顾及点位绝对关系求解最小二乘配置的协方差函数  

The Solution of Least Square Collocation’s Covariance with the Absolute Relation of Point Position

作　　者：闫占瑞 YAN Zhanrui(Tiezheng Testing Technology Co.Ltd.,Jinan Shandong 250014,China)

机构地区：[1]铁正检测科技有限公司,山东济南250014

出　　处：《铁道建筑技术》2023年第10期62-65,共4页Railway Construction Technology

基　　金：中国铁建股份有限公司科技研究开发计划项目(2019-C12)。

摘　　要：最小二乘配置(Least Square Collocation, LSC)广泛应用于GNSS高程拟合,其中协方差函数确定是其关键问题。传统的基于随机函数的各态历经平稳性求解协方差函数仅考虑信号间的距离,而忽略点位绝对关系对协方差函数的影响。基于此,本文顾及未测点与已测点之间的相对关系与绝对关系,提出一种在有限数据下求解未测点S*与已测点S协方差函数的方法。利用51个GNSS水准点进行试验验证,并与具有高度非线性化的GA-BP网络进行对比分析,结果表明本文方法可用于最小二乘配置的协方差函数求解。Least Square Collocation(LSC)is widely used in GNSS elevation fitting,and the determination of covariance function is the key problem.The traditional solution of covariance function is based on the stationarity of ergodic states of random function,which only takes the distance between signals into account,while the influence of the absolute relation of point position on the covariance function is ignored.Therefore,this paper takes into account the relative and absolute relations between unmeasured and measured points,and proposes a method to solve the covariance function of unmeasured point S∗and measured point S under limited data.There are 51 GNSS level points used for experimental analysis,and compared with GA-BP network with high nonlinearity,and the experimental results show that the proposed method in the paper can be used to solve the covariance function of least square collocation.

关 键 词：最小二乘配置 GNSS 协方差函数 GA-BP网络 

分 类 号：P258[天文地球—测绘科学与技术] P216