A.I. Kalinkin – Post-graduate Student, 

Department «Radio Systems», Ryazan State Radio Engineering University named after V.F. Utkin

E-mail: san_mozart@mail.ru

I.S. Kholopov – Ph.D.(Eng.), Dean of Department «Radioengineering and Telecommunications»,  Ryazan State Radio Engineering University named after V.F. Utkin E-mail: kholopov.i.s@rsreu.ru

The option of determining the location of the aircraft at the take-off or landing stage using optical tracking system is considered. Such an approach under the influence of natural or intentionally generated clutters to the global satellite navigation systems we can improve the reliability of determining the location of an aircraft relative to the runway at the stages of the pre-landing maneuver and landing. A method for solving the problem of determining the angular and spatial coordinates of an object from the image of two reference points obtained using one camera and information from an inertial measuring unit is presented. The formalization and geometric formulation of the problem of landing of an aircraft according to the image of reference points radiating in the same wavelength range is carried out. A method for solving the P2P problem is provided, provided that there is a priori information from the inclinometer. The conditions and restrictions on the process of solving the P2P problem are introduced, which make it possible to exclude solutions that do not satisfy the physical meaning of the problem. The analytical expression for the solution error arising due to the error in determining the glow centers of the projections of the frames in the image plane is presented. The error in determining the angular coordinates in solving the P2P problem by simulation is studied. It is shown that, within the framework of the mathematical model for solving the P2P problem with the standard deviation of determination of roll and pitch of not more than 0.05° and pixel coordinates of reference points of not more than 0.5 pixels, the measurement of the angular coordinate of the yaw with a standard deviation of not more than 0.2° is achieved.

1. Ivanov V.O. Optiko-elektronnoe ustroistvo avtomaticheskoi posadki avtonomnogo letayushchego robota. Izvestiya VUZov. Priborostroenie. 2012. T. 50. № 11. S. 23−28. (in Russian)
2. Zavalishin O., Zatuchnyi D. Metody povysheniya pomekhoustoichivosti navigatsionnykh sistem vozdushnykh sudov grazhdanskoi aviatsii. Radioelektronnye tekhnologii. 2019. № 2 (21). S. 70−75. (in Russian)
3. Antonov D.A., Zharkov M.V., Kuznetsov I.M., Lunev E.M., Pronkin A.N. Opredelenie navigatsionnykh parametrov bespilotnogo letatelnogo apparata na baze fotoizobrazheniya i inertsialnykh izmerenii. Trudy MAI. 2012. № 91. S. 1−26. (in Russian)
4. Belokurov V.A. Sistema uglovoi orientatsii na osnove gaussovskogo partsialnogo filtra. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2016. № 56. S. 11−16. DOI: 10.21667/1995-4565-2016-56-2-11-16. (in Russian)
5. GOST 20058-80. Dinamika letatelnykh apparatov v atmosfere. Terminy, opredeleniya i oboznacheniya. M., 1980. 54 s. (in Russian)
6. Kalinkin A.I., Koshelev V.I., Kholopov I.S. Issledovanie pogreshnosti izmereniya koordinat v sisteme avtonomnoi navigatsii po opticheskim metkam. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2016. № 58. S. 10−17. DOI: 10.21667/1995-4565-2016-58-4-10-17. (in Russian)
7. Pavlov O.V., Kholopov I.S. Sravnitelnyi analiz dvukh algoritmov vybora repernogo svetodiodnogo klastera v zadache navigatsii po opticheskim metkam. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2017. № 61. S. 13−18. DOI: 10.21667/1995-4565-2017-61-3-13-18. (in Russian)
8. Hartley R., Zisserman A. Multiple View Geometry in Computer Vision: 2nd edition. Cambridge: Cambridge University Press. 2003. 656 p. DOI: 10.1017/CBO9780511811685.
9. Brown D.C. Close-Range Camera Calibration. Photogrammetric Engineering. 1971. V. 37(8). P. 855−866. DOI: 10.1.1.14.6358.
10. Kuipers J.B. Quaternions and rotation sequences. A primer with applications to orbits, aerospace, and virtual reality. New Jersey: Princeton University. 1999. 391 p.
11. Chelnokov Yu.N. Kvaternionnye i bikvaternionnye modeli i metody mekhaniki tverdogo tela i ikh prilozheniya. Geometriya i kinematika dvizheniya. M.: FIZMATLIT. 2006. 512 s. (in Russian)
12. Kalinkin A.I., Kholopov I.S. Realizatsiya besplatformennoi inertsialnoi navigatsionnoi sistemy na mikromekhanicheskikh datchikakh dlya mobilnogo nazemnogo ob’ekta. Proektirovanie i tekhnologiya elektronnykh sredstv. 2015. № 2. S. 27−34. (in Russian)
13. Kukelova Z., Bujnak M., Pajdla T. Closed-form solutions to the minimal absolute pose problems with known vertical direction. ACCV'10 Proc. of the 10th Asian conference on Computer vision. Part II. Queenstown. 2010. P. 216−229.
14. Kalinkin A.I., Kholopov I.S. Otsenka pogreshnosti opredeleniya uglovykh koordinat ob’ekta s dvumya repernymi izluchatelyami. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2019. № 69. S. 52−59. DOI: 10.21667/1995-4565-2019-69-52-59. (in Russian)
15. Belokurov V.A. Primenenie avtokovariatsionnogo metoda naimenshikh kvadratov v invariantnoi skheme uglovoi orientatsii. Vestnik Ryazanskogo gosudarstvennogo radiotekhnicheskogo universiteta. 2018. № 64. S. 9−16. DOI: 10.21667/1995-4565-2018-64-2-9-16. (in Russian)