Minimum kernel risk sensitive mean p-power loss algorithms and their performance analysis

Abstract

The least mean square (LMS) algorithm is optimal for combating Gaussian noises owing to the used minimum mean square error (MSE) criterion in its loss function. However, the MSE criterion is not efficient for non-Gaussian noises. To this end, a new robust minimum kernel risk sensitive mean p-power loss (MKRSP) algorithm is proposed to provide robustness against impulsive noises and improve filtering accuracy, simultaneously. The MKRSP algorithm can generalize the minimum kernel risk sensitive loss (MKRSL) algorithm by setting p=2, and improve filtering accuracy by setting a proper p. Further, the random-Fourier-features MKRSP (RMKRSP) algorithm is developed for improving robustness and filtering accuracy of MKRSP. And the steady-state excess mean square errors (SEMSEs) of MKRSP and RMKRSP are calculated for theoretical analysis. The correctness of the obtained SEMSEs are verified by simulations, and the accuracy advantages of MKRSP and RMKRSP are also confirmed in different noise environments.