I. INTRODUCTION Section: Choose Top of page ABSTRACT I. INTRODUCTION << II. TELESCOPE POINTING ER... III. ANALYSIS OF THE EXPE... IV. CONCLUSION REFERENCES

2 in space and hundreds of millions of space debris with a radar cross section of <0.1 m2. The space debris mainly distributes in the geostationary earth orbit and low earth orbit. Their existence seriously affects the safety of a spacecraft in orbit. 1,2 Space debris collision avoidance using a three-filter sequence ,” Mon. Not. R. Astron. Soc. 442, 3235– 3242 (2014). 1. D. Casanova, C. Tardioli, and A. Lemaître, “,” Mon. Not. R. Astron. Soc., 3235–(2014). https://doi.org/10.1093/mnras/stu1065 Creation of a synthetic population of space debris to reduce discrepancies between simulation and observations ,” Celest. Mech. Dyn. Astron. 130, 1–19 (2018). 2. A. Petit, D. Casanova, M. Dumont, and A. Lemaître, “,” Celest. Mech. Dyn. Astron., 1–19 (2018). https://doi.org/10.1007/s10569-018-9873-1 Space debris is the space junk generated by human beings in space during space activities, and it mainly comes from an invalid spacecraft, the last stage arrow of a carrier rocket, and the debris of spacecraft disintegrating in the orbit. According to incomplete statistics, there are ∼17 000 space debris with a radar cross section of >0.1 min space and hundreds of millions of space debris with a radar cross section of <0.1 m. The space debris mainly distributes in the geostationary earth orbit and low earth orbit. Their existence seriously affects the safety of a spacecraft in orbit.Therefore, debris monitoring has attracted significant attention worldwide. Even though geodetic technologies have the highest measurement accuracy, laser ranging technology is widely used to detect space debris. At present, there are >50 global laser observation stations and a global satellite laser ranging measurement and tracking network that have been formed, and both of which are of great importance to the monitoring of space debris.

3,4 3. F. Qu, C. M. Zhao, and Z. B. Wei, “ Pointing correction of satellite laser ranging telescope system ,” Sci. Surv. Mapp. 31, 84– 85 (2006). Confidence limits for the pointing error of gimbaled sensors ,” IEEE Trans. Aerospace Electron. Syst. AES-2, 648– 654 (1996). 4. J. W. Fisk and A. K. Rue, “,” IEEE Trans. Aerospace Electron. Syst. AES-2, 648–(1996). https://doi.org/10.1109/TAES.1966.4501957 5 MMT pointing and tracking ,” Proc. SPIE 628, 9– 15 (1986). 5. A. D. Poyner, J. W. Montgomery, and B. L. Ulich, “,” Proc. SPIE, 9–(1986). https://doi.org/10.1117/12.963506 Laser ranging technology is one of the most accurate space technologies in space target tracking technology, and single ranging accuracy of cooperative targets such as in-orbit spacecraft and the noncooperative targets such as space debris can reach centimeter level and it is developing into the millimeter level.However, in the process of space debris detection by laser ranging technology, because of the small size, poor prediction accuracy, and no reflection prism on the surface of space debris, it belongs to a noncooperative target,making the pointing position of the telescope deviate from the actual position of the space debris, which prevents laser ranging systems from accurately detecting the space debris. Therefore, the precise pointing and guidance of the laser ranging system become the key to the accurate detection of space debris.

6,7 6. L. Huang, “ Research in pointing error and shafting technologies for large telescope ,” Ph.D. thesis, Institute of Optics and Electronics, Chinese Academy of Sciences , 2016. 7. R. L. Meeks, “ Improving telescope mechanical error estimation using pointing data ,” Ph.D. thesis, Colorado State University, Fort Collins, CO , 2003. 8,9 8. B. Deng, “ Research on the wide-band large-angle active phased array antenna ,” Ph.D. thesis, Nanjing University , 2018. Control and pointing challenges of large antennas and telescopes ,” IEEE Trans. Contr. Syst. Technol. 15, 276– 288 (2007). 9. W. Gawronski, “,” IEEE Trans. Contr. Syst. Technol., 276–(2007). https://doi.org/10.1109/TCST.2006.886434 et al. 10 Static pointing error of level mounting optoelectronic telescope ,” Chin. Opt. 8, 263– 269 (2015). 10. Z. W. Li, W. B. Yang, and N. Zhang, “,” Chin. Opt., 263–(2015). https://doi.org/10.3788/co.20150802.0263 11 11. B. Wang, “ Research on the pointing error of telescope mount in SLR system ,” Ph.D. thesis, Shanghai Astronomical Observatory , 2004. 12 12. C. G. Zhu, “ Research of pointing error modeling of the satellite laser ranging based on BP neural network ,” Ph.D. thesis, Institute of Seismology China Earthquake Administration , 2013. 13 13. K. Xu and Q. S. Zhu, “ An application of RBF neural network in global sky pointing model ,” Microcomput. Inf. 228–229, 227 (2008). 14 14. R. Prestage and I. Coulson, “ Treatment of pointing in the new JCMTTCS ,” Ph.D. thesis, James Clerk Maxwell Telescope TCS Design Note5 , 1998. et al. 15 Pointing and tracking performance of the W. M. Keck Telescope ,” Proc. SPIE 2199, 117– 125 (1994). 15. H. Lewis, W. Lupton, M. Sirota, T. S. Mast, J. Nelson, and P. Wallace, “,” Proc. SPIE, 117–(1994). https://doi.org/10.1117/12.176182 16 16. Y. Zhao, “ Research on modeling analysis and design of pointing errors for large radio telescope ,” Ph.D. thesis, Xidian University , 2008. et al., 17 17. N. Ukita, H. Ezawa, B. Ikenoue, and M. Saito, “ Thermal and wind effects on the azimuth axis tilt of the ASTE 10-m antenna ,” Publ. Natl. Astron. Observ. Jpn. 10, 25– 33 (2007). et al., 18 Subaru telescope improved pointing accuracy in open-loop and Az rail flatness ,” Proc. SPIE 6267, 62673K (2006). 18. T. Kanzawa, D. Tomono, T. Usuda, N. Ohshima, K. Namikawa, T. Ogasawara, and N. Itoh, “,” Proc. SPIE, 62673K (2006). https://doi.org/10.1117/12.670629 et al., 19 A new calibration model for pointing a radio telescope that considers nonlinear errors in the azimuth axis ,” Res. Astron. Astrophys. 14, 733– 740 (2014). 19. D. Q. Kong, S. G. Wang, J. Q. Wang, M. W. and H, and B. Zhang, “,” Res. Astron. Astrophys., 733–(2014). https://doi.org/10.1088/1674-4527/14/6/011 et al., 20 Azimuth-track level compensation to reduce blind-pointing errors of the deep space network antennas ,” IEEE Antennas Propag. Mag. 42, 28– 38 (2000). 20. W. Gawronski, F. Baher, and O. Quintero, “,” IEEE Antennas Propag. Mag., 28–(2000). https://doi.org/10.1109/74.842123 21 21. J. X. Gu, “ Research on the antenna pointing error of 25 m radio telescope ,” Ann. Shanghai Observ. Acad. Sin. 15, 205– 211 (1994). In view of the low pointing accuracy of the telescope of the laser ranging system at present, the method of correcting the telescope pointing error of the laser ranging system was proposed by Scholars to improve the pointing accuracy of the telescope. One is to improve the pointing accuracy of the telescope by improving the processing and assembly accuracy of the hardware equipment. The second is to establish a pointing error correction model to improve the pointing accuracy of the telescope.Since the first method is time-consuming and laborious and the accuracy improvement is limited, the second method is widely adopted to improve the pointing accuracy of the telescope in the laser ranging observation stations. The traditional telescope pointing error correction models include the spherical harmonic function model, the basic parameter model, and the mount model; among them, the spherical harmonic function model is simple in form and can be used to fit various errors; however, the correlation among the model coefficients is relatively large, the parameters have no actual physical meaning, and the model is not stable enough. In contrast, the basic parameter model and the mount model are relatively stable, and these two types of models are built on the basis of determining the interrelationship among the physical factors causing the pointing errors. In addition, these two types of model functions are clear in form, the convergence is fast in the process of solving function, and each parameter has a definite physical meaning. However, it is difficult to comprehensively consider the factors affecting the pointing accuracy and accurately describe all types of error laws. In addition, the overall accuracy of the model is not very high.On this basis, different laser ranging telescope pointing error correction models have been proposed. Liand Wangproposed the use of image processing to establish the telescope pointing error correction model; Zhuproposed the use of the back propagation (BP) neural network model to correct the telescope pointing error. Both methods were tested and applied in the mobile laser ranging station; Xu and Zhueproposed the use of radial basis function neural network for modeling; Prestage and Coulsonand Lewisadded several corrected empirical terms based on the description of the main sources of error and predicted the trajectory of space debris in the airspace; Zhaoused the quaternion method to model the pointing error of the radio telescope and analyzed and summarized the error items affecting the pointing accuracy of the radio telescope; Ukita.,Kanzawa.,Kong.,GawronskiGu,and others investigated the perspective of the effect of the azimuth rail irregularity error on the pointing accuracy of the telescope and proposed the look-up table method to improve the pointing accuracy of the telescope. The accuracy of the telescope pointing correction model proposed can reach about 10 in.

The investigation on telescope pointing correction has reached a certain level. However, since the satellite prediction accuracy is generally in the decimeter level, and the space debris prediction accuracy is in the kilometer level, the current pointing accuracy of the model is still difficult to meet the high-accuracy pointing requirements of the telescopes required for space debris detection. Therefore, on the basis of previous studies, the requirements of the telescope pointing correction with fast and real-time performance are taken into consideration, and the BP neural network model optimized by the genetic algorithm (GA) and Levenberg–Marquardt (LM) is proposed to establish the telescope pointing error correction model, in which GA can determine the optimal initial weight matrix of the BP neural network to avoid the deficiency that the BP neural network is too sensitive to the initial parameters; LM accurately trains the BP neural network in the local solution space to ensure that the global optimal solution can be searched. Based on the 60 cm aperture laser ranging system of the Beijing Fangshan station, the experimental research and application of the real-time pointing correction method for the laser ranging system telescope were carried out. The results show that the application of the BP neural network model optimized by the GA and LM into the modeling of the telescope pointing error in the laser ranging system can greatly improve the pointing accuracy of the telescope and meet the requirements of the telescope pointing accuracy for detecting space debris in the laser ranging system.