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

作　　者：吕建伟 张志华 张新秀 刘祖昱 Lü Jianwei;ZHANG Zhihua;ZHANG Xinxiu;LIU Zuyu(Faculty of Geoniatics,Lanzhou Jiaotong University,Lanzhou 730070,China;National-Local Joint Engineering Research Center of Technologies and Applications for National Geographic State Monitoring,Lanzhou 730070,China;Gansu Provincial Engineering Laboratory for National Geographic State Monitoring,Lanzhou 730070,China;Key Laboratory of Highway Network Monitoring,Gansu Province,Lanzhou 730030,China)

机构地区：[1]兰州交通大学测绘与地理信息学院,甘肃兰州730070 [2]地理国情监测技术应用国家地方联合工程研究中心,甘肃兰州730070 [3]甘肃省地理国情监测工程实验室,甘肃兰州730070 [4]甘肃省公路路网监测重点实验室,甘肃兰州730030

出　　处：《测绘通报》2020年第5期127-129,133,共4页Bulletin of Surveying and Mapping

基　　金：国家自然科学基金(41861059);兰州交通大学优秀平台支持(201806);甘肃省科技支撑计划(1604GKCA039)

摘　　要：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.

关 键 词：最小二乘配置 高程异常 二次曲面 残差 精度 

分 类 号：P228[天文地球—大地测量学与测量工程]