Recursive identification of overparametrized systems

A recursive identification algorithm based on extended least squares is proposed to deal with the contingency of overparametrization. The algorithm is relatively simple compared to those involving online order determination, being based on adaptively introducing suitable excitation into the algorithm to avoid ill-conditioning. In the case of extended-least-squares-based adaptive estimation, then the regressors are appropriately stochastically perturbed. The algorithm is shown to converge to a uniquely defined signal model with any pole-zero cancellations at the origin.<>