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.
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