星载GPS自主定轨理论及其软件实现
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摘要
随着我国航天科技的发展,航天任务不断增加,传统的地面测控系统一直处于高负荷工作状态。尤其是近年来迅猛发展的小卫星,需要全弧段高精度的轨道参数。如果仍采用地面测控系统测定全球覆盖的小卫星轨道,不仅消耗的费用与日俱增,而且地面站的布局难以达到全球覆盖。因此,发展高精度的航天器自主定轨技术迫在眉睫。
GPS卫星导航系统的发展和完善、精密轨道确定理论与方法的发展、星载GPS接收机技术的改进,为高精度自主定轨理论的研究创造了有利的条件。然而受星上处理器有限的计算能力和轨道参数的实时确定等条件限制,自主定轨理论与精密定轨存在着很大的区别。本文在现有轨道确定的理论基础上,针对自主定轨系统的工作环境,从理论上建立了星载GPS测量进行米级精度的自主定轨算法,在实践上成功研制出星载GPS自主定轨软件——SATODS。用大量的星载GPS实测数据模拟自主定轨试验,结果表明,使用GPS广播星历,低轨卫星自主定轨可以达到±1.5~3.0米的轨道精度,±3毫米/秒的速度精度;而且自主定轨软件可以应用于轨道机动期间的实时轨道确定。具体的研究内容和主要贡献如下:
1、在简要总结动力学定轨基本理论的基础上,通过数值模拟计算分析,提出了用4阶Runge-Kutta-Fehlberg单步积分法作为自主定轨系统的轨道积分方法,并用直接法计算状态转移矩阵。考虑到星上处理器有限的计算能力,论文对自主定轨系统进入工程应用的几个关键问题进行了细致研究。其中包括:在需要大量计算耗时的地球引力加速度计算中,引入了优化递推算法;针对不同轨道高度(低轨卫星),用大量数值积分模拟计算,在不影响轨道精度的情况下,确定合理的重力场模型的阶次和摄动力模型的取舍,确定合理的数值积分步长;给出了与轨道积分相等精度的5阶Hermite多项式轨道内插算法,实现高密度的轨道输出。
2、因为星载GPS接收机在地球的电离层中间运行,且其速度为每秒几公里,所以星载GPS测量与地面GPS测量存在一定的差异。本文详细讨论了星载GPS测量的各项误差源及其改正模型,给出了适用于单频星载GPS测量的电离层改正模型。推导了星载GPS伪距观测数据的实测精度的评价方法,用CHAMP和SAC-C星载GPS实测数据进行了验算,为自主定轨的观测噪声协方差矩阵确定以及精密定轨的观测数据加权提供了依据。
3、结合自主定轨的轨道预报信息,提出了伪距粗差的探测方法——新息序列探测法。用该方法对星载GPS实测数据进行了处理,结果表明,CHAMP和SAC-C卫星的伪距粗差观测值所占的比例分别达到1.2%和3.0%。如果不加以探测和剔除,几何法实时定轨将出现几百米甚至上千米的轨道偏差。新息序列探测法已经应用于星载GPS自主定轨软件,提高了自主定轨系统的定轨精度和稳定性。
4、讨论了几何法实时确定卫星轨道和卫星速度的原理,用星载GPS实测数据进行了模拟试验,总结了几何法实时定轨作为卫星的自主定轨系统存在因观测中断无法定轨、轨道预报精度差等主要问题。
5、在卡尔曼滤波的理论基础上,充分考虑了引起卡尔曼滤波发散的主要原因,提出了星载GPS自主定轨的揉合算法——DMC-UDEKF算法。在此理论基础上,使用标准C/C++编程语言,自主研制出一套星载GPS自主定轨软件SATODS。并用大量的星载GPS实测数据进行模拟自主定轨的试验,该算法和软件能够达到±1.5~3.0米轨道精度和±3毫米/秒的速度精度,与国外的自主定轨软件精度水平相当。而且SATODS软件具有较强的可移植性、源代码简洁、占用内存少和运行速度快等特点。
在本文的研究成果中,主要创新点可总结为:
(1)提出了星载GPS伪距粗差探测方法——新息序列探测法。新息序列探测法与自主定轨系统滤波测量更新阶段的粗差检验方法相结合,不仅可以消除星载GPS伪距观测值的粗差,而且可以消除质量较差的GPS广播星历和钟差对自主定轨系统的影响。
(2)提出了星载GPS测量自主定轨的揉合算法,它是动力学定轨理论、动力学补偿算法、推广卡尔曼滤波、U-D分解滤波与星载GPS观测模型等理论的集成应用。用大量的星载GPS实测数据模拟自主定轨计算表明,该算法不仅能够达到±1.5~3米的实时定轨精度,而且具有轨道机动期间的实时定轨能力。
(3)成功研发了星载GPS自主定轨软件SATODS,该软件已成功地对大量的星载GPS实测数据进行了模拟自主定轨计算。软件具有较强的可移植性、代码简洁、占用内存少和运行速度快等特点。
星载GPS自主定轨理论的建立和软件的成功研制,填补了我国在星载GPS自主定轨方面的一项空白,有助于推动GPS在我国航天领域的应用。
With the development of our country astronautics science and technology, the astronautical mission will increase unceasingly; so the traditional earth-based TT&C are in the high activity, especially the rapid development of small satellite which required the high accuracy parameters of the entire trajectory recently. If the earth-based TT&C will still be used to track these small satellites, not only it will take expensive cost day by day, but also it is much difficult to build the ground stations all over the world. Therefore, the technical development of the high accuracy spacecraft autonomous orbit determination is an imminent task.
The developed science and technology such as spaceborne GPS reciver, GPS satellite navigation system and the precise orbit determination theory, has provided the advantageous condition for the high accuracy autonomous navigation. However, the autonomous navigation system will determine satellite real-time trajectory on the processor onborne, so that the autonomous navigation theory is much different from the precise orbit determination. According to the existing orbit determination theory, this dissertation established the high accuracy autonomous algorithm with spaceborne GPS measurements theoretically, and developed spaceborne GPS autonomous navigation software (SATODS) practically. The autonomous navigation experimental results from plenty of data collected from CHAMP and SAC-C missions are presented. The results have demonstrated that the orbit accuracy can achieve±1.5~3.0 meter and velocity accuracy±3 millimeters/second with GPS broadcast ephemeris. Moreover the autonomous navigation software may apply in the period of orbit maneuver. The concrete contents and the main contributions are as follows:
On the basis of brief summary of dynamics orbit determination theory, 4 step Runge-Kutta-Fehlberg integrator was used as orbit integration method of autonomous navigation with numerical simulations and the state transition matrix was calculated directly instead of numerical integration method. In view of processor onboard with limited computation ability, serval key problems were researched in order that autonomous navigation will enter into practical application in the future. These problems include that: the optimized recursion algorithm was introduced to reduce computation consumes; the reasonable order of gravitational field model and which of the other perturbation forces were selected and the reasonable step time of integrator was determined with plenty of numerical analysises, 5 step Hermite polynomial interpolation algorithm was introduced to output high density trajectory parameters and so on.
Spaceborne GPS measurements are different from that on the ground because of spaceborne GPS receiver move at the speed of several kilometer/second. Therefore each erroneous source and the correction model in the spaceborne GPS measurements were discussed in detail. Ionospheric correction model for single frequency spaceborne GPS users was presented. A valuable accuracy assessment method of pseudorange of spaceborne GPS measurements was reduced. The results computed from data collected from CHAMP and SAC-C missions will contribute to determine the observation noise covariance matrix in autonomous navigation and support the design of optimal data weighting strategies in precise orbit determination applications.
Innovation sequence detecting outlier method was presented to delete outlier data of spaceborne GPS pseudorange measurements with orbit parameters predicted. The observation data collected from CHAMP and SAC-C onboard GPS receivers were tested with this method that code outliers amount to 1.2% and 3.0% respectively. The geometry real-time orbit determination will appear on several hundred meter even kilometer trajectory errors if these outlier can not be deleted.
The geometry real-time orbit determination with spaceborne GPS measurements was discussed and tested with two days data collected from CHAMP and SAC-C onboard GPS receivers. Serval key problems were summarized according to the results of simulation computation if the spacecraft had used geometry real-time orbit determination as main method of autonomous navigation.
Based on theory of Kalman filtering, the integration algorithm of autonomous navigation with spaceborne GPS measurements was presented and deduced. And autonomous navigation software (SATODS) was independently developed with standard C/C++ programming language according to this new algorithm. Many simulation experiments were carried on with observation data from CHAMP and SAC-C missions. The computation results demonstrated that the orbit accuracy could achieve±1.5~3.0 meter and velocity accuracy±3 millimeter/second with this algorithm and software. This accuracy of automous navigation with spaceborne GPS measurements is equal to international ones. Moreover because this algorithm had considered some resons of Kalman filtering divergence, the SATODS software has strong stability, replantability, fast computation speed and so on.
In this dissertation, main innovating points of some research contents were summarized as follows: Innovation sequence detecting outlier method was presented to delete outlier data of spaceborne GPS pseudorange measurements with orbit parameters predicted. This method can not only delete code outliers of spaceborne GPS measurements, with other methods in the measurement update of Kalman filtering, but also eliminate the effects of bad GPS broadcast ephemeris and clock error.
The integration algorithm of autonomous navigation with spaceborne GPS measurements was presented and deduced. It integrated serval theory such as dynamic orbit determination, dynamic model compensation, extended Kalman filtering, U-D decomposition filtering and spaceborne GPS measurement.
Autonomous navigation software with spaceborne GPS measurements was developed successfully. This software has successfully been carried on the simulation computation with plenty of data collected from CHAMP and SAC-C missions.
The autonomous navigation theory and software with spaceborne GPS measurements have filled in a blank of spaceborne GPS autonomous navigation in our country. It will be helpful to extend GPS to astronautics application.
GPS卫星导航系统的发展和完善、精密轨道确定理论与方法的发展、星载GPS接收机技术的改进,为高精度自主定轨理论的研究创造了有利的条件。然而受星上处理器有限的计算能力和轨道参数的实时确定等条件限制,自主定轨理论与精密定轨存在着很大的区别。本文在现有轨道确定的理论基础上,针对自主定轨系统的工作环境,从理论上建立了星载GPS测量进行米级精度的自主定轨算法,在实践上成功研制出星载GPS自主定轨软件——SATODS。用大量的星载GPS实测数据模拟自主定轨试验,结果表明,使用GPS广播星历,低轨卫星自主定轨可以达到±1.5~3.0米的轨道精度,±3毫米/秒的速度精度;而且自主定轨软件可以应用于轨道机动期间的实时轨道确定。具体的研究内容和主要贡献如下:
1、在简要总结动力学定轨基本理论的基础上,通过数值模拟计算分析,提出了用4阶Runge-Kutta-Fehlberg单步积分法作为自主定轨系统的轨道积分方法,并用直接法计算状态转移矩阵。考虑到星上处理器有限的计算能力,论文对自主定轨系统进入工程应用的几个关键问题进行了细致研究。其中包括:在需要大量计算耗时的地球引力加速度计算中,引入了优化递推算法;针对不同轨道高度(低轨卫星),用大量数值积分模拟计算,在不影响轨道精度的情况下,确定合理的重力场模型的阶次和摄动力模型的取舍,确定合理的数值积分步长;给出了与轨道积分相等精度的5阶Hermite多项式轨道内插算法,实现高密度的轨道输出。
2、因为星载GPS接收机在地球的电离层中间运行,且其速度为每秒几公里,所以星载GPS测量与地面GPS测量存在一定的差异。本文详细讨论了星载GPS测量的各项误差源及其改正模型,给出了适用于单频星载GPS测量的电离层改正模型。推导了星载GPS伪距观测数据的实测精度的评价方法,用CHAMP和SAC-C星载GPS实测数据进行了验算,为自主定轨的观测噪声协方差矩阵确定以及精密定轨的观测数据加权提供了依据。
3、结合自主定轨的轨道预报信息,提出了伪距粗差的探测方法——新息序列探测法。用该方法对星载GPS实测数据进行了处理,结果表明,CHAMP和SAC-C卫星的伪距粗差观测值所占的比例分别达到1.2%和3.0%。如果不加以探测和剔除,几何法实时定轨将出现几百米甚至上千米的轨道偏差。新息序列探测法已经应用于星载GPS自主定轨软件,提高了自主定轨系统的定轨精度和稳定性。
4、讨论了几何法实时确定卫星轨道和卫星速度的原理,用星载GPS实测数据进行了模拟试验,总结了几何法实时定轨作为卫星的自主定轨系统存在因观测中断无法定轨、轨道预报精度差等主要问题。
5、在卡尔曼滤波的理论基础上,充分考虑了引起卡尔曼滤波发散的主要原因,提出了星载GPS自主定轨的揉合算法——DMC-UDEKF算法。在此理论基础上,使用标准C/C++编程语言,自主研制出一套星载GPS自主定轨软件SATODS。并用大量的星载GPS实测数据进行模拟自主定轨的试验,该算法和软件能够达到±1.5~3.0米轨道精度和±3毫米/秒的速度精度,与国外的自主定轨软件精度水平相当。而且SATODS软件具有较强的可移植性、源代码简洁、占用内存少和运行速度快等特点。
在本文的研究成果中,主要创新点可总结为:
(1)提出了星载GPS伪距粗差探测方法——新息序列探测法。新息序列探测法与自主定轨系统滤波测量更新阶段的粗差检验方法相结合,不仅可以消除星载GPS伪距观测值的粗差,而且可以消除质量较差的GPS广播星历和钟差对自主定轨系统的影响。
(2)提出了星载GPS测量自主定轨的揉合算法,它是动力学定轨理论、动力学补偿算法、推广卡尔曼滤波、U-D分解滤波与星载GPS观测模型等理论的集成应用。用大量的星载GPS实测数据模拟自主定轨计算表明,该算法不仅能够达到±1.5~3米的实时定轨精度,而且具有轨道机动期间的实时定轨能力。
(3)成功研发了星载GPS自主定轨软件SATODS,该软件已成功地对大量的星载GPS实测数据进行了模拟自主定轨计算。软件具有较强的可移植性、代码简洁、占用内存少和运行速度快等特点。
星载GPS自主定轨理论的建立和软件的成功研制,填补了我国在星载GPS自主定轨方面的一项空白,有助于推动GPS在我国航天领域的应用。
With the development of our country astronautics science and technology, the astronautical mission will increase unceasingly; so the traditional earth-based TT&C are in the high activity, especially the rapid development of small satellite which required the high accuracy parameters of the entire trajectory recently. If the earth-based TT&C will still be used to track these small satellites, not only it will take expensive cost day by day, but also it is much difficult to build the ground stations all over the world. Therefore, the technical development of the high accuracy spacecraft autonomous orbit determination is an imminent task.
The developed science and technology such as spaceborne GPS reciver, GPS satellite navigation system and the precise orbit determination theory, has provided the advantageous condition for the high accuracy autonomous navigation. However, the autonomous navigation system will determine satellite real-time trajectory on the processor onborne, so that the autonomous navigation theory is much different from the precise orbit determination. According to the existing orbit determination theory, this dissertation established the high accuracy autonomous algorithm with spaceborne GPS measurements theoretically, and developed spaceborne GPS autonomous navigation software (SATODS) practically. The autonomous navigation experimental results from plenty of data collected from CHAMP and SAC-C missions are presented. The results have demonstrated that the orbit accuracy can achieve±1.5~3.0 meter and velocity accuracy±3 millimeters/second with GPS broadcast ephemeris. Moreover the autonomous navigation software may apply in the period of orbit maneuver. The concrete contents and the main contributions are as follows:
On the basis of brief summary of dynamics orbit determination theory, 4 step Runge-Kutta-Fehlberg integrator was used as orbit integration method of autonomous navigation with numerical simulations and the state transition matrix was calculated directly instead of numerical integration method. In view of processor onboard with limited computation ability, serval key problems were researched in order that autonomous navigation will enter into practical application in the future. These problems include that: the optimized recursion algorithm was introduced to reduce computation consumes; the reasonable order of gravitational field model and which of the other perturbation forces were selected and the reasonable step time of integrator was determined with plenty of numerical analysises, 5 step Hermite polynomial interpolation algorithm was introduced to output high density trajectory parameters and so on.
Spaceborne GPS measurements are different from that on the ground because of spaceborne GPS receiver move at the speed of several kilometer/second. Therefore each erroneous source and the correction model in the spaceborne GPS measurements were discussed in detail. Ionospheric correction model for single frequency spaceborne GPS users was presented. A valuable accuracy assessment method of pseudorange of spaceborne GPS measurements was reduced. The results computed from data collected from CHAMP and SAC-C missions will contribute to determine the observation noise covariance matrix in autonomous navigation and support the design of optimal data weighting strategies in precise orbit determination applications.
Innovation sequence detecting outlier method was presented to delete outlier data of spaceborne GPS pseudorange measurements with orbit parameters predicted. The observation data collected from CHAMP and SAC-C onboard GPS receivers were tested with this method that code outliers amount to 1.2% and 3.0% respectively. The geometry real-time orbit determination will appear on several hundred meter even kilometer trajectory errors if these outlier can not be deleted.
The geometry real-time orbit determination with spaceborne GPS measurements was discussed and tested with two days data collected from CHAMP and SAC-C onboard GPS receivers. Serval key problems were summarized according to the results of simulation computation if the spacecraft had used geometry real-time orbit determination as main method of autonomous navigation.
Based on theory of Kalman filtering, the integration algorithm of autonomous navigation with spaceborne GPS measurements was presented and deduced. And autonomous navigation software (SATODS) was independently developed with standard C/C++ programming language according to this new algorithm. Many simulation experiments were carried on with observation data from CHAMP and SAC-C missions. The computation results demonstrated that the orbit accuracy could achieve±1.5~3.0 meter and velocity accuracy±3 millimeter/second with this algorithm and software. This accuracy of automous navigation with spaceborne GPS measurements is equal to international ones. Moreover because this algorithm had considered some resons of Kalman filtering divergence, the SATODS software has strong stability, replantability, fast computation speed and so on.
In this dissertation, main innovating points of some research contents were summarized as follows: Innovation sequence detecting outlier method was presented to delete outlier data of spaceborne GPS pseudorange measurements with orbit parameters predicted. This method can not only delete code outliers of spaceborne GPS measurements, with other methods in the measurement update of Kalman filtering, but also eliminate the effects of bad GPS broadcast ephemeris and clock error.
The integration algorithm of autonomous navigation with spaceborne GPS measurements was presented and deduced. It integrated serval theory such as dynamic orbit determination, dynamic model compensation, extended Kalman filtering, U-D decomposition filtering and spaceborne GPS measurement.
Autonomous navigation software with spaceborne GPS measurements was developed successfully. This software has successfully been carried on the simulation computation with plenty of data collected from CHAMP and SAC-C missions.
The autonomous navigation theory and software with spaceborne GPS measurements have filled in a blank of spaceborne GPS autonomous navigation in our country. It will be helpful to extend GPS to astronautics application.
引文
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