基于约束平差的陀螺导线精度预计

Gyro traverse error prediction based on constraint adjustment

贯通测量精度预计使用传统的导线预计公式很不方便,特别是当导线加测陀螺边时更加繁琐复杂。本文提出基于间接平差原理的精度预计方法,通过列立水平角、边长和陀螺方位角的误差方程,进而组成法方程,计算协因数矩阵来求解导线终点的误差。由于法方程矩阵是秩亏矩阵,使用了坐标约束的方法,不仅有利于计算机编程处理,还能顾及起算点精度的影响。算例表明了新方法既正确又简单,便于推广使用。

It is not convenient to predict traverse error using traditional traverse error formula in heading-through surveying,especially when the traverse is added gyro leg.So an error prediction method based on the indirect adjustment principle is proposed.Firstly error equations of all horizontal angle,side length and gyro azimuth are formulated,and then the corresponding normal equation is obtained.At last,the co-factor matrix is used to estimate the errors at the end of the traverse.Normal equation matrix is rank deficient,so the coordinates of known points are constraint,which is not only helpful for computer programming,but also take into account the effect of the starting point error.Examples show that the new method is right and simple,easy to be popularized and applied.