基于拉格朗日的雷达方位超分辨方法研究

民用导航雷达的方位分辨率与天线孔径尺寸相关，大孔径天线在工程实践中受等多种条件制约，难以广泛应用。本文提出一种基于拉格朗日的方位超分辨方法。对方位信号向量进行数据补充，将卷积扫描模型转换为矩阵-向量乘积形式。对天线方向图奇异值分解，结合BFGS算法构造二次规划观测模型。利用拉格朗日法计算模型最优解，进而重建目标原始方位信号，实现目标方位超分辨。实验结果表明，在信噪比(Signal to noise ratio, SNR)为10~20 dB时，本文方法具有良好的分辨效果，与对偶-对数障碍法相比，该方法可获得较高的信号重构误差比(Signal reconstruction to error ratio, SRER)。

Research on the Method of Radar Azimuth Super-resolution via Lagrange Theory

The azimuth resolution of civil navigation radar depends on the size of antenna aperture. Large aperture antenna is restricted by many factors in engineering project, and it is difficult to be widely used. For this problem a super-resolution method based on Lagrange theory is proposed in this paper. The convolutional echo is converted into the form of matrix-vector product by supplementing elements to azimuth signal vector. Combining singular value decomposition (SVD) to antenna pattern with BFGS algorithm a new observed model is established, and Lagrange function is utilized to solve the new model for restoring original azimuth signals, by which azimuth super-resolution can be realized. Experimental performances manifest that the proposed method has good super-resolution, and a higher signal reconstruction to error ratio (SRER) is obtained comparing with dual-logarithmic method while the signal to noise ratio (SNR) ranges from 10dB to 20 dB.