Research And Software Implementation Of 3D Coordinate Transformation

With the continuous development of measurement technology,three-dimensional coordinate transformation in the mine measurement,engineering survey,GNSS,photogrammetry and three-dimensional laser scanning and other fields more widely used,and people are increasingly demanding for the measurement results.The traditional three-dimensional coordinate method cannot meet the requirements of the people,for example,the classic linear model,Bursa-Wolf,which is only applicable to the case of smaller rotation angle,and to solve the conversion parameters under large rotation angle,linear model will be seriously distorted,and even solved conversion parameters may cannot be used at all,eventually leading to the failure of conversion.The traditional three-dimensional coordinate transformation model is based on the principle of least squares(LS),and the Gauss-Markov model is used to solve the transformation parameters.Only the random errors in the observation vector are taken into account,and the observed values in the coefficient matrix make there is also a random error in the coefficient array,and the Gauss-Markov model does not take this into account.However,most of the coordinate transformation problems still depend on the traditional coordinate transformation model and method.The precision of conversion parameters is low,and the limitation of theory and application becomes more and more obvious.The total Least Squares(TLS)can take into account the random errors in the observation vector and the coefficient matrix,and consider the model as a whole and the comprehensive analysis.TLS can also be extended to a weighted total least squares(WTLS)estimate to solve the problem of unequal accuracy of observations.In this paper,we first introduce the linear model and the nonlinear model of the transformation parameters by introducing the basic principle of the three-dimensional coordinate transformation,and discuss the two solutions of the quadratic constraint model based on the Newton-Gauss weighted global least squares.First,the conditional equation is taken as the constraint condition;Second,the conditional equation as a virtual observation.By constructing the Lagrange objective function,the iterative method of WTLS is derived.In the three-dimensional coordinate transformation,because of the environment,man-made factors such as the existence of factors,often observed values will be mixed with gross error,classic LS,TLS,WTLS gross margin is not a good resistance,often due to the existence of gross errors Model distortion,conversion parameters failed to solve.The RWTLS algorithm of traditional three-dimensional coordinate transformation uses the residual to construct the weighting function,and cannot take into account the structural space robustness.In this paper,a Robust weighted total least squares with constraints(CRWTLS)based on the Newton-Gauss weighted global least squares orthogonal constraint model is proposed,and the expression of the residual covariance matrix is deduced to obtain the normalized residual,Based on the normalized residual constructor function,the robustness of observation space and structural space is realized.Through the case study,it is shown that the algorithm can construct the weighting function based on the normalized residuals,and the robustness of the observation space and the structure space can be realized.Compared with the existing research and the new algorithm,CRWTLS get more advantages.In the current sofftware market,the three-dimensional coordinate conversion software has not yet adopted the anti-difference solution conversion parameters.Based on the theoretical basis of this article,the author developed CooRTLS-high precision coordinate conversion software V1.0 which provides ellipsoid conversion,ellipsoid conversion,local coordinate system conversion,three parameters solving,four parameters solving,seven parameters solving,thirteen parameters solving,elevation fitting and other basic functions,including three-dimensional coordinate conversion of all needs,in order to provide users with high-precision three-dimensional coordinate conversion results.