N.M. Ivanov1, V.N. Shevchenko2

1,2 JSC «All-Russian Scientific Research Institute «Gradient» (Rostov-on-Don, Russia)

The problem of air object image acquisition in radiofrequency range when using passive radio engineering systems with external signal source, for example, digital television broadcast transmitters is considered in the paper. Moreover air object motion pattern, illumination emitter number, receiving station quantity and signal characteristics are essential.

Creation of two-dimensional image of objects, performing helical, in other words simultaneously translational as well as rotational, motion and creation of one-dimensional image of objects, running just progressively, on time intervals as short that object center position is not drastically varied is considered. It being understood that observable object is found in far zone relative to not only transmitters but also receivers. Illumination signals with narrowband envelope are under consideration. Pro hac vice frequency-domain integral equation to which complex scattering amplitude, considered as position function of scattering points within reference configuration, rigidly found with object, should be complied, is derived.

Superposition of translational and rotational motions with constant linear and angular speeds is taken as helical motion model. In this case Euler kinematical equation solution is in the explicit vector form that later is used in short time intervals. Model of isotropic local scattering centers («highlights») is used for the whole of such intervals. Considered problem is amounted to the linear equation system solution as a consequence of discretization. As a rule this system is proved to be undetermined, in other words the number of equations exceeds dimensionality that is «highlights» complex scattering amplitudes.

Obtained linear equation system pseudosolution is found out by quadratic functional minimization with regularizing summand addition that is pseudosolution in Holder norm space lg , where g > 0 – predetermined number. Differentiation of regularized functional by vector of complex scattering amplitudes and equating gradient to zero give rise after some transformations to quasi-linear equation system which matrix depends upon desired vector. This system is solved by iterative method. Linear system with matrix found using approximation to vector of unknowns obtained on the previous step is solved on every iteration except the first iteration. Quasisolution found in a such way offers property of superresolution as it pertains to regularization methods in Holder spaces lp when

1 ≤ p < 2. And what is more, it is possible to increase resolution in specific cases stepping over the bounds of Holder space, in other words if we set 0 < g < 1.

Imaging modeling of small-sized aircrafts for the cases of both transitional and helical motions was realized for proposed technique testing. One-dimensional image as distance function from the beginning of moving coordinates was obtained in the first instance. Satisfying two-dimensional image in coordinates «distance – speed» was obtained in the latter case. Images obtained in both cases make it possible to get an idea of both object shape and sizes, notwithstanding that object sizes are comparable to carrier radiated frequency wave length. By this means simulated results carry inference about crucial efficiency of analyzed technique of image acquisition of aircrafts in passive radiolocation.

Ivanov N.M., Shevchenko V.N. Image acquisition of aircrafts in passive radiolocation. Radioengineering. 2021. V. 86. № 11. P. 47−53. DOI: https://doi.org/10.18127/j00338486-202111-08 (in Russian)

1. Markeev A.P. Teoreticheskaya mekhanika. Moskva: CheRo. 1999. (in Russian)
2. Landau L.D., Lifshitz E.M. Course of Theoretical Physics. V. 1. Mechanics. Butterworth-Heinemann. 2000.
3. Walker J.L. Range-Doppler imaging of rotating objects. IEEE Transactions on Aerospace and Electronic Systems, AES-16. 1980. P. 23−52.
4. Martorella M., Giusti E. Theoretical Foundation of Passive Bistatic ISAR Imaging. IEEE Transactions on Aerospace and Electronic Systems. 50. 2014. P. 1647−1659.
5. Chen V.C and Martorella M. Inverse Synthetic Aperture Radar Imaging. NJ: SciTech Publishing. 2014. 304 r.
6. Qiu W., Giusti E., Bacci A., Martorella M., Berizzi F., Zhao HZ., Fu Q. Compressive sensing for passive ISAR with DVB-T signal. IEEE Transactions on Aerospace and Electronic Systems. 2015. 51. P. 2166−2180.
7. Ivanov N.M., Syrenko I.L., Shevchenko V.N. Visual representation of small aircrafts on straight segment of trajectory. IEEE Xplore Digital Library. Proceedings of International conference «Radiation and Scattering of Electromagnetic Waves» (RSEMW). 24−28 June 2019. Divnomorskoe (Krasnodar Region. Russia).
8. Ciucia P., Ider J. A half-quadratic block-coordinate descent method for spectral estimation. Signal processing. 2002. V. 82. № 7. P. 941.