Robust kernel adaptive filters based on mean p-power error for noisy chaotic time series prediction

Two robust kernel adaptive filter (KAF) algorithms, called the kernel least mean p-power (KLMP) and kernel recursive least mean p-power (KRLP), are developed by combining mean p-power error (MPE) criterion and kernel trick for noisy chaotic time series prediction (CTSP). The proposed algorithms employ the MPE to overcome the performance degradation of the CTSP when training data are corrupted by impulsive noises (especially the α-stable noises). First, the KLMP algorithm is proposed by the gradient decent method to improve the robustness of the traditional kernel least mean square (KLMS). Second, the recursion idea and the kernel method are utilized to develop a recursive KAF, namely KRLP, to improve the robustness of the traditional kernel recursive least squares (KRLS). Simulation results show that the proposed algorithms display notable robustness in CTSP when the training data contain different levels of noises, and can perform better in terms of testing MSE than other algorithms.