Evaluation of Orbit Determination Accuracy in Interplanetary Transfer Section of Mars Probe
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摘要: 天问一号是中国第一次实现地火转移行星际飞行的探测器，在长达202天的行星际转移飞行期间，共经历了4次中途修正及1次深空机动控制，在2021年2月10日成功进行了近火制动，被火星捕获而进入环火轨道。本文对探测器行星际转移期间的动力学模型进行了分析，制定了转移飞行期间定轨积分中心转换原则：在探测器飞出地球影响球后，定轨积分中心需要由地心更换为日心；对不同版本行星星历表的使用进行了分析，确定了使用DE436行星历表进行计算对定轨影响最小。根据探测器行星际转移飞行的特点，制定了一种基于逐日迭代定轨策略的精度评估方法。基于实测数据分析，验证了该方法的有效性，火星探测器行星际转移期间定轨位置误差优于2 km，速度误差优于20 mm·s–1 (1σ)。Abstract: Tianwen-1 is the first Chinese probe to realize interplanetary flight between Earth and Mars. During the 202-day long interplanetary transfer flight, it experienced four midway corrections and one deep space maneuver control. On 10 February 2021, it successfully applied braking near Mars and was captured by Mars. This paper, the dynamic model during interplanetary transfer is analyzed, and the principle of celestial center conversion during transfer flight is formulated. It is necessary to replace the celestial center with the Sun after leaving the Earth’s influence sphere. According to the analysis results, DE436 ephemeris is determined to be used, because it has the least impact on orbit determination. Based on the characteristics of the interplanetary transfer flight of the probe, this paper proposes an accuracy evaluation method based on a daily iterative orbit determination strategy. Based on the analysis of measured data, the effectiveness of this method has been verified. During the interplanetary transfer of the Mars probe, the orbit determination position error is better than 2 km, and the velocity error is better than mm·s–1 (1σ).
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图 1 行星际转移初期各摄动加速度演化
Figure 1. Evolution diagram of perturbed acceleration at the initial stage of interplanetary transfer of Mars probe
图 2 不同积分中心下定轨误差
Figure 2. Orbit determination error under different integration centers
图 4 火星探测器行星际转移段定轨精度评估策略
Figure 4. Orbit accuracy evaluation strategy for interplanetary transfer section of Mars probe
图 7 火星探测器行星际转移段轨道精度评估结果
Figure 7. Orbit accuracy evaluation results of the interplanetary transfer section of the Mars probe
表 1 不同行星历表下定轨预报误差
Table 1. Orbit determination prediction error under different ephemeris
比较项目 定轨 预报 位置误
差/m速度误
差/（m·s–1）位置误
差/m速度误
差/（m·s–1）DE421 VSDE436 261.4351 0.0000006 306.4832 0.0207 DE405 VSDE436 1172.0748 0.0002 2238.2650 0.0930 
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表 2 行星际转移轨道探测器动力学模型及参数
Table 2. Dynamics model and parameters of explorer in transfer orbit
积分中心 动力学 模型 参数 地球 地球质点 J2000地心惯性系 － 地球非球形 JGM-3 8×8阶次 日月及大行星 第三体引力 JPL-DE436历表 太阳 太阳光压 固定面质比 初值Cr = 1.34 太阳质点 J2000日心惯性系 － 大行星及月球 第三体引力 JPL-DE436历表 后牛顿效应 广义相对论 JPL-DE436历表 太阳光压 固定面质比 初值Cr = 1.34
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表 3 火星探测器行星际转移轨道定轨数据使用的选择情况分析
Table 3. Analysis on the selection of orbit determination data for interplanetary transfer orbit of Mars probe
数据使用策略 误差统计 位置/m 速度/（m·s–1） 测距、测速
时延率60209.2 0.057 测距、测速
时延161.5 0.0002 测距、测速 60309.1 0.059 测速
时延、时延率1864324.0 0.102 测距
时延、时延率74.8 0.0001
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表 4 天问一号探测器行星际转移段关键事件
Table 4. Orbit control time of the interplanetary transfer phase of “Tianwen-1” probe
序号 时间（BJT） 关键事件 1 2020-07-23 13:17 发射 2 2020-08-02 07:00 第一次中途修正 3 2020-09-20 23:00 第二次中途修正 4 2020-10-09 23:08 深空机动 5 2020-10-28 22:00 第三次中途修正 6 2021-02-05 20:00 第四次中途修正 7 2021-02-10 20:00 近火制动
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