GPS非差精密单点定位模糊度固定理论与方法研究
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摘要
精密单点定位技术(Precise Point Positioning, PPP)可以利用单台接收机在全球范围内进行静态或动态独立定位,能够直接获得静态厘米级、动态分米到厘米级的高精度的坐标结果,它在地壳形变监测、高精度导航定位、低轨卫星定轨、GNSS气象、精密授时等领域得到了广泛的应用。实时性和高精度是精密定位的研究重点之一。随着实时轨道确定和实时精密钟差估计等核心技术的发展与进步,精密单点定位技术已经逐渐发展成为一种实时的高精度定位手段。传统的精密单点定位中,由于相位未校准延迟偏差中小数部分FCBs (Fractional-cycle biases)的影响,模糊度参数为实数解。国内外学者通过研究指出,精密单点定位在E方向的精度仍然可以通过模糊度的固定得到提高。利用区域或全球的参考站网络,估计能够恢复非差模糊度整数特性的产品,实现区域内流动站PPP模糊度固定是一项非常有意义的工作,同时也是国内外GNSS领域的一个研究热点。
本文通过对PPP模糊度固定问题全面深入的研究指出,基于FCBs的PPP模糊度固定算法可以利用现有的精密轨道和精密钟差产品估计FCBs,流动站利用相应的精密轨道、精密钟差和FCBs产品就能够实现PPP模糊度固定。这种算法能够在现有的精密钟差估计方法和产品上展开,具有广泛的研究基础和发展空间。本文针对服务端FCBs估计和用户端PPP模糊度固定中存在的问题,提出有效的解决办法,并在“广域实时精密定位系统”的软件平台基础上,开发了一套从数据处理中心FCBs古计到用户端PPP模糊度固定的软件模块。利用实测数据验证了改进算法的正确性。在此基础上,针对目前关于精密单点定位的研究都是基于精密轨道和精密钟差产品的情况,探索和讨论了基于广播星历和区域钟差估计产品的精密单点定位的可行性和在一定范围内的有效性。
本文的研究内容主要包括：
1.系统地研究了精密单点定位模糊度固定的理论与技术。从最基本的函数模型出发,对导致模糊度非整数特性的各参数项及它们与其他待估参数之间的相互关系进行了详细的分析。
2.依据造成非差模糊度非整数特性的相位未校准延迟小数部分FCBs与其他参数耦合性质的不同,首次系统地对国内外PPP模糊度固定算法进行了分类,并做了详细的对比分析。
3.提出了一种附加M估计的FCBs估计方法。在PPP模糊度固定的实时应用中,由于一些因素的影响(如地震等),部分参考站的位置可能会发生突变,而服务端的参考站坐标并不能够实时更新,这就会导致部分参考站的模糊度估值存在较大的偏差。本文指出可以将含有较大偏差的浮点模糊度的小数部分当做粗差处理,引入稳健估计的理论,通过降低有偏差观测值的权比,排除有害观测值的影响,提高FCBs估计的稳健性。实验分析表明,与原有算法相比,该算法能降低可能的粗差的影响,可以降低PPP模糊度固定实时应用中参考站位置突变的影响。
4.提出采用一种改进的LAMBDA模糊度搜索算法解算PPP的模糊度,以Bootstrapping成功率做为LAMBDA降相关的性能指标,当该指标满足一定条件时才尝试模糊度的搜索与固定。实验分析表明,改进的LAMBDA算法能够提高PPP模糊度固定的成功率。
5.以“广域实时精密定位系统”的软件平台为基础,进一步精化了软件系统中的部分误差模型,并分析了相应的误差对窄巷模糊度估计的影响。采用改进FCBs估计方法与流动站模糊度固定算法,实现了一套从服务端FCBs产品估计到用户端模糊度固定的软件模块。
6.提出了基于广播星历与区域钟差的精密单点定位方法。口前PPP及PPP模糊度固定的研究都是基于全球跟踪站观测数据解算的精密的卫星轨道和卫星钟差产品,而采用广播星历与区域钟差估计产品进行精密单点定位的研究开展的较少。本文分别从理论和实验验证两个方面对基于广播星历轨道与区域钟差估计产品的PPP模糊度实数解与固定解的精度及其适用范围进行了详细的分析。初步认为在半径300km的范围内,采用广播星历与区域钟差估计产品的模糊度实数解PPP能够达到与采用IGS最终产品相当的精度；在半径100km以内的范围,模糊度固定可以提高精密单点定位的精度。
7.分别利用省级CORS网、中国大陆构造环境监测网络和模拟地震平台的动态实测数据,采用精密的卫星轨道和卫星钟差产品,对PPP模糊度固定算法进行了验证和分析。省级CORS网的实例分析表明,PPP模糊度固定解比浮点解在N、E、U三个方向上精度提高分别为23.7%、52.6%、26.6%;中国大陆构造环境监测网络数据的结果表明,PPP模糊度固定解在N、E、U方向上的提高分别为23.88%、38.64%和15.98%；地震平台动态数据N、E、U方向上的RMS分别从0.94cm、0.84cm、5.77cm提高到0.70cm、0.76cm3.60cm。采用市级CORS网数据对基于区域钟差的精密单点定位进行了验证,结果表明基于广播星历与区域钟钟差的PPP模糊度浮点解比采用IGS最终产品的定位精度高,固定解的精度比浮点解精度在N、E、U三个方向上进一步提高,分别为22.1%、46.4%、17.1%。
Precise Point Positioning (PPP) is a positioning technique processing the observations at solely a single receiver on a global scale by fixing precise satellite orbits and clocks. PPP can directly obtain centimeter-level accuracy coordinates for static positioning and decimeter to centimeter-level accuracy coordinates for dynamic modes. PPP has been widely used in the field of deformation monitoring, high-precision navigation and positioning, LEO satellite orbit determination, GNSS meteorology, precise time transferring and so on. Real-time and high precision are two of the main objectives of GNSS researches. With the development of real-time orbit determination and real-time clock estimation technology, PPP has gradually developed into a real-time high-precision positioning means. In the traditional PPP, because of the fractional part of the uncalibrated phase delays (FCBs), ambiguity parameters are estimated as real-valued constants. Scholars both at home and abroad pointed out that the accuracy of PPP at the E direction can still be improved by ambiguity fixing. The research of ambiguity-fixed PPP is a very rewarding work, and it is also a central issue of GNSS research all over the world.
Through comprehensive and in-depth study, the author pointed out that ambiguity resolution of PPP based on FCBs can be achieved with existing precise orbit and clock products. Rovers use the corresponding precise orbit, precise clock and FCBs products can achieve ambiguity-fixed PPP. This algorithm can be carried out on the basis of existing clock estimation technology, thus it has a widely foundation and huge development space. This paper comes up with effective solutions on some problems of FCBs estimates and ambiguity resolution of rover stations. A module with functions of both FCBs estimation and PPP with integer ambiguities is developed based on the Wide Area Real-Time Differential GPS software platform. The correctness of the improved algorithm is verified with experiments. In addition, the researches of PPP are all based on precise orbit and clock products currently, this paper has explored and discussed the feasibility of PPP based on broadcast ephemeris and clock products estimated with regional networks, and the precision and certain feasible range is studied.
The content of this study mainly includes:
1. The theory and technology of ambiguity-fixed PPP are studied systematically. Starts from the basic function model, a detailed analysis of the relationship between parameters which lead the ambiguities to non-integer values and the other parameters are analyzed in detail.
2. Based on the difference of the coupling characteristics between the fractional part of the uncalibrated phase delays (FCBs) and the other parameters, systematical classification for PPP ambiguity fixing algorithm both at home and abroad has been done. In addition, a detailed comparative analysis has been made.
3. A new method with M Estimator is proposed to estimate the FCBs. In the applications of real-time ambiguity-fixed PPP, the coordinates of reference stations should be fixed when the server estimates the FCBs. Biases of the coordinates can cause biases to narrow-lane ambiguities. Due to the influence of some irresistible factors (such as earthquake), the positions of some reference stations may change, while the server can not update the coordinates promptly. This will cause large deviations in the ambiguity estimation of some reference stations. This paper points out that the float ambiguities with large deviations can be treated as gross errors. The robust estimation theory is introduced into the estimation of FCBs and the influence of harmful observations can be reduced by reducing the weight of harmful observations to improve the robustness of FCBs estimation. Experimental results show that, compared with the original algorithm, this algorithm can reduce the possible influence of gross errors and the problem that reference station coordinates have sudden changes in real-time applications of PPP ambiguity-fixed solution can be solved.
4. An improved LAMBDA method was applied for the integer ambiguity resolution of PPP. This method uses bootstrapped probability as an indicator of the performance of LAMBDA decorrelation. The ambiguities are tried to be fixed only when the index of bootstrapping exceed the threshold. The results show that the improved LAMBDA method can improve the success rate of ambiguity resolution of PPP.
5. Based on the Wide Area Real-Time Differential GPS software System, which is developed by GNSS Center of Wuhan University for providing real-time precise satellite orbit and clock products, error models which have not been included in current version are added. For example, phase center variations (PCV), horizontal gradients of troposphere delay and etc. Furthermore, the impacts on the narrow-lane ambiguities estimation when neglecting them are analyzed. Based on the improved methods, a module with functions of both FCBs estimation and ambiguity-fixed PPP is added into the Wide Area Real-Time Differential GPS software.
6. Currently, the research of ambiguity-float and ambiguity-fixed PPP are all based on precise orbit and precision clock products estimated with observations of globally distributed tracking stations. However, there is hardly any research of PPP with broadcast ephemeris and clock products estimated with regional observations. In this paper, PPP with broadcast ephemeris and clocks estimated with regional networks is put forward. The precision and feasible range of ambiguity-float PPP and ambiguity-fixed PPP are verified both theoretically and experimentally. Preliminary view is that ambiguity-float PPP with broadcast ephemeris and clocks estimated with regional networks can achieve comparable result with PPP based on IGS final products within a region of300km radius. Ambiguity-fixed PPP based on broadcast (brdc) ephemeris and clock products estimated with regional observations is proposed within a region of100km radius.
7. Data of Provincial CORS network, Continental Tectonic Environment Monitoring Network Project of China and seismic experiment is used to verify the improved algorithm and the capability of the software. Results based on data of CORS network at the provincial level show that the accuracy of ambiguity-fixed PPP improved about52.6%,23.7%and26.6%in the East, North and Up components respectively than ambiguity-float PPP. The improvements decrease to38.64%,23.88%and15.98%in the East, North and Up components when the large area is used. Results of the earthquake simulation experiment show that the RMS deduce from0.84cm,0.94cm and5.77cm to0.76cm,0.70cm and3.60cm in the East, North and Up components, respectively. PPP with broadcast ephemeris and clocks products estimated with regional networks is verified with Municipal CORS network. The precision of ambiguity-float PPP with broadcast ephemeris and clocks estimated with regional networks is higher than that with IGS final products, the ambiguity-fixed PPP solution has a further increment of22.1%,46.4%,17.1%in N, E and U directions, respectively.
本文通过对PPP模糊度固定问题全面深入的研究指出,基于FCBs的PPP模糊度固定算法可以利用现有的精密轨道和精密钟差产品估计FCBs,流动站利用相应的精密轨道、精密钟差和FCBs产品就能够实现PPP模糊度固定。这种算法能够在现有的精密钟差估计方法和产品上展开,具有广泛的研究基础和发展空间。本文针对服务端FCBs估计和用户端PPP模糊度固定中存在的问题,提出有效的解决办法,并在“广域实时精密定位系统”的软件平台基础上,开发了一套从数据处理中心FCBs古计到用户端PPP模糊度固定的软件模块。利用实测数据验证了改进算法的正确性。在此基础上,针对目前关于精密单点定位的研究都是基于精密轨道和精密钟差产品的情况,探索和讨论了基于广播星历和区域钟差估计产品的精密单点定位的可行性和在一定范围内的有效性。
本文的研究内容主要包括：
1.系统地研究了精密单点定位模糊度固定的理论与技术。从最基本的函数模型出发,对导致模糊度非整数特性的各参数项及它们与其他待估参数之间的相互关系进行了详细的分析。
2.依据造成非差模糊度非整数特性的相位未校准延迟小数部分FCBs与其他参数耦合性质的不同,首次系统地对国内外PPP模糊度固定算法进行了分类,并做了详细的对比分析。
3.提出了一种附加M估计的FCBs估计方法。在PPP模糊度固定的实时应用中,由于一些因素的影响(如地震等),部分参考站的位置可能会发生突变,而服务端的参考站坐标并不能够实时更新,这就会导致部分参考站的模糊度估值存在较大的偏差。本文指出可以将含有较大偏差的浮点模糊度的小数部分当做粗差处理,引入稳健估计的理论,通过降低有偏差观测值的权比,排除有害观测值的影响,提高FCBs估计的稳健性。实验分析表明,与原有算法相比,该算法能降低可能的粗差的影响,可以降低PPP模糊度固定实时应用中参考站位置突变的影响。
4.提出采用一种改进的LAMBDA模糊度搜索算法解算PPP的模糊度,以Bootstrapping成功率做为LAMBDA降相关的性能指标,当该指标满足一定条件时才尝试模糊度的搜索与固定。实验分析表明,改进的LAMBDA算法能够提高PPP模糊度固定的成功率。
5.以“广域实时精密定位系统”的软件平台为基础,进一步精化了软件系统中的部分误差模型,并分析了相应的误差对窄巷模糊度估计的影响。采用改进FCBs估计方法与流动站模糊度固定算法,实现了一套从服务端FCBs产品估计到用户端模糊度固定的软件模块。
6.提出了基于广播星历与区域钟差的精密单点定位方法。口前PPP及PPP模糊度固定的研究都是基于全球跟踪站观测数据解算的精密的卫星轨道和卫星钟差产品,而采用广播星历与区域钟差估计产品进行精密单点定位的研究开展的较少。本文分别从理论和实验验证两个方面对基于广播星历轨道与区域钟差估计产品的PPP模糊度实数解与固定解的精度及其适用范围进行了详细的分析。初步认为在半径300km的范围内,采用广播星历与区域钟差估计产品的模糊度实数解PPP能够达到与采用IGS最终产品相当的精度；在半径100km以内的范围,模糊度固定可以提高精密单点定位的精度。
7.分别利用省级CORS网、中国大陆构造环境监测网络和模拟地震平台的动态实测数据,采用精密的卫星轨道和卫星钟差产品,对PPP模糊度固定算法进行了验证和分析。省级CORS网的实例分析表明,PPP模糊度固定解比浮点解在N、E、U三个方向上精度提高分别为23.7%、52.6%、26.6%;中国大陆构造环境监测网络数据的结果表明,PPP模糊度固定解在N、E、U方向上的提高分别为23.88%、38.64%和15.98%；地震平台动态数据N、E、U方向上的RMS分别从0.94cm、0.84cm、5.77cm提高到0.70cm、0.76cm3.60cm。采用市级CORS网数据对基于区域钟差的精密单点定位进行了验证,结果表明基于广播星历与区域钟钟差的PPP模糊度浮点解比采用IGS最终产品的定位精度高,固定解的精度比浮点解精度在N、E、U三个方向上进一步提高,分别为22.1%、46.4%、17.1%。
Precise Point Positioning (PPP) is a positioning technique processing the observations at solely a single receiver on a global scale by fixing precise satellite orbits and clocks. PPP can directly obtain centimeter-level accuracy coordinates for static positioning and decimeter to centimeter-level accuracy coordinates for dynamic modes. PPP has been widely used in the field of deformation monitoring, high-precision navigation and positioning, LEO satellite orbit determination, GNSS meteorology, precise time transferring and so on. Real-time and high precision are two of the main objectives of GNSS researches. With the development of real-time orbit determination and real-time clock estimation technology, PPP has gradually developed into a real-time high-precision positioning means. In the traditional PPP, because of the fractional part of the uncalibrated phase delays (FCBs), ambiguity parameters are estimated as real-valued constants. Scholars both at home and abroad pointed out that the accuracy of PPP at the E direction can still be improved by ambiguity fixing. The research of ambiguity-fixed PPP is a very rewarding work, and it is also a central issue of GNSS research all over the world.
Through comprehensive and in-depth study, the author pointed out that ambiguity resolution of PPP based on FCBs can be achieved with existing precise orbit and clock products. Rovers use the corresponding precise orbit, precise clock and FCBs products can achieve ambiguity-fixed PPP. This algorithm can be carried out on the basis of existing clock estimation technology, thus it has a widely foundation and huge development space. This paper comes up with effective solutions on some problems of FCBs estimates and ambiguity resolution of rover stations. A module with functions of both FCBs estimation and PPP with integer ambiguities is developed based on the Wide Area Real-Time Differential GPS software platform. The correctness of the improved algorithm is verified with experiments. In addition, the researches of PPP are all based on precise orbit and clock products currently, this paper has explored and discussed the feasibility of PPP based on broadcast ephemeris and clock products estimated with regional networks, and the precision and certain feasible range is studied.
The content of this study mainly includes:
1. The theory and technology of ambiguity-fixed PPP are studied systematically. Starts from the basic function model, a detailed analysis of the relationship between parameters which lead the ambiguities to non-integer values and the other parameters are analyzed in detail.
2. Based on the difference of the coupling characteristics between the fractional part of the uncalibrated phase delays (FCBs) and the other parameters, systematical classification for PPP ambiguity fixing algorithm both at home and abroad has been done. In addition, a detailed comparative analysis has been made.
3. A new method with M Estimator is proposed to estimate the FCBs. In the applications of real-time ambiguity-fixed PPP, the coordinates of reference stations should be fixed when the server estimates the FCBs. Biases of the coordinates can cause biases to narrow-lane ambiguities. Due to the influence of some irresistible factors (such as earthquake), the positions of some reference stations may change, while the server can not update the coordinates promptly. This will cause large deviations in the ambiguity estimation of some reference stations. This paper points out that the float ambiguities with large deviations can be treated as gross errors. The robust estimation theory is introduced into the estimation of FCBs and the influence of harmful observations can be reduced by reducing the weight of harmful observations to improve the robustness of FCBs estimation. Experimental results show that, compared with the original algorithm, this algorithm can reduce the possible influence of gross errors and the problem that reference station coordinates have sudden changes in real-time applications of PPP ambiguity-fixed solution can be solved.
4. An improved LAMBDA method was applied for the integer ambiguity resolution of PPP. This method uses bootstrapped probability as an indicator of the performance of LAMBDA decorrelation. The ambiguities are tried to be fixed only when the index of bootstrapping exceed the threshold. The results show that the improved LAMBDA method can improve the success rate of ambiguity resolution of PPP.
5. Based on the Wide Area Real-Time Differential GPS software System, which is developed by GNSS Center of Wuhan University for providing real-time precise satellite orbit and clock products, error models which have not been included in current version are added. For example, phase center variations (PCV), horizontal gradients of troposphere delay and etc. Furthermore, the impacts on the narrow-lane ambiguities estimation when neglecting them are analyzed. Based on the improved methods, a module with functions of both FCBs estimation and ambiguity-fixed PPP is added into the Wide Area Real-Time Differential GPS software.
6. Currently, the research of ambiguity-float and ambiguity-fixed PPP are all based on precise orbit and precision clock products estimated with observations of globally distributed tracking stations. However, there is hardly any research of PPP with broadcast ephemeris and clock products estimated with regional observations. In this paper, PPP with broadcast ephemeris and clocks estimated with regional networks is put forward. The precision and feasible range of ambiguity-float PPP and ambiguity-fixed PPP are verified both theoretically and experimentally. Preliminary view is that ambiguity-float PPP with broadcast ephemeris and clocks estimated with regional networks can achieve comparable result with PPP based on IGS final products within a region of300km radius. Ambiguity-fixed PPP based on broadcast (brdc) ephemeris and clock products estimated with regional observations is proposed within a region of100km radius.
7. Data of Provincial CORS network, Continental Tectonic Environment Monitoring Network Project of China and seismic experiment is used to verify the improved algorithm and the capability of the software. Results based on data of CORS network at the provincial level show that the accuracy of ambiguity-fixed PPP improved about52.6%,23.7%and26.6%in the East, North and Up components respectively than ambiguity-float PPP. The improvements decrease to38.64%,23.88%and15.98%in the East, North and Up components when the large area is used. Results of the earthquake simulation experiment show that the RMS deduce from0.84cm,0.94cm and5.77cm to0.76cm,0.70cm and3.60cm in the East, North and Up components, respectively. PPP with broadcast ephemeris and clocks products estimated with regional networks is verified with Municipal CORS network. The precision of ambiguity-float PPP with broadcast ephemeris and clocks estimated with regional networks is higher than that with IGS final products, the ambiguity-fixed PPP solution has a further increment of22.1%,46.4%,17.1%in N, E and U directions, respectively.
引文
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