UNDERMODELED ADAPTIVE FILTERING - AN A-PRIORI ERROR BOUND FOR THE STEIGLITZ-MCBRIDE METHOD

Practical applications of adaptive IIR filtering are confronted with u ndermodeled (or reduced-order) cases: the order chosen for the adaptiv e identifier is inferior to the true degree of the unknown system, Mos t known results for adaptive IIR filters concern only the sufficient o rder case, and rarely admit direct extensions to the undermodeled case , As exact matching is excluded by undermodeling, critical to the acce ptance of any algorithm are the approximation properties which result in the undermodeled case, In this direction, we establish an a priori error bound for the Steiglitz-McBride algorithm, In particular, if the input and disturbance are both white noise processes, and if M is the chosen order for the identifier, we show that the L(2)-norm of the er ror function at any stationary point can be no larger than the M + 1st Hankel singular value of the unknown system, This gives a meaningful bound, and yields the first formal result which affirms that the Steig litz-McBride method is capable of satisfactory approximation propertie s for the undermodeled case, Conditions under which the Steiglitz-McBr ide model is close to an optimal L(2)-norm or Hankel-norm approximant are obtained as an elementary consequence of our bound, Our result als o provides the first bound on the ''bias'' introduced by a colored dis turbance.