Accelerated Gradient Descent Estimation for Rational Models by Using Volterra Series: Structure Identification and Parameter Estimation

Abstract

This brief studies a rational model identification problem using a novel gradient descent algorithm. The rational model is approximated by a second-order Volterra system, whose parameters and structure are estimated through an accelerated gradient descent algorithm. This algorithm improves the convergence rates by computing an optimal step-size and introducing a preconditioning method. In addition, it can avoid the eigenvalue calculation if the preconditioning matrix is equal to the inverse of the information matrix. A numerical experiment is given to illustrate the performances of the proposed algorithm.