A Sparse Robust Adaptive Filtering Algorithm Based on the $q$ -Rényi Kernel Function

In this letter, a novel kernel function named $q$ -Renyi kernel is proposed. Based on it, a new online adaptive learning algorithm is presented, which is derived based on the recursive adaptive filtering paradigm under the reproducing kernel Hilbert space. The proposed learning algorithm is different from the conventional kernel-based learning paradigm in two senses: first, the reproducing kernel so-called $\boldsymbol {q}$ -Renyi kernel is firstly derived and employed; and second, a sparsity constraint is utilized to generate a small size of neural networks while maintaining a high learning performance. The effectiveness of the proposed algorithm is demonstrated via numerical simulations.