Recently, the kernel based constrained adaptive filtering algorithm has attracted a lot of attentions because of its robustness and superiority over traditional methods. As two classic kernel based algorithms, both constrained maximum correntropy criterion (CMCC) and constrained minimum error entropy (CMEE) have shown their superiorities in the case of non-Gaussian noise. However, both algorithms use only one kernel as the kernel function. To further improve the performance of the kernel based adaptive filtering algorithms, we first define the mixture kernel risk-sensitive loss (MKRSL) and study its properties. Then, we apply it to the constrained adaptive filtering and propose a novel constrained minimum MKRSL (CMM-KRSL) algorithm in this paper. Furthermore, we present the performance analysis of the CMM-KRSL algorithm, and provide the stability condition and the theoretical mean square deviation (MSD). Finally, we validate the accuracy of performance analysis and the superiorities of CMM-KRSL by simulations.

近年来，基于核的约束自适应滤波算法由于其鲁棒性和优于传统方法的优势而备受关注。作为两种经典的基于核的算法，在非高斯噪声的情况下，约束最大熵准则（CMCC）和约束最小误差熵（CMEE）都显示了它们的优势。但是，两种算法都仅使用一个内核作为内核功能。为了进一步提高基于内核的自适应过滤算法的性能，我们首先定义混合内核风险敏感损失（MKRSL）并研究其性质。然后，将其应用于约束自适应滤波，并提出了一种新的约束最小MKRSL（CMM-KRSL）算法。此外，我们介绍了CMM-KRSL算法的性能分析，并提供稳定性条件和理论均方差（MSD）。最后，我们通过仿真验证了性能分析的准确性以及CMM-KRSL的优越性。