多频GNSS精密定位理论与方法研究
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摘要
随着美国GPS现代化的推进,欧盟GALILEO系统的建立,俄罗斯GLONASS系统的恢复,中国北斗二代的实施,未来的导航卫星星座将包含有120多颗卫星,且将提供多个频率的无线电信号。多频多系统组合定位有望减少模糊度的初始化时间,提高定位精度及可靠性,已成为高精度卫星定位的发展方向。因此,多频多系统精密数据处理理论和方法,特别是多频GNSS模糊度解算已成为国际卫星导航定位的研究热点。
本文在此背景下,着重研究了GNSS多频精密定位模型及其模糊度解算方法,主要内容包含以下几个部分：
1. GNSS多频观测数据仿真
在深入分析了GNSS定位原理基础上,依据GNSS星座参数和卫星运动的开普勒定理,仿真了GPS/GLONASS/GALILEO/COMPASS四个卫星导航系统的星座,并由误差模型仿真了观测值误差,最后根据GNSS定位原理,编制仿真软件实现了四个GNSS系统的多频观测数据模拟,为论文的研究提供了实验数据。
2.多频载波相位混合伪距最优组合系数的求解
深入分析了载波相位混合伪距组合观测值的模型,针对原有的基于二阶导数求函数极值方法解算最优组合系数需要复杂的公式推导,且对组合的频率个数有要求,论文中提出了一种新的基于最小二乘求解最优组合系数方法。新的方法模型简单,且可以直接获得任意频率组合的最优组合系数。
3.三频周跳探测与修复的新方法——三频TurboEdit方法
深入分析了双频TuroEdit方法探测与修复周跳的方法,在此基础上,提出了三频TurboEdit方法。基于该方法处理实测的GPS三频数据,可有效的探测并修复大于1周(包含1周)的小周跳。
4.模糊度解算方法及其可靠性理论
1)提出了一种新的模糊度搜索方法——K-Bootstrap方法
系统介绍了球形模糊度搜索方法的理论基础,并针对高维情况下,球形模糊度搜索方法耗时较多的缺点,文中提出一种新的模糊度搜索方法——K-Bootstrap法。与MLAMBDA软件包中的球形搜索算法相比,新方法在损失较少模糊度解算的成功率情况下,极大地减少了模糊度的搜索时间。
2)引入了格理论以辅助整周模糊度解算
引入了格理论以辅助载波相位整周模糊度解算。讨论了LAMBDA方法中的多维高斯整数降相关法与LLL格基规约的关系,并进一步比较分析了LLL格基规约、多维高斯整数降相关、逆Cholesky整数降相关、统一整数降相关四种方法辅助模糊度解算的性能。结果表明：LLL格基规约不但耗时少,而且可以获得较高的Bootstrap成功率；统一整数降相关法消耗时间最多,但是获得的Bootstrap成功率最高；逆Cholesky整数降相关耗时较多,获得的Bootstrap成功率也较低。在高维情况下,虽然经格基规约后的模糊度方差协方差矩阵条件数较大,但是格基规约明显提高了模糊度的搜索效率,且可以很大程度上提高Bootstrap成功率,且当Bootstrap成功率较高时,球形搜索方法耗时也较少。
在此基础上提出一种混合降相关的方法,在保证模糊度降相关效率的同时,有效的提高Bootstrap成功率,减少球形搜索方法的耗时。
3)提出了一种新的序贯模糊度解算方法
针对在高维情况下,模糊度解算耗时较多的缺点,文中提出了一种降维的模糊度解算方法——序贯模糊度解算法。新方法在模糊度区域内对模糊度转换后,再对其分块序贯固定,不仅可减少模糊度解算时间,而且可以提高模糊度正确固定时的Ratio值,便于模糊度的检验。
4)采用Monte Carlo方法讨论了模糊度的成功率
深入讨论了模糊度固定成功率的问题,包括直接取整成功率,Bootstrap成功率,以及整数最小二乘成功率。针对Bootstrap成功率理论存在争议的问题,文中采用了Monte Carlo方法进行验证,结果表明：Bootstrap成功率低于但是接近于整数最小二乘成功率,可以作为其下边成功率。
5)提出了一种新的Bootstrap方法解算方法
深入研究了Bootstrap方法的解算模糊度的原理,针对在高维情况下,原有的直接基于Cholesky分解的Bootstrap解算方法,其模糊度解算成功率较低。文中提出了一种新的Bootstrap解算方法,新方法基于分块序贯Cholesky分解原理,可有效地提高Bootstrap方法解算模糊度的成功率。
6)采用Monte Carlo方法讨论了Ratio的经验取值
基于Monte Carlo方法,分析了不同维数下Ratio值的概率分布。结果表明：Ratio值与模糊度的维数、精度存在较大的相关性。当Bootstrap成功率一定时,模糊度维数越高,则Ratio值越小。最后指出在高维情况下,使用Ratio经验值检验模糊度将过于保守。在此基础上,分析了固定失败率的模糊度固定方法。
5.研究并分析了多频GNSS相对定位的性能
1)研究了GNSS不同基线长度条件下单历元模糊度固定的成功率
基于仿真的观测数据,分别研究了短基线与长基线条件下,GNSS单历元模糊度固定成功率。结果表明在短基线情况下,单系统双频与三频的单历元模糊度固定成功率都可以达到100%；在长基线情况下,GPS/GALILEO/COMPASS单系统模糊度固定成功率都较低。但在中国及周边地区,由于可视卫星数的增加,COMPASS系统模糊度固定成功率远优于GPS和GALILEO系统,三个系统组合可以显著提高模糊度解算的成功率。
2)研究了GNSS长基线多历元不同数据处理模式下模糊度固定的初始化时间
针对单系统长基线单历元模糊度固定成功率较低的问题,分析了长基线双频与三频多历元、不同数据处理模式下模糊度固定的初始化时间。比较了基于原始观测值的相对定位模型与基于无电离层组合观测值的相对定位模型的优缺点,仿真数据处理结果表明：如果忽略电离层过程变化的影响,两种模型获得的定位结果是一致的,但前者模糊度固定的初始化时间少于后者。
进一步分析了长基线条件下,双频与三频多历元模糊度固定的初始化时间；仿真数据处理结果表明：三频模糊度固定的初始化时间远少于双频需要的时间,且GALILEO系统模糊度固定的初始化时间少于GPS系统。
最后分析了不同模糊度解算方法对模糊度固定初始化时间的影响；数据处理结果表明：基于降维处理的序贯模糊度解算的方法可以有效的提高模糊度正确固定时的Ratio值,减少了模糊度固定的初始化时间；基于固定失败率的模糊度解算方法可以根据用户的需要获得Ratio域值,其模糊度的初始化时间取决于用户设置的失败率,失败率越小,其需要的初始化时间越长。
With the modernization of U.S. GPS, the establishment of European GALILEO system, the recovery of the Russian GLONASS system, and the implementation China COMPASSⅡ, four satellite navigation systems will provide 120 navigation satellites. multi-frequency multi-system combinations postioning not only can improve the navigation accuracy and reliability, but also can improve the success rate of fixing carrier phase integer ambiguity and reduce the initial time for ambiguity fixed. However, it is not easy to process so many observation data and resovel ambiguity in high dimension, which propose new problem in high-precision multi-frequency GNSS combined navigation and positioning.
The multi-frequency high-precision GNSS positioning theory and methods are reseached in this paper, which mainly contains the following sections:
1. Simulation of GNSS multi-frequency observations
The errors of GPS observation are analysis and simulated with the error model, and GNSS satellite constellation are simulated based on the orbit parameters, then the GNSS observation are simulated based on the theory of GNSS positioning, the GNSS simulation software can output multi-system multi-frequency pseudo-range and carrier phase observations.
2. New method for carrier phase mixed pseudo-range combination—the least square method
The original method to resolve the coefficients of carrier phase mixed pseudo-range combination is very complicated and can only resolve 3 frequency combinations, so new method which based on least square method is proposed to resolve the coefficients, it is very easy to understand and can resolve 4 or more frequency combinations.
3. New method to detect cycle slip of three-frequency data—Three frequency TurboEdit method
Analysis the limitations of cycle slip detection and repair for dual frequency carrier phase data, then the Three frequency TurboEdit method to detect and repair the three-frequency carrier phase cycle slip is introduced, the real observation of the GPS three frequency data (15s interval) is processed, which can effectively detect and repair half-cycle slips.
4. GNSS ambiguity resolution methods is studied
1) A new search method for ambiguity search—K-Bootstrap Method
Spherical ambiguity search method is analyzed, and for high-dimensional case, the spherical ambiguity search method takes a long time, the paper proposes a new method for ambiguity resolution-K-Bootstrap method, in high dimension case, the new method can greatly reducing search time for ambiguity fixed.
2) Introduction of lattice theory
the Lattice theory was introduced to aid the carrier phase integer ambiguity resolution, multi-dimensional Gaussian integers decorrelation is under the LLL reduce law, and further analysis of the performance of LLL reduce, Gaussian integers decorrelation,inverse Cholesky integer decorrelation, and unified integer decorrelation for ambiguity resolution, the results show that:LLL reduce is not only less time consuming, and the Bootstrap can get a higher success rate; uniform integer decorrelation method get the most time consuming, but receive the highest success rate of Bootstrap; inverse Cholesky decorrelation is time-consuming, and with lower success rate of Bootstrap. In high-dimensional case, when the Bootstrap success rate is low, it is more time-consuming to search ambiguity, when the Bootstrap success rate is high, less time-consuming to search ambiguity.
3) A new method of sequential ambiguity resolution
A sequential method of ambiguity resolution is proposed, which first transform the ambiguity to new ambiguity combination in the ambiguity region, and then fix them in sequential model, it can reduce ambiguity resolution time while increasing the value of Ratio.
4) using Monte Carlo method to validate success rate of ambiguity
Introduce the success rate for ambiguity resolution, including rounding, Bootstrap, integer least squares method. the Monte Carlo method is used to verify the theoretical, the results show that, Bootstrap ambiguity success rate is lower but close to the integer least squares method.
5) using Monte Carlo method to validate Ratio value
This paper analyzes the principle of Ratio test, and using Monte Carlo methods to obtain the distribution of Ratio value in different dimensions, in high-dimensional case, using the experience value of 2 in Ratio would be too conservative, and on this basis, the ambiguity resolve with fixed-failure rate method is introduced.
5. Analyzed the performance of multi-frequency GNSS relative positioning
1) Analyzed the success rate of single epoch ambiguity resolution
The success rate of single-epoch ambiguity fixed is analyzed, the success rate of ambiguity fixed in the European region is similar, but in the Chinese region and the surrounding areas, the success rate of ambiguity resolution for COMPASS is much better than the other three systems; relative to a single system, multiple systems can improve the success rate of single-epoch ambiguity resolution.
2) Analyzed the multi-epoch ambiguity reolution for long baseline
The KALMAN filter is used to process three-frequency data simulated, the initialization time for ambiguity fixed is studied, the results showed that:compared with dual-frequency, the three-frequency can largely reduce the initialization time for ambiguity fixed, it's RATIO values is lager than dual-frequency, which make it easy to fixed ambiguity when ambiguity is right.
本文在此背景下,着重研究了GNSS多频精密定位模型及其模糊度解算方法,主要内容包含以下几个部分：
1. GNSS多频观测数据仿真
在深入分析了GNSS定位原理基础上,依据GNSS星座参数和卫星运动的开普勒定理,仿真了GPS/GLONASS/GALILEO/COMPASS四个卫星导航系统的星座,并由误差模型仿真了观测值误差,最后根据GNSS定位原理,编制仿真软件实现了四个GNSS系统的多频观测数据模拟,为论文的研究提供了实验数据。
2.多频载波相位混合伪距最优组合系数的求解
深入分析了载波相位混合伪距组合观测值的模型,针对原有的基于二阶导数求函数极值方法解算最优组合系数需要复杂的公式推导,且对组合的频率个数有要求,论文中提出了一种新的基于最小二乘求解最优组合系数方法。新的方法模型简单,且可以直接获得任意频率组合的最优组合系数。
3.三频周跳探测与修复的新方法——三频TurboEdit方法
深入分析了双频TuroEdit方法探测与修复周跳的方法,在此基础上,提出了三频TurboEdit方法。基于该方法处理实测的GPS三频数据,可有效的探测并修复大于1周(包含1周)的小周跳。
4.模糊度解算方法及其可靠性理论
1)提出了一种新的模糊度搜索方法——K-Bootstrap方法
系统介绍了球形模糊度搜索方法的理论基础,并针对高维情况下,球形模糊度搜索方法耗时较多的缺点,文中提出一种新的模糊度搜索方法——K-Bootstrap法。与MLAMBDA软件包中的球形搜索算法相比,新方法在损失较少模糊度解算的成功率情况下,极大地减少了模糊度的搜索时间。
2)引入了格理论以辅助整周模糊度解算
引入了格理论以辅助载波相位整周模糊度解算。讨论了LAMBDA方法中的多维高斯整数降相关法与LLL格基规约的关系,并进一步比较分析了LLL格基规约、多维高斯整数降相关、逆Cholesky整数降相关、统一整数降相关四种方法辅助模糊度解算的性能。结果表明：LLL格基规约不但耗时少,而且可以获得较高的Bootstrap成功率；统一整数降相关法消耗时间最多,但是获得的Bootstrap成功率最高；逆Cholesky整数降相关耗时较多,获得的Bootstrap成功率也较低。在高维情况下,虽然经格基规约后的模糊度方差协方差矩阵条件数较大,但是格基规约明显提高了模糊度的搜索效率,且可以很大程度上提高Bootstrap成功率,且当Bootstrap成功率较高时,球形搜索方法耗时也较少。
在此基础上提出一种混合降相关的方法,在保证模糊度降相关效率的同时,有效的提高Bootstrap成功率,减少球形搜索方法的耗时。
3)提出了一种新的序贯模糊度解算方法
针对在高维情况下,模糊度解算耗时较多的缺点,文中提出了一种降维的模糊度解算方法——序贯模糊度解算法。新方法在模糊度区域内对模糊度转换后,再对其分块序贯固定,不仅可减少模糊度解算时间,而且可以提高模糊度正确固定时的Ratio值,便于模糊度的检验。
4)采用Monte Carlo方法讨论了模糊度的成功率
深入讨论了模糊度固定成功率的问题,包括直接取整成功率,Bootstrap成功率,以及整数最小二乘成功率。针对Bootstrap成功率理论存在争议的问题,文中采用了Monte Carlo方法进行验证,结果表明：Bootstrap成功率低于但是接近于整数最小二乘成功率,可以作为其下边成功率。
5)提出了一种新的Bootstrap方法解算方法
深入研究了Bootstrap方法的解算模糊度的原理,针对在高维情况下,原有的直接基于Cholesky分解的Bootstrap解算方法,其模糊度解算成功率较低。文中提出了一种新的Bootstrap解算方法,新方法基于分块序贯Cholesky分解原理,可有效地提高Bootstrap方法解算模糊度的成功率。
6)采用Monte Carlo方法讨论了Ratio的经验取值
基于Monte Carlo方法,分析了不同维数下Ratio值的概率分布。结果表明：Ratio值与模糊度的维数、精度存在较大的相关性。当Bootstrap成功率一定时,模糊度维数越高,则Ratio值越小。最后指出在高维情况下,使用Ratio经验值检验模糊度将过于保守。在此基础上,分析了固定失败率的模糊度固定方法。
5.研究并分析了多频GNSS相对定位的性能
1)研究了GNSS不同基线长度条件下单历元模糊度固定的成功率
基于仿真的观测数据,分别研究了短基线与长基线条件下,GNSS单历元模糊度固定成功率。结果表明在短基线情况下,单系统双频与三频的单历元模糊度固定成功率都可以达到100%；在长基线情况下,GPS/GALILEO/COMPASS单系统模糊度固定成功率都较低。但在中国及周边地区,由于可视卫星数的增加,COMPASS系统模糊度固定成功率远优于GPS和GALILEO系统,三个系统组合可以显著提高模糊度解算的成功率。
2)研究了GNSS长基线多历元不同数据处理模式下模糊度固定的初始化时间
针对单系统长基线单历元模糊度固定成功率较低的问题,分析了长基线双频与三频多历元、不同数据处理模式下模糊度固定的初始化时间。比较了基于原始观测值的相对定位模型与基于无电离层组合观测值的相对定位模型的优缺点,仿真数据处理结果表明：如果忽略电离层过程变化的影响,两种模型获得的定位结果是一致的,但前者模糊度固定的初始化时间少于后者。
进一步分析了长基线条件下,双频与三频多历元模糊度固定的初始化时间；仿真数据处理结果表明：三频模糊度固定的初始化时间远少于双频需要的时间,且GALILEO系统模糊度固定的初始化时间少于GPS系统。
最后分析了不同模糊度解算方法对模糊度固定初始化时间的影响；数据处理结果表明：基于降维处理的序贯模糊度解算的方法可以有效的提高模糊度正确固定时的Ratio值,减少了模糊度固定的初始化时间；基于固定失败率的模糊度解算方法可以根据用户的需要获得Ratio域值,其模糊度的初始化时间取决于用户设置的失败率,失败率越小,其需要的初始化时间越长。
With the modernization of U.S. GPS, the establishment of European GALILEO system, the recovery of the Russian GLONASS system, and the implementation China COMPASSⅡ, four satellite navigation systems will provide 120 navigation satellites. multi-frequency multi-system combinations postioning not only can improve the navigation accuracy and reliability, but also can improve the success rate of fixing carrier phase integer ambiguity and reduce the initial time for ambiguity fixed. However, it is not easy to process so many observation data and resovel ambiguity in high dimension, which propose new problem in high-precision multi-frequency GNSS combined navigation and positioning.
The multi-frequency high-precision GNSS positioning theory and methods are reseached in this paper, which mainly contains the following sections:
1. Simulation of GNSS multi-frequency observations
The errors of GPS observation are analysis and simulated with the error model, and GNSS satellite constellation are simulated based on the orbit parameters, then the GNSS observation are simulated based on the theory of GNSS positioning, the GNSS simulation software can output multi-system multi-frequency pseudo-range and carrier phase observations.
2. New method for carrier phase mixed pseudo-range combination—the least square method
The original method to resolve the coefficients of carrier phase mixed pseudo-range combination is very complicated and can only resolve 3 frequency combinations, so new method which based on least square method is proposed to resolve the coefficients, it is very easy to understand and can resolve 4 or more frequency combinations.
3. New method to detect cycle slip of three-frequency data—Three frequency TurboEdit method
Analysis the limitations of cycle slip detection and repair for dual frequency carrier phase data, then the Three frequency TurboEdit method to detect and repair the three-frequency carrier phase cycle slip is introduced, the real observation of the GPS three frequency data (15s interval) is processed, which can effectively detect and repair half-cycle slips.
4. GNSS ambiguity resolution methods is studied
1) A new search method for ambiguity search—K-Bootstrap Method
Spherical ambiguity search method is analyzed, and for high-dimensional case, the spherical ambiguity search method takes a long time, the paper proposes a new method for ambiguity resolution-K-Bootstrap method, in high dimension case, the new method can greatly reducing search time for ambiguity fixed.
2) Introduction of lattice theory
the Lattice theory was introduced to aid the carrier phase integer ambiguity resolution, multi-dimensional Gaussian integers decorrelation is under the LLL reduce law, and further analysis of the performance of LLL reduce, Gaussian integers decorrelation,inverse Cholesky integer decorrelation, and unified integer decorrelation for ambiguity resolution, the results show that:LLL reduce is not only less time consuming, and the Bootstrap can get a higher success rate; uniform integer decorrelation method get the most time consuming, but receive the highest success rate of Bootstrap; inverse Cholesky decorrelation is time-consuming, and with lower success rate of Bootstrap. In high-dimensional case, when the Bootstrap success rate is low, it is more time-consuming to search ambiguity, when the Bootstrap success rate is high, less time-consuming to search ambiguity.
3) A new method of sequential ambiguity resolution
A sequential method of ambiguity resolution is proposed, which first transform the ambiguity to new ambiguity combination in the ambiguity region, and then fix them in sequential model, it can reduce ambiguity resolution time while increasing the value of Ratio.
4) using Monte Carlo method to validate success rate of ambiguity
Introduce the success rate for ambiguity resolution, including rounding, Bootstrap, integer least squares method. the Monte Carlo method is used to verify the theoretical, the results show that, Bootstrap ambiguity success rate is lower but close to the integer least squares method.
5) using Monte Carlo method to validate Ratio value
This paper analyzes the principle of Ratio test, and using Monte Carlo methods to obtain the distribution of Ratio value in different dimensions, in high-dimensional case, using the experience value of 2 in Ratio would be too conservative, and on this basis, the ambiguity resolve with fixed-failure rate method is introduced.
5. Analyzed the performance of multi-frequency GNSS relative positioning
1) Analyzed the success rate of single epoch ambiguity resolution
The success rate of single-epoch ambiguity fixed is analyzed, the success rate of ambiguity fixed in the European region is similar, but in the Chinese region and the surrounding areas, the success rate of ambiguity resolution for COMPASS is much better than the other three systems; relative to a single system, multiple systems can improve the success rate of single-epoch ambiguity resolution.
2) Analyzed the multi-epoch ambiguity reolution for long baseline
The KALMAN filter is used to process three-frequency data simulated, the initialization time for ambiguity fixed is studied, the results showed that:compared with dual-frequency, the three-frequency can largely reduce the initialization time for ambiguity fixed, it's RATIO values is lager than dual-frequency, which make it easy to fixed ambiguity when ambiguity is right.
引文
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