On Resolution Method Of High Accurate Coordinate Transformation Based On Ill-posed Problem Resistance And Anti-error Estimation

Abstract:During the period of survey,design and construction of road and railway,it is of great necessary to build project control networks. Nowadays, several coordinate systems co-exist in our country. Coordinate transformation of high accuracy is of great importance for establishing project control networks. Bursa-wolf model, simple and feasible, turns out to be the most widely used geodetic coordinate transformation model.But in its application, Bursa-wolf model is easily disturbed by ill-posed problem of error equations and gross errors in common points, which turns down the precision and stability of transformation parameters. And the results are unreliable.The paper introduces the basic knowledge of geodetic coordinates. Based on the ill-posed problems and gross errors, it makes an intensive study on the effect of ill-posed problem of equations and gross errors towards coordinate transformation. It also studies coordinate transformation methods based on Bursa-wolf model to reduce their effects. The main points are as follows:(1) The paper analyzes ill-posed problem in coordinate transformation of error equations, and proposes the method of how to classify effects of ill-posed problem to parameter transformation, which evaluates the damage degree by analyzing the effect of parameters caused by the disturbance of known information.(2) By researching how the locations of different common points affect the ill-posedness, the paper comes up with the method of how to choose common points to weaken ill-pose problem. Large numbers of data simulations prove that in the target zone which surrounded by the common points, the results are less affected by ill-pose problem.(3) Analyzing the sources of gross errors in common points, summarizing the model of detecting and removing gross errors and applying the robust estimation theory in Bursa-wolf model, the paper deduces the formula of robust coordinate transformation parameter.(4) Based on the research of the limitations of common robust coordinate transformation methods, the paper combines hypothesis test and weight-reducing with resist gross errors in coordinate transformation, and proposes the variance ratio test and weight-reducing iteration, in which variance ratio test is more powerful to detect gross errors than regular methods, and weight-reducing iteration could meet the situation with few coordinates utilizing known information.(5) Using above algorithm under the language of Matlab makes them be easier applied. Examples in the paper prove that the method of variance ratio test and weight-reducing iteration are more practical and effective to test gross errors in coordinate transformation than regular methods. When gross errors take the percentage of1/3, regular methods always do not work, but the methods proposed by this paper are still useful to precisely test gross errors, and can effectively guarantee the accuracy of coordinate transformation.