Diffusion least mean kurtosis algorithm and its performance analysis

Adaptive filtering algorithms developed by using the negated kurtosis of the error signal as cost function can obtain good performance in some types of sub-Gaussian noise environments. This work extends the least mean kurtosis (LMK) algorithm to a diffusion network scenario to address the distributed estimation problem. To evaluate its stochastic behavior, we analyze the transient performance using Isserlis' theorem under some statistical assumptions. In addition, the theoretical steady-state performance indicators are also derived in closed form. Our established analytical models are also applicable to the diffusion least mean fourth (DLMF) algorithm which is a special case of our proposed diffusion LMK (DLMK) algorithm. The analytical models are more universal and reliable than the existing models in the literature. Simulation results are provided to show the superiority of DLMK and to corroborate our theoretical development of transient and steady-state performance.