Error propagation characteristic analysis of halo orbit based on condition number of state transition matrix

Abstract

The error propagation characteristics of different points of a halo orbit are studied in this paper. The condition number of state transition matrix after a period is used to estimate the sensitivity of different positions on a halo orbit to the state errors. Then the covariance propagation method is applied to compute the error covariance matrix under the initial state errors, and the results are validated by Monte Carlo simulation. The variations of the position error are compared with the variations of the condition number. The results show that the variation trend of the position error after a period of that halo orbit is the same as the variation trend of the condition number. Moreover, this identified property is verified by testing the halo orbits with different amplitudes and the halo orbits in systems with different mass ratios. Finally, the variation trends of the condition numbers against propagation time corresponding to different points on the halo orbit are analyzed. It is shown that the largest point in the negative \(z\) direction of the north halo orbit and its vicinity are more sensitive to state errors than other positions on the halo orbit, and they should not be selected as the injection point.