不同地方基准转换数值分析的计算研究

【作者】 张勇；

【导师】 施昆；

【作者基本信息】 昆明理工大学 ， 大地测量学与测量工程， 2008， 硕士

【摘要】 我国在不同时期、不同部门间都有自己独立的地方基准(地方独立坐标系),但随着“数字中国”、“数字城市”的发展,为了将原有的测绘资料统一到同一个基准下,必须将旧的坐标基准转换到新的坐标基准下,以实现测绘资料的“平稳过渡”,达到测绘数据的充分共享。在不同地方基准间的转换过程中,由于一般坐标基准点的数值位数较大,导致转换模型运算的有效数位不足或计算过程中约数误差较大,使模型的设计矩阵或信息矩阵在计算过程中产生病态,进而导致转换参数的不可靠。为了解决这种运算有效数位不足或计算中约数误差较大对转换参数的影响,本文做了如下几个方面的工作:1)为了实现不同基准的转换,通过对常用坐标基准转换模型的分析,本文在多元线性回归分析模型的基础上推导了不同地方基准转换的回归模型,利用C#开发了模型的计算程序并为了后面的数值分析的计算研究提供了基础。2)本文在分析间接平差Gauss-Markov模型中设计矩阵的病态性及回归方程中信息矩阵病态性的基础上,找出了矩阵病态性产生的原因主要是:过度化参数的选择和计算方法(计算机字长和有效数位)两个方面,同时给出几种判断矩阵病态性的方法,这为后面对模型中数值的计算分析奠定了理论基础。3)研究利用对坐标基准进行整体缩放的方法来解决运算有效数位不够的这一问题。通过对不同缩放比例来求解转换参数里信息矩阵的分析,找出导致结果偏差或偏离真值的原因,从而获得地方基准最佳缩放比例。4)通过分析转换参数对转换点精度的影响,即对点位转换残差进行评定和未知点与其它相邻点间的导线相对精度的分析,证明采用坐标基准整体缩放的方法求解出的转换参数是可靠和有效的,同时该方法下转换点的点位精度能够满足一般工程转换的要求,模型对转换参数的求解过程也是稳定的。5)通过用不同公共点数求解出不同的转换参数对转换点精度的分析,证明了不同公共点数求解出不同的转换参数在对应的控制范围内都是有效的。在公共点不存在粗差的情况下,参与转换公共点数越多,求解出转换参数的可靠性就越高,相对应的点位在转换过程中损失的精度就越小。更多还原

【Abstract】 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.更多还原