椭球大地测量学计算机代数分析化

计算机科学技术和空间科学技术的发展，使大地测量发生了深刻和巨大的变化，将计算机代数分析应用于大地测量进行公式推导，相较于以前的人工推导，极大的提高了大地测量的计算效率与精度，但作为大地测量基础的椭球大地测量学却仍然固守着传统的几何分析和经典的数学分析方法。从国家建设出发，为解决椭球大地测量学在工程应用中由于人工分析导致的数学公式繁琐、精度不高等问题，本项目将在传统椭球大地测量经典分析的基础上，引入计算机代数分析方法，对椭球上的点、线、面、体等几何实体元素之间的关系进行研究，对各纬度间的表达式进行革新，采用适合计算代数分析的计算机语言进行表达，提高模型精度的同时尽可能使表达式简洁；充分发掘微分方程间的内在联系，实现大地线解算方法的创新；丰富和发展椭球大地测量学中的数学基础，并将理论成果应用于实际工程中。利用计算机代数系统实现椭球大地测量从传统人工推导向利用计算机进行分析的革新。

Profound and dramatic changes have taken place in geodesy with the development of space science and computer science. The application of computer algebra analysis system significantly improves the mathematical analysis efficiency and accuracy in the field of geodesy. However, the Ellipsoid Geodesy, as the foundation of geodesy, still uses the traditional methods to solve problems. The project will solve the problem of complexation in formula and low precision caused by manual analysis, especially in the practical engineering application of Ellipsoid Geodesy. Based on traditional analysis of Ellipsoid Geodesy, the theory of computer algebra will be introduced into the project. The relationship among points, lines, surfaces, and other geometric entities on the ellipsoid will be analyzed, and new expressions among different latitudes will be established in terms of computer algebra analysis. This project will fully discover the inherent relationships in differential equations and find innovative methods of Geodesic calculation. By introducing the computer algebra analysis, the theoretical research on Ellipsoid Geodesy can be enriched and developed. Therefore, the innovative transformation from traditional manual formulation to artificial intelligence formulation can be made in the field of Ellipsoid Geodesy.