Parameter Identification for Inverse Scattering Problem of Electrically-Large Curved Surfaces

Inverse scattering problems (ISP) often suffer from severe ill-posedness and nonlinearity. In this paper, a parameter identification method that determines the necessary conditions of observation for obtaining a unique solution in parameter inversion of general electrically-large curved surface is proposed. The method analyzes the relationship between surface geometry and position parameters with observation angles, frequency bands, and polarization modes. It includes two main steps. First, it divides curved surfaces into singly-curved and doubly-curved surfaces based on their dispersion effect, and concludes that the length of singly-curved surfaces can be inverted when frequency points satisfy the Nyquist sampling theorem. Second, it employs algebraic transformations to convert the nonlinear terms into linear expressions for the inversion of other curvature and position parameters. Furthermore, the measurement schemes required to achieve unique solutions for curved surface parameter inversion under typical monostatic and bistatic observation modes is explored. It also investigates the relationship between the robustness of the method and factors such as radar signal-to-noise ratio (SNR) and the amount of radar data. Numerical simulations verify the effectiveness of the proposed method. This study reveals the physical mechanisms underlying the ISP of curved surfaces parameter inversion. It can be used to guide the design of measurement schemes and parameter inversion methods of general curved structures.