LAUSR

This paper addresses a general sampling method of the unscented Kalman filter (UKF) for nonlinear state estimation. The sampling method for standard UKF is analyzed, and we propose a theorem to address the conditions that UKF provides a third order accuracy in terms of Taylor series expansion for expectation estimation by changing the number and placements of the sampling points. This theorem can be used to develop new UKF. Based on this theorem, we propose a method to design the placements of the sampling points, including the directions and lengths by optimization strategies. Simulation studies demonstrate that the proposed UKF is effective and can significantly improve the filter performance.