A third order range model for high speed and high maneuvering SAR using Chebyshev approximation

To obtain high-accuracy spectrum, the slant range must be expanded to high order (usually fourth order) using Taylor polynomials for high speed and high maneuvering (HSHM) SAR. But the corresponding spectrum is too complex for image formation. So it´s profound to reduce the order of Taylor expansion with the accuracy reserved. The Chebyshev approximation is an optimal uniform approximation method in the sense of least mean square. This paper presents a third order slant range model for HSHM SAR utilizing the Chebyshev approximation. Compared with the third order Taylor expansion, the accuracy of this new range model is much higher and the complexity is not added. The 2D-spectrum is also simply given at last. The simulation results validate the proposed slant range model.