N.M. Ivanov 1, V.N. Shevchenko 2

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

1 qkivanov@list.ru, 2 vnsh1952@yandex.ru

The paper is concerned with the problem of synthesis of radio images for visual representation of airborne objects on the basis of inverse aperture synthesis in passive radio systems with outside illumination. The problem of visual representation is turned out to be bi-static while signal processing of single emission source and multiway (multi-static) while processing of signals of several sources by single receiving system or several ones. Herewith airborne object motion pattern is of the essence.

Two-dimensional visual representation of objects, performing simultaneously translational movement as well as rotational movement, at short time differences, and one-dimensional visual representation of objects, moving straight, as its special case, but the object under observation resides in far zone of transmitter as well as receiver, is considered. Derivation of integral equation, that is in accord with complex scattering amplitude as function of object coordinates, is formulated for signal with narrowband envelope using frequency domain transition.

Solution of kinematic Euler equation at uniform angular rate, that is useful for the problem concretization at short time differences, is found in vectorial form. Considered problem, for the whole of such differences by object triaxial coordinates discretization using model of isotropic local scattering centers (highlights), is reduced to linear equation system solution, where the number of system’s equations usually exceeds the number of unknown complex scattering amplitudes of highlights. Obtained underdetermined linear equation system is solved by regularization method in Holder space 1. System pseudosolution is searched through regularizing functional minimization by its differentiation on vector of complex scattering amplitudes and gradient setting equal to zero. Quasilinear equation system, the matrix of which is depended on desired vector, is determined by result transformation using matrix inversion lemma. This quasilinear equation system is solved by iterative method at every step of whom, with exception of first, new system matrix is found that is calculated on the basis of approximation to vector of unknowns obtained at preceding step. Quasisolution, finding out in this way, possesses superresolution property, as it appropriate to regularization method in Holder space p at 1 p 2 .

Proposed technics was tested by visual representation simulation of small-sized airborne objects for cases of helical (translational and rotational) and linear movement. Satisfying two-dimensional image in distance-rate coordinates was obtained in the first instance. One-dimensional image as distance function from origin of moving coordinates was obtained in the latter case. In both cases obtained images make it possible to get an idea of object shape as well as dimensions notwithstanding that object dimensions are comparable to wave length of radiated carrier frequency. Thus simulation results make it possible to infer about efficiency of analyzed technics of radio image synthesis.

Ivanov N.M., Shevchenko V.N. Synthesis of radio images of small-sized airborne objects. Radioengineering. 2020. V. 84. № 11(22). P. 13−19. DOI: 10.18127/j00338486-202011(22)-03. (in Russian)

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