Two Modifications of the Unscented Kalman Filter that Specialize to the Kalman Filter for Linear Systems

Abstract

Although the unscented Kalman filter (UKF) is applicable to nonlinear systems, it turns out that, for linear systems, UKF does not specialize to the classical Kalman filter. This situation suggests that it may be advantageous to modify UKF in such a way that, for linear systems, the Kalman filter is recovered. The ultimate goal is thus to develop modifications of UKF that specialize to the Kalman filter for linear systems and have improved accuracy for nonlinear systems. With this motivation, this paper presents two modifications of UKF that specialize to the Kalman filter for linear systems. The first modification (EUKF-A) requires the Jacobian of the dynamics map, whereas the second modification (EUKF-C) requires the Jacobian of the measurement map. For various nonlinear examples, the accuracy of EUKF-A and EUKF-C is compared to the accuracy of UKF.