Robust adaptive filtering with variable risk-sensitive parameter and kernel width

Similarity measures play a significant role in adaptive filtering. Previous work such as correntropy and kernel risk-sensitive loss (KRSL), has successfully improved the technology of adaptive filtering in terms of robustness against outliers, fast convergence speed and high filtering accuracy. Based on KRSL, a newly raised similarity measure, complex KRSL (CKRSL), was proposed by extending KRSL to the complex domain. It successfully gains superior performance than other similarity measures in adaptive filtering algorithms. However, the minimum CKRSL (MCKRSL) algorithm may result in poor performance when the parameters are not properly chosen. In this Letter, an adaptive parameter selection is proposed to help the MCKRSL algorithm improve performance while overcoming the uncertainty in artificial selection. The proposed MCKRSL with variable parameters (MCKRSL-VP) algorithm updates the risk-sensitive parameter and kernel width by making the iteratively squared bias as small as possible. A moving average scheme is further used to smoothly update the risk-sensitive parameter and kernel width. Finally, the authors verify that MCKRSL-VP performs better than other algorithms by simulations.