The Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Ensemble Kalman Filter (EnKF) are commonly implemented practical solutions for solving nonlinear state space estimation problems; all based on the linear state space estimator, the Kalman Filter. Often, the UKF and EnKF are cited as a superior methods to the EKF with respect to error-based performance criteria. The UKF in turn has the advantage over the EnKF of smaller computational complexity. In practice however the UKF often fails to live up to this expectation, with performance which does not surpass the EKF and estimates which are not as robust as the EnKF. This work explores the geometry of alternative sigma point sets, which form the basis of the UKF, contributing several new sets along with novel methods used to generate them. In particular, completely novel systems of sigma points that preserve higher order statistical moments are found and evaluated. Additionally a new method for scaling and problem specific tuning of sigma point sets is introduced as well as a discussion of why this is necessary, and a new way of thinking about UKF systems in relation to the other two Kalman Filter methods. An Iterated UKF method is also introduced, similar to the smoothing iterates developed previously for the EKF. The performance of all of these methods is demonstrated using problem exemplars with the improvement of the contributed methods highlighted.
Worcester Polytechnic Institute
Electrical & Computer Engineering
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Lowe, M. (2015). Extended and Unscented Kalman Smoothing for Re-linearization of Nonlinear Problems with Applications. Retrieved from https://digitalcommons.wpi.edu/etd-dissertations/457
Kalman Filter, EKF, UKF, Tracking, Iterative, Sigma Point