GPS水准拟合模型及其优选理论的研究
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摘要
全球定位系统(GPS)能为用户提供精确的三维坐标、速度和时间信息。然而,GPS提供的高程是以参考椭球为基准的大地高,而在实际工程应用中的高程是以似大地水准面为基准的正常高;大地高与正常高之间的差值称为高程异常,如何有效地利用已知信息计算高程异常是目前测绘界研究的一个热点。目前,国内外用于高程异常计算的方法主要有数学模型拟合法(GPS水准)、重力法和几何与重力混合转化法,由于一般的工程机构很难获得精确的重力数据,所以现在最常用的方法还是通过GPS水准来计算高程异常。
本文首先简介了GPS测量的基本原理、三种常用高程系统及其相互关系、影响GPS水准的误差因素和拟合模型的精度评定,研究了稳健估计用于GPS水准的方法;其次,研究了曲线拟合法、曲面拟合法、多面函数法、移动曲面法、协方差推估法、最小二乘配置法、BP神经网络法的算法;重点研究了拟合模型的优选,包括多项式阶次模型检验法、AIC准则、多面函数法核函数的优选原理和基于均方误差的函数模型优选准则;然后,应用MATLAB语言对本文涉及的所有算法进行了编程并进行了实例分析、比较和研究。另外,本文设计并改进了一种用于GPS高程异常拟合的BP神经网络算法——“基于加权平均的改进BP神经网络法”。
最后,本文得出了一些结论,以及对该研究方向下一步工作进行了展望。
GPS can provide three dimensional coordinates of space point,the speed of surveying object and the time for each kind of user.But the height information of GPS is ellipsoidal height which based on the reference ellipsoid and as we know it is not the normal height in the project needs.The difference between the geoid height and normal height is called geoidundulations. How effective use of the known information transfor height abnormity is a new focus in the area of surveying.At present, common methods of this area contain the following list: the method of mathematical model fitting (GPS leveling), gravitic method and the mixed method of the geometric and gravitic.As the common groups hard to obtain the accurate data of gravity, therefore the conventional methods of transformation of height abnormity is the geometric method now.
This paper has introduced the fundamental knowledge theory of GPS,the difference between three commonly used height system,the factors of error in GPS leveling ,the precision evaluation of fitting model ,the application of robust estimation used for GPS height abnormity gross error detection.Second,this paper has research curve fitting, surface fitting, polyhedral function method, mobile interpolation,the covariance method,the least-squares collocation(LSC) and BP neural network algorithm; then studied the preferred model fitting, including the use of statistical test for the optimum degree of polynomial surface model, AIC guidelines and based on minimum mean squared error theory to obtain the best model.Moreover,this paper has improved a new method named Based on weighted average model and BP nets.Also,this paper has programmed by MATLAB on the use of all the algorithms and examples.
At last, the conclusions of this paper are presented and potential prospects of this subject are discussed.
本文首先简介了GPS测量的基本原理、三种常用高程系统及其相互关系、影响GPS水准的误差因素和拟合模型的精度评定,研究了稳健估计用于GPS水准的方法;其次,研究了曲线拟合法、曲面拟合法、多面函数法、移动曲面法、协方差推估法、最小二乘配置法、BP神经网络法的算法;重点研究了拟合模型的优选,包括多项式阶次模型检验法、AIC准则、多面函数法核函数的优选原理和基于均方误差的函数模型优选准则;然后,应用MATLAB语言对本文涉及的所有算法进行了编程并进行了实例分析、比较和研究。另外,本文设计并改进了一种用于GPS高程异常拟合的BP神经网络算法——“基于加权平均的改进BP神经网络法”。
最后,本文得出了一些结论,以及对该研究方向下一步工作进行了展望。
GPS can provide three dimensional coordinates of space point,the speed of surveying object and the time for each kind of user.But the height information of GPS is ellipsoidal height which based on the reference ellipsoid and as we know it is not the normal height in the project needs.The difference between the geoid height and normal height is called geoidundulations. How effective use of the known information transfor height abnormity is a new focus in the area of surveying.At present, common methods of this area contain the following list: the method of mathematical model fitting (GPS leveling), gravitic method and the mixed method of the geometric and gravitic.As the common groups hard to obtain the accurate data of gravity, therefore the conventional methods of transformation of height abnormity is the geometric method now.
This paper has introduced the fundamental knowledge theory of GPS,the difference between three commonly used height system,the factors of error in GPS leveling ,the precision evaluation of fitting model ,the application of robust estimation used for GPS height abnormity gross error detection.Second,this paper has research curve fitting, surface fitting, polyhedral function method, mobile interpolation,the covariance method,the least-squares collocation(LSC) and BP neural network algorithm; then studied the preferred model fitting, including the use of statistical test for the optimum degree of polynomial surface model, AIC guidelines and based on minimum mean squared error theory to obtain the best model.Moreover,this paper has improved a new method named Based on weighted average model and BP nets.Also,this paper has programmed by MATLAB on the use of all the algorithms and examples.
At last, the conclusions of this paper are presented and potential prospects of this subject are discussed.
引文
[1]李征航,黄劲松.GPS测量与数据处理.武汉:武汉大学出版社,2005
[2]刘基余,李征航,王跃虎等.全球定位系统原理及其应用.北京:测绘出版社,1993
[3]梁振英,董鸿闻.精密水准测量的理论和实践.北京:测绘出版社,2004
[4]匡翠林.高精度GPS水准算法研究及其应用:[硕士学位论文].长沙.中南大学,2004
[5] T. Kavzoglu, M. H. Saka.Modelling local GPS/levelling geoid undulations using artificial neural Networks.Journal of Geodesy,2005
[6]杨国清,控制测量学.郑州:黄河水利出版社,2005
[7] Rapp R H,A conceptual formulation of a World Height System. OSU Report,1992,(421)
[8]胡伍生.GPS测量原理及其应用.北京:人民交通出版社,2002
[9]高伟.GPS高程测量的理论与方法研究:[博士学位论文].武汉.武汉大学,2004
[10]武汉测绘科技大学测量平差教研室.测量平差基础(第三版).北京:测绘出版社,1996
[11]崔希璋,於宗俦,陶本藻等.广义测量平差(新版).武汉:武汉大学出版社,2001
[12]周江文.经典误差理论与抗差估计.测绘学报,1989,Vol.18(2): 115～119
[13]刘大杰,陶本藻.实用测量数据处理方法.北京:测绘出版社,2000
[14]李庆扬,王能超,易大义.数值分析(第四版).北京:清华大学出版社,2001
[15]李广杰,何群,郭甲媵. GPS水准多项式曲面拟合模型实验研究.鞍山科技大学学报,2007
[16]陶本藻.GPS水准似大地水准面拟合和正常高计算.测绘通报,1992
[17] Hardy R.L,The Application of Multiquadic Equations and point Mass Anomaly Models to Crustal Movement Studies. NOAA Technical Report NOS76,NGS11,1978
[18]黄筱蓉,周光文.用多面函数法内插GPS点的高程异常.工程勘察,1995
[19]金时华.多面函数拟合法转换GPS高程.测绘与空间地理信息,2005
[20]聂桂根,祝永刚,徐绍铨.改进的移动插值法及应用.测绘通报,1998
[21]王殊伟,陈正阳.基于移动曲面模型的GPS高程拟合.海洋测绘,2005
[22]刘长建,吴洪举,陈少明.GPS水准移动曲面法功能新探.全球定位系统,2006
[23]陶本藻,姚宜斌,赵美超.论多面函数推估与协方差推估.测绘通报,2002
[24]李丽华,高井祥,刘晋斌.协方差函数拟合高程异常方法探析.测绘工程,2005
[25]李丽华,高井祥,陈健等.协方差推估在高程异常拟合中的应用.测绘通报,2006
[26]孙正明,高井祥,王坚等.最小二乘配置法GPS高程异常推估中的应用.测绘科学,2007
[27]沙月进.最小二乘配置法在GPS高程拟合中的应用.测绘信息与工程,2000
[28]潘雄,孙海燕.最小二乘配置模型的参数估计.测绘工程,2004
[29]段虎荣,郭新成,丁宁.最小二乘预估法在GPS高程转换中的应用.西安科技大学学报,2006
[30] Martin,T.Hagan Howard,B.Demuth Mark,H.Beale.神经网络设计.北京:机械工业出版社,2005
[31]张良均,曹晶,蒋世忠.神经网络实用教程.北京:机械工业出版社,2008
[32]吴微.神经网络计算.北京:高等教育出版社,2003
[33]韩力群.人工神经网络教程.北京:北京邮电大学出版社,2006
[34]王旭,王宏,王文辉.沈阳:东北大学出版社,2007
[35]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:[硕士学位论文].成都.西南交通大学,2006
[36]秦永宽,黄声享,张书毕.利用MATLAB神经网络实现GPS高程转换设计.海洋测绘,2008
[37]高宁,高彩云,吴良才.关于BP神经网络转换GPS高程的若干问题.测绘工程,2006
[38]飞思科技产品研发中心.神经网络理论与MATLAB 7实现.北京:电子工业出版社,2005
[39]飞思科技产品研发中心.MATLAB 6.5神经网络分析与设计.北京:电子工业出版社,2003
[40]罗成汉.基于MATLAB神经网络工具箱的BP网络实现.计算机仿真,2004
[41]高宁.基于BP神经网络的农作物虫情预测预报及其MATLAB实现:[硕士学位论文].合肥.安徽农业大学,2004
[42]胡伍生,华锡生,张志伟.平坦地区转换GPS高程的混合转换方法.测绘学报,2002,
[43]潘宝玉,丁先伟.GPS水准高程拟合的精度研讨.地矿测绘,1996
[44]李晓桓.GPS水准拟合模型的优选.测绘通报,2003
[45]刘帅,王礼江,朱建军等.GPS高程拟合模型的优选.测绘工程,2006
[46] AKAIKE,H.Information Theory and an Extension of theMaximum LikelihoodPrinciple[A].B.N.PETROV ANDF.CSAKI.Second International Symposium on InformationTheory. Akademia Hiado, Budapest, 1973, 267-281.
[47] AKAIKE. A new look at the statistical model identification.IEEE Trans. Autom. Control, 1974,AC-19:716-723.
[48]周光文,黄筱蓉.一种改进的多面函数法.测绘通报,1996
[49]陶本藻.地球重力场平差模型误差的控制.武汉大学学报信息科学版,2003
[50]陶本藻,蔡凤萍.大范围GPS水准拟合模型的选取及其实验研究,2005
[51] C.Kotsakis. On the trade-off between model expansion,model shrinking,and paramenter estimation accuracy in least-squares data analysis.Journal of Geodesy, 2005.
[52] Yamin Dang,Chuanlu Cheng,Junyong Chen. Geodetic height determination in 2005 Qomolangma survey .Geo-Spatial Information Science, 2007.
[2]刘基余,李征航,王跃虎等.全球定位系统原理及其应用.北京:测绘出版社,1993
[3]梁振英,董鸿闻.精密水准测量的理论和实践.北京:测绘出版社,2004
[4]匡翠林.高精度GPS水准算法研究及其应用:[硕士学位论文].长沙.中南大学,2004
[5] T. Kavzoglu, M. H. Saka.Modelling local GPS/levelling geoid undulations using artificial neural Networks.Journal of Geodesy,2005
[6]杨国清,控制测量学.郑州:黄河水利出版社,2005
[7] Rapp R H,A conceptual formulation of a World Height System. OSU Report,1992,(421)
[8]胡伍生.GPS测量原理及其应用.北京:人民交通出版社,2002
[9]高伟.GPS高程测量的理论与方法研究:[博士学位论文].武汉.武汉大学,2004
[10]武汉测绘科技大学测量平差教研室.测量平差基础(第三版).北京:测绘出版社,1996
[11]崔希璋,於宗俦,陶本藻等.广义测量平差(新版).武汉:武汉大学出版社,2001
[12]周江文.经典误差理论与抗差估计.测绘学报,1989,Vol.18(2): 115～119
[13]刘大杰,陶本藻.实用测量数据处理方法.北京:测绘出版社,2000
[14]李庆扬,王能超,易大义.数值分析(第四版).北京:清华大学出版社,2001
[15]李广杰,何群,郭甲媵. GPS水准多项式曲面拟合模型实验研究.鞍山科技大学学报,2007
[16]陶本藻.GPS水准似大地水准面拟合和正常高计算.测绘通报,1992
[17] Hardy R.L,The Application of Multiquadic Equations and point Mass Anomaly Models to Crustal Movement Studies. NOAA Technical Report NOS76,NGS11,1978
[18]黄筱蓉,周光文.用多面函数法内插GPS点的高程异常.工程勘察,1995
[19]金时华.多面函数拟合法转换GPS高程.测绘与空间地理信息,2005
[20]聂桂根,祝永刚,徐绍铨.改进的移动插值法及应用.测绘通报,1998
[21]王殊伟,陈正阳.基于移动曲面模型的GPS高程拟合.海洋测绘,2005
[22]刘长建,吴洪举,陈少明.GPS水准移动曲面法功能新探.全球定位系统,2006
[23]陶本藻,姚宜斌,赵美超.论多面函数推估与协方差推估.测绘通报,2002
[24]李丽华,高井祥,刘晋斌.协方差函数拟合高程异常方法探析.测绘工程,2005
[25]李丽华,高井祥,陈健等.协方差推估在高程异常拟合中的应用.测绘通报,2006
[26]孙正明,高井祥,王坚等.最小二乘配置法GPS高程异常推估中的应用.测绘科学,2007
[27]沙月进.最小二乘配置法在GPS高程拟合中的应用.测绘信息与工程,2000
[28]潘雄,孙海燕.最小二乘配置模型的参数估计.测绘工程,2004
[29]段虎荣,郭新成,丁宁.最小二乘预估法在GPS高程转换中的应用.西安科技大学学报,2006
[30] Martin,T.Hagan Howard,B.Demuth Mark,H.Beale.神经网络设计.北京:机械工业出版社,2005
[31]张良均,曹晶,蒋世忠.神经网络实用教程.北京:机械工业出版社,2008
[32]吴微.神经网络计算.北京:高等教育出版社,2003
[33]韩力群.人工神经网络教程.北京:北京邮电大学出版社,2006
[34]王旭,王宏,王文辉.沈阳:东北大学出版社,2007
[35]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:[硕士学位论文].成都.西南交通大学,2006
[36]秦永宽,黄声享,张书毕.利用MATLAB神经网络实现GPS高程转换设计.海洋测绘,2008
[37]高宁,高彩云,吴良才.关于BP神经网络转换GPS高程的若干问题.测绘工程,2006
[38]飞思科技产品研发中心.神经网络理论与MATLAB 7实现.北京:电子工业出版社,2005
[39]飞思科技产品研发中心.MATLAB 6.5神经网络分析与设计.北京:电子工业出版社,2003
[40]罗成汉.基于MATLAB神经网络工具箱的BP网络实现.计算机仿真,2004
[41]高宁.基于BP神经网络的农作物虫情预测预报及其MATLAB实现:[硕士学位论文].合肥.安徽农业大学,2004
[42]胡伍生,华锡生,张志伟.平坦地区转换GPS高程的混合转换方法.测绘学报,2002,
[43]潘宝玉,丁先伟.GPS水准高程拟合的精度研讨.地矿测绘,1996
[44]李晓桓.GPS水准拟合模型的优选.测绘通报,2003
[45]刘帅,王礼江,朱建军等.GPS高程拟合模型的优选.测绘工程,2006
[46] AKAIKE,H.Information Theory and an Extension of theMaximum LikelihoodPrinciple[A].B.N.PETROV ANDF.CSAKI.Second International Symposium on InformationTheory. Akademia Hiado, Budapest, 1973, 267-281.
[47] AKAIKE. A new look at the statistical model identification.IEEE Trans. Autom. Control, 1974,AC-19:716-723.
[48]周光文,黄筱蓉.一种改进的多面函数法.测绘通报,1996
[49]陶本藻.地球重力场平差模型误差的控制.武汉大学学报信息科学版,2003
[50]陶本藻,蔡凤萍.大范围GPS水准拟合模型的选取及其实验研究,2005
[51] C.Kotsakis. On the trade-off between model expansion,model shrinking,and paramenter estimation accuracy in least-squares data analysis.Journal of Geodesy, 2005.
[52] Yamin Dang,Chuanlu Cheng,Junyong Chen. Geodetic height determination in 2005 Qomolangma survey .Geo-Spatial Information Science, 2007.