Research On The Total Least Squares Collocation And Its Applications

Compared with the traditional least squares method, the total least squares method considered the error contained in the coefficient matrix and the observation vector, it makes the minimum sum of squares of all random variables as the guidelines to constraint all of the random variable in minimize. In recent years, the total least squares method has developed into a new data processing method and widely used in various fields. However, in some measurement data processing problems, if we only use the simple total least squares method, there are still some shortcomings. For example in the GPS height transformation based on quadric surface polynomial fitting problem, traditional methods are usually will be the calculation of transformation parameters and the height anomaly to the abnormal height of fixed-point calculation is divided into two steps, and only considering the error of coefficient matrix which used to calculate the parameters, the errors in the coordinate of the checkpoint are ignored.This paper based on the shortage which may exist in the measurement data processing method, the main research content includes: 1)Go through the basic idea of the theory,such as the least squares,the total least squar-es, the weighted total least squares, including the application of the method of measu-rement in the data processing.This parper indicates the basic idea of the total least squares collocation and describes the process of calculating. 2)On the basis of the seamless model in three-dimensional datum transformation,this paper verified the feasibility of the application which total least squares collocation could be built in the plane coordinate transformation by using the simulation examles. Then,this paper also expouds some common method of this area to demonstrate the effectiveness of this approach. 3)In order to solve the deficiencies of the quadric polynomial surface which being applied in the GPS elevation transformation,this paper puts forward the airthmetic of the total leastsquares to match the estimable model of GPS height transformation combining by the calculation of fitting parameters through the calculation of elevation abnormity of inspection points.It also introduces the calculated process of the GPS height transfor-mation combine model's covariance matrix in order to describe the progress of the simulation examples and calculation.By comparing with another methods to demonstrate the validity of this method. 4)With the guide of the GM(1,1) associated model, this paper carries out the GM(1.1)joint modle covariance matrix by using the method of total least squares collocation in the process of subsidence monitoring data. Besides, it indicates the calculative proc-ess and the covariance of the GM(1,1) combine model, through comparing with the o-ther method to demonstrate the superiority of the method.