On the existence of stationary points for the Steiglitz-McBride algorithm

Most convergence results for adaptive identification algorithms have been developed in sufficient order settings, involving an unknown system with known degree. Reduced-order settings, in which the degree of the unknown system is underestimated, are more common, but more difficult to analyze. Deducing stationary points in these cases typically involves solving nonlinear equations, hence the sparseness of results for reduced-order cases. If we allow ourselves the tractable case in which the input to an identification experiment is white noise, we shall show that the Steiglitz-McBride method (1965) indeed admits a stationary point in reduced-order settings for which the resulting model is stable. Our interest in this study stems from a previous result, showing an attractive a priori bound on the mismodeling error at any such stationary point.