Robust Adaptive Filtering under Least q-Gaussian Kernel Mean p-Power Error Criterion

Owing to their superior approximation capability, kernel adaptive filters (KAFs) have been widely applied to the nonlinear systems modeling. Traditional KAFs are generally developed under the mean square error (MSE) criterion. However, the MSE criterion merely performs well under the Gaussian assumption. For non-Gaussian situations, an information theoretic measure called correntropy has been proposed and applied in robust adaptive filtering, which uses the Gaussian kernel as the default kernel. Of course, Gaussian kernel is not always the optimal choice. To enhance the approximation capability of KAFs, The q-Gaussian kernel is derived from the q-Gaussian distribution which arises from the maximization of the Tsallis entropy under appropriate constraints. With a proper shape parameter $q$ , the q-Gaussian kernel can get better performance than the Gaussian kernel. In this paper, the least q-Gaussian kernel mean q-power error (LQKMP) criterion is proposed with the help of correntropy and the q-Gaussian kernel. Furthermore, a recursive KAF algorithm, named as recursive least q-Gaussian kernel mean p- power (RQKMP), is derived under the LQKMP criterion for robust learning in noisy environment. This new proposed algorithm reveals superior performance against large outliers. Simulations about time series prediction are utilized to demonstrate the effectiveness of the proposed algorithm.