A Study & Application About Hight Precise GPS Leveling Arithmetic

As the appearance of GPS has great impact to the conventional technology surveying, geometry leveling has no exception. Firstly, GPS has a lot of advantages in efficiency , saving money, saving time, even precision. If normal height is not necessary for some cases, GPS leveling can replace geometry leveling to solve the problems of engineering or scientific research. Secondly, if the abnormal height has been computed by quasi-geoid, geodetic height computed from GPS surveying can been translated into normal height. The method is an alternative for leveling.The development of GPS technology, especially the development of quasi-geoid with centimeter accuracy, provides the basic technology for evaluating the normal height with GPS, but which method is the best and how to control the translating quality should be studied further. The paper will deal with the two problems in detail.After concluding some problems relating to GPS leveling, the paper discusses three methods in three chapters respectively. The methods are: numerical approximations method , remove-restore method , BP neural network method. Numerical approximations include functional approximations and statistical approximations. The former are suitable for approaching the trends, but with proper models, the latter are easy to calculate and appropriate to approximate the stochastic behavior, but with proper covariance functions. Basing on the above factors, chapter 3 gives an integrated method which has the advantages of functional approximations and statistical approximations. The methods of calculating abnormal height are divided two types according to the source of data: gravitational methods and geometrical methods. The merits and demerits of them are complementary for each other. The remove-restore method in chapter 4 has the merits of both methods. It implementing like this: firstly to remove long and medium wave of abnormal height by global gravity models, then to fit and interpolate the remain of abnormal height, at last to restore long and medium wave at the interpolated points, and obtain abnormal height value. BP neural network is a kind of nonlinear mapping for its inputs and outputs. As we know, GPS leveling, in fact, is a mapping from coordinate to abnormal height. Therefore, BP neural network is a high precise method for translating height. But there are no standards for constructing the structure of neural network. Chapter 5 will discuss the problem by trials.