A. D. Vinogradov – Dr.Sc. (Eng.), Professor, Chief Research Scientist

Military Air Force Academy n.a. Prof. N.E. Zhukovsky and Y.A. Gagarin (Voronezh)

E-mail: mvvad@mail.ru

A. Yu. Vostrov – Chief Designer,

JSC «Concern «Sozvezdie» (Voronezh)

E-mail: a.y.vostrov.1988@mail.ru

I. S. Dmitriev – Ph.D. (Eng.), Leading Research Scientist,

JSC «Concern «Sozvezdie» (Voronezh)

E-mail: dmiv@mail.ru

Satellite radio navigation systems are currently used to determine with high accuracy the coordinates and angular orientation of mobile air-based objects and equipment placed on them (in particular, on-board direction finding antennas). Under the conditions of loss of signals from satellite radio navigation systems, the coordinates and angular orientation of moving objects can be determined using onboard autonomous navigation sensors and systems (inertial, geomagnetic). However, a disadvantage of on-board autonomous navigation sensors and systems is the deterioration in the accuracy of determining navigation parameters with an increase in the time interval since the calibration of sensors or systems. If a radio-direction finder with an on-board direction-finding antenna is placed on a mobile object, it is possible to determine the azimuth and elevation angle of radio sources with known coordinates, the coordinates in space and the angular orientation of both the on-board direction-finding antenna and the mobile object on which it is located can be determined by an angular method based on the use of results of the radio direction finding of reference sources of radio emission in the azimuth and elevation planes.

In the article the task of determining the coordinates and angular orientation of an on-board direction finding antenna placed on a mobile air-based object based on the results of the azimuth-elevation radio direction finding of reference radio-emission sources has been considered. The analytical relationships describing the relationship between azimuth and elevation angle of a reference radio source measured by an onboard azimuth-elevation radio direction finder with parameters of spatial position and angular orientation of an on-board direction finding antenna have been determined and the corresponding expression for the conditional probability density function of the measurement errors of the azimuth-angular elevation direction finder has been obtained. The expressions for the lower boundary of the covariance matrix of errors of determination of the onboard direction finding antenna coordinates and the angular orientation, which correspond to the Rao–Cramer inequality, have been defined. The tables and graphs of the dependences of the on-board direction finding antenna coordinates and the angular orientation errors in determining on its spatial location relative to the three reference radio-emission sources with different configurations of their placement and accuracy of azimuth and elevation measurements have been given. The expressions for the maximum likelihood method target functions of estimating the onboard direction finding antenna coordinates and the angular orientation when using the results of radio direction finding of reference radio emission sources by the onboard azimuth elevation direction finder separately, as well as when used together with the onboard altimeter and inclinometer have been obtained. The results of statistical experiments for comparing the target functions by the magnitude of the errors in estimating the onboard direction finding antenna coordinates and the angular orientation have been given.

1. Yatsenkov V.S. Osnovy sputnikovoj navigatsii. Sistema GPS NAVSTAR i GLONASS. M.: Goryachaya liniya – Telekom. 2005.
2. Tyapkin V.N., Garin E.N. Metody opredeleniya navigatsionnykh parametrov podvizhnykh sredstv s ispol'zovaniem sputnikovoj radionavigatsionnoj sistemy GLONASS. Monografiya. Krasnoyarsk: Sibirskij federal'nyj universitet. 2012.
3. Branets V.N., Shmyglevskij I.P. Vvedenie v teoriyu besplatformennykh inertsial'nykh navigatsionnykh sistem. M.: Nauka. 1992.
4. Orientatsiya i navigatsiya podvizhnykh ob''ektov: sovremennye informatsionnye tekhnologii. Pod red. B.S. Aleshina, K.K. Veremeenko, A.I. Chernomorskogo. M.: FIZMATLIT. 2006.
5. Belavin O.V. Osnovy radionavigatsii. Ucheb. posobie dlya vuzov. Izd. 2-e, pererab. i dop. M.: Sov. radio. 1977.
6. Belyaevskij L.S., Novikov V.S., Olyanyuk P.V. Osnovy radionavigatsii. Uchebnik dlya vuzov grazhd. aviatsii. M.: Transport. 1982.
7. Yarlykov M.S. Statisticheskaya teoriya radionavigatsii. M.: Radio i svyaz'. 1985.
8. Sosulin Yu.G. Teoreticheskie osnovy radiolokatsii i radionavigatsii. Ucheb. posobie dlya vuzov. M.: Radio i svyaz'. 1992.
9. Bakulev P.A., Sosnovskij A.A. Radiolokatsionnye i radionavigatsionnye sistemy. Ucheb. posobie dlya vuzov. M.: Radio i svyaz'. 1994.
10. Kondrat'ev V.S., Kotov A.F., Markov L.N. Mnogopozitsionnye radiotekhnicheskie sistemy. Pod red. V.V. Tsvetnova. M.: Radio i svyaz'. 1986.
11. Bubnov I.A., Bogatov S.F., Dubov S.D., Kalinin A.K., Savchenko P.T. Voennaya topografiya. M.: Voenizdat. 1977.
12. Vinogradov A.D., Vostrov A.Yu., Dmitriev I.S. Obobshchennaya struktura radiopelengatora i osnovnye terminy, ispol'zuemye v teorii radiopelengovaniya. Antenny. 2018. № 5 (249). S. 5–20. [in Russian]
13. GOST 20058–80. Dinamika letatel'nykh apparatov v atmosfere. Terminy, opredeleniya i oboznacheniya. M.: Izdatel'stvo standartov. 1981.
14. Tikhonov V.I. Statisticheskaya radiotekhnika. Izd. 2-e, pererab. i dop. M.: Radio i svyaz'. 1982.
15. Korn G., Korn T. Spravochnik po matematike. M.: Nauka. 1974.
16. Sejdzh E., Mels Dzh. Teoriya otsenivaniya i ee primenenie v svyazi i upravlenii. M.: Svyaz'. 1976.
17. Bandi B. Metody optimizatsii. Pod red. V.A. Volynskogo. Per. s angl. O.V. Shikheevoj. M.: Radio i svyaz'. 1988.
18. Dokumentatsiya na funktsiyu MATLAB randn. Ofitsial'nyj sajt MathWorks [Elektronnyj resurs] / URL: http://www.mathworks.com/help/ matlab/ref/randn.html (data obrashcheniya: 01.10.2018).
19. Dokumentatsiya na funktsiyu MATLAB fminsearch. Ofitsial'nyj sajt MathWorks [Elektronnyj resurs] / URL: http://www.mathworks.com/ help/matlab/ref/fminsearch.html (data obrashcheniya: 01.10.2018).