Kernel robust mixed-norm adaptive filtering

Kernel methods are powerful for developing a nonlinear learning algorithm in a high-dimensional linear space. The least mean square (LMS) and the least absolute deviation (LAD) are two well-known linear adaptive filtering algorithms. The former performs very well when the noise is Gaussian, while the later possesses desirable performance when the noise has a long-tailed distribution (e.g. alpha-stable distribution). The combination of the LMS and LAD yields a robust mixed-norm (RMN) algorithm. In this paper, we combine the popular kernel methods and the RMN algorithm to develop a new kernel adaptive filtering algorithm, namely the kernel RMN (KRMN) algorithm, which is a robust adaptive algorithm in reproducing kernel Hilbert space (RIOTS). The mean square convergence is analyzed, and the excellent and robust performance of the new algorithm is demonstrated by the simulation results of nonlinear time series prediction.