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

In this letter, a novel information theoretic measure, namely $\boldsymbol {q}$ -Gaussian kernel mean $\boldsymbol {p}$ -power error (QKMPE), is proposed by defining the mean $\boldsymbol {p}$ -power error in the $\boldsymbol {q}$ -Gaussian kernel space, which is a generalization of the kernel mean $\boldsymbol {p}$ -power error measure. Furthermore, a recursive kernel adaptive filter algorithm, named as recursive least $\boldsymbol {q}$ -Gaussian kernel mean $\boldsymbol {p}$ -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 non-Gaussian 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.