X射线脉冲星导航算法研究
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摘要
本文研究了X射线脉冲星导航算法,包括观测数据处理、误差修正、模糊度搜索、导航定位等。主要工作及创新点概括如下:
1.通过对脉冲星的特性分析,总结了适宜于X射线脉冲星导航的脉冲星所应具备的条件。分析了X射线脉冲星导航的原理、基本要素、算法流程及其与其他导航系统的异同点。导出了脉冲星差分观测方程,分析了它们对测量误差的消除或减弱能力。概述了X射线脉冲星导航在定时、定姿、测速、定位方面的导航算法。
2.以地面射电观测数据处理及时间模型建立精化为目标,研究了将脉冲到达时间观测量转换到太阳系质心处TCB/TDB时间尺度的计算方法及时间模型精化算法。统计分析了Einstein延迟、Shapiro延迟、Roemer延迟、色散延迟以及大气延迟改正的量级及变化特点,对比了不同双星模型及行星星历对脉冲星参数拟合的影响,以期为数据处理提供依据。
3.阐述了X射线巡天观测数据从数据提取到时间转换的处理流程。导出了周期搜索的计算方法,并利用Crab脉冲星的实测数据实现了轮廓折叠。发现当搜索周期未达到一定精度时,受观测光子数在折叠周期内平均作用,不能形成准确的脉冲轮廓。分析了折叠轮廓区间数及观测总光子数对折叠轮廓信噪比及时间分辨率的影响。
4.给出了判断脉冲星是否受航天器自身及第三天体遮挡的计算公式。通过计算分析,总结了脉冲星可见性的变化规律。发现航天器自身遮挡是影响脉冲星可见性的主要因素。提出了提高脉冲星可见性的探测器架设方法,将脉冲星可见性由50%提高到了92%。
5. GPS卫星导航系统通常利用精度衰减因子(DOP)进行选星,其计算方法是建立在所有卫星观测值都具有基本相同的测量误差的基础上的。本文利用SNR估算法对各脉冲星的测量误差进行了计算。分析得出不同脉冲星具有特定的观测误差,且从几十米至上千公里差异较大。因此本文导出了同时顾及不同脉冲星测量误差的差异及空间几何结构的DOP计算公式。总结了DOP随观测脉冲星的变化情况。最终通过计算给出了采用3~6颗脉冲星进行导航时的最优脉冲星组合,为X射线脉冲星导航应用提供了参考依据。
6.编制完成了脉冲星相位模糊度搜索算法库。分析了模糊度搜索随观测误差、检核脉冲星数、时间误差、脉冲星位置误差、脉冲周期、脉冲星几何结构的变化情况。利用先双差后单差检验法以及钟差辅助检验法解决了单差检验中模糊度搜索正确性受测相误差影响较大的难点,有效降低了通过阈值的模糊度组合数,提高了模糊度搜索的成功率。基于整周期数关系式的模糊度搜索方法,可避免解算航天器位置,有效提高模糊度搜索速度,便于工程实现,但也同时失去了解算航天器位置对观测误差的平差作用。因此该方法受测量误差的影响较大。
7.几何法定位可以解决航天器故障或轨道机动期间的航天器轨道确定问题,本文导出了脉冲星几何法定位的计算公式,编制完成了脉冲星几何法定位软件。发现星表误差对定位精度影响随航天器到时间模型基准点距离的增大而增大,应尽量将时间模型设定在距离航天器轨道较近的参考点以有利于改善定位精度。相位误差对定位精度具有严重影响。测量误差较小时,增加观测脉冲星可以降低定位误差,相反当测量误差较大时,增加观测脉冲星对提高定位精度并不一定有利。
8.导出了利用三差观测量测速的计算公式。由于在三差测速中采样率高,观测量偶然误差对三差测速精度影响较大。采样率越高,测速精度受偶然误差影响越大,计算结果越不稳定。而采样率越低越不能反映航天器的瞬时速度。
9.提出了基于互相关技术的脉冲星相对定位方法。该方法可以通过观测任何具有时变信号的天体进行定位,突破了X射线脉冲星绝对定位中需要选取具有稳定周期脉冲星的限制,增大了被选星源的数量。可以达到简化计算过程,缩小探测器面积的作用。
10.在相对定位中,分别利用仿真及实测数据进行了互相关时延计算分析。发现时变信号变化幅度是影响时延测定精度的重要因素。提出了改进的时延计算方法。利用观测数据并道,在提高数据信噪比的同时可达到将时延测量精度提高到脉冲到达时间测量精度的效果,避免了数据采样间隔对时延测量精度的影响。
11.编制完成了脉冲星动力学定轨软件。评定了各项误差对定轨精度的影响。通过计算得出:在解算航天器位置的同时,对每颗脉冲星进行钟差全弧段二次多项式参数估计,可吸收脉冲星误差系统部分,提高定轨精度。但由于增加了解算参数,当脉冲星测量误差较大时,增大了导致定轨矩阵奇异的可能性。测量误差对定轨精度的影响在动力学方程的约束下明显降低。定轨精度由几何法的几十公里提高到100米。
12.利用单脉冲星定轨方法,在X射线脉冲星导航试验阶段具有重要的实际意义。但不同脉冲星的定轨误差从几公里至几十公里不等,精度不稳定。为解决该问题,分析了脉冲星几何位置与定轨精度的关系,发现在RTN坐标系内,R、N方向以及位置定轨误差表现出当脉冲星方向单位向量与航天器轨道面Z轴夹角接近90°时误差增大,远离90°时误差减小的变化规律,而T方向误差变化与此相反,解决了单脉冲星定轨时的选星问题。提出了提高单星定轨精度的单探测器准多星定轨方法,有效解决了单星定轨中几何结构不佳,精度较低的缺点,定轨精度可与多星定轨相媲美。
This thesis deals with the X-ray pulsar navigation algorithms including data processing, error corrections, phase ambiguity resolution, and navigation and positioning methods. The main works and contributions are summarized as follows.
1. Necessary qualifications of pulsars for the X-ray pulsar navigartion are proposed through the analysis of pulsar character. The principle and basic elements and navigation algorithmic flow of the X-ray pulsar navigation are described. The comparisions between the X-ray pulsar navigation and other navigation systems are made. Differential observation equations are derived and their ability of eliminating and reducing observation errors is investigated. The X-ray pulsar navigation algorithms about the timing correction, attitude determination, velocity determination and positioning are generally summarized.
2. Aimed at data processing for ground radio observations and timing model setting-up, the transformation of the time of arrival(TOA) observed onboard spacecraft to the TCB/TDB time at the barycenter of the solar system and the pulsar timing model refining are researched. The magnitude of order and variations of Einstein delay, Shapiro delay, Roemer delay, dispersion delay and atmospheric delay are statistically analysed. The influences of varying timing models for binary pulsars and of planetary ephemeris on pulsar parameter fitting are compared. These analyses constitute a reference for henceforth data processing.
3. The X-ray surveying data processing flows from data selection to time transformation are expounded. Computing method for the period search is educed. And the pulse profile folding is realized using real data of Crab pulsar. The results show that pulse profile can not exactly formed if the period of pulse is not known to a certain precision due to the insufficiency of observed photons. The influence of profile subinterval numbers and total number of observed photons on the signal-noise ratio and time resolution of profile are analysed.
4. Equations judging whether a pulsar is sheltered by itself or by the third celestial body are given. Variations in pulsar visibility are analysed by means of calculation. It is pointed out that the main factor which affects pulsar visibility is the spacecraft itself, and that a proper detector setting can improve the visibility from 50% to 92%.
5. GPS satellite navigation system ususlly selects satellites by a factor called the dilution of precision(DOP) based on the assumption that all satellite measurements have equal observation error. Pulsar’s observation error are calculated using the SNR estimation method. Results show that various pulsar has normally a large observation error, from several tens of meters to thousands of kilometers. The DOP formula is deduced considering both unequal observation errors for various pulsars and their geometry configuration. Changes of DOP with the pulsar configuration are also summarized. Finally the best navigation pulsar configurations including three to six pulsars are selected through analysis, which provide a reference for the application of X-ray pulsar navigation.
6. A library of phase ambiguity resolution algorithms is furnished. The situation about ambiguity searching are analysed which are affected by the observation error, number of pulsars, clock error, pulsar position error, pulse period, and pulsars’geometry configuration. In the single difference checkout method the ambiguity resolution correctness is severely influenced by the phase error. Using double-difference measurements followed by using single-difference measurements or using the spacecraft-clock-offset-aided single difference checkout method can solve this problem. These two methods can efficiently reduce the number of ambiguity combination that pass the threshold and improve the success ratio. Using the ambiguity resolution method based on the full-period number relation formula can avoid calculating spacecraft position. This method can effectively speed up searching and is convenient for implement, but fails to adjust observation errors during spacecraft position computation. So it suffer severely the influence of observation error.
7. Geometric orbit determination is useful when spacecraft has a failure or in maneuver. Equations associated with the geometric orbit determination are derived and related software is developed. It is pointed out that the influence of pulsar ephemeris error is severer if the distance between the spacecraft and the point to which the timing model refers is very large. So we should manage to set the timing model reference point to the position closer to the running spacecraft. The phase error severely affects position precision. Increasing observing pulsars can reduce orbit determination error if the observation error is small. However if observation error is large, increasing observing pulsars may not benefit the orbit determination precision.
8. Equations for the speed determination using triple-difference measurements are given. Random measurement error may bring severe influence on the triple-difference speed determination due to high sampling data rate. The higher the sampling rate the severer the influence on speed determination precision, and the results are more unstable. On the other hand the lower sampling rate may not reflect the instantaneous speed of spacecraft.
9. Pulsar relative positioning based on the cross correlation method is presented. The spacecraft position can be determined through observing any celestial body which radiates variable signal. Thus it breaks away from the limitation of having to use pulsars that have stable period in absolute positioning. This method can use a wide range of pulsar sources. It also can simplify the calculation process and reduce the detector area as well.
10. For the relative positioning, cross correlation calculation is carried out using simulated and real data. Results show that the amplitude of temporal signal is the main factor limiting the time delay determination precision. An improved time delay calculation method is presented. Using combined bins of observations can raise the signal-noise ratio of data and improve the time delay precision to such a level at which precision of time of arrival can be achieved. It avoid the influence of data sampling interval on time delay determination precision.
11. A dynamic orbit determination software package is developed. The influence of all kinds of error sources on the orbit determination is assessed. It is found that the estimation of clock parameters with a second order polynomial for each pulsar in conjunction with the spacecraft position determination can absorb partial systematic errors and improve orbit determination precision. But because this method will increase the number of estimated parameters, the possibility of orbit determination matrix becoming singular is increased. The influence of observation error on the orbit determination precision is significantly reduced because of the dynamic equations. The orbit determination precision is improved from several kilometers to one hundred meters.
12. The orbit determination by a single pulsar is very useful in the test phase of X-ray pulsar navigation. But in this case the orbit precision is not stable, varying from several kilometer to tens of kilometers. In trying to solve this problem the relationship between the palsar geometry and orbit determination precision is analysed. It is found that in RTN coordinate system the errors in R and T direction and position determination become larger when the angle between the unit vector in pulsar direction and Z-axis of orbit plane gets closer to 90°. While the errors will decrease when the angle is apart from 90°. And that the variation in T direction precision is opposite. Then the selecting pulsar problem with the single pulsar orbit determination error is investigated. A quasi-multiple pulsar orbit determination method is put forward which can improve the orbit determination precision. This method can effectively overcome the disadvantage of bad geometry configuration. And yield a precision comparable with that of the multi-pulsar orbit determination.
1.通过对脉冲星的特性分析,总结了适宜于X射线脉冲星导航的脉冲星所应具备的条件。分析了X射线脉冲星导航的原理、基本要素、算法流程及其与其他导航系统的异同点。导出了脉冲星差分观测方程,分析了它们对测量误差的消除或减弱能力。概述了X射线脉冲星导航在定时、定姿、测速、定位方面的导航算法。
2.以地面射电观测数据处理及时间模型建立精化为目标,研究了将脉冲到达时间观测量转换到太阳系质心处TCB/TDB时间尺度的计算方法及时间模型精化算法。统计分析了Einstein延迟、Shapiro延迟、Roemer延迟、色散延迟以及大气延迟改正的量级及变化特点,对比了不同双星模型及行星星历对脉冲星参数拟合的影响,以期为数据处理提供依据。
3.阐述了X射线巡天观测数据从数据提取到时间转换的处理流程。导出了周期搜索的计算方法,并利用Crab脉冲星的实测数据实现了轮廓折叠。发现当搜索周期未达到一定精度时,受观测光子数在折叠周期内平均作用,不能形成准确的脉冲轮廓。分析了折叠轮廓区间数及观测总光子数对折叠轮廓信噪比及时间分辨率的影响。
4.给出了判断脉冲星是否受航天器自身及第三天体遮挡的计算公式。通过计算分析,总结了脉冲星可见性的变化规律。发现航天器自身遮挡是影响脉冲星可见性的主要因素。提出了提高脉冲星可见性的探测器架设方法,将脉冲星可见性由50%提高到了92%。
5. GPS卫星导航系统通常利用精度衰减因子(DOP)进行选星,其计算方法是建立在所有卫星观测值都具有基本相同的测量误差的基础上的。本文利用SNR估算法对各脉冲星的测量误差进行了计算。分析得出不同脉冲星具有特定的观测误差,且从几十米至上千公里差异较大。因此本文导出了同时顾及不同脉冲星测量误差的差异及空间几何结构的DOP计算公式。总结了DOP随观测脉冲星的变化情况。最终通过计算给出了采用3~6颗脉冲星进行导航时的最优脉冲星组合,为X射线脉冲星导航应用提供了参考依据。
6.编制完成了脉冲星相位模糊度搜索算法库。分析了模糊度搜索随观测误差、检核脉冲星数、时间误差、脉冲星位置误差、脉冲周期、脉冲星几何结构的变化情况。利用先双差后单差检验法以及钟差辅助检验法解决了单差检验中模糊度搜索正确性受测相误差影响较大的难点,有效降低了通过阈值的模糊度组合数,提高了模糊度搜索的成功率。基于整周期数关系式的模糊度搜索方法,可避免解算航天器位置,有效提高模糊度搜索速度,便于工程实现,但也同时失去了解算航天器位置对观测误差的平差作用。因此该方法受测量误差的影响较大。
7.几何法定位可以解决航天器故障或轨道机动期间的航天器轨道确定问题,本文导出了脉冲星几何法定位的计算公式,编制完成了脉冲星几何法定位软件。发现星表误差对定位精度影响随航天器到时间模型基准点距离的增大而增大,应尽量将时间模型设定在距离航天器轨道较近的参考点以有利于改善定位精度。相位误差对定位精度具有严重影响。测量误差较小时,增加观测脉冲星可以降低定位误差,相反当测量误差较大时,增加观测脉冲星对提高定位精度并不一定有利。
8.导出了利用三差观测量测速的计算公式。由于在三差测速中采样率高,观测量偶然误差对三差测速精度影响较大。采样率越高,测速精度受偶然误差影响越大,计算结果越不稳定。而采样率越低越不能反映航天器的瞬时速度。
9.提出了基于互相关技术的脉冲星相对定位方法。该方法可以通过观测任何具有时变信号的天体进行定位,突破了X射线脉冲星绝对定位中需要选取具有稳定周期脉冲星的限制,增大了被选星源的数量。可以达到简化计算过程,缩小探测器面积的作用。
10.在相对定位中,分别利用仿真及实测数据进行了互相关时延计算分析。发现时变信号变化幅度是影响时延测定精度的重要因素。提出了改进的时延计算方法。利用观测数据并道,在提高数据信噪比的同时可达到将时延测量精度提高到脉冲到达时间测量精度的效果,避免了数据采样间隔对时延测量精度的影响。
11.编制完成了脉冲星动力学定轨软件。评定了各项误差对定轨精度的影响。通过计算得出:在解算航天器位置的同时,对每颗脉冲星进行钟差全弧段二次多项式参数估计,可吸收脉冲星误差系统部分,提高定轨精度。但由于增加了解算参数,当脉冲星测量误差较大时,增大了导致定轨矩阵奇异的可能性。测量误差对定轨精度的影响在动力学方程的约束下明显降低。定轨精度由几何法的几十公里提高到100米。
12.利用单脉冲星定轨方法,在X射线脉冲星导航试验阶段具有重要的实际意义。但不同脉冲星的定轨误差从几公里至几十公里不等,精度不稳定。为解决该问题,分析了脉冲星几何位置与定轨精度的关系,发现在RTN坐标系内,R、N方向以及位置定轨误差表现出当脉冲星方向单位向量与航天器轨道面Z轴夹角接近90°时误差增大,远离90°时误差减小的变化规律,而T方向误差变化与此相反,解决了单脉冲星定轨时的选星问题。提出了提高单星定轨精度的单探测器准多星定轨方法,有效解决了单星定轨中几何结构不佳,精度较低的缺点,定轨精度可与多星定轨相媲美。
This thesis deals with the X-ray pulsar navigation algorithms including data processing, error corrections, phase ambiguity resolution, and navigation and positioning methods. The main works and contributions are summarized as follows.
1. Necessary qualifications of pulsars for the X-ray pulsar navigartion are proposed through the analysis of pulsar character. The principle and basic elements and navigation algorithmic flow of the X-ray pulsar navigation are described. The comparisions between the X-ray pulsar navigation and other navigation systems are made. Differential observation equations are derived and their ability of eliminating and reducing observation errors is investigated. The X-ray pulsar navigation algorithms about the timing correction, attitude determination, velocity determination and positioning are generally summarized.
2. Aimed at data processing for ground radio observations and timing model setting-up, the transformation of the time of arrival(TOA) observed onboard spacecraft to the TCB/TDB time at the barycenter of the solar system and the pulsar timing model refining are researched. The magnitude of order and variations of Einstein delay, Shapiro delay, Roemer delay, dispersion delay and atmospheric delay are statistically analysed. The influences of varying timing models for binary pulsars and of planetary ephemeris on pulsar parameter fitting are compared. These analyses constitute a reference for henceforth data processing.
3. The X-ray surveying data processing flows from data selection to time transformation are expounded. Computing method for the period search is educed. And the pulse profile folding is realized using real data of Crab pulsar. The results show that pulse profile can not exactly formed if the period of pulse is not known to a certain precision due to the insufficiency of observed photons. The influence of profile subinterval numbers and total number of observed photons on the signal-noise ratio and time resolution of profile are analysed.
4. Equations judging whether a pulsar is sheltered by itself or by the third celestial body are given. Variations in pulsar visibility are analysed by means of calculation. It is pointed out that the main factor which affects pulsar visibility is the spacecraft itself, and that a proper detector setting can improve the visibility from 50% to 92%.
5. GPS satellite navigation system ususlly selects satellites by a factor called the dilution of precision(DOP) based on the assumption that all satellite measurements have equal observation error. Pulsar’s observation error are calculated using the SNR estimation method. Results show that various pulsar has normally a large observation error, from several tens of meters to thousands of kilometers. The DOP formula is deduced considering both unequal observation errors for various pulsars and their geometry configuration. Changes of DOP with the pulsar configuration are also summarized. Finally the best navigation pulsar configurations including three to six pulsars are selected through analysis, which provide a reference for the application of X-ray pulsar navigation.
6. A library of phase ambiguity resolution algorithms is furnished. The situation about ambiguity searching are analysed which are affected by the observation error, number of pulsars, clock error, pulsar position error, pulse period, and pulsars’geometry configuration. In the single difference checkout method the ambiguity resolution correctness is severely influenced by the phase error. Using double-difference measurements followed by using single-difference measurements or using the spacecraft-clock-offset-aided single difference checkout method can solve this problem. These two methods can efficiently reduce the number of ambiguity combination that pass the threshold and improve the success ratio. Using the ambiguity resolution method based on the full-period number relation formula can avoid calculating spacecraft position. This method can effectively speed up searching and is convenient for implement, but fails to adjust observation errors during spacecraft position computation. So it suffer severely the influence of observation error.
7. Geometric orbit determination is useful when spacecraft has a failure or in maneuver. Equations associated with the geometric orbit determination are derived and related software is developed. It is pointed out that the influence of pulsar ephemeris error is severer if the distance between the spacecraft and the point to which the timing model refers is very large. So we should manage to set the timing model reference point to the position closer to the running spacecraft. The phase error severely affects position precision. Increasing observing pulsars can reduce orbit determination error if the observation error is small. However if observation error is large, increasing observing pulsars may not benefit the orbit determination precision.
8. Equations for the speed determination using triple-difference measurements are given. Random measurement error may bring severe influence on the triple-difference speed determination due to high sampling data rate. The higher the sampling rate the severer the influence on speed determination precision, and the results are more unstable. On the other hand the lower sampling rate may not reflect the instantaneous speed of spacecraft.
9. Pulsar relative positioning based on the cross correlation method is presented. The spacecraft position can be determined through observing any celestial body which radiates variable signal. Thus it breaks away from the limitation of having to use pulsars that have stable period in absolute positioning. This method can use a wide range of pulsar sources. It also can simplify the calculation process and reduce the detector area as well.
10. For the relative positioning, cross correlation calculation is carried out using simulated and real data. Results show that the amplitude of temporal signal is the main factor limiting the time delay determination precision. An improved time delay calculation method is presented. Using combined bins of observations can raise the signal-noise ratio of data and improve the time delay precision to such a level at which precision of time of arrival can be achieved. It avoid the influence of data sampling interval on time delay determination precision.
11. A dynamic orbit determination software package is developed. The influence of all kinds of error sources on the orbit determination is assessed. It is found that the estimation of clock parameters with a second order polynomial for each pulsar in conjunction with the spacecraft position determination can absorb partial systematic errors and improve orbit determination precision. But because this method will increase the number of estimated parameters, the possibility of orbit determination matrix becoming singular is increased. The influence of observation error on the orbit determination precision is significantly reduced because of the dynamic equations. The orbit determination precision is improved from several kilometers to one hundred meters.
12. The orbit determination by a single pulsar is very useful in the test phase of X-ray pulsar navigation. But in this case the orbit precision is not stable, varying from several kilometer to tens of kilometers. In trying to solve this problem the relationship between the palsar geometry and orbit determination precision is analysed. It is found that in RTN coordinate system the errors in R and T direction and position determination become larger when the angle between the unit vector in pulsar direction and Z-axis of orbit plane gets closer to 90°. While the errors will decrease when the angle is apart from 90°. And that the variation in T direction precision is opposite. Then the selecting pulsar problem with the single pulsar orbit determination error is investigated. A quasi-multiple pulsar orbit determination method is put forward which can improve the orbit determination precision. This method can effectively overcome the disadvantage of bad geometry configuration. And yield a precision comparable with that of the multi-pulsar orbit determination.
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