Conventional slant range models has difficulty in accurately describing the motion characteristics of the Synthetic Aperture Radar (SAR) with three-dimensional velocity and acceleration, and the curve trajectory increases the range-walk phenomenon and the high-order terms of azimuth time in the slant range equation, further complicating the two-dimensional coupling of the echo signal. Therefore, this paper proposes an improved Chirp Scaling algorithm to solve the imaging problem of the curvilinear trajectory SAR which moves with the three-dimensional velocity and acceleration. The slant range expression for the curvilinear trajectory SAR is firstly established based on the motion equation, followed by the obtainment of the slant range model in the form of equivalent hyperbolic equation based on the Chebyshev approximation of the slant range equation. The range cell migration function with spatial variability and the chirp scaling factor are finally derived, on the basis of which an improved Chirp Scaling algorithm is proposed. Simulation results confirm the effectiveness of the extended equivalent slant range model and the Chirp Scaling algorithm for large synthetic aperture time, and provide the boundary value of 3D acceleration.
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