Applications of Square Root Filtering/Smoothing/ Bidirectional Filtering on GPS-based Orbit Determination for LEO

In the paper,the improvements of square root filtering,Kalman smoothing and bidirectional filtering on Kalman filtering is discussed.Two GRACE satellites orbits are computed by using square root filtering/ smoothing/ bidirectional filtering.The results are compared with the orbits provided by JPL and independently validated with k-band ranging(KBR) data.By comparison and analysis,we find that POD using fixed-interval Kalman smoothing can improve the accuracy of square root extended Kalman filtering(SR-EKF) result at the beginning of the data arc.The result of bidirectional filtering can not only improve the accuracy of SR-EKF result at the beginning of the data arc evidently,but also improve the accuracy of orbits after steady of SR-EKF.We also find that the orbits of GRACE which computed using SR-EKF are at a level of about 20 cm in 3-Dimension position and about 10 cm in radial(R),transverse(T) and normal(N) direction respectively.The result of fixed-interval Kalman smoothing can get 15 cm in 3-Dimension position and about 8 cm in radial(R),transverse(T) and normal(N) direction respectively.The result of bidirectional filtering can get 10 cm in 3-Dimension position and about 5 cm in radial(R),transverse(T) and normal(N) direction respectively.