基于克里格方法的GPS高程拟合研究.doc

摘 要 GPS测量可以获得高精度的三维坐标，它的平面相对定位精度已经非常高，但是它得到的高精度的大地高与我国采用的正常高系统不一致，只具有几何意义。为了充分的发挥GPS测量的优点，需要将大地高转化成正常高，应用于实际的工程项目。目前，将大地高转换为正常高最好的方法是利用重力测量法。但在小范围内，不具备重力资料的情况下，数学模型拟合方法仍然是一般单位进行GPS高程拟合的首选方案。 本文针对GPS大地高转换为正常高的相关问题，结合近几年快速发展的地理信息技术，利用ArcGIS软件内置的地统计学工具，分析数据结构，试图探索其内在规律，获取小区域的高程异常拟合模型。 首先，系统介绍了GPS水准高程应用理论，并对目前数学模型拟合的主要方法进行了简单介绍和比较，突出克里格法的优越性。 其次，深入探讨了克里格法的基础理论，从前提假设到半变异函数都进行了详细论述，克里格法以样点空间相关性为前提，拟合估值具有线性、无偏、最优的特点。 最后，详细介绍了三种克里格方法(普通克里格、简单克里格、泛克里格)的数学模型。在对校园实测GPS数据仔细分析的基础上，进行了基于克里格方法的GPS高程拟合相关试验，通过分析得到的结果精度，获得了最佳拟合模型。 关键词：GPS高程拟合；克里格法；ArcGISAbstract GPS measurements can obtain the three-dimensional coordinates of high precision, the plane relative positioning precision is very high, but it gets high precision geodetic height and our country the normal height system inconsistent, only have a geometric meaning.?In order to give full play to?the advantages?of GPS measurement,?to?earth will be transformed into high normal,?applied to the actual?project.?At present,?the earth?into?normal height?is the best?use of gravity?measurement.?But in a small range, do not have the gravity data and mathematical model fitting method is still units are generally the preferred solution for GPS height fitting. This paper for GPS high conversion to normal height related issues, combined with geographic information technology rapid development in recent years, using ArcGIS softwares built-in geostatistical tools. Analysis data structure, tries to explore the inherent law, access to the small area of height anomaly fitting model. First of all, the paper introduces the GPS level elevation and the application of the theory, and gives a brief introduction and comparison of the main method of the mathematical model fitting, the superiority of the prominent Kriging. Secondly, in-depth study of the basic theory of Kriging method, from the premise hypothesis to semi variation function are discussed in detail, Kriging method to spatial correlation as the premise, the estimate with linear, unbiased,