基于拉格朗日反演的宽波束多子阵合成孔径声纳成像算法研究

The research on wide beam synthetic aperture sonar (SAS) imaging algorithm is of great significance to improve imaging resolution, imaging range and the ability of detecting buried objects, but the existing wide beam multi-aperture SAS imaging algorithm can not take into account the imaging quality and efficiency. Aiming at this problem, this project studies the imaging algorithm of the wide beam multi-aperture SAS based on Lagrange inversion theorem. The main content include: ① On the premise that the accurate range history is not approximated, the two-dimensional spectrum of the wide beam multi-aperture SAS is deduced by using Lagrange inversion theorem, which can solve the problem that ignoring the azimuth spatial variation of the azimuth moving distance during sending and receiving influence the two-dimensional spectrum. ② To reduce aperture dependence, range dependence and element dependence of the differential range curvature, the correction algorithm of the differential range curvature is studied, so that the multi-aperture can be transformed into the monostatic signal, to solves the problem of low computational efficiency caused by the existing algorithms where each element need to image respectively. ③ On the basis of equivalent wide-beam monostatic signal, the wavenumber domain and chirp scaling algorithm of wide beam multi-aperture based on Lagrange inversion theorem are proposed by modifying the classical wavenumber domain and chirp scaling algorithm. After this project, the imaging efficiency can be improved on the premise of guaranteeing the imaging quality, which provides the key theoretical support for the development and application of multi-aperture SAS with high resolution, long range and the better ability of detecting buried objects.

研究宽波束合成孔径声纳（SAS)成像算法对提高成像分辨率、成像距离和掩埋物探测能力具有重要的意义，而现有宽波束多子阵SAS成像算法不能兼顾成像质量和效率。针对该问题，本申请研究基于拉格朗日反演的宽波束多子阵SAS成像算法。主要内容有：①在精确距离史不进行近似的前提下，借用拉格朗日反演定理，推导宽波束多子阵SAS二维谱，解决忽略声纳收发期间横向走动量的方位空变影响二维谱的问题；②研究差分距离弯曲校正算法，降低差分距离弯曲的孔径依赖、距离依赖和阵元依赖，在宽波束条件下，通过预处理将多子阵信号等效为单阵信号，解决各子阵单独成像带来效率低的问题；③在等效单阵信号的基础上，对经典波数域和线频调变标算法进行修正，提出基于拉格朗日反演的宽波束多子阵波数域和线频调变标算法。通过本研究，在保证成像质量的前提下提高成像效率，为高分辨、远距离和高掩埋物探测能力多子阵SAS研发与应用提供关键理论支撑。

本项目围绕宽波束多子阵合成孔径声纳（SAS）模型、相对距离偏移和差分距离弯曲校正方法和成像算法问题展开研究。研究成果在一定程度上丰富了SAS成像算法理论，能够为国内外同行进行宽波束多子阵SAS成像算法理论研究提供参考和借鉴，同时为宽波束SAS的研制提供一定的技术支撑。主要工作和创新点如下：.（1）提出了宽波束多子阵SAS模型和二维谱求解方法。首先考虑了声基阵在信号发射与接收期间移动的距离和信号伸缩效应，建立了多子阵SAS精确距离史和信号模型；然后通过对伸缩因子、时延和相位进行处理，首次得到了实用的宽波束多子阵SAS信号模型；接着利用拉格朗日反演定理，推导出宽波束多子阵SAS二维谱解析式；最后通过仿真实验结果验证了宽波束多子阵SAS模型的有效性。.（2）提出了相对距离偏移（RRO）和差分距离弯曲（DRC）校正方法。首先通过相位相乘的方式在距离多普勒域精确地校正每个子阵信号中RRO和DRC导致的方位调制量；然后使用距离向子孔径的方式校正RRO和DRC带来的距离徙动量和DRC带来的距离/方位高阶耦合量；最后通过仿真实验结果验证了提出方法的有效性。.（3）提出了基于拉格朗日反演的宽波束多子阵ωKA。首先用提出的RRO和DRC校正方法对从基于拉格朗日反演的二维谱中推导出的RRO和DRC进行校正；然后利用参考子阵模型和各子阵相干叠加的方式，完成多子阵信号向单阵信号的等效，得到等效宽波束单阵合成孔径信号；接着根据该等效信号模型对原始ωKA进行修正，实现了对宽波束多子阵SAS的精确成像；最后通过仿真和实测数据结果验证了提出算法的有效性。.（4）提出了基于拉格朗日反演的宽波束多子阵CSA。首先在经过RRO和DRC校正后将等效宽波束单阵合成孔径信号的二维谱展开成距离频率的高阶幂级数形式，将距离向等效调频斜率展开成距离向时间的高阶幂级数形式；然后在幂级数展开形式的二维谱和距离向等效调频斜率的基础上，结合Chirp Scaling原理，推导出高阶CS算法。最后通过仿真和实测数据结果验证了所提算法的有效性。