Keywords: 
• GPS leveling /
• normal height /
• abnormal height /
• height interpolation

Abstract: As we know,global positioning system (GPS) can be used to get precise relative position in a three-dimensional system. The results of many field-tests and applied projects have already shown that, GPS survey method can take the place of classical horizontal terrain survey method. But how to interpolate the abnormal height of GPS leveling, so as to take the place of classical leveling survey method, has attracted many geodesists in the past ten years. Up to now, a lot of methods have been discussed and applied.According to the development of GPS height abnormal height interpolation system (GANHIS),this paper discusses some mathematical models and the key techniques of GPS leveling.Firstly, the general design of GANHIS is illustrated with DFD (data flow diagram). Secondly, the mathematical models of GANHIS, including the polynomial curve interpolation method, the three-spline curve interpolation method, the curve interpolation of Akima method, the polynomial curved surface interpolation method, the multidimensional function curved surface interpolation method,the motion curved surface interpolation method, etc. are presented in brief. The characteristics of each method are offered as the mathematical expression.In succession, the key techniques of implemention GANHIS are stated briefly:1) To adopt the rotation of coordinates to ensure the precision of curve interpolation methods;2) To adopt the correction of terrain to ensure the precision of curved surface interpolation methods in mountainous areas, and its calculation, method is provided;3) To adopt the reliability testing of GPS bench marks to exclude blunders;4) The method of assessing precision is provided;5) The method of protracting the isoline of GPS normal height is introduced.GANHIS has come int use since 1998. In this paper, an application example is given, and it is proved that the result is good:both the internal precision and the outside precision are superior to the limit error of IV-order leveling. Finally, some significant conclusions are drawn:①For localGPS net, if the design of GPS net is reasonable, we can achieve IV-order leveling precision with GPS leveling method. ②GANHIS provides lots of interpolation models, so we can verify the interpolation result with different methods. The example in the paper proves that the precision of the polynomial curved surface interpolation method is approximate to that of the motion curved surface interpolation method. ③GANHIS has not only prominent economic benefit, but also important application and popularization value.