GPS高程拟合及其在交通工程中的应用研究
|
摘要
长期以来,解决高程测量的主要方法是水准测量,其优点是精度较高,缺点是劳动强度大,成本高、效率低,尤其是对于测区大、线路长、沿线地形复杂多样的交通工程。近来年,GPS以其提供全天候、全球性、高精度、高速度、高效益的实时导航定位服务等优点被广泛应用于各个领域。
然而令人遗憾的是GPS在高程定位精度方面还不尽人意,由于似大地水准面是一个不规则的曲面,它无法用一个精准的曲面来模拟,这就使得GPS只能提供给我们高精度的大地高,而不是我们工程中需要的正常高。因此如何有效利用GPS测量的高程信息把大地高转换成正常高,直接为测绘生产服务,实现GPS观测时能同时获得实用的三维坐标,是一个非常实际而又有意义的课题。
目前针对面状测区利用GPS转换高程拟合方法把GPS高程信息转换成工程项目需要的正常高这种方法比较常见,技术也较为成熟。而针对长达几十公里甚至几百公里且穿越崇山峻岭的交通工程,如何有效利用大量的GPS高程信息使其成为工程项目需要的正常高,是测量工作者非常关心的问题,也正是本文所研究的问题。
本论文介绍了大地高、正常高和正高等高程系统的概念及其相互关系,阐述了GPS测高的相关理论以及GPS水准(GPS高程拟合)的原理,并将GPS高程拟合模型分为函数模型、统计模型、组合模型、重力模型四类,详细阐述了各种模型的拟合方法,并对GPS高程拟合的可行性和各种模型的适用性进行了深入分析,给出了GPS水准拟合精度的评定方法和指标。结合杭州湾跨海大桥工程实例,用Matlab语言编程实现不同的GPS水准拟合方案,对结果进行综合比较、分析和研究,给出了不同拟合模型的精度评价。
本文还着重讨论了顾及地球重力场模型的GPS高程拟合方法,从理论上讲,实现GPS大地高向正常高转换的最好方法是综合利用GPS测量数据和地球重力场模型,但对一般工程单位而一言,不具备获得地球重力场模型的能力。文中还结合某高速公路工程数据,利用“移去-恢复”法进行高程转换,采用不同拟合模型与直接拟合结果进行综合比较和分析研究,给出了不同拟合模型的精度评价,并提出了具体的结论和建议。
For a long time,the standard measurement to solve the Height Survey is leveling.Though it is precise,it has some shortcomings,such as high labor-intensity,high cost and low efficiency,especially for the traffic engineering which locate in a large measurement area with long range and complicated terrain,In recent years,the GPS,by virtue of such advantages as all-weather service,global observation,high-precision,high-efficiency, low-cost,timely navigation and positioning services,has been widely used in various areas.
However,it is regrettable that the positioning accuracy of GPS in elevation is not satisfactory.For example,as the geoid is not a regular surface,the GPS can not find a precise model to simulate it.We could only get the high-precise altitude,which is not essential for our project.It is practical and meaningful subject for us to turn the geodetic height,which we obtain from the GPS,into normal height,make the latter directly serve the mapping and get three-dimensional coordinates through the GPS observation.
At present,in the plane measurement area,it is common to use the GPS conversion elevation fitting method to turn GPS height information into a suitable one to the project,for its technology is relatively mature.But when we face the large traffic engineering which goes a few dozen kilometers or even hundreds of kilometers across the mountains,it is a very concerned issue that how tO get the normal height by using quantitative GPS height information.
This essay mainly introduces the concepts,mutual relationships of geodetic height、normal height and orthometrie height elevation systems,narrates related theories of the GPS height fitting and the principles of GPS standard(GPS elevation fitting).In addition,GPS elevation model,which has been divided into the function model,the statistical model,the combination model and gravity model,elaborates the fitting methods of various models, deeply analyzes the feasibility of GPS elevation fitting model,applicability of various models presenting the evaluation method and indicators of accuracy of GPS standard fitting. With the Hangzhou Bay Bridge Project and different fitting methods of GPS standard using Matlab programming language,the results have been comprehensively compared,analyzed, researched.The evaluation methods of accuracy of various fitting models have also been presented.
Besides,this essay particularly describes the GPS height fitting method,in which the Earth's gravity have always been taken into consideration.The best way to get GPS land height from the conversion of the normal height is to utilize GPS measurements and Earth's gravity field model comprehensively in theory.But for the ordinary project department,it does not have access to Earth's gravity field model.The author illustrates the data of one highway engineering and makes the elevation conversation with the "remove-restore" method in the essay.What's more,he compares and analyzes those in direct fitting results and different fitting models comprehensively.At last,the accuracy of evaluation of different fitting models have been given and specific conclusions and recommendations have been made.
然而令人遗憾的是GPS在高程定位精度方面还不尽人意,由于似大地水准面是一个不规则的曲面,它无法用一个精准的曲面来模拟,这就使得GPS只能提供给我们高精度的大地高,而不是我们工程中需要的正常高。因此如何有效利用GPS测量的高程信息把大地高转换成正常高,直接为测绘生产服务,实现GPS观测时能同时获得实用的三维坐标,是一个非常实际而又有意义的课题。
目前针对面状测区利用GPS转换高程拟合方法把GPS高程信息转换成工程项目需要的正常高这种方法比较常见,技术也较为成熟。而针对长达几十公里甚至几百公里且穿越崇山峻岭的交通工程,如何有效利用大量的GPS高程信息使其成为工程项目需要的正常高,是测量工作者非常关心的问题,也正是本文所研究的问题。
本论文介绍了大地高、正常高和正高等高程系统的概念及其相互关系,阐述了GPS测高的相关理论以及GPS水准(GPS高程拟合)的原理,并将GPS高程拟合模型分为函数模型、统计模型、组合模型、重力模型四类,详细阐述了各种模型的拟合方法,并对GPS高程拟合的可行性和各种模型的适用性进行了深入分析,给出了GPS水准拟合精度的评定方法和指标。结合杭州湾跨海大桥工程实例,用Matlab语言编程实现不同的GPS水准拟合方案,对结果进行综合比较、分析和研究,给出了不同拟合模型的精度评价。
本文还着重讨论了顾及地球重力场模型的GPS高程拟合方法,从理论上讲,实现GPS大地高向正常高转换的最好方法是综合利用GPS测量数据和地球重力场模型,但对一般工程单位而一言,不具备获得地球重力场模型的能力。文中还结合某高速公路工程数据,利用“移去-恢复”法进行高程转换,采用不同拟合模型与直接拟合结果进行综合比较和分析研究,给出了不同拟合模型的精度评价,并提出了具体的结论和建议。
For a long time,the standard measurement to solve the Height Survey is leveling.Though it is precise,it has some shortcomings,such as high labor-intensity,high cost and low efficiency,especially for the traffic engineering which locate in a large measurement area with long range and complicated terrain,In recent years,the GPS,by virtue of such advantages as all-weather service,global observation,high-precision,high-efficiency, low-cost,timely navigation and positioning services,has been widely used in various areas.
However,it is regrettable that the positioning accuracy of GPS in elevation is not satisfactory.For example,as the geoid is not a regular surface,the GPS can not find a precise model to simulate it.We could only get the high-precise altitude,which is not essential for our project.It is practical and meaningful subject for us to turn the geodetic height,which we obtain from the GPS,into normal height,make the latter directly serve the mapping and get three-dimensional coordinates through the GPS observation.
At present,in the plane measurement area,it is common to use the GPS conversion elevation fitting method to turn GPS height information into a suitable one to the project,for its technology is relatively mature.But when we face the large traffic engineering which goes a few dozen kilometers or even hundreds of kilometers across the mountains,it is a very concerned issue that how tO get the normal height by using quantitative GPS height information.
This essay mainly introduces the concepts,mutual relationships of geodetic height、normal height and orthometrie height elevation systems,narrates related theories of the GPS height fitting and the principles of GPS standard(GPS elevation fitting).In addition,GPS elevation model,which has been divided into the function model,the statistical model,the combination model and gravity model,elaborates the fitting methods of various models, deeply analyzes the feasibility of GPS elevation fitting model,applicability of various models presenting the evaluation method and indicators of accuracy of GPS standard fitting. With the Hangzhou Bay Bridge Project and different fitting methods of GPS standard using Matlab programming language,the results have been comprehensively compared,analyzed, researched.The evaluation methods of accuracy of various fitting models have also been presented.
Besides,this essay particularly describes the GPS height fitting method,in which the Earth's gravity have always been taken into consideration.The best way to get GPS land height from the conversion of the normal height is to utilize GPS measurements and Earth's gravity field model comprehensively in theory.But for the ordinary project department,it does not have access to Earth's gravity field model.The author illustrates the data of one highway engineering and makes the elevation conversation with the "remove-restore" method in the essay.What's more,he compares and analyzes those in direct fitting results and different fitting models comprehensively.At last,the accuracy of evaluation of different fitting models have been given and specific conclusions and recommendations have been made.
引文
[1]张勤,李家权.GPS测量原理及应用[M].北京:科学出版社,2005:212-219,220-266
[2]孔祥元,郭际明,刘宗泉.大地测量学基础[M].武汉:武汉大学出版社,2001:1-2
[3]宫雨声.GPS水准模型及其应用研究[D].阜新:辽宁工程技术大学,2006:2-3
[4]贾翔.GPS水准拟合模型的误差分析与研究[D].昆明:昆明理工大学,2007:2-3
[5]Featherstone W.E.Absolute and relative testing ofgravimetrie geoid Models using Global Positioning System and orthometrie height data[J].Computers &Geoseienees,2001(27)
[6]熊伟,宁镇亚.美国国家大地测量局的十年规划[N].中国测绘报,2008-7-22(3)
[7]马新莹.局部大地水准面精化中几个问题的探讨[D].武汉:武汉大学,2005:3-4
[8]李冲.基于CQC2000的区域似大地水准面精化理论与应用研究[D].西安:长安大学,2006
[9]李建成.我国现代高程测定关键技术若干问题的研究及进展[J].武汉大学学报(信息科学版),2001,32(11):984-985
[10]张小红,程世来,许晓东.基于kriging统计的GPS高程拟合方法研究[J].大地测量与地球动力学,2007,27(2):47
[11]曹月玲,王解先.利用球冠谐分析拟合GPS水准高程[J].武汉大学学报(信息科学版),2008,33(7):740-743
[12]周世健,鲁铁定.有限元法拟合GPS水准高程分析[J].江西科学,2007,25(5):248
[13]赵超英,刘雷.GPS水准拟合优化法探讨[J].工程勘察,2006(2):64
[14]刘长建,吴洪举,张俊.GPS水准拟合方法的比较与软件编制[J].信息工程大学学报,2006,7(1):85-87
[15]刘珍贵.关于两种GPS高程拟合改进模型的探讨[J].建材与装饰,2007,(9):278-279
[16]冯光财,陈正阳.一种GPS高程拟合计算的新方法[J].矿山测量,2005(4):6-8
[17]焦明连.一种利用小波变换和Kriging估计转换GPS高程的方法[J].工程勘察,2007(11):50
[18]李胜.GPS高程异常拟合研究[D].大连:大连理工大学,2006:29-30
[19]陶本藻.GPS测高原理及其算法[J].地矿测绘,1998(1)
[20]胡伍生,高成发.GPS测量原理及应用[M].北京:人民交通出版社,2002:161-164
[21]高智广,刘艳坤.GPS测高的限制性与可行性研究[J].煤炭技术,2003,22(6):107-108
[22]许跃民.GPS水准在线路工程高程测量中的应用研究[D].武汉:武汉大学,2005:8-9,17-19
[23]杨元喜,刘念.重力异常的一种逼近方法[J].测绘学报,2001,30(3):192-195
[24]于小平等.GPSRTK高程拟合方法精度研究[J].测绘通报,2006,(11):19
[25]乔仰文,辛久志,王晓辉.GPS高程拟合的几种常用方法[J].东北测绘,1999,22(2):10-11
[26]RAPP R H.Use of Potential.Coefficients Models for Geoid Undulation Determinations Using a Spherical Harmonic Representation of the Height Anomaly/Geoid Undulation Difference[J].Journal of Geodesy.1997,71:282-289.
[27]雷晓霞.基于重力与GPS水准组合法的大地水准面精化研究[D].西安:长安大学,2005
[28]金时华.多面函数拟合法转换GPS高程[J].测绘与空间地理信息,2005,28(6):45-47
[29]车延国.GPS高程水准拟合模型与精度分析[J].辽宁工程技术大学学报(自然科学版),2008,27(1):35-36
[30]Xu Shaoquan,LI Zhenhong,WU Yunsun.Research of GPS Abnormal Height Interpolation System[J].Journal of Wuhan Technical University of Surveying and Mapping.1999,24(4):337
[31]胡晓民,葛斌.抗差移动曲面法在局部似大地水准面中应用[J].淄博学院学报,2001,3(4):65-68
[32]刘念.拟合推估的质量理论[D].郑州:信息工程大学2001:6-49
[33]边少锋,Joachim Menz。克立格估计的分析解释与协方差函数的代数确定[J].中国地质大学学报.2000(2):195-200
[34]Forsberg R,Tseherning C.The use of height data in gravity field approximation by collocation[J].Geophys Res,1981,86:7 843-7 854
[35]刘念,胡荣明.拟合推估在GPS高程解算中的应用[J].测绘通报,2001,(7):29
[36]沙月进.最小二乘配置法在GPS高程拟合中的应用[J].测绘信息与工程2000(3):3-5
[37]文汉江.最小二乘配置法中局部协方差函数的计算[J].测绘科学.2000(3)
[38]姚道荣等.最小二乘配置与普通K r i g i n g法的比较[J].大地测量与地球动力学,2008,28(6):77-78
[39]胡宏昌.半参数模型的估计方法及其应用[D].武汉:武汉大学,2004
[40]胡宏昌,孙海燕.正规化矩阵R及平滑因子a的选取[J].测绘工程,2003,12(4):5-8.
[41]王振杰,欧吉坤.半参数模型与拟合推估模型的比较[J].测绘通报,2004,(9):4-5
[42]武汉大学测绘学院测量平差学科组.误差理论与测量平差基础[M].武汉:武汉大学出版社,2003
[43]魏子卿,王刚.用地球位模型和GPS/水准数据确定我国大陆似大地水准面[J].测绘学报,2003(33)
[44]王爱生,欧吉坤,赵长胜.“移去-拟合-恢复”算法进行高程转换和地形改正计算公式探讨[J].测 绘通报,2005.(4):5-7
[45]花向红,王新洲,王泽民等.GPS水准及其在武汉轨道交通一号线工程中应用研究[J].黑龙江工程学院学报,2001,15(1):33
[46]Vermeer M,Li J G,Guo C X.Geoid determination by FFT techniques and MGM in the Western China Test Area.Finish[J].Geodetic Institute Report 1997,Helsinki
[47]黄垣,王兴旺.浅谈GPS高程拟合技术[J].辽宁交通科技,2005,(3):11
[48]蒋强,胡润强.数学方法在GPS高程拟合研究中的应用[J].甘肃科技,2006,22(10):110-112
[49]熊小莉,吴迪军.GPS高程拟合模型的精度分析[J].铁道勘察,2007(2):27-28
[50]匡翠林.高精度GPS水准算法研究及其应用[J].长沙:中南大学,2004:33-36
[51]Denker H.Regional and Local Gravity Field Modeling.National Report of the Federal Republic of Germany onthe Geodetic Activities in the Years[J].1995-1999,Munchen,1999
[52]NGS.Guidelines for Geodetic Network Surveying Using GPS.DRAFT 4,2000
[53]Tao Benzao.Determination of Quasi-geoid and Calculation of Normal Heights with GPS Leveling[J].Bulleti of Surveying and Mapping,1992(4):14-18.
[54]Kuroishi Y,Ando H,Fukuda Y.A new hybrid geoid model for Japan.GSIGE02000[J].Journal of Geodesy.2002(76):428-436.
[55]Hu J G,Cheng Y Y,Ding J X,et al.The establishment and the precision analysis of Chinese High Precision Vertical continent-Ocean Movement Monitoring Network.Asia-Pacific space geodynamics program,Shang hal.14-19 May,2001(ASPG 2001)
[56]Omang OCD,Forsberg R.The northern European geoid:a case study onlong-wavelength geoid errors[J].Journal of Geodesy,2002(76):369-380.
[57]徐卫明,陆秀平,朱穆华等.利用地球重力场模型精化GPS水准[J].海洋测绘,2003,23(2):5-8
[58]蔡群,张书毕.基于Matlab的GPS水准高程拟合程序设计[J].科技资讯,2006,(32):2-3
[59]来米芳.GPS在大型桥梁工程控制测量中的应用研究[D].杭州:浙江大学,2005
[60]杨天宇.基于BP神经网络的GPS高程拟合及其在杭州湾跨海大桥中的应用[D].成都:西南交通大学,2006
[61]王爱生,欧吉坤,赵长胜.“移去-拟合-恢复”算法进行高程转换和地形改正计算公式探讨[J].测绘通报,2005(4):5-7
[62]伍吉仓,王解先,陆彩萍.基于EGM96模型的GPS水准拟合方法[J].GPS world of china,2002(4):28-30
[2]孔祥元,郭际明,刘宗泉.大地测量学基础[M].武汉:武汉大学出版社,2001:1-2
[3]宫雨声.GPS水准模型及其应用研究[D].阜新:辽宁工程技术大学,2006:2-3
[4]贾翔.GPS水准拟合模型的误差分析与研究[D].昆明:昆明理工大学,2007:2-3
[5]Featherstone W.E.Absolute and relative testing ofgravimetrie geoid Models using Global Positioning System and orthometrie height data[J].Computers &Geoseienees,2001(27)
[6]熊伟,宁镇亚.美国国家大地测量局的十年规划[N].中国测绘报,2008-7-22(3)
[7]马新莹.局部大地水准面精化中几个问题的探讨[D].武汉:武汉大学,2005:3-4
[8]李冲.基于CQC2000的区域似大地水准面精化理论与应用研究[D].西安:长安大学,2006
[9]李建成.我国现代高程测定关键技术若干问题的研究及进展[J].武汉大学学报(信息科学版),2001,32(11):984-985
[10]张小红,程世来,许晓东.基于kriging统计的GPS高程拟合方法研究[J].大地测量与地球动力学,2007,27(2):47
[11]曹月玲,王解先.利用球冠谐分析拟合GPS水准高程[J].武汉大学学报(信息科学版),2008,33(7):740-743
[12]周世健,鲁铁定.有限元法拟合GPS水准高程分析[J].江西科学,2007,25(5):248
[13]赵超英,刘雷.GPS水准拟合优化法探讨[J].工程勘察,2006(2):64
[14]刘长建,吴洪举,张俊.GPS水准拟合方法的比较与软件编制[J].信息工程大学学报,2006,7(1):85-87
[15]刘珍贵.关于两种GPS高程拟合改进模型的探讨[J].建材与装饰,2007,(9):278-279
[16]冯光财,陈正阳.一种GPS高程拟合计算的新方法[J].矿山测量,2005(4):6-8
[17]焦明连.一种利用小波变换和Kriging估计转换GPS高程的方法[J].工程勘察,2007(11):50
[18]李胜.GPS高程异常拟合研究[D].大连:大连理工大学,2006:29-30
[19]陶本藻.GPS测高原理及其算法[J].地矿测绘,1998(1)
[20]胡伍生,高成发.GPS测量原理及应用[M].北京:人民交通出版社,2002:161-164
[21]高智广,刘艳坤.GPS测高的限制性与可行性研究[J].煤炭技术,2003,22(6):107-108
[22]许跃民.GPS水准在线路工程高程测量中的应用研究[D].武汉:武汉大学,2005:8-9,17-19
[23]杨元喜,刘念.重力异常的一种逼近方法[J].测绘学报,2001,30(3):192-195
[24]于小平等.GPSRTK高程拟合方法精度研究[J].测绘通报,2006,(11):19
[25]乔仰文,辛久志,王晓辉.GPS高程拟合的几种常用方法[J].东北测绘,1999,22(2):10-11
[26]RAPP R H.Use of Potential.Coefficients Models for Geoid Undulation Determinations Using a Spherical Harmonic Representation of the Height Anomaly/Geoid Undulation Difference[J].Journal of Geodesy.1997,71:282-289.
[27]雷晓霞.基于重力与GPS水准组合法的大地水准面精化研究[D].西安:长安大学,2005
[28]金时华.多面函数拟合法转换GPS高程[J].测绘与空间地理信息,2005,28(6):45-47
[29]车延国.GPS高程水准拟合模型与精度分析[J].辽宁工程技术大学学报(自然科学版),2008,27(1):35-36
[30]Xu Shaoquan,LI Zhenhong,WU Yunsun.Research of GPS Abnormal Height Interpolation System[J].Journal of Wuhan Technical University of Surveying and Mapping.1999,24(4):337
[31]胡晓民,葛斌.抗差移动曲面法在局部似大地水准面中应用[J].淄博学院学报,2001,3(4):65-68
[32]刘念.拟合推估的质量理论[D].郑州:信息工程大学2001:6-49
[33]边少锋,Joachim Menz。克立格估计的分析解释与协方差函数的代数确定[J].中国地质大学学报.2000(2):195-200
[34]Forsberg R,Tseherning C.The use of height data in gravity field approximation by collocation[J].Geophys Res,1981,86:7 843-7 854
[35]刘念,胡荣明.拟合推估在GPS高程解算中的应用[J].测绘通报,2001,(7):29
[36]沙月进.最小二乘配置法在GPS高程拟合中的应用[J].测绘信息与工程2000(3):3-5
[37]文汉江.最小二乘配置法中局部协方差函数的计算[J].测绘科学.2000(3)
[38]姚道荣等.最小二乘配置与普通K r i g i n g法的比较[J].大地测量与地球动力学,2008,28(6):77-78
[39]胡宏昌.半参数模型的估计方法及其应用[D].武汉:武汉大学,2004
[40]胡宏昌,孙海燕.正规化矩阵R及平滑因子a的选取[J].测绘工程,2003,12(4):5-8.
[41]王振杰,欧吉坤.半参数模型与拟合推估模型的比较[J].测绘通报,2004,(9):4-5
[42]武汉大学测绘学院测量平差学科组.误差理论与测量平差基础[M].武汉:武汉大学出版社,2003
[43]魏子卿,王刚.用地球位模型和GPS/水准数据确定我国大陆似大地水准面[J].测绘学报,2003(33)
[44]王爱生,欧吉坤,赵长胜.“移去-拟合-恢复”算法进行高程转换和地形改正计算公式探讨[J].测 绘通报,2005.(4):5-7
[45]花向红,王新洲,王泽民等.GPS水准及其在武汉轨道交通一号线工程中应用研究[J].黑龙江工程学院学报,2001,15(1):33
[46]Vermeer M,Li J G,Guo C X.Geoid determination by FFT techniques and MGM in the Western China Test Area.Finish[J].Geodetic Institute Report 1997,Helsinki
[47]黄垣,王兴旺.浅谈GPS高程拟合技术[J].辽宁交通科技,2005,(3):11
[48]蒋强,胡润强.数学方法在GPS高程拟合研究中的应用[J].甘肃科技,2006,22(10):110-112
[49]熊小莉,吴迪军.GPS高程拟合模型的精度分析[J].铁道勘察,2007(2):27-28
[50]匡翠林.高精度GPS水准算法研究及其应用[J].长沙:中南大学,2004:33-36
[51]Denker H.Regional and Local Gravity Field Modeling.National Report of the Federal Republic of Germany onthe Geodetic Activities in the Years[J].1995-1999,Munchen,1999
[52]NGS.Guidelines for Geodetic Network Surveying Using GPS.DRAFT 4,2000
[53]Tao Benzao.Determination of Quasi-geoid and Calculation of Normal Heights with GPS Leveling[J].Bulleti of Surveying and Mapping,1992(4):14-18.
[54]Kuroishi Y,Ando H,Fukuda Y.A new hybrid geoid model for Japan.GSIGE02000[J].Journal of Geodesy.2002(76):428-436.
[55]Hu J G,Cheng Y Y,Ding J X,et al.The establishment and the precision analysis of Chinese High Precision Vertical continent-Ocean Movement Monitoring Network.Asia-Pacific space geodynamics program,Shang hal.14-19 May,2001(ASPG 2001)
[56]Omang OCD,Forsberg R.The northern European geoid:a case study onlong-wavelength geoid errors[J].Journal of Geodesy,2002(76):369-380.
[57]徐卫明,陆秀平,朱穆华等.利用地球重力场模型精化GPS水准[J].海洋测绘,2003,23(2):5-8
[58]蔡群,张书毕.基于Matlab的GPS水准高程拟合程序设计[J].科技资讯,2006,(32):2-3
[59]来米芳.GPS在大型桥梁工程控制测量中的应用研究[D].杭州:浙江大学,2005
[60]杨天宇.基于BP神经网络的GPS高程拟合及其在杭州湾跨海大桥中的应用[D].成都:西南交通大学,2006
[61]王爱生,欧吉坤,赵长胜.“移去-拟合-恢复”算法进行高程转换和地形改正计算公式探讨[J].测绘通报,2005(4):5-7
[62]伍吉仓,王解先,陆彩萍.基于EGM96模型的GPS水准拟合方法[J].GPS world of china,2002(4):28-30