Abstract: 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.