Different Parts Of The Datum Transformation Calculation Of The Numerical Analysis

At different times our country have their own independent local datum(independent local coordinate system)in different departments.But with the development of "Digital China","Digital City",and also to unify all surveying and mapping data into one datum,it need to convert all the old coordinates datum to the new one so that it can realize a "smooth transition" and share the data of surveying and mapping fully.In the process of transforming different local datum,there are many digits in coordinate datum point value,resulting in conversion model of the effective digit is not enough or divisor error is biggish.It also cause errors in the computing process of modeling designed matrix and information matrix,and then the errors reduce the reliability of transformation parameters.In order to overcome this problem and to provide a solution, this paper has made the following effort:1)To realize the transformation from old datum to new datum,the writer has analyzed commonly coordinate datum transition model and then deduced conversion model of regression between two local datum at the base of analyzing multiple linear regression model.Writer also programmed computing model with C#,which provided a basis for value computation in the future.2)At the base of analyzing ill-conditioned for design matrix with Gauss-Markov model in adjustment of observation and information matrix in regression equation,the writer has found that the reason for ill-conditioned matrix are of 2 factors:Over selective of parameters and calculation method(computer's word length and effective digital).At the same time,the writer established method to overcome and eliminate this problem and it laid a theoretical foundation for model of the numerical computational analysis.3)The paper has studied a method of the overall scaling for coordinate datum to resolve the problem that the effective digit is insufficiency and divisor error is biggish.In the different scaling conditions,the writer has analyzed the information matrix of transformation parameters to detect the true reasons for results deviating from the true value and to ultimately obtain the best local datum scaling.4)Through analyzing the affection of conversion parameters on the accuracy of conversion points,which is assessment the conversion residuals error for point position and analyzing the relative accuracy of the traverse between unknown point and its adjacent points,the writer has proved the reliability and availability solving conversion parameters by coordinates datum scaling.Simultaneously the conversion point accuracy with this method can meet the requirements for general conversion project,furthermore this method is stable to calculate transformation parameters by using the model.5)Through analyzing the conversion point accuracy of different conversion parameters by using different public points,the writer has proved that the different public points for the conversion of different parameters in the control of the corresponding are effective.If there is no blunder in public points,the more number of the public points participate in,the higher reliability the parameters for conversion and the smaller accuracy of corresponding to the point position lose in the conversion process.