To estimate and analyze the orbit of a spacecraft in the ascent phase, three algorithms are proposed in this paper: a two-satellite point-by-point intersection positioning algorithm, single-satellite positioning algorithm, and multiple-point intersection collaborative positioning algorithm. Meanwhile, two mathematic models of the spacecraft orbit are presented based on the kinematics characteristic and the least square method. Besides, by combining the results of the proposed satellite positioning algorithms with mathematic models of the spacecraft orbit, the particle filtering based on the Monte Carlo algorithm is applied to filtering of the final results of the spacecraft. Finally, the effectiveness of the two-satellite point-by-point intersection positioning algorithm and the single-satellite positioning algorithm is verified through the experiment simulation on the real data.