基于多项式曲面拟合模型的高程转换方法及其结果分析

本文针对影响多项式高程转换精度的两个主要因素(拟合模型选择和拟合点选取),在分析不同阶次多项式表达特征的基础上,基于一次多项式拟合残差信息,提出了综合不同多项式曲面模型的GNSS高程转换方法,并通过实例验证了该方法的有效性。结果表明,利用一次多项式拟合残差空间分布信息反映的测区高程异常变化特征,作为二次多项式分区拟合区域划分或三次多项式拟合点选取的依据,进行高程拟合,可以将高程拟合精度从厘米级提高至毫米级。

Height conversion method and result analysis based on polynomial surface fitting model

Considering the impacts of selection of fitting models and fitting points on the precision of height conversion based on polynomial surface fitting, this study proposed GNSS height fitting methods by integrating different polynomial curved surface models based on the analysis of their features and the information about fitting residuals of fist order polynomial. The effectiveness of the proposed model was evaluated by a case study. The results show that the spatial distribution of fitting residuals of fist order polynomial, which reflects the feature of regional height anomalies, can provide a basis for dividing sub-regions for quadratic polynomial fitting or the selection of fitting points for cubic polynomial, and the fitting precision can be increased from centimeter level to millimeter level.