Quaternion Kernel Normalized Minimum Error Entropy Adaptive Algorithms

Information Theoretic Learning (ITL) [1][2] is gaining popularity for designing adaptive filters for a non-stationary or non-Gaussian environment. ITL cost functions such as the Minimum Error Entropy (MEE) have been applied to both linear and nonlinear adaptive filtering with better overall performance compared with the typical minimum mean squared error (MSE) and least-squares type adaptive filtering [3][4] especially for nonlinear systems and in higher-order statistic noise environments. In this paper, we develop a kernel adaptive filter for quaternion data based on normalized minimum error entropy cost function. We apply generalized Hamilton-real (GHR) calculus that is applicable to Hilbert space for evaluating the cost function gradient to develop the quaternion kernel normalized minimum error entropy (QKNMEE) algorithm. The new proposed algorithm enhanced MEE algorithm where the filter update stepsize selection will be independent of the input power and the kernel size.