基于Chebyshev正交分解的曲线运动轨迹SAR的Chirp Scaling算法

针对具有三维速度和加速度的曲线运动轨迹合成孔径雷达（SAR），传统的斜距模型无法精确描述其运动特性，曲线历程增加了距离走动现象和方位向时间的高次项，使二维耦合现象更为复杂。本文提出了一种考虑载体平台三维速度和加速度的Chirp Scaling算法以解决曲线运动轨迹SAR成像问题。首先根据运动方程建立斜距表达式，然后对其进行Chebyshev近似，并构造其等效双曲方程形式的斜距模型，推导了具有空变性的距离徙动函数，Chirp Scaling因子以及适用于曲线轨迹的Chirp Scaling成像算法。仿真结果证实了此扩展的等效斜距模型和Chirp Scaling算法在大合成孔径时间下的有效性，并给出了三维加速度的边界值。

Chirp Scaling algorithm based on Chebyshev orthogonal decomposition for curve trajectory SAR

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.