A Unified Approach to Set-Membership and Selective Partial Update Adaptive Filtering Algorithms

In this paper we show how the classical and modern adaptive filter algorithms can be introduced in a unified way. The Max normalized least mean squares (MAX-NLMS), N-Max NLMS, the family of SPU-NLMS, SPU transform domain adaptive filter (SPU-TDAF), and SPU subband adaptive filter (SPU-SAF) are particular algorithms are established in a unified way. Following this, the concept of set-membership (SM) adaptive filtering is extended to this framework, and a unified approach to derivation of SM and SM-SPU adaptive filters is presented. The SM-NLMS, SM-TDAF, SM-SAF, SM-SPU-NLMS, and SM-SPUSAF are presented based on this approach. Also, this concept is extended to the SPU affine projection (SPU-AP) and SPUTDAF algorithms and two new algorithms which are called SM-SPU-AP and SM-SPU-TDAF algorithms, are established. These novel algorithms are computationally efficient. The good performance of the presented algorithms is demonstrated in system identification application.