A new NLMS algorithm for slow noise magnitude variation

A set-membership (SM) normalized least-mean-square (NLMS) (SMNLMS) algorithm is developed using SM theory in the class of optimal bounding ellipsoid (OBE) algorithms. This signed version of NLMS algorithm requires a priori knowledge of a bound for the error magnitude, which is unknown in most applications. A very simple algorithm is proposed for the case in which the unknown magnitude of the measurement noise is slowly time-varying. The proposed algorithm is able to extract the noise magnitude information and exploit this magnitude to enhance or accelerate the learning process without risk of overbounding or performance loss due to underbounding. The performance of the proposed algorithm is compared with that of SMNLMS using some simulation examples.