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斜距多普勒定位模型是实现SAR图像无控制点定位的基本模型,因此如何高效准确地获得RD方程组的解成为实现SAR图像无控制点几何定位的根本问题,也是实现SAR自动图像定位的关键。首先利用地固坐标系下目标速度为零的特性,简化RD模型并整理为一元四次方程,然后利用一元四次方程求根方法,推导出斜距多普勒定位模型的明确数学解析解,并与常用的数值迭代求解方法进行比较分析,仿真结果验证了推导的正确性。新解法具有无需设置初始值,易于编程实现,鲁棒性高的特点。
Oblique distance Doppler localization model is the basic model to realize uncontrolled point location of SAR images. Therefore, how to obtain the solution of RD equations efficiently and accurately becomes the fundamental problem to realize the geometric location of uncontrolled points in SAR image, and also realize the automatic image location of SAR The essential. Firstly, by using the characteristic that the target velocity is zero under the geodetic coordinate system, the RD model is simplified and sorted into a quadratic equation, and then the explicit mathematical analytical solution of the oblique-range Doppler localization model is deduced by using the quadratic equation. Compared with commonly used numerical iterative methods, the simulation results verify the correctness of the derivation. The new solution has no need to set the initial value, easy programming, high robustness.