Position and Velocity estimation of Re-entry Vehicles using Fast Unscented Kalman Filters

Accurate position and velocity estimation of a re-entry vehicle is essential for realizing its deviation from the desired descent trajectory and providing necessary guidance command in real-time. Generally the Extended Kalman Filter (EKF) is utilized for position and velocity estimation of a space vehicle. However, in the EKF the error covariance is predicted by linearizing the non-linear dynamic model of the system, which results in less accurate state estimation when the dynamics is highly non-linear. As the dynamics of a re-entry vehicle is particularly non-linear in nature, a more accurate position and velocity estimation is expected using a non-linear estimator. The Unscented Kalman Filter (UKF) predicts the mean state vector and the error covariance by deterministic sampling and utilizing the non-linear dynamics of the system. This results in better estimation accuracy than the EKF. However, the processing time of the UKF is much higher than the EKF because of the requirement of multiple state propagations in each measurement time interval. In this paper, application of two new UKF based estimation techniques with reduced processing time in re-entry vehicle position and velocity estimation problem using ground-based range and elevation measurements is presented. The first method is called the Single Propagation Unscented Kalman Filter (SPUKF) where, the a postiriori state is propagated only once and then the sampled sigma points at the next time state are approximated by the first-order Taylor Series terms. In the second method called the Extrapolated Single Propagation Unscented Kalman Filter (ESPUKF), the sigma points are approximated to the second-order Taylor Series terms using the Richardson Extrapolation. The EKF, SPUKF, ESPUKF and the UKF are utilized in a re-entry vehicle navigation scenario using range and elevation measurements. The estimation accuracies and the processing times for different algorithms are compared for the scenario. The result demonstrates that the UKF provides better accuracy than the EKF but requires more processing time. The SPUKF accuracy is better than the EKF and the processing time is significantly less than the UKF. However, the accuracy of the SPUKF is less than the UKF. The ESPUKF provides estimation accuracy comparable to the UKF and the processing time is also significantly reduced.