GEO卫星精密定轨技术研究
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摘要
本文主要研究了10米至1米的GEO精密定轨包括机动后数小时内的快速轨道恢复技术和方法。利用文中推导建立的动力法定轨的误差协方差分析模型和简化解析算法，重点进行了地基测距定轨和高精度干涉测角定轨以及各种综合定轨方案的特性比较和精度分析；采用蒙特卡罗仿真，研究了天基测距(测速)以及各种天地基联合测轨技术的特点及其对GEO卫星精密定轨的贡献；最后对GEO位置保持机动后的快速轨道恢复这一热点问题进行了探讨。论文的主要内容和创新点如下：
1．推导了自校准定轨的状态参数估计和协方差公式，从理论上证明了自校准定轨的优越性。针对GEO卫星的“高轨"和“静地”特性，分析研究了测量误差对轨道确定精度的影响，建立了动力法定轨的误差协方差分析模型和简化解析算法。
2．综合分析了几种地基测定轨技术用于GEO卫星精密定轨的优缺点，指出了常规雷达测距定轨体制中存在的系统误差表现形式，提出了短基线CEI干涉测角技术与单站激光测距技术联合定轨方案，分析了满足10米定轨精度要求的可行性。结果表明，制约10米定轨精度的主要因素是等效测量偏差。随观测站个数和分布的不同，测量偏差可以8至20倍放大在卫星横向位置上。其中轨道面法向位置分量(即南北位置)误差在一天弧段的保证下能控制到10米以内，但星下点经度(即东西位置)的确定精度得不到改善。相位干涉差分技术可以将系统偏差减小1至2个数量级，以相位干涉测量为主的测角／测距综合定轨能够显著提高轨道精度，从独立CEI定轨的一两百米提高到优于10米。
3．研究了GEO／LEO联合定轨方法，利用星间测量数据对LEO位置变化的敏感性，通过模拟仿真计算，分析了LEO测量星的轨道改进对GEO卫星精密定轨的作用和影响。结果表明，星间测量利用LEO空间测轨站的在轨运行，打破了传统地基的静地测量模式，能够增加观测几何的强度和GEO卫星动力学模型的约束作用。其中利用星间测距数据仅对GEO定轨，10米的精度指标对LEO测量星的精密星历和动力学模型要求苛刻；采用GEO／LEO联合定轨，对LEO轨道的改进明显优于对GEO的改进。组网的多颗GEO和LEO卫星的联合定轨，能够加密可连续跟踪的弧段，进一步提高GEO的定轨精度。
4．针对GEO机动后的快速轨道恢复问题，讨论了仅利用机动后数小时短弧数据定轨的各种潜在的轨道优化策略，指出机动期间推力模型和机动参数的优化估计对提高机动轨道精度的作用。结果表明，在常规的机动后数小时短弧定轨中，必须应用某些特殊的策略来控制卫星的沿迹分量和轨道面法向分量误差。其中在较频繁的东西位置保持后，引进轨道面定向参数的强约束以及增加高精度Doppler测速观测，对控制卫星的法向分量误差效果明显，而利用前次机动后标定的测距偏差改进观测数据，对控制卫星的沿迹分量误差效果显著。
This dissertation mainly focuses on Precision Orbit Determination (POD) and fast post-maneuver orbit recovery of GEO satellites with the accuracy of 10-1 meter. Two commonly used yet powerful tools, variance-covariance matrix analysis and Monte-Carlo simulation, are used to investigate orbital errors and precision comparison. The former is specifically utilized to analyze the data set of ground-based range and VLBI/CEI phase with a simplified analytic algorithm developed in this paper, while the latter is applied to inter-satellites range and range rate (RARA). Finally the fast orbit recovery within several hours after station-keeping maneuvers of GEO is discussed. The main works and contributions are summarized as follows:
1. The estimate and covariance formula of self-calibration POD are derived by using QR factorization. It is proven that, compared with POD without self-calibration, self-calibration POD has the merits of calibrating some systematic errors in the measurement model or force model and improving the accuracy of orbit determination simultaneously. With the constraints of geostationary orbit and high altitude, the effects onto POD resulting from observational errors are investigated. The covariance analysis formula and its approximate algorithm of orbit determination are established.
2. Both advantages and weakness are analysed among several groung-based GEOs'tracking techniques. The formal behavior of systematic errors in classical range-based POD is pointed out, namely, at the first-order approximation, constant or piecewise constant range biases will be equivalently modeled for the representative of the summation of all kinds of error sources in the measurement residuals (O-C), due to the difficulty of distinguishing one error from another. It is presented that mini-scale network of two sets CEIs with large span of longitude will be a novel tracking and orbit determination solution, along with one set CEI augmented with few quantity of SLR data.The feasibility and potential application are discussed for VLBI and CEI in the 10m POD of GEOs' solutions. Results show that systematic errors (namely, range biases or interferometric phase biases) are the dominant factors to achieve 10m-level POD. They may be 8-20 times magnified to the transversal position uncertainty according to different number and distribution of the tracking sites. With the arc length enlarged to 24 hours, the uncertainty of cross-track positional component can be decreased to no more than 10 meters, while along-track position can not be improved apparently.
1．推导了自校准定轨的状态参数估计和协方差公式，从理论上证明了自校准定轨的优越性。针对GEO卫星的“高轨"和“静地”特性，分析研究了测量误差对轨道确定精度的影响，建立了动力法定轨的误差协方差分析模型和简化解析算法。
2．综合分析了几种地基测定轨技术用于GEO卫星精密定轨的优缺点，指出了常规雷达测距定轨体制中存在的系统误差表现形式，提出了短基线CEI干涉测角技术与单站激光测距技术联合定轨方案，分析了满足10米定轨精度要求的可行性。结果表明，制约10米定轨精度的主要因素是等效测量偏差。随观测站个数和分布的不同，测量偏差可以8至20倍放大在卫星横向位置上。其中轨道面法向位置分量(即南北位置)误差在一天弧段的保证下能控制到10米以内，但星下点经度(即东西位置)的确定精度得不到改善。相位干涉差分技术可以将系统偏差减小1至2个数量级，以相位干涉测量为主的测角／测距综合定轨能够显著提高轨道精度，从独立CEI定轨的一两百米提高到优于10米。
3．研究了GEO／LEO联合定轨方法，利用星间测量数据对LEO位置变化的敏感性，通过模拟仿真计算，分析了LEO测量星的轨道改进对GEO卫星精密定轨的作用和影响。结果表明，星间测量利用LEO空间测轨站的在轨运行，打破了传统地基的静地测量模式，能够增加观测几何的强度和GEO卫星动力学模型的约束作用。其中利用星间测距数据仅对GEO定轨，10米的精度指标对LEO测量星的精密星历和动力学模型要求苛刻；采用GEO／LEO联合定轨，对LEO轨道的改进明显优于对GEO的改进。组网的多颗GEO和LEO卫星的联合定轨，能够加密可连续跟踪的弧段，进一步提高GEO的定轨精度。
4．针对GEO机动后的快速轨道恢复问题，讨论了仅利用机动后数小时短弧数据定轨的各种潜在的轨道优化策略，指出机动期间推力模型和机动参数的优化估计对提高机动轨道精度的作用。结果表明，在常规的机动后数小时短弧定轨中，必须应用某些特殊的策略来控制卫星的沿迹分量和轨道面法向分量误差。其中在较频繁的东西位置保持后，引进轨道面定向参数的强约束以及增加高精度Doppler测速观测，对控制卫星的法向分量误差效果明显，而利用前次机动后标定的测距偏差改进观测数据，对控制卫星的沿迹分量误差效果显著。
This dissertation mainly focuses on Precision Orbit Determination (POD) and fast post-maneuver orbit recovery of GEO satellites with the accuracy of 10-1 meter. Two commonly used yet powerful tools, variance-covariance matrix analysis and Monte-Carlo simulation, are used to investigate orbital errors and precision comparison. The former is specifically utilized to analyze the data set of ground-based range and VLBI/CEI phase with a simplified analytic algorithm developed in this paper, while the latter is applied to inter-satellites range and range rate (RARA). Finally the fast orbit recovery within several hours after station-keeping maneuvers of GEO is discussed. The main works and contributions are summarized as follows:
1. The estimate and covariance formula of self-calibration POD are derived by using QR factorization. It is proven that, compared with POD without self-calibration, self-calibration POD has the merits of calibrating some systematic errors in the measurement model or force model and improving the accuracy of orbit determination simultaneously. With the constraints of geostationary orbit and high altitude, the effects onto POD resulting from observational errors are investigated. The covariance analysis formula and its approximate algorithm of orbit determination are established.
2. Both advantages and weakness are analysed among several groung-based GEOs'tracking techniques. The formal behavior of systematic errors in classical range-based POD is pointed out, namely, at the first-order approximation, constant or piecewise constant range biases will be equivalently modeled for the representative of the summation of all kinds of error sources in the measurement residuals (O-C), due to the difficulty of distinguishing one error from another. It is presented that mini-scale network of two sets CEIs with large span of longitude will be a novel tracking and orbit determination solution, along with one set CEI augmented with few quantity of SLR data.The feasibility and potential application are discussed for VLBI and CEI in the 10m POD of GEOs' solutions. Results show that systematic errors (namely, range biases or interferometric phase biases) are the dominant factors to achieve 10m-level POD. They may be 8-20 times magnified to the transversal position uncertainty according to different number and distribution of the tracking sites. With the arc length enlarged to 24 hours, the uncertainty of cross-track positional component can be decreased to no more than 10 meters, while along-track position can not be improved apparently.
引文
1 本章部分内容发表于《飞行器测控学报》，2005，6
1 本章部分内容发表于《飞行器测控学报》，2005，2；《上海航天》，2006，5。
1 本章部分内容发表于《测绘科学技术学报》，2006，4
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1 本章部分内容发表于《飞行器测控学报》，2005，2；《上海航天》，2006，5。
1 本章部分内容发表于《测绘科学技术学报》，2006，4
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