A class of improved least sum of exponentials algorithms

•An improved least sum of exponentials (ILSE) algorithm is proposed.•The specific mean square convergence performance analysis for ILSE is given.•The theoretical values of the steady-state EMSE for ILSE are validated by simulations.•A variable scaling factor strategy is incorporated into ILSE to generate VS-ILSE.•The kernel extensions of ILSE and VS-ILSE are developed.

A class of improved least sum of exponentials (ILSE) algorithms is proposed by incorporating a scaling factor into the cost function of LSE in this paper. The even-order moment information regarding error is influenced by the scaling factor. However, the ILSE algorithm based on a fixed scaling factor can only provide a tradeoff between the convergence rate and steady-state excess-mean-square error (EMSE). Therefore, a variable scaling factor ILSE (VS-ILSE) algorithm is also proposed to improve the convergence rate and steady-state EMSE, simultaneously. To facilitate analysis, the energy conservation relation of ILSE is established, providing a sufficient condition for mean square convergence and a theoretical value of the steady-state EMSE. In addition, the kernel extensions of ILSE and VS-ILSE are further developed for performance improvement. Simulation results illustrate the theoretical analysis and the excellent performance of the proposed methods.