The Quarternion Maximum Correntropy Algorithm

We develop a kernel adaptive filter for quaternion data based on maximizing correntropy. We apply a modified form of the HR calculus that is applicable to Hilbert spaces for evaluating the cost function gradient to develop the quaternion kernel maximum correntropy (KMC) algorithm. The KMC method uses correntropy to measure similarity between the filter output and the desired response. Here, the approach is applied to quaternions for improving performance for biased or non-Gaussian signals compared with the minimum mean square error criterion of the kernel least-mean-square algorithm. Simulation results demonstrate the improved performance with non-Gaussian inputs.