Does the unscented Kalman filter converge faster than the extended Kalman filter? A counter example

The relative effects of initialization error on the Extended and Unscented Kalman filters were investigated for an example scalar system. Analytical methods were applied in order to derive the conditions under which one filter outperformed the other in response to initial error. Some simulation results were presented to support the analytically derived results. For the considered example, the Extended Kalman filter was able to outperform the Unscented Kalman filter when the assumed initial state was greater in magnitude than the actual initial state, and vice versa. Additionally, cases with larger measurement noise demonstrated further performance advantage of the Extended Kalman Filter.