  In recent years, correntropy has been seccessfully applied to robust adaptive
filtering to eliminate adverse effects of impulsive noises or outliers.
Correntropy is generally defined as the expectation of a Gaussian kernel
between two random variables. This definition is reasonable when the error
between the two random variables is symmetrically distributed around zero. For
the case of asymmetric error distribution, the symmetric Gaussian kernel is
however inappropriate and cannot adapt to the error distribution well. To
address this problem, in this brief we propose a new variant of correntropy,
named asymmetric correntropy, which uses an asymmetric Gaussian model as the
kernel function. In addition, a robust adaptive filtering algorithm based on
asymmetric correntropy is developed and its steady-state convergence
performance is analyzed. Simulations are provided to confirm the theoretical
results and good performance of the proposed algorithm.
