Kernel least-mean mixed-norm algorithm

The Kernel method is a powerful tool for extending an algorithm from linear to nonlinear case. The least-mean mixed-norm (LMMN) algorithm possesses good performance when the system measurement noise shows distribution with a linear combination of long tails and short tails. In this paper, we combine the famed kernel trick and the LMMN algorithm to present the kernel LMMN (KLMMN) algorithm, which is an adaptive filtering algorithm in reproducing kernel Hilbert space (RKHS). The optimal norm-mixing parameter is derived. To demonstrate the effectiveness and superiorities of the proposed algorithm, we apply the algorithm to nonlinear system identification when the environment noise composed of a linear combination of Gaussian and Bernoulli distributions.