Study on curved surface fitting model using GPS and leveling in local area
(1.Department of Territory Information and Surveying Engineering, Xuzhou Normal Universit, Xuzhou 221009, China2.Chinese Academy of Surveying and Mapping, Beijing 100039, China3.Shandong University of Science and Technology, Qingdao 266510, China)
Abstract: The height anomaly surface is fitt and the quasi-geoid can be obtained when the height anomaly is determined with the geometric analytic method. Therefore, some mathematical models to fit height anomaly surface using GPS, leveling and terrain data in a local area, including the polynomial fitting model, the multi-surface function fitting model, the motion surface fitting model and the fitting model of little flexibility deformation of thin board, are given. Then the digital characteristics are analyzed with the curved surface theory. The General curvature and the mean curvature of surface are concluded. The advantage, disadvantage and application of the above models are discussed. The effect of terrain undulation on height anomaly is considered in the surface fitting models. The practical case indicates that these models are of validity and practicability. It is concluded that the above models can give the good fitting results at the centimeter level. But the polynomial fitting model is worse than the other models.
Key words: GPS； height anomaly； terrain effect； curve surface fitting