Experimental Refinement of a Mathematical Model of the Signal Reflected from Quadcopter Rotor Blade

Introduction. In order to solve a number of problems arising in the process of airspace control, it is necessary to determine the class (type) of the objects observed. In addition, differentiation between targets located in the same element of the spatial resolution of a radar system is highly relevant. Construction of radar images of aircraft blades based on the method of inverse synthetic aperture radar (ISAR) can become an efficient tool in solving this problem. The development of resolution algorithms using the ISAR method requires a sufficiently accurate model of the reflected signal that would take into account the design features of the aircraft rotor blade. The available mathematical models for the signal reflected from the rotating blades of an aircraft are, as a rule, over-simplified, thus inhibiting the implementation of an adequate ISAR-based algorithm.
Aim. Refinement of a mathematical model of the signal reflected from the quadcopter rotor blade based on experimental studies in application to the ISAR method.
Materials and methods. The rotor blade in the considered model is represented by a set of point reflectors located on the approximating segments of the front and rear edges of the blade. When developing a reflected signal model, changes in the phase structure of the reflected signal are taken into account due to the translational motion of the quadcopter and the rotation of the propeller blades, as well as the spread of the blades in space.
Results. A mathematical model of the signal reflected from the quadcopter rotor blade was obtained, which demonstrates good convergence with reality. By means of modeling, the implementations of signals reflected from one quadcopter blade are obtained. The temporal and spectral structures of the reflected signals obtained as a result of modeling and experimental studies are compared.
Conclusion. The refined mathematical model of the reflected signal, which takes into account the design features of the quadcopter blade, can serve as a basis for developing an algorithm for imaging quadcopter blades using the method of ISAR.

1. Plotnitskaya E. S., Heister S. R., Veremyev V. I. Mathematical Model for a Radar Signal Reflected from Drone Propellers as Applied to the Method of Inverse Synthetic Aperture Radar in Bistatic Radar. J. of the Russian Universities. Radioelectronics. 2023, vol. 26, no. 6, pp. 41–53. doi: 10.32603/1993-8985-2023-26-6-41-53

2. Chen V. C., Martorella M. Inverse Synthetic Aperture Radar Imaging: Principles, Algorithms, and Applications. Raleigh, USA, SciTech Publishing, 2014, 303 p. doi: 10.1049/SBRA504E

3. Ozdemir C. Inverse Synthetic Aperture Radar Imaging with MATLAB Algorithms. 2nd ed. Hoboken, USA, John Wiley and Sons, 2021, 672 p.

4. Zhu H., Hu W., Guo B., Jiao L., Zhu X., Zhu C. Research on Bi–ISAR Sparse Aperture High Resolution Imaging Algorithm under Low SNR. Electronics. 2022, vol. 11, iss. 18, art. no. 2856. doi: 10.3390/electronics11182856

5. Rong J. J., Wang Y., Han T. Iterative Optimization-based ISAR Imaging with Sparse Aperture and Its Application in Interferometric ISAR Imaging. IEEE Sens. J. 2019, vol. 19, iss. 19, pp. 8681–8693. doi: 10.1109/JSEN.2019.2923447

6. Sayed A. N., Ramahi O. M., Shaker G. In the Realm of Aerial Deception: UAV Classification via ISAR Images and Radar Digital Twins for Enhanced Security. IEEE Sensors Let. 2024, vol. 8, no. 7, pp. 1–4, art. no. 6007704. doi: 10.1109/LSENS.2024.3416381

7. Wang H., Li K., Luo Y., Liu Y., Zhang Q., Zhang Q. Removal of Micro-Doppler Effect in ISAR Imaging Based on Data-Driven Deep Network. IEEE Sensors J. 2023, vol. 23, no. 12, pp. 13198–13209. doi: 10.1109/JSEN.2023.3270226

8. Finkelstein M. I. Osnovy radiolocatsii [Radar Basics]. 2 nd ed. Moscow, Radio i svyaz, 1983, 536 p. (In Russ.)

9. Heister S. R., Thai T. Nguyen. Mathematical Models of the Radar Signal Reflected from a Helicopter Main Rotor in Application to Inverse Synthesis of Antenna Aperture. J. of the Russian Universities. Radioelectronics. 2019, vol. 22, no. 3, pp. 74–87. doi: 10.32603/1993-8985-2019-22-3-74-87

10. Heister, S. R., Nguyen T. T. The Radar Image Formation Algorithms for Screws of an Aerial Vehicle in Horizontal and Vertical Planes in the Radar Sensor with Inverse Synthesis of Antenna Aperture. Doklady BGUIR. 2018, vol. 115, no. 5, pp. 92–98. (In Russ.)

11. Okhrimenko A. Ye. Osnovy radiolokatsii i radioelektronnaya bor'ba. Chast' 1. Osnovy radiolokatsii [Fundamentals of Radar and Electronic Warfare. Pt 1. Fundamentals of Radar]. Moscow, Voyennoye izdatel'stvo, 1983, 456 p. (In Russ.)

12. Barton D. K. Radar System Analysis. Englewood Cliffs, NJ: Prentice Hall, 1964.

13. Shirman Ya. D., Losev Yu. I., Minervin N. N., Moskvitin S. V., Gorshkov S. A., Lekhovitskii D. I., Levchenko L. S. Radioelektronnyye sistemy: Osnovy postroyeniya i teoriya [Radio Electronic Systems. Basics of Construction and Theory] ed. by Ya. D. Shirman. Moscow, MAKVIS, 1998, 828 p. (In Russ.)

14. Bakulev P. A. Radiolokatsiya dvizhushchikhsya tseley [Radar Detection of Moving Targets]. Moscow, Sovetskoye radio, 1964, 336 p. (In Russ.).

15. Radar handbook: ed by M. I. Skolnik. In 4 vol. Vol. 1. New York, McGraw-Hill, 1970, 1536 p.