GLMS adaptive alogrithm in linear prediction

This paper proposes a new version of an adaptive LMS algorithm, based on a modified estimate of the performance function gradients. This modification leads to the GLMS (geometrically median LMS) adaptive algorithm. This algorithm causes smaller gradient noise into an adaptive filter, thus leading to more stable convergence of an adaptive process. This property makes the GLMS algorithm more stable and superior in some applications than the LMS algorithm. The convergence analysis of GLMS algorithm is also performed, and the comparative simulation results (with respect to the LMS algorithm) presented, confirming the mentioned advantages. GLMS turned out to be most suitable for prediction of a random signal with large Gaussian noise.