Accurate Attitude Detection of Telescope Azimuth Axis Using Beidou Differential Positioning System and Pointing Error Correction

The precise detection of telescope azimuth axis attitude is paramount in astronomy and ground-based observations, as it directly influences the accuracy of telescope pointing. To ascertain the overall tilt attitude of the azimuth axis, the Beidou differential positioning system is utilized to gather the telescope positioning data. However, the acquired positioning data are not always dependable when utilized in practical analysis. To address this issue, a novel approach that integrates ensemble empirical mode decomposition (EEMD) and variational mode decomposition (VMD) is proposed to extract effective signals from Beidou differential positioning data. Initially, the positioning data are decomposed using EEMD, aiming to separate harmonic-like signals and wave crest signals. Subsequently, VMD is applied to eliminate noise signals. Moreover, a 3-D discrete point fitting algorithm is introduced to derive the telescope trajectory fitting curve from effective signals, which aids in determining the tilt attitude of the azimuth axis. Additionally, to correct the pointing error induced by azimuth axis tilt, both an azimuth error model and a pitch error model are established in this study. The experimental results show that the correlation coefficient between EEMD processed signals and original signals is less than 12.66% of the VMD result, and the result of EEMD-VMD is higher than 3.51% of the EEMD result. Before pointing correction, the maximum azimuth pointing error and the maximum pitch pointing error caused by the azimuth axis tilt are 0.0736 degrees. Using the established pointing error correction model, the corrected maximum azimuth pointing error is 0.0028 degrees, the maximum pitch pointing error is 0.0054 degrees, and the pointing accuracy is improved by 0.0708 degrees and 0.0682 degrees, respectively. The results indicate that EEMD-VMD can effectively remove the harmonic-like signals, wave crest signals, and noise signals, and the pointing error models can accurately rectify the pointing error caused by azimuth axis tilt, thereby significantly enhancing the telescope pointing accuracy.