Sufficient excitation and stable reduced-order adaptive IIR filtering

Department of Electrical Engineering Department of Electrical Engineering Virginia Polytechnic Institute and State University University of Newcastle Blacksburg, VA 24061 New South Wales, 2308 Australia n ABSTRACT v(k) = y(k) — z(k) + c.[y(k—i) — z(k—i)I i=l A perturbed error system is developed to de— (4) scribe the parameter and output error behaviors of -. n reduced—order application of adaptive identifier! y(k) — y(k) + c.[y(k—i) — z(k—i)] 1 filters such..as the hyperstable adaptive recursive i1 filter (IIARF). Given satisfaction of a sufficient xi m 2 excitation condition, this error system is shown to 1 + p.z2(k—i) + p.u (k—j) exhibit a bounded—input, bounded—output (BIBO) il jl property. This implies that despite ofder insuffi— xi m ciency the output and parameter estimates of HARF z(k) = a.(k+l)z(k—i) ÷ b (k+l)u(k—j) (5) 1 (and similar adaptive identifier/filter algorithms) il j=l remain bounded.