二次曲面与最小二乘配置的组合模型在GPS高程异常拟合中的应用

Application of combination model of quadric surfaces and least squares collocation in GPS height anomaly fitting

在工程实践应用中,为了有效利用GPS高程数据,减少对传统水准测量的依赖,提高GPS高程异常的拟合精度便显得十分重要。为此,本文在介绍二次曲面拟合和最小二乘配置拟合基本原理分析、算法过程推导的基础上,提出了一种新的高程异常拟合方法。首先在二次曲面拟合的基础上,计算得到原始观测数据与拟合数据之间的残差序列,然后采用最小二乘配置模型对包括二次曲面拟合模型误差的综合误差进行优化减弱,最后得到新的高程异常。通过实例,将二次曲面拟合法,最小二乘配置法与文中提出的新方法进行比较分析。结果表明:新的组合方法的拟合预测精度要明显优于最小二乘配置及二次曲面拟合。

In engineering practice,in order to make the best of GPS elevation data and reduce the dependence on traditional leveling,it is very important to improve the fitting accuracy of GPS height anomaly.Therefore,based on the analysis of the basic principle of quadric surfaces fitting and least squares collocation fitting and the derivation of algorithm process,a new height anomaly fitting method is proposed.According to quadric surfaces fitting,the residual value sequence between the original observation data and the fitting data is calculated,and then the comprehensive error including the quadric surfaces fitting model error is optimized and weakened by using the least squares collocation model.Finally,a new height anomaly is obtained.Through an example,the quadric surfaces fitting method and the least squares collocation method are compared with the new method separetely proposed in this paper.The results show that the fitting prediction accuracy of the new combination method is obviously better than that of the least squares collocation and quadric surfaces fitting.