基于数字天顶仪的星点图像坐标误差分析

星点图像坐标的准确性与数字天顶仪的定位精度紧密相关。根据数字天顶仪成像原理，严格推导出星点图像坐标表达式，在此基础上推导了星点图像坐标在4个误差因素及综合误差下的误差方程，分析结果表明各误差之间相互独立。通过仿真4个误差因素及综合误差情况下的星图数据进行分析，仿真结果表明:焦距误差与转位误差对各星点图像坐标的影响各不相同，焦距引起的坐标变化值x和y相对其平均值的最大波动值分别为2.38、3.04 pixel；转位误差引起的坐标变化值x和y相对其平均值的最大波动值为1.06、1.41 pixel；光轴倾斜误差与主点偏移引起的星点图像坐标变化是整体性偏移。另外，提出了一种误差参数求解的方法，利用解算出来的误差参数对星点图像坐标进行补差，数字天顶仪的定位经度精度提高了约1.98 m，纬度精度提高了约1.65 m。

Error analysis of star image coordinate based on digital zenith camera

The accuracy of the star image coordinates is closely related to the positioning accuracy of the digital zenith camera. On the basis of the principle of digital zenith camera imaging, the star image coordinate expression was deduced strictly. The error equations of the image coordinates under four error factors and composite error factor were deduced based on the star image coordinate expression. The analysis results showed that the errors were independent of each other. Star map data was obtained through the simulation under four error factors and composite error factor. The simulation results show that:The influence of the image coordinates of each star point caused by the focal distance error and the transposition error is different. Compared to average value of the coordinate change values of x and y, the maximum fluctuation values of x and y caused by the focal distance error were about 2.38 pixel and 3.04 pixel. The maximum fluctuation values of x and y caused by the transposition error were about 1.06 pixel and 1.41 pixel. The error of the optical axis tilt and the main point offset made the change of the star image coordinates as whole migration. In addition, a method for solving the error parameters was proposed. The calculated error parameters were used to compensate the star image coordinates. The longitude accuracy of the digital zenith camera was improved by about 1.98 m, and the latitude accuracy was improved by about 1.65 m.