A Homotopy Approach to Identification of ARMAX Systems

Abstract

This paper presents a homotopy approach to identification of ARMAX systems. The idea is to construct a homotopy connection of the identification based on ARMAX model with the one based on ARX model. LS (least squares) estimate of ARX model, which guarantee to be global minimum of the loss function, is mapped to the estimate of ARMAX model. By tracking paths of LS estimate gradually transformed into the estimate of ARMAX model, it is shown to have very good convergence properties in estimation. Monte Carlo simulations are carried out to demonstrate the effectiveness of the proposed approach.