基于方差-协方差阵的宝林隧洞控制点稳定性分析

Control point stability analysis of Baolin Tunnel based on variance-covariance matrix

为分析水利工程建设中测量控制点稳定性,提出了一种基于方差-协方差阵的坐标较差法稳定性分析方法,并推导了计算模型。以宝林隧洞两期GNSS观测数据为例,经过控制网平差得到控制点坐标及其方差、协方差,采用本文方法给出了计算结果,并与已有坐标较差法进行比对分析。结果表明:已有方法由于未考虑协方差的影响,计算得到的中误差明显大于方差-协方差阵法计算得到的中误差,而且控制点坐标分量间的协方差对中误差的影响甚至可以达到已有坐标较差法的1/3,因而采用所提出的方法进行测量控制点稳定性分析更可靠。

In order to study and analyze the stability of measurement control points in hydraulic engineering constructions, this paper proposed a stability analysis method based on variance-covariance matrix for coordinate difference method, and derived the calculation model. At the same time, taking the two-phase GNSS observation data of Baolin tunnel as an example, the control point coordinates and its variance and covariance were obtained through the control network adjustment. The calculation results were given by the presented method of this paper, and compared with the existing coordinate difference method. The result showed that the RMSE calculated by the existing coordinate difference method is significantly larger than the RMSE by the variance-covariance matrix method because the existing method does not consider the influence of covariance. And the influence of the covariance of the control point coordinate components on the RMSE can even reach 1/3 of the existing coordinate difference method. Therefore, the proposed method is more reliable to measuring the stability of the control points.