Computationally Efficient Unscented Kalman Filtering Techniques for Launch Vehicle Navigation using a Space-borne GPS Receiver

Abstract

The Extended Kalman Filter (EKF) is a well established technique for position and velocity estimation. However, the performance of the EKF degrades considerably in highly non-linear system applications as it requires local linearisation in its prediction stage. The Unscented Kalman Filter (UKF) was developed to address the non-linearity in the system by deterministic sampling. The UKF provides better estimation accuracy than the EKF for highly non-linear systems. However, the UKF requires multiple propagations of sampled state vectors in the measurement interval, which results in higher processing time than for the EKF. This paper proposes an application of two newly developed UKF variants in launch vehicle navigation. These two algorithms, called the Single Propagation Unscented Kalman Filter (SPUKF) and the Extrapolated Single Propagation Unscented Kalman Filter (ESPUKF), reduce the processing time of the original UKF significantly and provide estimation accuracies comparable to the UKF. The estimation performance of the SPUKF and the ESPUKF is demonstrated using Falcon 9 V1.1 launch vehicle in CRS-5 mission scenario. The launch vehicle trajectory for the mission is generated using publicly available mission parameters. A SPIRENT GNSS simulator is used to generate the received GPS signal on the trajectory. Pseudo-range observations are used in the EKF, UKF, SPUKF and the ESPUKF separately and the estimation accuracies are compared. The results show that the estimation errors of the SPUKF and the ESPUKF are 15.44% and 10.52% higher than the UKF respectively. The processing time reduces by 83% for the SPUKF and 69.14% for the ESPUKF compared to the UKF.