Circular Correntropy: Definition and Application in Impulsive Noise Environments

Circular statistics has been applied to several areas of knowledge in which the input data is circular or directional. Noisy measurements are still a problem in circular data applications and, like non-circular data, second-order statistics have some limitations to deal with non-Gaussian noise. Recently, a similarity function called correntropy has been successfully employed in applications involving impulsive noise for being capable of extracting more information than second-order methods. However, correntropy has not been studied from the perspective of circular data so far. This paper defines a novel statistical measure called circular correntropy (CC). It uses the von Mises density function in order to redefine correntropy in this domain. In particular, it is proved analytically that the CC contains information regarding second-order and higher-order moments, being a generalization of the circular correlation measure. The performance of this novel similarity measure is evaluated as a cost function in a nonlinear regression problem, where the signals are contaminated with additive impulsive noise. The simulations demonstrate that the CC is more robust than circular correlation in impulsive noise environments.