  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.
