基于Legendre正交分解的曲线运动轨迹SAR的频域算法

高分辨率是合成孔径雷达（synthetic aperture radar，SAR）成像技术的重要指标.由于加速度的存在，SAR平台呈现曲线运动轨迹.结合SAR系统几何模型，提出了一个曲线运动轨迹斜距模型及其Taylor展开式，推导了曲线SAR回波信号精确的二维频谱表达式.复杂的斜距历程导致SAR回波信号产生了更为复杂的高阶二维耦合现象，利用Legendre正交多项式分解二维频谱，以解除耦合现象，由此推导出相应的频域算法，得到良好的聚焦效果.通过与Taylor展开二维频谱频域算法的仿真结果对比，Legendre多项式改善了聚焦性能.

Frequency domain algorithm for curved trajectories SAR based on Legendre orthogonal decomposition

High resolution is the main purpose of studying synthetic aperture radar imaging. Due to the existence of acceleration, the SAR platform presents a curvilinear trajectory. Combined with the geometrical model of SAR system, the slant range equation and its Taylor expansion of the airborne SAR on curve trajectory are put forward. Besides, the precise expression of the two-dimensional spectrum of the curved SAR echo is deduced. The complex slant range history leads to more complex high order coupling of SAR echo signal in range and azimuth. Legendre orthogonal polynomial is used to decompose the 2D spectrum, which eliminates the coupling phenomenon. The corresponding frequency domain algorithm is deduced, and better focusing effect is obtained. In conclusion, compared with the Taylor expansion, Legendre polynomials can improve the focusing performance.