A new composite gradient algorithm to achieve global convergence

Insufficient-order system identification can result in a multimodal mean square error surface on which a gradient-type algorithm may converge to a local minimum. In this letter a new composite gradient algorithm (CGA) is presented which is due to achieve global convergence when the output error surface contains local minima. The proposed algorithm combines the useful properties of the output error (OE) and equation error (EE) adaptive filtering methods using a new dynamic error surface. The CGA provides a single convergence point for the gradient-search algorithm independently of the initial conditions. The “global convergence” conjecture is illustrated by simulation examples showing good global convergence properties even in such undermodeled cases when the Steiglitz-McBride algorithm fails