平面四参数反算的精度分析及其控制方法研究

平面四参数坐标转换模型具有计算方便和模型精度高等特点，已广泛应用于不同平面坐标系成果的转换。大量的研究成果提高了模型的精度和适用范围，而忽视了高精度转换成果对参数保密的影响。针对转换参数的保密需求，则有必要分析参数反算的精度及其控制方法。本文首先推导了转换模型的内符合误差和外推误差；然后分别采用无误差和有误差的原始转换参数对坐标成果进行转换，并对转换后的成果附加不同的坐标误差；最后选择不同分布和数量的坐标点参与转换参数反算，从而分析不同方案参数反算的精度。试验结果表明，参数反算的精度可以通过增加转换点的数量和扩大其转换范围得到不断的提高，最高能达到原始转换参数的精度。因此，参数保密的有效方式为首先需要降低原始转换参数精度；然后根据转换成果的分布范围、数量及精度应用需求，对坐标成果附加不同的误差，从而达到参数保密的效果。

Precision analysis and control method of inverse calculation of plane four parameter

Planar four-parameter coordinate transformation model has the advantages of convenient calculation and high precision. It has been widely used in the transformation of different planar coordinate systems. A lot of research work has been done to improve the accuracy and applicability of the model, while ignore the impact of high-precision conversion results on parameter confidentiality. It is necessary to analyze the precision and control method of parameter inversion in order to meet the requirement of conversion parameter confidentiality. Firstly, the internal coincidence error and extrapolation error of the transformation model are deduced. Then, the coordinate results are transformed by the original conversion parameter without error and with error respectively, and different coordinate errors are added to the transformed results. Finally, different coordinate points with different distribution and number are selected to participate in the conversion parameter inversion, so as to analyze the accuracy of the parameters inversion of different schemes. The experimental results show that the accuracy of parameter inversion can be continuously improved by increasing the number of conversion points and expanding the conversion range, but the accuracy is as the same as the original conversion parameter achieved. Therefore, the effective way of parameter confidentiality firstly needs to reduce the accuracy of the original conversion parameter, and then add different errors to the coordinate results according to the distribution range, quantity and accuracy application requirements of the converted results, so as to achieve the effect of parameter confidentiality.