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.