Higher-Order Unscented Estimator

Abstract

This paper introduces a new extension of the unscented Kalman filter with asymmetric sample points and weights chosen to match third- and fourth-order moments in addition to the mean and covariance. Explicit solutions are obtained for sample points and weights, making their evaluation efficient and robust, and rigorous constraints are derived for their applicability. The use of the new filter is demonstrated with three dynamic systems (an aircraft coordinated turn model, a rotating rigid body, and a projectile with drag), and filter performance is compared with that of the conventional unscented Kalman filter and conjugate unscented transform filters. The new filter is found to be more robust in most cases where the initial distribution, process noise, and measurement noise have a high kurtosis, in that it does not generate extreme outliers in the estimation error. Also, execution times for the new filter are found to be only slightly longer than for the conventional unscented Kalman filter and significantly shorter than for the conjugate unscented transform filters.