差分GPS/INS组合定位定姿及其在MMS中的应用
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摘要
随着科学技术的进步，传统的测绘科学正发展成为以GPS、RS(遥感)和GIS(地理信息系统)为代表的空间信息科学，同时数据获取与更新的制约问题日益明显，尤其在中国这样的发展中国家，这个问题尤为突出，传统测绘方式已经不能满足人们空间信息快速获取与更新的需要，测绘科技工作者必须寻求新的高效廉价的空间数据获取技术和方式。
在这种需求下，MMS(移动测图系统)应运而生，成为制图新技术的典型代表。在MMS中，摄影平台的定位定姿是整个系统的重要的组成部分之一，如何通过GPS、INS等传感器来直接计算摄影平台的位置姿态等空间信息，是当前的研究热点。这种直接计算方式，和传统的通过地面控制点间接计算方式相比，具有极大的优越性。它结合多个学科的理论，为摄影平台外方位元素的获取提供了全新的手段，必将给测绘行业带来一场新的技术革命，对此研究具有重要的学术价值和实际意义。
本文通过对GPS、SINS、DR的数据处理方法的深入研究，系统地讨论了通过GPS／INS／DR组合实现摄影平台高精度定位定姿理论与应用，提出了适合MMS系统的GPS／INS和GPS／DR的数据集成方案。论文的最突出贡献是首次从测量领域的角度系统地研究了GPS／INS等传感器的高精度组合理论并将之应用于MMS这一测绘新技术，并在其中实现了一系列的理论创新。论文的主要研究内容包括高精度GPS动态定位测速理论、差分GPS／INS组合理论、差分GPS／DR组合理论以及这些理论在MMS特别是陆地MMS中的应用实践，具体有：
1、以线性方程的形式推导了单点、单差和双差定位模型，说明了不同模型不同数据类型的处理方法和结果。得出对于单历元码定位而言，如果使用最小二乘估计方法，单差模型和双差模型的定位结果和精度相同的结论，说明了双差模型在卡尔曼滤波方法中，可以减少对接收机钟差的建模，数据处理比单差简便的优点。提出了在单差模型中接收机钟差和接收机相位偏差不可分离的理论，解释了GPS短时间高精度时间比对困难的原因。说明了载波相位双差定位中初始相位模糊度具有整数特性，为模糊度的解算提供了理论基础。
2、讨论了GPS测速方法，重点讨论了多普勒测速法，首次以线性方程的形式推导了多普勒单点、单差和双差测速方程。分析了GPS多普勒测速的主要误差源，讨论了差分测速的精度、效果和意义。由于静态应用无需测速，所以在GPS测速应用中，一般都是对于动态情况而言，因此难以像静态定位那样顾及时域信息，即不能使用多个历元的观测信息统一处理，文章首次指出此时如果不顾及接收机钟差变率的变化特性，即不在时域内对其建模，而是直接使用最小二乘进行处理，则多普勒测速单差模型和双差模型是等效的。同时GPS多普勒测速方程中的设计矩阵和随机模型与GPS差分定位中相同，因而具有类似的统计特性，即GPS多普勒测速与GPS定位一样，受着GPS卫星图形分布和观测噪声的影响。
3、对目前现有GPS模糊度动态解法(OTF)进行了系统的研究和总结，对分属于观测值域、坐标域、模糊度域的不同OTF方法进行了归纳，特别对LAMBDA方法进行了细致的研究，指出了LAMBDA的理论前提、技术核心和实际贡献。
4、在深入分析、研究和总结目前GPS模糊度动态解法的基础上，根据双频相位数据的内在关系和统计特性，提出了一种高效可靠的独立于其他算法的单历元解算GPS模糊度的新方法——双频数据相关法(Dual Frequency Correlation Method,DUFCOM)。DUFCOM属于观测值域的压缩方法，其压缩率为观测卫星数的指数函数，在观测7颗星的情况下，压缩率可以达到千分之一，同时具有较强的伪值剔除能力。DUFCOM可以使用一个历元的C／A码和双频相位数据以较高的成功率解算模糊度，较好地解决了GPS高
精度动态定位中多年来的一个难题，这个方法对于不能获取美国精码的包括中国用户在内的普通用户具有
重要意义。并对DUFcOM方法在GPS现代化后的使用效果进行了讨论，通过对模拟数据的测试分析，预
言在GPS现代化后的三频观测相位中，模糊度解算效果将更好。
5、介绍了INS的常用坐标系统，以矢量方程的形式推导了不同坐标系中的导航方程，针对MMS中
GPS超联INS集成的实际应用，分析了在地固系及当地水平坐标系导航计算的优缺点，详细地讨论了捷联
INS在地固系的导航算法.说明了基于效率、精度和开发简化的原因，在MMS的事后数据处理的测量中，
宜选择地固系作为捷联INS导航计算坐标系统。指出载体姿态角在当地水平坐标系到制图坐标系的转换必
须顾及子午线收敛角的影响。针对NIMS的事后数据处理的特点，对具体的导航数值计算方法进行了讨论，
并提出了适合在MMS中使用的载体姿态角提取公式.
6、在介绍离散系统和连续系统经典卡尔曼滤波的基础上，详细讨论了非线性系统的卡尔曼数据处理
方法。结合M扮正A的要求和最小二乘线性化的特点，提出了按前一步状态最优估计线性化的新方法，并
推导了相应的滤波方程。该方法使得最小二乘和卡尔曼滤波的线性观测方程趋于一致，便于数据处理，适
用于多模型(MMAE)自适应滤波方法，在空间状态变化不大的情况下，此方法的线性化精度和广义卡尔
曼滤波类似，在低速度的GPS动?
It's increasingly difficult for the data acquirement and update to meet the requirement, while the traditional surveying growing into the spatial information science represented by GPS, RS and GIS. As a new typical mapping technology, MMS (Mobile Mapping System) can resolve this issue efficiently.
In MMS, one of the most important models is the positioning and orientation of the photogrammetry platform, which focus on how to calculate directly the position and attitude information with GPS, INS, etc. sensors, and is also the research hot point currently. Compared with the traditional method needing ground control point, the direct reference method has great superiority, which combines the theories of various fields and can provide a complete new way for the acquirement of exterior elements of photogrammetry platform.
This dissertation is mainly focused on the data processing models for GPS, SINS and DR, as well as systematical discussion on the GPS/INS/DR integration theory and proposed the corresponding solutions regarding the implement of high precision positioning and orientation of photogrammetry platform in MMS. The most important contribution this dissertation presents is that the high precision GPS/INS/etc. sensors integration theory has been systematically introduced into the survey field for the first time and has been applied to a new survey technology -MMS, and during the research, a series of creative theories and methods has been proposed. The main work and innovations done by the author are presented as follows:
1. The author deduced firstly the single point, single differenced and double-differenced positioning models with the linear equations, explained the processing methods and results corresponding to various models and various data type. Point out that the results will be the same for the single epoch positioning in single differential model or double differential model using least square method. The conclusion shows that using double differential model in Kalman filter can reduce the process for receivers clock errors, as well as the advantage of more simple data processing comparing to single differential model. Proposed that the receivers clock errors and receivers carrier phase bias cannot be processed separately, explaining the reason of the difficult of high precision GPS time comparison during short time. Described the integer characteristic of the phase ambiguity in the double differential model, which is the theory fundamental base for ambiguity resolution in this paper.
2. Discussed the GPS velocity measurement method emphasized in the Doppler observation. For the first time deduced the Doppler single point, single differential and double differential velocity equations with linear equation. Analyzed the main error sources of GPS Doppler velocity measurement, and discussed the accuracy, efficient and value of the differentia] velocity measurement The author points out for the first time that the Doppler velocity measurement of single differential model using least square method will lead to the same result as that of double differential model. Because the design matrix and random model in the GPS Doppler velocity measurement equation are the same with those in GPS differential position, so they have similar
statistic characteristic, i.e. both GPS Doppler velocity measurement and GPS position are affected by the GPS satellites distribution and observation noise.
3. The author systematically studied and summarized the current on-the-fly (OTF) GPS ambiguity methods, cataloged the various OTF methods according to observation space, coordinates space and ambiguity space. Especially attention has been place on the LAMBDA method, whose theoretic precondition, core technology and practical contribution have been concluded in this paper.
4. On the basis of analyzing the current OTF method, according to the inner relationship and statistic characteristic of dual frequency phase observation, the author proposed a new method - Dual Frequency Correlation Method (DUFCOM), which is indep
在这种需求下，MMS(移动测图系统)应运而生，成为制图新技术的典型代表。在MMS中，摄影平台的定位定姿是整个系统的重要的组成部分之一，如何通过GPS、INS等传感器来直接计算摄影平台的位置姿态等空间信息，是当前的研究热点。这种直接计算方式，和传统的通过地面控制点间接计算方式相比，具有极大的优越性。它结合多个学科的理论，为摄影平台外方位元素的获取提供了全新的手段，必将给测绘行业带来一场新的技术革命，对此研究具有重要的学术价值和实际意义。
本文通过对GPS、SINS、DR的数据处理方法的深入研究，系统地讨论了通过GPS／INS／DR组合实现摄影平台高精度定位定姿理论与应用，提出了适合MMS系统的GPS／INS和GPS／DR的数据集成方案。论文的最突出贡献是首次从测量领域的角度系统地研究了GPS／INS等传感器的高精度组合理论并将之应用于MMS这一测绘新技术，并在其中实现了一系列的理论创新。论文的主要研究内容包括高精度GPS动态定位测速理论、差分GPS／INS组合理论、差分GPS／DR组合理论以及这些理论在MMS特别是陆地MMS中的应用实践，具体有：
1、以线性方程的形式推导了单点、单差和双差定位模型，说明了不同模型不同数据类型的处理方法和结果。得出对于单历元码定位而言，如果使用最小二乘估计方法，单差模型和双差模型的定位结果和精度相同的结论，说明了双差模型在卡尔曼滤波方法中，可以减少对接收机钟差的建模，数据处理比单差简便的优点。提出了在单差模型中接收机钟差和接收机相位偏差不可分离的理论，解释了GPS短时间高精度时间比对困难的原因。说明了载波相位双差定位中初始相位模糊度具有整数特性，为模糊度的解算提供了理论基础。
2、讨论了GPS测速方法，重点讨论了多普勒测速法，首次以线性方程的形式推导了多普勒单点、单差和双差测速方程。分析了GPS多普勒测速的主要误差源，讨论了差分测速的精度、效果和意义。由于静态应用无需测速，所以在GPS测速应用中，一般都是对于动态情况而言，因此难以像静态定位那样顾及时域信息，即不能使用多个历元的观测信息统一处理，文章首次指出此时如果不顾及接收机钟差变率的变化特性，即不在时域内对其建模，而是直接使用最小二乘进行处理，则多普勒测速单差模型和双差模型是等效的。同时GPS多普勒测速方程中的设计矩阵和随机模型与GPS差分定位中相同，因而具有类似的统计特性，即GPS多普勒测速与GPS定位一样，受着GPS卫星图形分布和观测噪声的影响。
3、对目前现有GPS模糊度动态解法(OTF)进行了系统的研究和总结，对分属于观测值域、坐标域、模糊度域的不同OTF方法进行了归纳，特别对LAMBDA方法进行了细致的研究，指出了LAMBDA的理论前提、技术核心和实际贡献。
4、在深入分析、研究和总结目前GPS模糊度动态解法的基础上，根据双频相位数据的内在关系和统计特性，提出了一种高效可靠的独立于其他算法的单历元解算GPS模糊度的新方法——双频数据相关法(Dual Frequency Correlation Method,DUFCOM)。DUFCOM属于观测值域的压缩方法，其压缩率为观测卫星数的指数函数，在观测7颗星的情况下，压缩率可以达到千分之一，同时具有较强的伪值剔除能力。DUFCOM可以使用一个历元的C／A码和双频相位数据以较高的成功率解算模糊度，较好地解决了GPS高
精度动态定位中多年来的一个难题，这个方法对于不能获取美国精码的包括中国用户在内的普通用户具有
重要意义。并对DUFcOM方法在GPS现代化后的使用效果进行了讨论，通过对模拟数据的测试分析，预
言在GPS现代化后的三频观测相位中，模糊度解算效果将更好。
5、介绍了INS的常用坐标系统，以矢量方程的形式推导了不同坐标系中的导航方程，针对MMS中
GPS超联INS集成的实际应用，分析了在地固系及当地水平坐标系导航计算的优缺点，详细地讨论了捷联
INS在地固系的导航算法.说明了基于效率、精度和开发简化的原因，在MMS的事后数据处理的测量中，
宜选择地固系作为捷联INS导航计算坐标系统。指出载体姿态角在当地水平坐标系到制图坐标系的转换必
须顾及子午线收敛角的影响。针对NIMS的事后数据处理的特点，对具体的导航数值计算方法进行了讨论，
并提出了适合在MMS中使用的载体姿态角提取公式.
6、在介绍离散系统和连续系统经典卡尔曼滤波的基础上，详细讨论了非线性系统的卡尔曼数据处理
方法。结合M扮正A的要求和最小二乘线性化的特点，提出了按前一步状态最优估计线性化的新方法，并
推导了相应的滤波方程。该方法使得最小二乘和卡尔曼滤波的线性观测方程趋于一致，便于数据处理，适
用于多模型(MMAE)自适应滤波方法，在空间状态变化不大的情况下，此方法的线性化精度和广义卡尔
曼滤波类似，在低速度的GPS动?
It's increasingly difficult for the data acquirement and update to meet the requirement, while the traditional surveying growing into the spatial information science represented by GPS, RS and GIS. As a new typical mapping technology, MMS (Mobile Mapping System) can resolve this issue efficiently.
In MMS, one of the most important models is the positioning and orientation of the photogrammetry platform, which focus on how to calculate directly the position and attitude information with GPS, INS, etc. sensors, and is also the research hot point currently. Compared with the traditional method needing ground control point, the direct reference method has great superiority, which combines the theories of various fields and can provide a complete new way for the acquirement of exterior elements of photogrammetry platform.
This dissertation is mainly focused on the data processing models for GPS, SINS and DR, as well as systematical discussion on the GPS/INS/DR integration theory and proposed the corresponding solutions regarding the implement of high precision positioning and orientation of photogrammetry platform in MMS. The most important contribution this dissertation presents is that the high precision GPS/INS/etc. sensors integration theory has been systematically introduced into the survey field for the first time and has been applied to a new survey technology -MMS, and during the research, a series of creative theories and methods has been proposed. The main work and innovations done by the author are presented as follows:
1. The author deduced firstly the single point, single differenced and double-differenced positioning models with the linear equations, explained the processing methods and results corresponding to various models and various data type. Point out that the results will be the same for the single epoch positioning in single differential model or double differential model using least square method. The conclusion shows that using double differential model in Kalman filter can reduce the process for receivers clock errors, as well as the advantage of more simple data processing comparing to single differential model. Proposed that the receivers clock errors and receivers carrier phase bias cannot be processed separately, explaining the reason of the difficult of high precision GPS time comparison during short time. Described the integer characteristic of the phase ambiguity in the double differential model, which is the theory fundamental base for ambiguity resolution in this paper.
2. Discussed the GPS velocity measurement method emphasized in the Doppler observation. For the first time deduced the Doppler single point, single differential and double differential velocity equations with linear equation. Analyzed the main error sources of GPS Doppler velocity measurement, and discussed the accuracy, efficient and value of the differentia] velocity measurement The author points out for the first time that the Doppler velocity measurement of single differential model using least square method will lead to the same result as that of double differential model. Because the design matrix and random model in the GPS Doppler velocity measurement equation are the same with those in GPS differential position, so they have similar
statistic characteristic, i.e. both GPS Doppler velocity measurement and GPS position are affected by the GPS satellites distribution and observation noise.
3. The author systematically studied and summarized the current on-the-fly (OTF) GPS ambiguity methods, cataloged the various OTF methods according to observation space, coordinates space and ambiguity space. Especially attention has been place on the LAMBDA method, whose theoretic precondition, core technology and practical contribution have been concluded in this paper.
4. On the basis of analyzing the current OTF method, according to the inner relationship and statistic characteristic of dual frequency phase observation, the author proposed a new method - Dual Frequency Correlation Method (DUFCOM), which is indep
引文
1．陈小明(1997)．高精度GPS动态定位的理论和实践．[博士学位论文]武汉测绘科技大学，1997．
2．耿延睿(2001)．GPS／SINS组合系统算法与工程设计研究．[博士学位论文]北京航空航天大学，2001．
3．董绪荣，张守信，华仲春(1998)．GPS／INS组合导航定位及其应用．长沙：国防科技大学出版社，1998．
4．段志勇(2000)．GPS航姿系统及多天线GPS／惯性组合技术研究．[博士学位论文]南京航空航天大学，2000．
5．房建成，万德钧(1996)．GPS／SINS组合导航系统的动基座快速初始对准方法．中国惯性技术学报，1996，4(3)，pp．4-10．
6．房建成．申功勋(1998a)．车载DR系统自适应扩展卡尔曼滤波模型的建立及仿真研究．中国惯性技术学报，1998，6(3)，pp．24-28．
7．房建成，申功勋，万德钧(1998b)．一种自适应联合卡尔曼滤波器及其在车载GPS／DR组合导航系统中的应用研究．中国惯性技术学报，1998，6(4)，pp．1-6．
8．房建成，周锐，祝世平(1999a)．捷联惯导系统动基座对准的可观测性分析．北京航空航天大学学报，1999，25(16)，pp．714-719．
9．房建成，李学恩，申功勋，房建果，王庆，万德钧 (1999b)．市区车辆GPS／DR组合导航系统的研究．中国公路学报，1999，12(1)，pp．84-89．
10．冯绍军(1999)．低成本IMU／GPS组合导航系统研究．[博士学位论文]南京航天航空大学，1999．
11．高星伟(2002)．GPS／GLONASS网络RTK的算法研究与程序实现．[博士学位论文]武汉大学，2002．
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17．李德仁(1988)．误差处理与可靠性理论．北京：测绘出版社，1988．
18．李德仁(1996)．GPS用于摄影测量与遥感．北京：测绘出版社，1996．
19．刘基余，李征航，王跃虎，桑吉章(1993)．全球定位系统及其应用．北京：测绘出版社，1992．
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