星载GPS低轨卫星定轨理论及方法研究
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摘要
本文研究了星载GPS低轨卫星定轨技术的基本理论和方法,研制了星载GPS低轨卫星约化动力法定轨软件,针对约化动力法和推广卡尔曼滤波存在的问题,开展了星载GPS低轨卫星自适应事后和实时定轨研究,论文最后对星载GPS编队卫星相对定位技术进行了研究。主要工作及创新点概括如下:
1.介绍了星载GPS低轨卫星定轨的基本理论和方法,比较分析了卫星定轨中批处理和序贯处理的优缺点,讨论了星载GPS低轨卫星实时定轨和事后定轨的异同,阐述了星载GPS编队卫星相对定位的研究状况,分析认为以卡尔曼滤波形式进行的约化动力法研究,既可以满足事后定轨和实时定轨的需求,而且便于软件开发;以GRACE卫星为对象开展研究,既可以满足单颗卫星定轨的研究需要,又可以满足编队卫星相对定位的研究需要。
2.分析了不同因素对单点定位的影响,讨论了动力平滑定轨中估计参数的设置问题,计算结果表明:在动力平滑中可以不考虑太阳光压、大气阻力的影响,通过求解经验参数获得了较好的结果;增加估计径向经验加速度可能造成过度化参数,降低动力平滑精度。
3.研究了基于单点定位结果的动力学定轨方法,计算结果表明:利用动力学模型平滑单点定位结果,可以极大地减少单点定位结果的随机误差,提高单点定位结果精度。与JPL轨道的比较结果表明,动力平滑轨道在径向和法向的轨道精度优于10cm,沿迹方向的轨道精度优于20cm。
4.研究了抗差估计在动力平滑单点定位结果中的应用,计算结果表明:抗差估计可以有效地减弱观测粗差的影响,从而提高卫星定轨精度。但是,由于没有采用抗差动力平滑时,已经删除了超过3倍中误差的观测数据,因此采用抗差后的结果提高有限。
5.提出并实现了附有动力学信息的几何法定轨。计算结果表明:附有动力学信息的几何法定轨虽然能够解决运动学轨道的断点现象,但几何法轨道的跳变现象并没有得到很好的解决,指出提高动力学轨道精度可望解决跳变现象;采用附有动力学信息的几何法定轨所获得的卫星轨道在径向、法向和沿迹方向的精度均优于10cm。
6.从卫星运动方程、经验加速度处理和观测方程入手详细研究了约化动力法,介绍了约化动力法计算步骤,编制了星载GPS低轨卫星约化动力法(RDT)定轨软件。采用GRACE卫星实测数据验证了本文约化动力法软件的可行性,初步计算表明:本文约化动力法采用推广卡尔曼滤波算法收敛速度较快,定轨精度在径向、法向和沿迹方向的精度优于10cm。
7.研究分析了初始方差、稳态方差、相关时间对约化动力法定轨的影响。研究表明:RTN经验力稳态方差对定轨的影响较大,无论是增大经验力稳态方差还是减小都会影响到定轨精度,但存在一个适当的稳态方差使观测信息和动力学模型信息具有最佳的权比,从而得到一个高精度的定轨结果。
8.讨论了卡尔曼滤波平滑、双向滤波和抗差估计对约化动力法的改进。研究表明:卡尔曼滤波平滑和双向滤波可以提高约化动力法定轨精度,其中卡尔曼滤波平滑可以显著提高约化动力法开始阶段的定轨精度,而双向滤波不仅能显著提高约化动力法开始阶段的定轨精度,而且可以显著提高整个弧段的定轨精度。双向滤波定轨在径向、法向和沿迹方向的精度约4-6cm。当卫星出现异常观测时,约化动力法的定轨结果会受到较大影响,而此时抗差约化动力法定轨能够通过对观测向量等价协方差阵和卫星状态预报值等价协方差阵的调节达到抑制异常观测影响的目的。
9.提出了不求解随机过程参数的推广卡尔曼滤波(EKF)定轨方法。试验计算表明,该方法较约化动力法结果平滑,但是在轨道法向存在系统差,采用双向滤波可以消除系统差,两颗GRACE卫星的7天实测数据计算表明:双向滤波定轨在径向、法向和沿迹方向的精度可以达到5cm,3维位置精度优于10cm;推广双向卡尔曼滤波定轨精度优于约化动力法双向滤波定轨精度。
10.利用状态不符值构造自适应因子,实现了星载GPS低轨卫星的自适应(AKF)定轨。试验计算表明,推广卡尔曼滤波定轨(EKF)、自适应定轨(AKF)、约化动力法(RDT)定轨三者精度基本相当,但前两者的轨道相对后者较为平滑;采用AKF、EKF、RDT双向滤波定轨,GRACE-A、GRACE-B卫星的3维位置精度分别优于9cm、7cm;AKF、EKF双向滤波的定轨结果优于RDT双向滤波定轨结果。提出并实现了以单点定位结果为观测值,采用自适应定轨方法的实时定轨方案。试验计算表明,自适应定轨避开了状态噪声补偿矩阵设置的难题,具有较好的实时性和稳定性。
11.研究了编队卫星相对定位,实现了编队卫星相对定位软件。GRACE卫星10天实测数据的相对定位计算表明:固定模糊度参数后,采用本文软件可以得到5mm的编队卫星相对定位结果。
In the paper, the basic principle and methods of precision orbit determination (POD) of low earth orbiter (LEO) based on GPS technique are studied. The software of reduced dynamic technique for precise orbit determination of LEO using GPS is developed. To resolve the problems of reduced dynamic technique and extended Kalman filtering (EKF) technique in the LEO satellite orbit determination using GPS, the adaptive Kalman filtering (AKF) technique for LEO post-facto and real-time POD using GPS is researched. The technique for precise relative positioning of formation flying satellites using GPS is researched in the end of thesis. The main works and contributions are summarized as follows.
1. The basic theory and method for this paper are presented. The advantages and disadvantages of batch and sequential estimation in the satellite orbit determination are compared and analyzed. The similarities and differences of LEO post-facto and real-time POD using GPS are discussed. The status of research on precise relative positioning of formation flying satellites using GPS is described. The paper points out that reduced dynamic EKF method which is easily realized bu software can meet the demand of post-facto and real-time POD research. Researching orbit determination about GRACE satellites can not only satisfy the needs of single satellite POD, but also satisfy the needs of relative positioning of formation flying satellite.
2. Some influence factors on point positioning are analyzed. The parameter choice in the dynamic smoothing method is researched. The results show that the solar radiation pressure and atmospheric drag may not be taken into account in the dynamic smoothing. The dynamic smoothing can obtain high precise result by estimation the parameters of empirical forces. The precision of dynamic smoothing may be reduced when the parameters of empirical forces in radial(R) direction are increased, because of the number of parameter overabundance.
3. The method of dynamic orbit determination using point positioning solutions is studied. The results show that point positioning solutions smoothed by the dynamic model can reduce random error effects and improve the point positioning solutions significantly. The accuracy of the dynamic smoothing orbit is better than 10 cm in both radial and normal direction, and 20 cm in the transverse direction compared to the orbit results provided by JPL.
4. The application of robust estimation in the dynamic orbit determination using point positioning solutions is studied. The results show that the precision of orbit determination is improved with robust estimation which resists the outlying influences of the observations. But the improvement is limited if the observations are clean in which the measurements with errors larger than three times of root mean square (RMS) values are deleted.
5. The method of kinematic orbit determination based on GPS with dynamics information is put forward and realized. The results show that the method of kinematic orbit determination with dynamics information can solve the phenomenon of discontinuity in pure kinematic orbit, but can not solve the steep disturbances. The steep disturbances may be solved by improved dynamics orbit. The precision of the orbit is at a level of better 10 cm in radial, transverse and normal direction respectively.
6. The reduced dynamic technique (RDT) is researched in detail from the equations of satellite motion, empirical accelerations and observation equations. The steps of calculation LEO orbit using reduced dynamic technique are presented. The software of reduced dynamic technique (RDT) for precise orbit determination of LEO using GPS is developed. The feasibility of the software is validated by GRACE satellite orbit determination. The results show that the convergence speed is improved when the extended Kalman filtering (EKF) is employed. The accuracy of reduced dynamic orbit is better than 10 cm in radial, transverse and normal direction respectively.
7. The influences of priori variance, steady state variance and correlation time on reduced dynamic approach are analyzed. The results show that the steady state variances of RTN empirical accelerations have significant sffects on the reduced dynamic orbit. The precision of orbit will be affected whether increase or decrease the value of the steady state variance of RTN empirical accelerations. An opportune steady state variance value exists which can provide properly weight between the information of observation and dynamic model to get high precision orbit.
8. The improvements of Kalman smoothing, bidirectional filtering and robust estimation on reduced dynamic approach are discussed. The results show that POD using Kalman smoothing can improve the accuracy of reduced dynamic result at the beginning of the data arc. The result of bidirectional filtering can not only improve the accuracy of reduced dynamic result at the beginning of the data arc evidently, but also improve the accuracy of orbits in the all arc. The result of bidirectional filtering is about 4-6 cm in radial(R), transverse(T) and normal(N) direction respectively. The orbit of RDT is influenced when outlying measurements appear. While the influences of outlying measurements are resisted by using the equivalent covariance matrices of the observations and the satellite predicted states when introduce robust estimation in RDT.
9. The method of extended Kalman filtering(EKF) POD which don’t compute the parameter of random processes is put forward. The results show that the orbit is more smoothed than the orbit resolved by reduced dynamic method. Systematic error appears in normal direction in the orbit of the EKF method, but this systematic error can be removed by using bidirectional filtering. The orbit results of two GRACE satellites which computed using seven days data show that the result of bidirectional filtering can get 10 cm in 3-Dimension position and about 5 cm in radial(R), transverse(T) and normal(N) direction respectively. The precision of the orbit by EKF bidirectional filtering is better than the orbit by using reduced dynamic bidirectional filtering.
10. An adaptive factor based on the discrepancy between the predicted state vector and the estimated state vector is constructed. The adaptive Kalman filtering (AKF) technique for LEO POD using GPS is realized. The results show that the precision of the orbit computed by EKF, AKF and reduced dynamic technique (RDT) is equivalent approximately, but the orbit corresponding to the first two methods is more smoothed than the orbit provided by the last method. When satellite orbit determined by using AKF, EKF and RDT bidirectional filtering, the orbit precision of GRACE-A and GRACE-B is better than 9 cm and 7 cm (3-dimensional) respectively.The precision of the orbit from the first two methods is better than that from the last method. The project of LEO real time POD using AKF technique, which using point positioning solutions as observation, is put forward and realized. The results show that the AKF technique can avoid setting the state noise compensation matrix, and the solution of AKF POD is more stable than the solution of EKF POD.
11. The technique for post-factor precise relative positioning of formation flying satellites using onboard GPS is researched. The software of precise relative positioning of formation flying satellites is realized. The orbits of two GRACE satellites which computed using data with ten days show that the precision of relative positioning can get 5.0mm after the ambiguities fixed to integer values.
1.介绍了星载GPS低轨卫星定轨的基本理论和方法,比较分析了卫星定轨中批处理和序贯处理的优缺点,讨论了星载GPS低轨卫星实时定轨和事后定轨的异同,阐述了星载GPS编队卫星相对定位的研究状况,分析认为以卡尔曼滤波形式进行的约化动力法研究,既可以满足事后定轨和实时定轨的需求,而且便于软件开发;以GRACE卫星为对象开展研究,既可以满足单颗卫星定轨的研究需要,又可以满足编队卫星相对定位的研究需要。
2.分析了不同因素对单点定位的影响,讨论了动力平滑定轨中估计参数的设置问题,计算结果表明:在动力平滑中可以不考虑太阳光压、大气阻力的影响,通过求解经验参数获得了较好的结果;增加估计径向经验加速度可能造成过度化参数,降低动力平滑精度。
3.研究了基于单点定位结果的动力学定轨方法,计算结果表明:利用动力学模型平滑单点定位结果,可以极大地减少单点定位结果的随机误差,提高单点定位结果精度。与JPL轨道的比较结果表明,动力平滑轨道在径向和法向的轨道精度优于10cm,沿迹方向的轨道精度优于20cm。
4.研究了抗差估计在动力平滑单点定位结果中的应用,计算结果表明:抗差估计可以有效地减弱观测粗差的影响,从而提高卫星定轨精度。但是,由于没有采用抗差动力平滑时,已经删除了超过3倍中误差的观测数据,因此采用抗差后的结果提高有限。
5.提出并实现了附有动力学信息的几何法定轨。计算结果表明:附有动力学信息的几何法定轨虽然能够解决运动学轨道的断点现象,但几何法轨道的跳变现象并没有得到很好的解决,指出提高动力学轨道精度可望解决跳变现象;采用附有动力学信息的几何法定轨所获得的卫星轨道在径向、法向和沿迹方向的精度均优于10cm。
6.从卫星运动方程、经验加速度处理和观测方程入手详细研究了约化动力法,介绍了约化动力法计算步骤,编制了星载GPS低轨卫星约化动力法(RDT)定轨软件。采用GRACE卫星实测数据验证了本文约化动力法软件的可行性,初步计算表明:本文约化动力法采用推广卡尔曼滤波算法收敛速度较快,定轨精度在径向、法向和沿迹方向的精度优于10cm。
7.研究分析了初始方差、稳态方差、相关时间对约化动力法定轨的影响。研究表明:RTN经验力稳态方差对定轨的影响较大,无论是增大经验力稳态方差还是减小都会影响到定轨精度,但存在一个适当的稳态方差使观测信息和动力学模型信息具有最佳的权比,从而得到一个高精度的定轨结果。
8.讨论了卡尔曼滤波平滑、双向滤波和抗差估计对约化动力法的改进。研究表明:卡尔曼滤波平滑和双向滤波可以提高约化动力法定轨精度,其中卡尔曼滤波平滑可以显著提高约化动力法开始阶段的定轨精度,而双向滤波不仅能显著提高约化动力法开始阶段的定轨精度,而且可以显著提高整个弧段的定轨精度。双向滤波定轨在径向、法向和沿迹方向的精度约4-6cm。当卫星出现异常观测时,约化动力法的定轨结果会受到较大影响,而此时抗差约化动力法定轨能够通过对观测向量等价协方差阵和卫星状态预报值等价协方差阵的调节达到抑制异常观测影响的目的。
9.提出了不求解随机过程参数的推广卡尔曼滤波(EKF)定轨方法。试验计算表明,该方法较约化动力法结果平滑,但是在轨道法向存在系统差,采用双向滤波可以消除系统差,两颗GRACE卫星的7天实测数据计算表明:双向滤波定轨在径向、法向和沿迹方向的精度可以达到5cm,3维位置精度优于10cm;推广双向卡尔曼滤波定轨精度优于约化动力法双向滤波定轨精度。
10.利用状态不符值构造自适应因子,实现了星载GPS低轨卫星的自适应(AKF)定轨。试验计算表明,推广卡尔曼滤波定轨(EKF)、自适应定轨(AKF)、约化动力法(RDT)定轨三者精度基本相当,但前两者的轨道相对后者较为平滑;采用AKF、EKF、RDT双向滤波定轨,GRACE-A、GRACE-B卫星的3维位置精度分别优于9cm、7cm;AKF、EKF双向滤波的定轨结果优于RDT双向滤波定轨结果。提出并实现了以单点定位结果为观测值,采用自适应定轨方法的实时定轨方案。试验计算表明,自适应定轨避开了状态噪声补偿矩阵设置的难题,具有较好的实时性和稳定性。
11.研究了编队卫星相对定位,实现了编队卫星相对定位软件。GRACE卫星10天实测数据的相对定位计算表明:固定模糊度参数后,采用本文软件可以得到5mm的编队卫星相对定位结果。
In the paper, the basic principle and methods of precision orbit determination (POD) of low earth orbiter (LEO) based on GPS technique are studied. The software of reduced dynamic technique for precise orbit determination of LEO using GPS is developed. To resolve the problems of reduced dynamic technique and extended Kalman filtering (EKF) technique in the LEO satellite orbit determination using GPS, the adaptive Kalman filtering (AKF) technique for LEO post-facto and real-time POD using GPS is researched. The technique for precise relative positioning of formation flying satellites using GPS is researched in the end of thesis. The main works and contributions are summarized as follows.
1. The basic theory and method for this paper are presented. The advantages and disadvantages of batch and sequential estimation in the satellite orbit determination are compared and analyzed. The similarities and differences of LEO post-facto and real-time POD using GPS are discussed. The status of research on precise relative positioning of formation flying satellites using GPS is described. The paper points out that reduced dynamic EKF method which is easily realized bu software can meet the demand of post-facto and real-time POD research. Researching orbit determination about GRACE satellites can not only satisfy the needs of single satellite POD, but also satisfy the needs of relative positioning of formation flying satellite.
2. Some influence factors on point positioning are analyzed. The parameter choice in the dynamic smoothing method is researched. The results show that the solar radiation pressure and atmospheric drag may not be taken into account in the dynamic smoothing. The dynamic smoothing can obtain high precise result by estimation the parameters of empirical forces. The precision of dynamic smoothing may be reduced when the parameters of empirical forces in radial(R) direction are increased, because of the number of parameter overabundance.
3. The method of dynamic orbit determination using point positioning solutions is studied. The results show that point positioning solutions smoothed by the dynamic model can reduce random error effects and improve the point positioning solutions significantly. The accuracy of the dynamic smoothing orbit is better than 10 cm in both radial and normal direction, and 20 cm in the transverse direction compared to the orbit results provided by JPL.
4. The application of robust estimation in the dynamic orbit determination using point positioning solutions is studied. The results show that the precision of orbit determination is improved with robust estimation which resists the outlying influences of the observations. But the improvement is limited if the observations are clean in which the measurements with errors larger than three times of root mean square (RMS) values are deleted.
5. The method of kinematic orbit determination based on GPS with dynamics information is put forward and realized. The results show that the method of kinematic orbit determination with dynamics information can solve the phenomenon of discontinuity in pure kinematic orbit, but can not solve the steep disturbances. The steep disturbances may be solved by improved dynamics orbit. The precision of the orbit is at a level of better 10 cm in radial, transverse and normal direction respectively.
6. The reduced dynamic technique (RDT) is researched in detail from the equations of satellite motion, empirical accelerations and observation equations. The steps of calculation LEO orbit using reduced dynamic technique are presented. The software of reduced dynamic technique (RDT) for precise orbit determination of LEO using GPS is developed. The feasibility of the software is validated by GRACE satellite orbit determination. The results show that the convergence speed is improved when the extended Kalman filtering (EKF) is employed. The accuracy of reduced dynamic orbit is better than 10 cm in radial, transverse and normal direction respectively.
7. The influences of priori variance, steady state variance and correlation time on reduced dynamic approach are analyzed. The results show that the steady state variances of RTN empirical accelerations have significant sffects on the reduced dynamic orbit. The precision of orbit will be affected whether increase or decrease the value of the steady state variance of RTN empirical accelerations. An opportune steady state variance value exists which can provide properly weight between the information of observation and dynamic model to get high precision orbit.
8. The improvements of Kalman smoothing, bidirectional filtering and robust estimation on reduced dynamic approach are discussed. The results show that POD using Kalman smoothing can improve the accuracy of reduced dynamic result at the beginning of the data arc. The result of bidirectional filtering can not only improve the accuracy of reduced dynamic result at the beginning of the data arc evidently, but also improve the accuracy of orbits in the all arc. The result of bidirectional filtering is about 4-6 cm in radial(R), transverse(T) and normal(N) direction respectively. The orbit of RDT is influenced when outlying measurements appear. While the influences of outlying measurements are resisted by using the equivalent covariance matrices of the observations and the satellite predicted states when introduce robust estimation in RDT.
9. The method of extended Kalman filtering(EKF) POD which don’t compute the parameter of random processes is put forward. The results show that the orbit is more smoothed than the orbit resolved by reduced dynamic method. Systematic error appears in normal direction in the orbit of the EKF method, but this systematic error can be removed by using bidirectional filtering. The orbit results of two GRACE satellites which computed using seven days data show that the result of bidirectional filtering can get 10 cm in 3-Dimension position and about 5 cm in radial(R), transverse(T) and normal(N) direction respectively. The precision of the orbit by EKF bidirectional filtering is better than the orbit by using reduced dynamic bidirectional filtering.
10. An adaptive factor based on the discrepancy between the predicted state vector and the estimated state vector is constructed. The adaptive Kalman filtering (AKF) technique for LEO POD using GPS is realized. The results show that the precision of the orbit computed by EKF, AKF and reduced dynamic technique (RDT) is equivalent approximately, but the orbit corresponding to the first two methods is more smoothed than the orbit provided by the last method. When satellite orbit determined by using AKF, EKF and RDT bidirectional filtering, the orbit precision of GRACE-A and GRACE-B is better than 9 cm and 7 cm (3-dimensional) respectively.The precision of the orbit from the first two methods is better than that from the last method. The project of LEO real time POD using AKF technique, which using point positioning solutions as observation, is put forward and realized. The results show that the AKF technique can avoid setting the state noise compensation matrix, and the solution of AKF POD is more stable than the solution of EKF POD.
11. The technique for post-factor precise relative positioning of formation flying satellites using onboard GPS is researched. The software of precise relative positioning of formation flying satellites is realized. The orbits of two GRACE satellites which computed using data with ten days show that the precision of relative positioning can get 5.0mm after the ambiguities fixed to integer values.
引文
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