Research On GPS Normal Height Fitting Method Based On Total Least Squares Criterion

For nearly 10 years,GPS technology with its height efficiency,height precision,easy to operate,all-weather,low cost,no need of visual communication and a series of advantages in the field of engineering survey each related got rapid application development,however,in the aspect of height data acquisition,the WGS-84 coordinate system adopted by GPS is different from the normal height system in China and is affected by the abnormal elevation in different regions,for a long time,it has been difficult for GPS observations to be used directly in engineering surveys.Since the birth of GPS,how to acquire normal height with high accuracy based on GPS observation data has attracted the close attention of many domestic and foreign scholars.At present,some scholars take the least squares criterion as a constraint to realize the conversion of GPS geodetic height to normal height by fitting and adjustment,which makes GPS occupy a place in the field of elevation survey.Considering that the GPS normal height fitting method based on the general least squares criterion constraints only considers the errors of observation vectors and ignores the errors that may exist in the coefficient matrix itself,this may reduce the calculation accuracy of normal height results,in view of this,this paper,on the basis of in-depth analysis of the existing GPS normal height fitting model and adjustment calculation methods,proposes a new method,aiming at the high accuracy of the solution results,the total least squares is selected as the basic constraint criterion of GPS normal high fitting,the research on GPS normal high fitting based on the global least squares constraint is carried out,the specific work is as follows:(1)normal height fitting of GPS based on the constraint of general least squares criterionBased on the general least squares criterion constraints,the solution formula of normal height fitting model is deduced for the linear distribution height fitting model and the plane distribution height fitting model.The operation results of the algorithm are compared and analyzed by simulation data.(2)GPS normal height fitting based on the constraint of total least squares criterion.For the polynomial curve fitting model,based on the singular value decomposition method in the total least square and Lagrange's iteration method,the polynomial curve fitting formulas are derived.For polynomial surface fitting and polyhedral function fitting,the polynomial surface fitting and polyhedral function fitting formulas are derived based on the singular value decomposition method in the total least squares.(3)comparison and analysis of experimental resultsIn view of the measurement point is linear distribution and shape distribution in plane area,in the mountains is planar distribution of three types of experimental sites,respectively based on the general least squares criterion and total least squares criterion constraints to realize the normal height fitting solution,the running results of algorithm has carried on the contrast and analysis,and made evaluation of the applicability of the algorithm.Through the above research,the feasibility of the total least squares criterion in GPS normal height calculation is verified,and a GPS normal height fitting model based on the total least squares criterion constraint is constructed.It is concluded that the GPS normal height fitting model based on the total least squares criterion constraint is superior to the classical GPS normal height fitting model based on the general least squares criterion constraint.