关键词: 平面四参数, 坐标转换, 相似变换, 参数反算, 精度分析

Abstract: 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.

Key words: plane four-parameter, coordinate transformation, similarity transformation, parameter inversion, accuracy analysis