A.A. Mardiev1, V.D. Kuptsov2
1,2 Peter the Great St. Petersburg Polytechnic University (St. Petersburg, Russia)
1 mardiev.aa@edu.spbstu.ru; 2 kuptsov@spbstu.ru
Problem statement. Passive radio direction-finding systems usin g the time-difference-of-arrival (TDOA) method require solution s to improve accuracy and eliminate "blind spots" where small errors in TDOA measurements lead to significant errors in position or bearing determination. A promising approach to addressing these iss ues is adaptive baseline selection in direction-finding systems based on TDOA fusion. A key issue, understudied in the context of adaptive baseline selection, is the comprehensive consideration of the influence of the range-to-baseline ratio (R/d) and the angle of a rrival on the local accuracy of TDOA measurements and, conseque ntly, on the accuracy of direction-finding.
Objective. Develop a comprehensive methodology that identifies the most sensitive angular bearing baselines and quantifies the reliability of measurements on each a vailable baseline, taking into account the influence of SNR, bandwidth, the ratio of the dist ance from the source to the length of the baseline, and the angle of arrival.
Results. It was found that the root mean square error (RMSE) of the direction finding estimate using the proposed method, base d on adaptive selection of optimal baselines and weighted fusion of TDOA estimates, exceeds that of the non-adaptive method by more than 2-5 times. Furthermore, the proposed method allows for the virtual elimination of angular blind spots and ensures uniform accuracy across the entire angular range. Practical application. Optimal adaptive selection and weighted fusion of TDOA estimates can significantly improve the accuracy of direction finding, especially in conditions where the radio source is located at different distances and angles relative to the receiving antennas.
Mardiev A.A., Kuptsov V.D. Adaptive baseline selection based on the fusion of TDOA estimat es in direction finding systems. Radiotekhnika. 2026. V. 90. № 3. P. 90−106. DOI: https://doi.org/10.18127/j00338486-202603-08 (In Russian)
- Van Trees H.L. Detection, estimation, and modulation theory. Pa rt IV: Optimum array processing. New York. NY: Wiley-Interscien ce. 2002. DOI: 10.1002/0471221104.
- Ho K.C., Nguyen A.N.D.T. TDOA-based localization: a review. Pos itioning and Localization for Wireless Communications. G. Seco Ed. Berlin. Germany: Springer. 2011. P. 1–32.
- Manolakis D.G., Ingle V.K., Kogon S.M. Statistical digital signal processing and modeling. Hoboken. NJ: Wiley. 2005.
- Kuptsov V., Badenko V., Ivanov S., Fedotov A. Method for remote determination of object coordinates in space based on exact an alytical solution of hyperbolic equations. Sensors. 2020. V. 20. № 19. P. 5472. DOI: 10.3390/s20195472.
- Kuptsov V.D., Ivanov S.I. Multichannel multistatic combined TSo A and TDoA positioning system based on precise analytical solut ion of positioning equations. Computing, Telecommunications and Control. 2023. V. 16. № 2. P. 40−-54. DOI: 10.18721/JCSTCS.16204.
- Ivanov S., Kuptsov V., Badenko V., Fedotov A. RSS/TDoA-Based So urce Localization in Microwave UWB Sensors Networks Using Two Anchor Nodes. Sensors. 2022. V. 22. № 8. P. 3018. DOI: 10.3390/s22083018.
- Mardiev A.A., Kuptsov V.D. Povyshenie tochnosti opredeleniya ko ordinat vozdushnyh ob"ektov metodom vtorichnoj passivnoj bistaticheskoj radiolokacii po signalam upravleniya vozdushnym dvizhenie m. Radiotekhnika. 2025. T. 89. № 3. S. 32 −43. DOI: 10.18127/j00338486-202503-04 (in Russian).
- Kim S., Chong J.-W. An efficient TDOA-based localization algori thm without synchronization between base stations. Int. J. Dist rib. Sens. Netw. 2015. V. 11. № 9. P. 1−6. DOI: 10.1155/2015/832251.
- Zhuravlev A.V., Kiryushkin V.V., Krasov E.M., Smolin A.V., Shuv aev V.A. Opredelenie koordinat vozdushnogo sudna po signalam nesinhronizirovannyh peredatchikov pomekh global'nym navigacion nym sputnikovym sistemam. Radiotekhnika. 2025. T. 89. № 7. S. 147−155. DOI: 10.18127/j00338486-202507-24 (in Russian). 1
- Smith J.O., Abel J.S. Closed-form least-squares source location estimation from range-difference measurements. IEEE Trans. Aco ust., Speech, Signal Process. 1987. V. 35. №. 12. P. 1661–1669. DOI: 10.1109/TASSP.1987.1165089. 1
- Chan Y.T., Ho K.C. A simple and efficient estimator for hyperbo lic position finding. IEEE Trans. Aerosp. Electron. Syst. 1996. V. 32. № 1. P. 1–6. 1
- Kay S.M. Fundamentals of statistical signal processing. V. I: Estimation theory. Englewood Cliffs. NJ: Prentice Hall. 1993. 1
- Knapp C.H., Carter G.C. The generalized correlation method for estimation of time delay. IEEE Trans. Acoust., Speech, Signal P rocess. 1976. V. 24, № 4. P. 320–327. 1
- Kustkov I.A. Model' ocenki pogreshnosti opredeleniya koordinat nazemnyh istochnikov radioizlucheniya bazovo-korrelyacionnym metodom. Radiotekhnika. 2025. T. 89. № 5. S. 45−54. DOI: 10.18127/j00338486-202505-05 (in Russian). 1
- Artemov M.L., Gordienko D.Yu., Slichenko M.P., Trushin S.P. Obn aruzhenie istochnikov radioizlucheniya po rezul'tatam mnogokana l'noj prostranstvenno-korrelyacionnoj obrabotki radiosignalov v dinam icheski menyayushchejsya elektromagnit-noj obstanovke. Radiotekhnika. 2025. T. 89. № 9. S. 70−77. DOI: 10.18127/j00338486-202509-07 (in Russian). 1
- Filonovich A.V., Vornacheva I.V., Bukreev Z.V., Vojnash S.A., S okolova V.A. Adaptivnye sistemy ustraneniya lozhnyh pe-lengov v bazovo-korrelyacionnyh sistemah passivnoj radiolokacii s ispol'zo vaniem dvumernogo sledyashchego porogovogo urovnya. Izvestiya Tul'skogo gosudarstvennogo universiteta. Tekhnicheskie nauki. 2024. № 7. S. 309−314. DOI: 10.24412/2071-6168-2024-7-309-310 (in Russian). 1
- Cao S., Chen S., Liu Y., Chen R. Clustering combined weighted T DoA localization for outlier suppression. IEEE Transactions on Instrumentation and Measurement. 2025. V. 74. P. 1− 1
- Art № 9701613. DOI: 10.1109/TIM.2025.3619247. 1
- Kalman R.E. A new approach to linear filtering and prediction problems. J. Basic Eng. 1960. V. 82. № 1. P. 35–45. 1
- Feng D., Peng J., Zhuang Y., Guo C., Zhang T., Chu Y., Zhou X., Xia X.-G. An adaptive IMU/UWB fusion method for NLOS indoor po sitioning and navigation. IEEE Internet of Things Journal. 2023. V. 10. № 13. P. 11414−11428. DOI: 10.1109/JIOT.2023.3245144. 2
- Sharp I., Yu K., Guo Y.J. GDOP analysis for positioning system design. IEEE Trans. Veh. Technol. 2009. V. 58. № 7, P. 3371–338 2. DOI: 10.1109/TVT.2009.2017270. 2
- Lee J., Choi J., Bhattacharya S. NLOS-robust DL-TDOA localizati on using adaptive anchor selection. Proc. IEEE Global Commun. C onf. (GLOBECOM). Cape Town. South Africa. 2024. P. 3625–3630. DOI: 10.1109/GLOBECOM52923.2024.10900965. 2
- Ding Y., Shen D., Pham K., Chen G. Optimal placements for minim um GDOP with consideration on the elevations of access nodes. IEEE Transactions on Instrumentation and Measurement. 2025. V. 74. P. 1− 1
- Art № 9501210. DOI: 10.1109/TIM.2024.3497055. 2
- Afanas'ev O.V., Kozlov M.I., Slichenko M.P. Uglomestnoe pelengo vanie istochnikov radioizlucheniya na osnove integral'nogo oper atora preobrazovaniya harakteristik napravlennosti antennoj reshetki. Radiotekhnika. 2025. T. 89. № 9. S. 163 −169. DOI: 10.18127/j00338486-202509-17 (in Russian). 2
- Podstrigaev A.S., Astaf'ev I.A. Obnaruzhenie signalov na osnove tekhnologii subdiskretizacii bez poiska po naprav-leniyu i cha stote. Radiotekhnika. 2025. T. 89. № 9. S. 102−112. DOI: 10.18127/j00338486-202509-11 (in Russian). 2
- Duan X., Du Y., Yu X. Antenna layout for partial discharge loca lization in substations based on bayesian optimization. Proc. 4 4th Chinese Control Conference (CCC). Chongqing. China. 2025. P. 1−6. DOI: 10.23919/CCC64809.2025.11178921. 2
- Bahrampour R., Madani M.H., Bahr amgiri H. An iterative approach to enhance the accuracy of TDOA -based localization by averagin g and reducing noise. Proc. 32nd Int. Conf. Elect. Eng. (ICEE). Tehran. Iran. 2024. P. 1–5. DOI: 10.1109/ICEE63041.2024.10668226. 2
- Mardiev A.A., Kuptsov V.D. Adaptive operating baseline selectio n and estimate fusion in a TDOA direction finding system based on local uncertainty. 2025 International Conference on Electrical Engineering and Photonics (EExPolytech). Saint Petersburg. Russ ian Federation. 2025. P. 228−231. DOI: 10.1109/EExPolytech66949.2025.11252471. 2
- Wiley R. ELINT: The interception and analysis of radar signals. Artech. 2006.

