This paper explores the influence of unstable dynamics on orbit determination. A halo orbit about the Earth-Moon L2 is considered to be the nominal orbit and the dynamics model is constructed based on the Earth-Moon circular restricted three body problem. X-ray pulsar navigation method is introduced for orbit determination that is performed by Kalman filter. Simulation results show that unstable manifold of halo orbit dominates the growth of orbit-determination error and the corresponding uncertainty. However, when the orbit-determination measurements are incorporated in, the results change and are greatly influenced by the characteristic of the X-ray pulse measurements.