V.S. Pavlov1, A.Yu. Fedorov2, P.I. Bakulina3

1,3 Moscow branch of JSC “VNIIR-Progress” (Moscow, Russia)

2 JSC “VNIIR-Progress” (Cheboksary, Russia).

1 Vpavlov@abselectro.ru; 2 ayfedorov@vniir.ru; 3 pshivrina@abselectro.ru

Determining the position of a radio signal source using a digital antenna array mounted on an unmanned aerial vehicle represents a modern alternative to classical stationary multi-position radio monitoring systems. Previously, the authors proposed an algorithm for determining the coordinates of a radio signal source that is optimal according to the maximum likelihood function criterion. In this paper, the potential characteristics of the algorithm are analyzed.

The parameters influencing the error in measuring the position of the radio signal source include the shape of the unmanned aerial vehicle’s trajectory, the error in determining the orientation of the unmanned aerial vehicle, and the directional pattern of the digital antenna array. To study the potential characteristics of the algorithm, simulation modeling and analytical calculation of the Cramér-Rao bound were applied. Both methods mutually confirmed the validity of the results.

The main parameter affecting the error in determining the coordinates of the radio signal source is the shape of the unmanned aerial vehicle’s trajectory. The greater the diversity of observation angles of the radio signal source, the smaller the error in estimating the coordinates. Combining trajectories from multiple unmanned aerial vehicles also helps reduce the error in determining the position of the radio signal source.

Another significant parameter influencing the algorithm’s performance in practice is the error in determining the unmanned aerial vehicle’s orientation. For small aircraft, unstable flight conditions can lead to orientation errors of up to 10°.

Knowledge of the radiation pattern of the digital antenna array forms the basis of the algorithm. When measuring the directional pattern in an open area, inaccuracies in determining the directional pattern in amplitude terms can reach 6 dB. This leads to an increase in the root mean square error of direction finding to 18° and causes anomalous bearing measurements.

The results of the study of the potential characteristics of the algorithm for determining the position of a radio signal source will allow selecting the optimal trajectory for exploring an area during field tests to detect radio signal sources.

Pavlov V.S., Fedorov A.Yu., Bakulina P.I. Theoretical performance bounds for the radio source localization algorithm. Radiotekhnika. 2025. V. 89. № 12. P. 98−109. DOI: https://doi.org/10.18127/j00338486-202512-12 (In Russian)

1. Pavlov V.S., Fedorov A.Ju., Harisov V.N., Shivrina P.I. Algoritm opredelenija mestopolozhenija istochnika radiosignala. Nauchnye chtenija po aviacii, posvjashhennye pamjati N.E. Zhukovskogo. 2024. № 12. S. 215-227 (in Russian).
2. Bakulev P.A. Radiolokacionnye sistemy: Uchebnik. M.: Radiotehnika. 2007. 375 s. (in Russian).
3. Al'-Odhari A.H., Fokin G.A., Fedorenko I.V., Rjabenko D.S., Lavrov S.V. Issledovanie vlijanija geometricheskogo raspredelenija punktov priema i istochnika radioizluchenija na tochnost' pozicionirovanija. Vestnik Polockogo gos. un-ta. Ser. S. Fundamental'nye nauki. 2017. № 4. S. 2-7 (in Russian).
4. Semenjuk S.S., Hristichan E.V., Saniev R.R. Obosnovanie podhoda k snizheniju variativnosti geometricheskogo faktora sistemy opredelenija koordinat vozdushnyh ob'ektov s ispol'zovaniem tehnologii MLAT. Zhurnal Radiojelektroniki. 2021. № 4. URL: http://jre.cplire.ru/jre/apr21/14/text.pdf (data obrashhenija: 07.02.2025) (in Russian).
5. Semenjuk S.S., Eremeev I.Ju., Kozlov A.V., Kosynkin A.I., Veselov I.D. Vybor topologii izmerenij raznostno-dal'-nomernoj sistemy dlja opredelenija mestopolozhenija istochnikov radioizluchenija s fakticheski zadannymi polozhenijami priemnyh tochek. Zhurnal radiojelektroniki. URL: http://jre.cplire.ru/jre/jun23/5/text.pdf (data obrashhenija: 07.02.2025) (in Russian).
6. Dvornikov S.V., Fokin G.A., Al'-Odhari A.H., Fedorenko I.V. Issledovanie zavisimosti geometricheskogo faktora topologii dlja raznostno-dal'nomernogo metoda pozicionirovanija. Voprosy radiojelektroniki. Ser. Tehnika televidenija. 2017. № 2. S. 86-93 (in Russian).
7. Al'-Odhari A.H. Issledovanie vlijanija geometricheskogo faktora snizhenija tochnosti pozicionirovanija v raznostno-dal'nomernom metode. Aktual'nye problemy infotelekommunikacij v nauke i obrazovanii. SPb: SPbGUT. 2017. S. 44-48 (in Russian).
8. Fokin G.A., Al'-odhari A.H. Obrabotka RDM izmerenij dlja pozicionirovanija s ispol'zovaniem bespilotnyh letatel'nyh apparatov. T-Comm. 2018. № 7 (in Russian).
9. Fokin G., Lazarev V. Positioning Accuracy Evaluation of radio emission sources using time difference of arrival and angle of arrival methods. Part 2. 2D-Simulation. Proceedings of Telecommunication Universities. V. 5. P. 65-78. DOI:10.31854/1813-324X-2019-5-4-65-78.
10. Fokin G.A., Lazarev V.O. Ocenka tochnosti pozicionirovanija istochnika radioizluchenija raznostno-dal'nomernymi i uglomernymi metodami. Ch. 3. 3D-Modelirovanie. Trudy uchebnyh zavedenij svjazi. 2020. T. 6. № 2. S. 87-102 (in Russian).
11. Dubrovin A.V. Potencial'naja tochnost' izmerenija napravlenija na izluchatel' dlja pelengacionnyh sredstv s kol'cevymi antennymi reshetkami. Antenny. 2006. № 2. S. 29-31 (in Russian).
12. Nechaev Ju.B., Peshkov I.V. Ocenka granicy Kramera-Rao dlja 2D-radiopelengacii v ploskih antennyh reshetkah. Vestnik NTUU «KPI». 2016. № 67. S. 12-17 (in Russian).
13. Peshkov I.V. Minimizacija nizhnej granicy Kramera-Rao pri proektirovanii antennyh reshetok s napravlennymi izluchateljami dlja povyshenija tochnosti ocenki napravlenija prihoda signala. Zhurnal radiojelektroniki. 2022. № 2. http://jre.cplire.ru/jre/feb22/10/text.pdf (data ob-rashhenija: 07.02.2025) (in Russian).
14. Weiss A.J., Friedlander B. On the Cramer Rao bound for direction finding of correlated signals. Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers. 1990. P. 941-945. DOI: 10.1109/acssc.1990.523476.
15. Weiss A.J., Friedlander B. On the Cramer-Rao bound for direction finding of correlated signals. IEEE Transactions on Signal Processing. 1993. № 41(1). P. 495-499. DOI: 10.1109/tsp.1993.193187.
16. Mirkin A.N., Sibul L.H. Cramer-Rao bounds on angle estimation with a two-dimensional array. IEEE Transactions on Signal Processing, 1991. № 39(2). Р. 515–517. DOI: 10.1109/78.80843.
17. Nechaev Yu.B., Peshkov I.W., Fortunova N.A. Estimation of the Cramer-Rao bound for radio direction-finding on the azimuth and elevation of planar antenna arrays of the symmetric form. IEEE East-West Design & Test Symposium (EWDTS). 2018. P. 1-5. DOI: 10.1109/ewdts.2018.8524799.
18. Nechaev Yu.B., Peshkov I.W., Fortunova N.A. Evaluation and minimization of Cramer-Rao bound for conformal antenna arrays with directional emitters for DOA-Estimation. Progress in Electromagnetics Research. 2019. P. 139-154. DOI: 10.2528/PIERC18111802.
19. Nechaev Yu.B., Peshkov I.V. An approach of DOA-estimation accuracy improving via conformal antenna arrays with directional emitters. Systems of Signals Generating and Processing in the Field of on Board Communications. 2020. P. 1-6. DOI: 10.1109/ieeeconf48371.2020.90.
20. Friedlander B. On the Cramer-Rao bound for sparse linear arrays. 54th Asilomar Conference on Signals, Systems, and Computers. 2020. P. 1255-1259, DOI: 10.1109/IEEECONF51394.2020.9443292.
21. Li S., Liu Y., You L., Wang W. Optimal three-dimensional antenna array for direction finding with geometric constraint. IEEE Access. 2020. V. 8. P. 31948-31956, DOI: 10.1109/ACCESS.2020.2973820.
22. Nechaev Yu.B., Peshkov I.W. Novel planar antenna arrays geometries improving DOA estimation accuracy of narrowband sources on the azimuth. 42nd International Conference on Telecommunications and Signal Processing. 2019. P. 420-423.
23. Gazzah H., Marcos S. Cramer-Rao bounds for antenna array design. IEEE Transactions on Signal Processing, 2006. № 54(1). P. 336–345. DOI:10.1109/tsp.2005.861091.
24. Van Trees H.L. Detection, Estimation, and Modulation Theory. Part IV. Optimum Array Processing. John Wiley & Sons. 2004. P. 1470.