  A priori state vector and error covariance computation for the Unscented
Kalman Filter (UKF) is described. The original UKF propagates multiple sigma
points to compute the a priori mean state vector and the error covariance,
resulting in a higher computational time compared to the Extended Kalman Filter
(EKF). In the proposed method, the posterior mean state vector is propagated
and then the sigma points at the current time step are calculated using the
first-order Taylor Series approximation. This reduces the computation time
significantly, as demonstrated using two example applications which show
improvements of 90.5% and 92.6%. This method shows the estimated state vector
and the error covariance are accurate to the first-order Taylor series terms. A
second method using Richardson Extrapolation improves prediction accuracy to
the second-order Taylor series terms. This is implemented on the two examples,
improving efficiency by 85.5% and 86.8%.
