分数阶傅里叶变换在水下多目标方位估计中的应用研究

线性调频（Linear Frequency Modulation，LFM）信号作为一种具有大时宽带宽积的信号被广泛应用于主动声纳中以进行水下目标方位估计。分数阶傅里叶变换（Fractional Fourier Transform，FRFT）技术对LFM信号分析具有独特的优势，本文通过对FRFT的理论研究，分析其应用于水下多目标方位估计领域的可行性。对于FRFT最优阶次搜索中存在的误差影响，本文研究范数约束Capon波束形成技术（Norm Constrained Capon Beamforming，NCCB），利用NCCB算法提高FRFT预处理后的目标方位估计的稳健性。最后，本文将分数阶预处理与稳健波束形成算法结合，通过计算机仿真验证了基于FRFT预处理的NCCB算法在低信噪比环境下仍然可以实现水下多目标方位的稳健估计。 

The application of FRFT in DOA Estimation of Underwater Multi-Targets

As a kind of signal with large time-bandwidth product, linear frequency modulation (LFM) signal is widely used in active sonar for underwater direction of arrival (DOA) estimation. Fractional Fourier Transform (FRFT) has unique advantages for LFM signal analysis. In this paper, the feasibility of its application to the field of underwater multi-targets DOA estimation is explored based on the theory of FRFT. For the possible increased errors of optimal order searching in the FRFT, norm constrained Capon beamforming (NCCB) is studied in this paper, and it is used to improve the robustness of the DOA based on FRFT preprocessing. Finally, fractional order preprocessing and robust beamforming algorithm are combined in the paper. Computer simulation proves that the NCCB based on FRFT preprocessing can still achieve robust underwater multi-targets DOA estimation in low SNR.