基于GPS/GLONASS集成的CORS网络大气建模与RTK算法实现
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摘要
随着GLONASS卫星星座的逐步恢复,GLONASS卫星系统有望在2010年年底之前再次实现满星座运行状态,同时第一颗加载了码分多址(CDMA)信号的GLONASS-K型卫星也有望在2010年12月发射。众多证据显示,GLONASS系统将再次成为能够与GPS系统相抗衡的全球卫星定位系统。而对于民用的终端用户而言,如果能够充分的利用GPS和GLONASS卫星,可视卫星数量的增加,将意味着其导航定位结果的准确性和可靠性的增强。
本文以GPS/GLONASS集成的网络RTK算法实现为主线,系统研究网络RTK在实现过程中的理论和技术,具体内容有：
1. GPS/GLONASS集成双差方程的建立
本文GPS/GLONASS集成的函数模型和随机模型是建立在最小二乘模型的基础上的。首先研究了GPS/GLONAS系统的观测值,双频信号的线性组合和时空基准的统一方法。然后对GNSS测量中的各误差项进行逐一分析,针对各误差站间差分后的特性与模型改正后的残差量级,分别用四种方法来进行分类处理,分别为：不做模型改正并将残差并入随机模型中,模型改正后残差并入随机模型中,利用先验信息预处理和作为待估参数进行估计。同时还讨论了GPS/GLONASS实时系统中,参考卫星的选取方法。最后介绍基线解算的三种基本模型,几何无关模型,几何固定模型和几何相关模型,其中几何无关模型主要用于长基线宽巷整周模糊度解算,几何固定模型适用以CORS站间的基线解算,几何相关模型是RTK相对定位最常用的模型。
2. GPS/GLONASS伪距观测值的预处理
在GNSS数据处理中,伪距观测值的精度往往是决定整周模糊度能否正确解算的关键。本文首先对GNSS观测值的预处理方法进行研究,其中主要包括利用恒星日滤波对伪距多路径进行降噪方法和考虑电离层变化的载波相位平滑伪距方法。实际测试数据表明,通过载波相位平滑和恒星日滤波处理,可以将伪距观测值的精度提高到厘米级,从而保证宽巷整周模糊度快速固定。
3. GPS/GLONASS集成的整周模糊度解算
对于GPS/GLONASS集成的双差整周模糊度解算,本文将Leick等人1995年提出的GLONASS数据处理方法应用到网络RTK的CORS基线解算中。首先用伪距估计参考卫星的站间单差整周模糊度,可以证明用伪距求得的参考卫星的站间单差整周模糊度的误差不会影响最终GLONASS双差整周模糊度的固定。在GPS/GLONASS集成的整周模糊度解算中,依照传统的“三步法”实现先固定宽巷,后固定L1,L2整周模糊度的解算,本文推导了用卡尔曼滤波方法实现上述“三步法”整周模糊度解算的方法,最后对CORS基线的周跳探测与修复方法进行了分析。
4.大气延迟的网络插值模型的分析比较
在网络RTK的插值算法比较过程中,本文研究比较了几种常用的网络插值方法,其中包括基于基线长度的线性插值DIM(Distance-Based Linear Interpolation Model)模型,基于平面二维坐标线性组合的LCM(Linear Combination Model)模型,基于平面二维坐标线性插值的LIM(Linear Interpolation Model)模型,基于低阶地表LSM(Low-Order Surface Model)模型和基于最小二乘配置的LSC(Least Squares Collocation)模型和Kriging模型。基于实测数据的分析比较表明,尽管各种插值模型的插值精度量级相当,但就电离层的插值而言,Kriging模型的精度相对较好,而考虑了高程因素LSM3模型在对流层插值效果上相对较好。
5.VRS虚拟观测值的生成算法
为了保证VRS虚拟观测值的精度,本文不仅提出进一步对各双差大气延迟项进行分解,构建单差大气延迟项,同时在轨道和伪距多路径延迟上做进一步处理。从而保证VRS虚拟观测值的精度。
6. GPS/GLONASS集成的RTK实现
与GPS/GLONASS集成的CORS基线解算类似,在GPS/GLONASS集成的RTK需要首先借助伪距求得GLONASS参考卫星的站间单差整周模糊度,然后才能保证GLONASS观测值双差整周模糊度的整数特性。而在实现过程中,RTK的观测值与待定坐标参数之间的关系为非线性模型,因此本文使用扩展卡尔曼滤波方法实现RTK的动态基线解算。
As the recovery of the GLONASS constellation, it's possible for GLONASS system to get Full Operational Capability (FOC) before the end of 2010, and also the first GLONASS-K satellite which can broadcast CDMA signal will be launched on December 2010. All these evidences show that the GLONASS system will come back to compete with GPS system again. For the civilian users, it could be good news as there will be more visible satellites, which mean the improvement of the precision and reliability for the positioning.
This paper mainly focused on the implementation of GPS/GLONASS integrated Network RTK system and the contribution of this work can be list as following:
1. The Construction of GPS/GLONASS Integrated Double Difference Equations
In this paper, we use the least square method to construct the function model and stochastic model. The paper firstly has a brief description for the GPS/GLONASS integrated measurements, the linear combination of the dual frequencies and also the datum difference between the two systems. The paper also analysis the physical influences of the GNSS measurements, and use four different method to deal with the different physical influences. For the double difference equation construction, we also discuss the method for the reference satellite selection. Finally, three different models including geometry free model, geometry fixed model and geometry based model are introduced for GNSS resolution models, and all of these three models will be use in the following implementation of the Network-RTK system.
2. Data Pre-processing for GPS/GLONASS Pseudo-range Measurements
For GNSS data processing, the quality for the pseudo-range is very important for the carrier phase ambiguity resolutions. In this paper, the data pre-processing including the sidereal day filter to reduce the pseudo-range multi-path effect and also the carrier phase smoothing pseudo-range. The test data shows that with the sidereal day filter, the precision for the pseudo-range can be improved to several centimeters level, and this can faster the wide-lane ambiguity resolution.
3. GPS/GLONASS Integrated Ambiguity Resolution
For the GPS/GLONASS integrated ambiguity resolution, we use the method Leick proposed in 1995 (Leick 1995):firstly, the reference satellite's single difference ambiguities are estimate with the pseudo-range and carrier-phase measurements. It can be proved that, the precision of the estimated single different ambiguities will not influence the integer property of the double difference ambiguities. After the GLONASS reference satellite single difference ambiguities are fixed to a approximate value, the traditional "three step" (bootstrap) method are implemented with Kalman filter. And finally, the cycle-slip detection and recovery for CORS baseline are discussed.
4. The Comparison of the Network Interpolation Method for Atmosphere Delays
In this paper, we compared several interpolation method which are commonly used for the Network-RTK, including DIM(Distance-Based Linear Interpolation Model) model, LCM(Linear Combination Model) model, LIM (Linear Interpolation Model) model, LSM (Low-Order Surface Model) model, LSC(Least Squares Collocation) model and Kriging model. The tested data show that, although most interpolation method are quite similar, for the SYDNET data, the Kriging method's perform best for ionospheric delay interpolation and LSM3 model performs best for tropospheric delay interpolation.
5. The Generation of the VRS Measurements
To guarantee the precision of the VRS observation, the paper proposes to decompose the double difference atmospheric delay to single difference delay between two stations. In the meantime, the difference between precise orbit and broadcast orbit are added to the VRS observation. And also the sidereal day filter is proposed to be added to the VRS observation pseudo-range measurements.
6. The Implementation of GPS/GLONASS Integrated RTK
The same as CORS baseline resolution, the GPS/GLONASS integrated RTK need firstly solved the GLONASS reference satellite's single difference ambiguities, and then the double difference ambiguity can be fixed to be integer for the GLONASS satellites. As the relationship between the measurements and the rover station's coordinate is not linearism, the extended Kalman filter is proposed for the implementation work of the GPS/GLONASS integrated RTK algorithm.
本文以GPS/GLONASS集成的网络RTK算法实现为主线,系统研究网络RTK在实现过程中的理论和技术,具体内容有：
1. GPS/GLONASS集成双差方程的建立
本文GPS/GLONASS集成的函数模型和随机模型是建立在最小二乘模型的基础上的。首先研究了GPS/GLONAS系统的观测值,双频信号的线性组合和时空基准的统一方法。然后对GNSS测量中的各误差项进行逐一分析,针对各误差站间差分后的特性与模型改正后的残差量级,分别用四种方法来进行分类处理,分别为：不做模型改正并将残差并入随机模型中,模型改正后残差并入随机模型中,利用先验信息预处理和作为待估参数进行估计。同时还讨论了GPS/GLONASS实时系统中,参考卫星的选取方法。最后介绍基线解算的三种基本模型,几何无关模型,几何固定模型和几何相关模型,其中几何无关模型主要用于长基线宽巷整周模糊度解算,几何固定模型适用以CORS站间的基线解算,几何相关模型是RTK相对定位最常用的模型。
2. GPS/GLONASS伪距观测值的预处理
在GNSS数据处理中,伪距观测值的精度往往是决定整周模糊度能否正确解算的关键。本文首先对GNSS观测值的预处理方法进行研究,其中主要包括利用恒星日滤波对伪距多路径进行降噪方法和考虑电离层变化的载波相位平滑伪距方法。实际测试数据表明,通过载波相位平滑和恒星日滤波处理,可以将伪距观测值的精度提高到厘米级,从而保证宽巷整周模糊度快速固定。
3. GPS/GLONASS集成的整周模糊度解算
对于GPS/GLONASS集成的双差整周模糊度解算,本文将Leick等人1995年提出的GLONASS数据处理方法应用到网络RTK的CORS基线解算中。首先用伪距估计参考卫星的站间单差整周模糊度,可以证明用伪距求得的参考卫星的站间单差整周模糊度的误差不会影响最终GLONASS双差整周模糊度的固定。在GPS/GLONASS集成的整周模糊度解算中,依照传统的“三步法”实现先固定宽巷,后固定L1,L2整周模糊度的解算,本文推导了用卡尔曼滤波方法实现上述“三步法”整周模糊度解算的方法,最后对CORS基线的周跳探测与修复方法进行了分析。
4.大气延迟的网络插值模型的分析比较
在网络RTK的插值算法比较过程中,本文研究比较了几种常用的网络插值方法,其中包括基于基线长度的线性插值DIM(Distance-Based Linear Interpolation Model)模型,基于平面二维坐标线性组合的LCM(Linear Combination Model)模型,基于平面二维坐标线性插值的LIM(Linear Interpolation Model)模型,基于低阶地表LSM(Low-Order Surface Model)模型和基于最小二乘配置的LSC(Least Squares Collocation)模型和Kriging模型。基于实测数据的分析比较表明,尽管各种插值模型的插值精度量级相当,但就电离层的插值而言,Kriging模型的精度相对较好,而考虑了高程因素LSM3模型在对流层插值效果上相对较好。
5.VRS虚拟观测值的生成算法
为了保证VRS虚拟观测值的精度,本文不仅提出进一步对各双差大气延迟项进行分解,构建单差大气延迟项,同时在轨道和伪距多路径延迟上做进一步处理。从而保证VRS虚拟观测值的精度。
6. GPS/GLONASS集成的RTK实现
与GPS/GLONASS集成的CORS基线解算类似,在GPS/GLONASS集成的RTK需要首先借助伪距求得GLONASS参考卫星的站间单差整周模糊度,然后才能保证GLONASS观测值双差整周模糊度的整数特性。而在实现过程中,RTK的观测值与待定坐标参数之间的关系为非线性模型,因此本文使用扩展卡尔曼滤波方法实现RTK的动态基线解算。
As the recovery of the GLONASS constellation, it's possible for GLONASS system to get Full Operational Capability (FOC) before the end of 2010, and also the first GLONASS-K satellite which can broadcast CDMA signal will be launched on December 2010. All these evidences show that the GLONASS system will come back to compete with GPS system again. For the civilian users, it could be good news as there will be more visible satellites, which mean the improvement of the precision and reliability for the positioning.
This paper mainly focused on the implementation of GPS/GLONASS integrated Network RTK system and the contribution of this work can be list as following:
1. The Construction of GPS/GLONASS Integrated Double Difference Equations
In this paper, we use the least square method to construct the function model and stochastic model. The paper firstly has a brief description for the GPS/GLONASS integrated measurements, the linear combination of the dual frequencies and also the datum difference between the two systems. The paper also analysis the physical influences of the GNSS measurements, and use four different method to deal with the different physical influences. For the double difference equation construction, we also discuss the method for the reference satellite selection. Finally, three different models including geometry free model, geometry fixed model and geometry based model are introduced for GNSS resolution models, and all of these three models will be use in the following implementation of the Network-RTK system.
2. Data Pre-processing for GPS/GLONASS Pseudo-range Measurements
For GNSS data processing, the quality for the pseudo-range is very important for the carrier phase ambiguity resolutions. In this paper, the data pre-processing including the sidereal day filter to reduce the pseudo-range multi-path effect and also the carrier phase smoothing pseudo-range. The test data shows that with the sidereal day filter, the precision for the pseudo-range can be improved to several centimeters level, and this can faster the wide-lane ambiguity resolution.
3. GPS/GLONASS Integrated Ambiguity Resolution
For the GPS/GLONASS integrated ambiguity resolution, we use the method Leick proposed in 1995 (Leick 1995):firstly, the reference satellite's single difference ambiguities are estimate with the pseudo-range and carrier-phase measurements. It can be proved that, the precision of the estimated single different ambiguities will not influence the integer property of the double difference ambiguities. After the GLONASS reference satellite single difference ambiguities are fixed to a approximate value, the traditional "three step" (bootstrap) method are implemented with Kalman filter. And finally, the cycle-slip detection and recovery for CORS baseline are discussed.
4. The Comparison of the Network Interpolation Method for Atmosphere Delays
In this paper, we compared several interpolation method which are commonly used for the Network-RTK, including DIM(Distance-Based Linear Interpolation Model) model, LCM(Linear Combination Model) model, LIM (Linear Interpolation Model) model, LSM (Low-Order Surface Model) model, LSC(Least Squares Collocation) model and Kriging model. The tested data show that, although most interpolation method are quite similar, for the SYDNET data, the Kriging method's perform best for ionospheric delay interpolation and LSM3 model performs best for tropospheric delay interpolation.
5. The Generation of the VRS Measurements
To guarantee the precision of the VRS observation, the paper proposes to decompose the double difference atmospheric delay to single difference delay between two stations. In the meantime, the difference between precise orbit and broadcast orbit are added to the VRS observation. And also the sidereal day filter is proposed to be added to the VRS observation pseudo-range measurements.
6. The Implementation of GPS/GLONASS Integrated RTK
The same as CORS baseline resolution, the GPS/GLONASS integrated RTK need firstly solved the GLONASS reference satellite's single difference ambiguities, and then the double difference ambiguity can be fixed to be integer for the GLONASS satellites. As the relationship between the measurements and the rover station's coordinate is not linearism, the extended Kalman filter is proposed for the implementation work of the GPS/GLONASS integrated RTK algorithm.
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