A Mathematical Model in the Problem of Aircraft Shape Identification Based on a Sound Field Scattered Diagram

This paper proposes a mathematical model to solve an inverse problem reconstructing the shape and size of possible models of an unmanned aerial vehicle based on its acoustic trail. To simplify the calculations, four two-dimensional simplest geometric shapes were chosen for numerical experiments - a circle, an ellipse, a square and a four-petal rose. The scattering diagrams of the sound field, as a solution to direct diffraction problem for each contour, were taken as the input data. A residual functional is constructed as a difference between the true data of the scattered sound field and the data obtained using the semi-analytical boundary integral equation method and the Fredholm integral equation of the second kind, in the direct diffraction problem. The minimization of this functional leads to the inverse diffraction problem. After discretizing the boundary curve, the problem is reduced to a linear algebraic equation system, from which a function is found that numerically describes the shape of the object.