整体最小二乘法平面坐标转换在基坑水平位移监测中的应用

Application of Total Least Squares Plane Coordinate Transformation in Pit Horizontal Displacement Monitoring

在参数求解过程中,经常遇到参数估计模型的观测向量和系数矩阵都可能存在误差的情况,于是人们在20世纪80年代提出了整体最小二乘方法。近几年,整体最小二乘才被引入测量领域。本文详细阐述了整体最小二乘法平面坐标转换基于奇异值分解原理的解算过程。在此基础上,把整体最小二乘法平面直角坐标转换应用到基坑水平位移监测中,改进了传统的变形监测数据处理方法,并运用工程实例验证了该方法的可行性。

We often encounter in some estimation models that both the observation and design matrix are subject to errors in parameter solution process. So the total least -square （TLS） method was proposed in early 80＇s of twenty century. The TLS was introduced into measurement only in recent years. This paper describes systematically the commutation process of the TLS plane coordinate transforma- tion based on singular value decomposition principle. On this basis, we apply the TLS plane rectangular coordinate transformation to the pit horizontal displacement monitoring, improve the traditional method of deformation monitoring data processing, and validate the feasibility of the method using engineering instance.