Nonlinear adaptive filtering techniques with multiple kernels

In this paper, we propose a novel approach using multiple kernels to nonlinear adaptive filtering problems. We present two types of multi-kernel adaptive filtering algorithms, both of which are based on the kernel normalized least mean square (KNLMS) algorithm (Richard et al., 2009). One is a simple generalization of KNLMS, adopting the coherence criterion for dictionary selection. The other is derived by applying the adaptive proximal forward-backward splitting method to a certain squared distance function penalized by a weighted block ℓ₁ norm. The latter algorithm operates the weighted block soft-thresholding which encourages the sparsity of dictionary at the block level. Numerical examples demonstrate the efficacy of the proposed approach.