The Extended Kalman Filter (EKF) is a widely used estimation technique which combines the knowledge of the dynamics of the user vehicle motion with the GNSS measurements for robust and more accurate position solutions. However, the EKF approximates the error covariance by linearisation and thus it has limited accuracy. A more rigorous technique is the Unscented Kalman Filter (UKF) which calculates the propagated mean and error covariance of the states more accurately than the EKF. Unscented Kalman Filtering for continuous time systems involves propagation of multiple sigma points at each time step, which incurs a substantial amount of processing time. This paper presents an application of a modified UKF algorithm referred as the Single Propagation Unscented Kalman Filter (SPUKF) with reduced processing time compared to the UKF. In a multiGNSS based Low Earth Orbit (LEO) satellite position estimation scenario the computational performance of the SPUKF is demonstrated. A SPIRENT GNSS simulator was used to simulate the trajectory and the GPS and Galileo measurements for the LEO user satellite. The UNSW Namuru V3.3 multi-GNSS receiver was used to receive the simulated GNSS signals. The pseudorange measurements from the multi-GNSS receiver were used in the UKF and the SPUKF for position estimation. The results indicate that the SPUKF reduces the satellite position computation time by approximately 92.6% compared to the conventional UKF.