基于坐标协因数阵的GPS网隧道横向贯通中误差严密计算方法研究  

Study on Calculating Rigorously Lateral Link-up Error in GPS Tunnel Control Network Based on Variance-covariance Matrix of Coordinates

作　　者：刘成龙[1] 王鹏[1] 

机构地区：[1]西南交通大学土木工程学院,四川成都610031

出　　处：《铁道学报》2009年第1期74-77,共4页Journal of the China Railway Society

基　　金：国家自然科学基金项目(50478085)

摘　　要：针对GPS网隧道横向贯通误差近似计算方法在理论上的不足,本文根据GPS控制网平差和坐标协因数阵计算隧道横向贯通误差的原理,运用坐标转换方法和协因数传播定律,探讨隧道GPS网验后单位权中误差的计算方法和GPS网点在WGS84坐标系下的空间直角坐标协因数阵转换为隧道独立坐标系下的平面直角坐标协因数阵的方法,推导用于严密计算横向贯通误差的坐标协因数阵公式,实现隧道GPS网洞外横向贯通误差的严密计算,并据此对北天山隧道GPS网的横向贯通误差进行严密计算。Aiming at covering the insufficiency of the approximating theory in calculation of the mean square error of lateral link-up in the GPS tunnel control network, considering the principium of GPS control network adjustment and calculation of the mean square error of tunnel lateral link-up utilizing the variance-covariance matrix of coordinates, this paper discusses a method to calculate the posterior mean square error of weight unit in the GPS tunnel control network, and to transfer the space rectangular coordinates variance-covariance matrix of the GPS control network in WGS84 to the plane rectangular coordinates variance-covariance matrix in the tunnel independent coordinate system by employing the theory of coordinate transformation and law of variance-covariance propagation. This method educes the formulae of the variance-covariance matrix of coordinates, which is used for calculating rigorously the mean square error of lateral link-up. The algorithm is developed to implement the rigorous calculation of the mean square error of lateral link-up in the GPS tunnel control network, which is also operated in the Beitian Mountain GPS tunnel control network.

关 键 词：隧道 GPS控制网 横向贯通误差 坐标协因数阵 

分 类 号：U452.13[建筑科学—桥梁与隧道工程]