  We consider the robust filtering problem for a nonlinear state-space model
with outliers in measurements. To improve the robustness of the traditional
Kalman filtering algorithm, we propose in this work two robust filters based on
mixture correntropy, especially the double-Gaussian mixture correntropy and
Laplace-Gaussian mixture correntropy. We have formulated the robust filtering
problem by adopting the mixture correntropy induced cost to replace the
quadratic one in the conventional Kalman filter for measurement fitting errors.
In addition, a tradeoff weight coefficient is introduced to make sure the
proposed approaches can provide reasonable state estimates in scenarios where
measurement fitting errors are small. The formulated robust filtering problems
are iteratively solved by utilizing the cubature Kalman filtering framework
with a reweighted measurement covariance. Numerical results show that the
proposed methods can achieve a performance improvement over existing robust
solutions.
