Abstract: The dual-frequency GPS carrier phase and pseudorange measurements have become the primary observations for accurately determining the position and velocity of satellites in low Earth orbit (LEO). Reduced dynamic batch least squares (LSQ) technique is used for LEO orbit determination using pseudorange and carrier phase ionosphere-free measurements, which combines the merits of kinematic positioning technique with pure dynamic orbit determination. In order to compensate for any unmodelling or inaccuracy of the employed dynamic model, piece-wise constant accelerations are estimated in consecutive subintervals on the basis of a precise deterministic force model in the batch LSQ method. Particularly, the paper introduces two methods for calculating the sensitive matrix related to empirical accelerations and solving for the inverse of a banded sparse matrix. GRACE-A real flight data has been used to evaluate the positioning performance of the proposed method. Positioning accuracy of less than 5cm in terms of 3D RMS was achieved. The magnitudes of empirical accelerations were all less than 40nm·s^-2 in radial, along-track and cross-track directions. The extra dynamic parameters C_D and C_R were estimated within a reasonable range and the space-borne receiver's clock offset was linear with small periodic fluctuations.