method, rooted in empirical copula, is applied, creating a robust framework for parameter estimation. Following this, an innovative stochastic gradient algorithm that incorporates a flexible stacking length is presented to enhance the accuracy of parameter estimates. This algorithm adapts stacking length dynamically according to the optimization progress, which enhances both convergence and accuracy. Additionally, a criterion based on the decrease of the cost function is proposed to determine the optimal variable stacking length, ensuring better performance. Extensive experimental results confirm the effectiveness of the proposed methods.