E.I. Minakov1, А.V. Zyuzin2, V.B. Tichonov3, S.V. Bogdanovsky4

1 Tula State University (Tula, Russia)

2,3 Yaroslavl Higher Military School of Air Defense n.a. Marshal of the Soviet Union L.A. Govorov (Yaroslavl, Russia)

4 Military Order of Zhukov University of Radio Electronics (Cherepovets, Vologda Region, Russia)

1 eminakov@bk.ru, 2 aleksey.zyuzin@mail.ru, 3 kaktus38@yandex.ru, 4 bogdan141@mail.ru

Problem formulation. The relevance of this research stems from the need to ensure reliable positioning of airborne passive radar systems in the presence of interference and a limited number of reference stations. Traditional computational geometry methods encounter measurement noise and a large number of false positives, leading to a significant reduction in accuracy.

Purpose., the objective of this study is to develop, implement, and evaluate an algorithm for determining the coordinates and attitude angles of an airborne passive radar system based on angular measurements using cluster analysis, as well as to evaluate its effectiveness in comparison with existing methods.

Results. The proposed algorithm, based on an analytical solution to the «Perspective-3-Point» problem for generating an array of possible positions followed by filtering based on physical feasibility, is implemented in software and analyzed using mathematical modeling. The method is based on a modified cluster analysis algorithm for grouping geometrically consistent positions, with the resulting coordinates and attitude angles calculated using the criterion of minimum internal variance of the cluster.

Practical significance. The obtained results demonstrated the method's high immunity to measurement noise and false positives, and confirmed a 5-20 % increase in position determination accuracy compared to traditional approaches, depending on the number of reference stations, their placement topology, and signal-to-noise ratio.The key conclusion of the study was the demonstrated advantage of the developed algorithm over traditional methods due to the effective elimination of geometrically inconsistent solutions and the optimal selection of the final position from an arbitrary number of reference stations. These results confirm the high potential for the proposed algorithm in the design of navigation systems for unmanned aerial vehicles equipped with passive radar systems, and also open up opportunities for increasing the autonomy and accuracy of their operation in complex electronic environments.

The work was carried out with the financial support of a Grant in the form of a research grant from the Committee on Science and Innovation of the Tula Region No. 15 dated June 21, 2024.

Minakov E.I., Zyuzin А.V., Tichonov V.B., Bogdanovsky S.V. Algorithm for determining the coordinates and orientation angles of an airborne passive radar system based on angular measurements using cluster analysis // Radioengineering. 2026. V. 90. № 9. P. 96−107. DOI: https://doi.org/10.18127/j00338486-202609-10

1. Tyapkin V.N., Garin E.N. Metody opredeleniya navigacionnyh parametrov podvizhnyh sredstv s ispol'zovaniem sputnikovoj radionavigacionnoj sistemy GLONASS. Krasnoyarsk: Sib. feder. un-t. 2012. 260 s. (in Russian).
2. Dyatlov A.P., Dyatlov P.A., Kul'bikayan B.H. Radioelektronnaya bor'ba so sputnikovymi radionavigacionnymi sistemami. M.: Radio i svyaz', 2004. 226 s. (in Russian).
3. Sagdeev K.M., Linec G.I., Mel'nikov S.V. i dr. Sposob opredeleniya fakta iskazheniya navigacionnogo polya i identifikacii pomekhovogo vozdejstviya na priemnik RBLA. Infokommunikacionnye tekhnologii. 2020. T. 18. № 2. S. 166–177 (in Russian).
4. Filippov A.A., Bazhin D.A., Hlobystov A.N. Povyshenie effektivnosti upravleniya bespilotnogo letatel'nogo apparata v usloviyah pomekh. Informacionno-upravlyayushchie sistemy. 2014. № 6(73). S. 45–50 (in Russian).
5. Andreev S.V., Il'inyh V.V., Il'inyh O.A., Chertkov M.S., Klyuchnikov A.V. Ocenka vliyaniya pogreshnostej inercial'nyh datchikov na tochnost' besplatformennoj inercial'noj navigacionnoj sistemy. Vestnik Koncerna VKO «Almaz Antej». 2018. № 2. S. 29–34 (in Russian).
6. Mathematical Problems in Engineering. Hindawi Publishing Corporation. 2015. V. 2015. Article ID 147397. 6 p.
7. Svidetel'stvo o gosudarstvennoj registracii programmy dlya EVM № 2019614758. Pervichnaya obrabotka pelengovoj informacii na bortu bespilotnogo letatel'nogo apparata. Cherepaha I.N., Bogdanovskij S.V., Antipov N.S., Marenkov I.A.; zayavl. 01.04.2019 g.; opubl. 11.04.2019 g. (in Russian).
8. Bogdanovskij S.V., Simonov A.N., Teslevich S.F., Mahetov A.B. Sposob opredeleniya koordinat bespilotnogo letatel'nogo apparata na osnove polyarizacionnoj obrabotki radioizluchenij repernyh stancij. Naukoemkie tekhnologii. 2017. T. 18. № 11. S. 16–21 (in Russian).
9. Tyapkin V.N., Vinogradov A.D. Determinirovannyj podhod k resheniyu zadachi opredeleniya koordinat i uglovoj orientacii bortovoj pelengatornoj antenny po rezul'tatam radiopelengovaniya radioorientirov. Radiotekhnika. 2019. № 6. S. 112–120 (in Russian).
10. Bogdanovskij S.V., Simonov A.N., Sevidov V.V.Polyarizacionnyj sposob opredeleniya orientacii bespilotnogo letatel'nogo apparata. Uspekhi sovremennoj radioelektroniki. 2017. № 10. S. 15–19 (in Russian).
11. Svidetel'stvo o gosudarstvennoj registracii programmy dlya EVM № 2018660515, Model' polyarizacionnogo pelengatora na bortu bespilotnogo letatel'nogo apparata. Antipov N.S., Simonov A.N., Bogdanovskij S.V. i dr.; zayavl. 08.08.2018 g.; opubl. 23.08.2018 g. (in Russian).
12. Svidetel'stvo o gosudarstvennoj registracii programmy dlya EVM № 2025619175, Programmnyj modul' formirovaniya prostranstvenno-polyarizacionnyh parametrov radiosignala. Antipov N.S.; zayavl. 30.03.2025 g.; opubl. 14.04.2025 g. (in Russian).
13. Svidetel'stvo o gosudarstvennoj registracii programmy dlya EVM № 2025662464, Programmnyj modul' priema i obrabotki prostranstvenno-polyarizacionnyh parametrov radiosignalov. Antipov N.S.; zayavl. 12.05.2025 g.; opubl. 21.05.2025 g. (in Russian).
14. Dvornikov S.V., Simonov A.N., Bogdanovskij S.V. Sposob pozicionirovaniya bespilotnogo letatel'nogo apparata na osnove polyarizacionno-adaptivnoj obrabotki radiosignalov ot repernyh stancij. Telekommunikacii. 2017. № 8. S. 36–42 (in Russian).
15. Patent № 2827103 (RF), MPK G01C 21/08 (2006.01), G01R 29/08 (2006.01), G01S 1/08 (2006.01), G01S 13/06 (2006.01). Sposob opredeleniya sobstvennogo mestopolozheniya ob"ekta v prostranstve: № 2023134072: zayavl. 18.12.2023: opubl. 23.09.2024. Bogdanovskij S.V., Sevidov V.V., Ivanov V.A.; zayavitel' VAS im. S.M. Budennogo. 12 s. (in Russian).
16. Patent № 2821640 (RF), MPK G01C 21/04 (2006.01), G01S 5/02 (2010.01), G01R 29/08 (2006.01). Sposob opredeleniya uglovoj orientacii letatel'nogo apparata: № 2024103172: zayavl. 08.02.2024: opubl. 25.06.2024. Bogdanovskij S.V., Zyuzin A.V., Sevidov V.V. i dr.; zayavitel' YaVVU PVO. 16 s. (in Russian).
17. Svidetel'stvo o gosudarstvennoj registracii programmy dlya EVM № 2023680128, Programmnyj modul' rascheta sobstvennyh koordinat radiotekhnicheskogo ob"ekta v prostranstve na osnove polyarizacionnyh izmerenij. Bogdanovskij S.V.; zayavl. 12.09.2023 g.; opubl. 26.09.2023 g. (in Russian).
18. Svidetel'stvo o gosudarstvennoj registracii programmy dlya EVM № 2023684577, Programmnyj modul' rascheta uglov orientacii letatel'nogo apparata v prostranstve na osnove polyarizacionnyh izmerenij. Bogdanovskij S.V.; zayavl. 14.11.2023 g.; opubl. 16.11.2023 g. (in Russian).