拍星残差数据相关性分析的大气折光差修正

靶场通常采用夜间静态拍星的方式检测光电经纬仪的静态测角总误差。受大气折射率变化的影响，俯仰方向测角数据通常采用大气折光差经验公式进行修正。不同地区和时间的大气环境差异使得该经验公式存在较大误差，导致拍星解算得到的俯仰方向测角误差偏大，且影响俯仰方向测角误差因素的进一步分离。为此，提出了一种基于多台光电经纬仪同步拍星数据相关性分析的大气折光差修正方法。基于经纬仪拍星方位角和俯仰角测量残差模型推导得到了大气折光差修正误差模型。根据该误差模型，利用分布在同一区域不同点位的多台光电经纬仪拍星俯仰角残差数据，采用最小二乘法拟合得到大气折光差的修正系数并修正俯仰角测量残差数据。实测数据表明：采用该方法对俯仰角测量残差进行大气折光差修正后，光电经纬仪俯仰角测角总误差显著降低，且由垂直轴倾斜误差修正错误引起的方位角和俯仰角残差特性得以显现。文中提出的方法无需使用探空气球等获取大气参数，即可对同一地域分布的多台光电经纬仪拍星俯仰角残差数据进行修正，修正后的数据可用于进一步分离其他误差因素，具有较强的工程应用价值。

Correction of atmospheric refraction error based on correlation analysis of star measurement residual data

  Objective  The static angle measurement error for an optical electronic theodolite is generally measured by the star calibration method in the shooting range. Affected by the change of atmospheric refractive index, the empirical formula of atmospheric refraction error is usually used to correct the angle measurement data in the pitching direction of stars. However, the difference between the atmospheric composition in various areas and over time leads to a significant error in the empirical formula. This error results in a significant error in the pitch angle measurement results obtained by the star calibration procedure and affects the separation of other error factors. Therefore, the correction of atmospheric refraction error, which is obtained by the empirical formula, is very important to calculate the total error in measuring the pitch angle of an optical electronic theodolite. To precisely correct atmospheric refraction error, it is usually necessary to use sounding balloons or meteorological aircraft to collect atmospheric parameters at different altitudes. But this traditional method is complicated to organize and difficult to implement. For this purpose, a new method for correcting the empirical formula of atmospheric refraction error is proposed in this paper.  Methods  A method for correcting the empirical formula of atmospheric refraction error is built in this paper. The method is based on the correlation analysis of star measuring data from multiple theodolites. According to the residual error model for measuring the azimuth and pitch angle of the theodolite, the atmospheric refraction error correction model is derived. Based on this error model, using the residual data of the pitch angle from multiple photoelectric theodolites distributed at different points in the same area, the coefficient for correcting atmospheric refraction error is obtained by fitting the pitch angle measurement residuals and the tangent of the pitch angle with the least square method, and the residual pitch angle data are corrected with the atmospheric refraction error correction model.   Results and Discussions   Analysis results based on the data of six phototheodolites distributed in the same area show that there were obvious components of the pitch angle measurement residuals that varied linearly with the tangent of the pitch angle (Fig.1). According to the atmospheric refraction error correction model, the pitch angle measurement residuals of the six phototheodolites were linearly fitted to obtain six correction coefficients (Tab.1), and the average value was taken as the comprehensive correction coefficient. After using the comprehensive correction coefficient to correct the atmospheric refraction error, the correlation between the pitch angle residuals and the tangent of pitch angle was significantly decreased (Fig.2), and the total static angle measurement error of the pitch angle of the six devices was significantly reduced (Tab.1). Moreover, before the atmospheric refraction error correction, the peak values of the normalized correlation curves (Fig.6) of the azimuth and pitch angle measurement residuals of each phototheodolites were generally under 0.7 (Tab.2). After the correction of atmospheric refraction error, the peak values of the normalized correlation curves of the azimuth and pitch angle measurement residuals were greater than 0.7, indicating that the correlation of azimuth and pitch angle measurement residuals is enhanced, and this correlation is mainly caused by the correction error of vertical axis tilt angle.  Conclusions  A method for the correction of atmospheric refraction error based on the correlation analysis of star measurement residual data is proposed. The atmospheric refraction error correction model is derived based on the residual error model for measuring the azimuth and pitch angle of the theodolite. With the residual data of the pitch angle obtained from multiple photoelectric theodolites distributed at different points in the same area, the coefficient for correcting atmospheric refraction error is obtained by the least square method and the residual pitch angle data are corrected. As a result, the total error in measuring the pitch angle of an optical electronic theodolite is significantly reduced after correction of the atmospheric refraction error, and the features of the azimuth and pitch angle residuals caused by the error in correcting the vertical axis tilt error are revealed. The proposed method makes it possible to correct residual pitch angle data of multiple optical electronic theodolites distributed in the same area without using sounding balloons to obtain atmospheric parameters, and the corrected data can be used to separate other error factors, which is of high engineering application value.