Combined Fitting Based on Robust Trend Surface and Orthogonal Multiquadric with Applications in DEMs Fitting

Juqing Zhang 1 + and Pingzhi Liu 2
1 School of Geology Engineering and Geomatics, Chang’an University, Yanta Road, Xi’an 710054, China
2 Xi’an Research Institute of Surveying and Mapping, No.1 Mid-Yanta Road, Xi’an 710054, China

Abstract. Spatial data interpolation is an indispensable process in DEM. A combining fitting with trend surface and multiquadric fitting is proposed, which removes the trend influence of the DEM in the research area then re-fit the residuals by surface fitting. In order to control the influence of some outstanding points to surface fitting, a robust fitting of the  trend surface by using an equivalent weight is adopted. An adaptive node choosing method is proposed based on the effect of every node to the curve fitting calculated by using the orthogonal least squares. It cannot only ensure the stability, but also improve the precision of fitting. A practical example of terrain fitting shows that the proposed combined method is effective in improving the quality of DEM fitting. 

Keywords: trend surface fitting, multiquadric, node, fitting

In: Wan, Y. et al. (eds) Proceeding of the 8th international symposium on spatial accuracy assessment in natural resources and environmental sciences, World Academic Union (Press).

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