Robust Adaptive Filtering With $q$ -Gaussian Kernel Mean $p$-Power Error

In this letter, a novel information theoretic measure, namely q-Gaussian kernel mean p-power error (QKMPE), is proposed by defining the mean p-power error in the q-Gaussian kernel space, which is a generalization of the kernel mean p-power error measure. Furthermore, a recursive kernel adaptive filter algorithm, named as recursive least q-Gaussian kernel mean p-power, is derived under the least QKMPE criterion for robust learning in noisy environment. This new proposed algorithm reveals superior performance against Gaussian-type noise as well as the nonGaussian perturbation, especially when the data contain large outliers. Experimental results in the context of Mackey-Glass time series prediction confirm the effectiveness of the proposed algorithm.