A new family of robust sequential partial update least mean M-estimate adaptive filtering algorithms

The sequential-LMS (S-LMS) family of algorithms are designed for partial update adaptive filtering. Like the LMS algorithm, their performance will be severely degraded by impulsive noises. In this paper, we derive the nonlinear least mean M-estimate (LMM) versions of the S-LMS family from robust M-estimation. The resultant algorithms, named the S-LMM family, have the improved performance in impulsive noise environment. Using the Pricepsilas theorem and its extension, the mean and mean square convergence behaviors of the S-LMS and S-LMM families of algorithms are derived both for Gaussian and contaminated Gaussian (CG) additive noises.