Stability of some system identification techniques for underparameterized IIR adaptive filters

Stability for reduced-order identification is addressed. In particular, three system identification/adaptive filtering algorithms-the Steiglitz-McBride method (SMM), the recursive gradient method (RGM), and the instrumental variable method (IVM)-are revisited. It is shown that for some classes of reduced-order cases SMM and RGM yield stable solutions, whereas IVM can misbehave, although it has very good performance in sufficiently high-order cases. Thus it is concluded that no individual algorithm is superior, and that it is merely a tradeoff to choose one against the others in a specific application