Least mean [formula omitted]-power algorithms with generalized correntropy

Abstract

A family of least mean p-power (LMP) algorithms including the sign algorithm (SA, p=1), the least mean square (LMS, p=2) and the LMP (1<p<2), have been widely applied in system identification because of their advantages for easy implementation. In some application systems on the basis of sparse features, the generalized correntropy (GC) which is a good measure to address sparse problem, is applied to these LMP-type algorithms in order to improve algorithms’ performance with response to convergence rate or filtering accuracy. And the LMP-type algorithms with GC are proposed in this paper, called as GCSA, GCLMS and GCLMP respectively. In addition, simplified versions of these proposed algorithms (written as SGCSA, SGCLMS and SGCLMP) are also derived to save lots of computations. To overcome the limitation of fixed step size in filtering precision and convergence speed, a variable-step-size method is derived. Furthermore, the convergence of proposed algorithms are analysed. For white input signals, simulation results are demonstrated to verify the good performance of proposed algorithms.