Unbiased Equation - Error Adaptive IIR FilteringBased on Moni

35 Unbiased Equation-Error Adaptive IIR Filtering Based on Moni Normalization Hyoung-Nam Kim, Student Member, IEEE, and Woo-Jin Song, Member, IEEE Abstra t| We present a novel way to remove the bias in equation-error based adaptive in nite impulse response (IIR) ltering by on eiving a s heme alled moni normalization. It is found that normalizing all the oeÆ ients of the denominator lter by the rst oeÆ ient after ea h adaptation removes the bias and leads to unbiased estimates. The analysis of stationary points is presented to show that the proposed method an indeed produ e unbiased parameter estimates in the presen e of noise. The omputer simulation results also demonstrate that the proposed method performs better than or omparable to existing algorithms, while requiring mu h lower omputational omplexity. Keywords| Adaptive IIR ltering, equation error, unbiased estimate. I. Introdu tion EQUATION-ERROR adaptive in nite impulse response (IIR) ltering has some attra tive features su h as a unimodal error surfa e, good onvergen e, and guaranteed system stability, ompared to output-error adaptive IIR ltering [1℄. In spite of those advantages, the equationerror approa h has not been widely used sin e it may generate biased oeÆ ient estimates in the presen e of noise. Most existing algorithms in equation-error adaptive IIR ltering have tried to remove the bias through additional ltering or umbersome noise suppression pro edures [2℄{ [4℄. Re ently, the unit-norm onstraint has drawn mu h interest as an appropriate alternative for solving the bias problem without resorting to ltering or noise suppression [5℄, [6℄. The fo us of development of su h algorithms is to make the pro ess of oeÆ ients update una e ted by noise. In this letter, we introdu e a novel s heme alled moni normalization for unbiased equation-error adaptive IIR ltering. The proposed method is inspired by the moni onstraint ommonly used in the existing equation-error algorithms in whi h the rst oeÆ ient of the denominator lter is xed to unity. In adaptive IIR ltering with moni normalization, all the denominator oeÆ ients of an adaptive IIR lter in luding the rst oeÆ ient are adapted and normalized by the updated rst oeÆ ient after ea h iteration. In this way, the noise e e t on the updated oeÆ ients an be removed be ause the noise e e t is shown to be approximately identi al for all those oeÆ ients. Manus ript re eived O tober 5, 1998. The asso iate editor oordinating the review of this manus ript and approving it for publi ation was Prof. G. Ramponi. The authors are with the Department of Ele troni and Ele tri al Engineering, Pohang University of S ien e and Te hnology, Pohang, Kyungbuk, 790-784, Korea (e-mail: wjsong poste h.a .kr). Publisher Item Identi er S 1070-9908(99)01235-3. ) ( ˆ z Bg + ⊕ ) (n x ) (z H