GPS水准拟合模型及其优选理论的研究

【作者】 谢忠俍；

【导师】 刘小生；

【作者基本信息】 江西理工大学 ， 大地测量与测量工程， 2009， 硕士

【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。更多还原

【Abstract】 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.更多还原