A Kernel-Width Adaption Diffusion Maximum Correntropy Algorithm

Abstract

Impulsive noises are widely existing in various systems like noise cancellation system and wireless communication systems, where adaptive filtering (AF) is always employed to identify specific systems. Additionally, the impulsive noises will affect the performance for estimating these systems, resulting in slow convergence or worse identification accuracy. In this paper, a diffusion maximum correntropy criterion (DMCC) algorithm with adaption kernel width is proposed, denoting as DMCC adapt algorithm, to find out a solution for dynamically choosing the kernel width. The DMCC adapt algorithm chooses small kernel width at initial stage to improve its convergence speed rate, and uses large kernel width at completion stage to reduce its steady-state error. To render the proposed DMCC adapt algorithm suitable for sparse system identifications, the DMCC adapt algorithm based on proportional coefficient adjustment is realized and named as diffusion proportional maximum correntropy criterion (DPMCC adapt). The theoretical analysis and simulation results are presented to show that the DPMCC adapt and DMCC adapt algorithms have better convergence than the traditional diffusion AF algorithms under impulse noise and sparse systems. INDEX TERMS Adaptive kernel width, diffusion algorithm, impulse noise, maximum correntropy criterion, sparse system identification.

Developing a multi-step recurrent algorithm to maximize the criteria of correntropy

“…Therefore, when applying a given algorithm in practice, one should use the estimates of these parameters. However, the estimates derived from (40) to (42) allow the researcher to pre-evaluate the limits of a given algorithm and the effectiveness of its application when solving practical tasks.…”

“…Numerous studies [36][37][38][39][40][41][42][43][44] have shown that with non-Gaussian noise in measurements an informational approach is very effective. At the same time, the criterion used should take into consideration the statistics of the error signal not only of the second but also of a higher order.…”

“…Correntropy was introduced in [36,37] as a generalized measure of similarity, maximizing which underlies the production of sufficiently effective robust algorithms. However, while a gradient algorithm was used in [38][39][40][41][42] to maximize functionality, the algorithm of the recurring LSM was used in [43] to maximize functionality. It should be noted that due to the low convergence rate, both algorithms are quite ineffective in assessing non-stationary parameters.…”

“…If, in the n-th step, the matrix taking into consideration the designations in (40), consider the scalar value…”

Diffusion Generalized MCC with a Variable Center Algorithm for Robust Distributed Estimation

“…A robust DE method based on MCC, called diffusion MCC (DMCC), was developed in [15] to mitigate the robustness of the traditional DAF algorithms. In addition, a proportional DMCC algorithm with adaptable kernel width was proposed for sparse distributed system identification in the cases of impulse noise [16]. The diffusion subband adaptive filtering (DSAF) algorithm, based on symmetrical MCC with individual weighting factors, was developed for colored input signals [17].…”