Sufficient excitation and stable reduced-order adaptive IIR filtering

A perturbed error system is developed to describe the parameter and output error behaviors of reduced-order application of adaptive identifier/ filters such as the hyperstable adaptive recursive filter (HARF). Given satisfaction of a sufficient excitation condition, this error system is shown to exhibit a bounded-input, bounded-output (BIBO) property. This implies that despite order insufficiency the output and parameter estimates of HARF (and similar adaptive identifier/filter algorithms) remain bounded.