The Surface Fitting Base On Totoal Least Squares And ITS Application In GPS Elevation Fitting

The Least squares method is one of the most basic and widely used data processing method now in the field of Surveying and mapping, but it requires a premise in the application. That is, there is error only in the observation vector, but none in the coefficient matrix. But in reality, error caused by interference coefficient matrix due to personnel, environment and the instrument in most measurement problems, so the coefficient matrix is not entirely accurate, which makes the application of least squares method of data processing theory have a defect. The results obtained can not achieve the optimal characteristics. Based on this situation, the total least squares presents a reasonable and effective model. In the field of surveying and mapping, the applied research on the total least squares just started in recent years, but it also received the attention of many scholars, and it became a hot issue of data processing research in the field of surveying and mapping. On the problem of solving the parameters by related matching, many documents all solved the balancing by the least squares method. This paper will be in line with the characteristics of the measured data, solving the parameters of related matching by adopting the mathematical model which is the total least square theory and the rules of balancing. Then, drawing the more reasonable and reliable parameter, and finally applying in the engineering project combining with the example.This paper mainly introduces the overall least squares method of total least square theory, and gives a more detailed exposition. On the problem of the total least squares solution, generally obtaining the total least squares solution by the use of the singular value decomposition method. Introducing the iterative algorithm of total least squares in order to facilitate the realization of programming, and then programming by use of VB. Based on the total least squares method, this paper use the least squares method on the plane fitting and surface fitting, and analyzing the example combining with the simulation data, and then contrasting the fitting results by the analysis of examples to the fitting results by the traditional least squares, thus verifying the accuracy of solving the parameters by the overall least squares method, and getting a parameter with higher precision. Finally, with the discussion of the total least square in the fitting(plane and planar), this paper applying the overall least squares theory in the GPS elevation fitting, and calculating by actual example. This paper compared the difference between the results by the least squares and the traditional least squares, and also comparing to the precision of analysis. Then confirming the rationality of the total least square not only on theory but also on the fitting results.