Adaptive Nonlinear Estimation Based on Parallel Projection Along Affine Subspaces in Reproducing Kernel Hilbert Space

We propose a novel algorithm using a reproducing kernel for adaptive nonlinear estimation. The proposed algorithm is based on three ideas: projection-along-subspace, selective update, and parallel projection. The projection-along-subspace yields excellent performances with small dictionary sizes. The selective update effectively reduces the complexity without any serious degradation of performance. The parallel projection leads to fast convergence/tracking accompanied by noise robustness. A convergence analysis in the non-selective-update case is presented by using the adaptive projected subgradient method. Simulation results exemplify the benefits from the three ideas as well as showing the advantages over the state-of-the-art algorithms. The proposed algorithm bridges the quantized kernel least mean square algorithm of Chen et al. and the sparse sequential algorithm of Dodd et al.