空域移变反卷积水下阵列信号处理算法及应用研究

Convolution and deconvolution are fundamental problems in signal processing. Conventional beamforming results can be seen as the convolution of the array directivity function and the objective function, and the resolution ability of the array directivity is limited by array physical aperture. Depending on the duality of time sampling and spatial sampling, time domain deconvolution can be used for the spatial array. Using deconvolution technique to remove the effect of array directivity and get rid of the limitation of physical aperture provides a new idea for robust high resolution signal processing of underwater array. This project intends to carry out research work on signal processing algorithm and application of deconvolution underwater arrays. Firstly, the deconvolution beamforming modeling is studied, and a unified mathematic model of arbitrary spatial array deconvolution beamforming is established, especially for the spatial shift variant array (the shift invariant model can be considered as a special case); Then, the research on the algorithm of deconvolution beamforming algorithm of spatial shift variant model is carried out. Aiming at the mathematical model of underwater array signal, combining with the traditional deconvolution algorithm and likelihood estimation, sparse reconstruction and other mathematical tools to form a variety of new algorithms, and the performance of the algorithm such as robustness, resolution, gain, and calculation amount is compared and analyzed through simulation; In order to verify the actual performance of algorithm in the marine environment, deconvolution beamforming algorithm application performance test of various array shapes are carried out.

卷积和反卷积是信号处理中的基本问题。常规波束形成结果可以看成是阵列指向性函数与目标函数的卷积，阵列指向性受物理孔径的限制导致分辨能力受限。根据时间采样与空间采样的对偶性，可将时间序列反卷积用于空间阵列。利用反卷积技术去除阵列指向性的影响，摆脱物理孔径限制，为水下阵列稳健高分辨信号处理提供了一种新的思路。本课题拟开展反卷积水下阵列信号处理算法及应用研究工作。首先，开展反卷积波束形成理论建模研究，建立空间任意阵列反卷积波束形成的统一数学模型，特别针对空域移变模型阵列（移不变模型可视为其特例）；然后，开展空域移变模型反卷积波束形成解算算法研究，针对水下阵列信号数学模型，结合传统反卷积算法与似然估计、稀疏重构等数学工具形成多种新的算法，并通过仿真对比分析算法的鲁棒性、分辨率、增益和计算量等性能；最后，开展多种具体阵列形式反卷积波束形成算法应用性能试验研究。验证方法在实际海洋环境下的应用性能。

卷积和反卷积是信号处理中的基本问题。常规波束形成结果可以看成是阵列指向性函数与目标函数的卷积，阵列指向性受物理孔径的限制导致分辨能力受限。根据时间采样与空间采样的对偶性，可将时间序列反卷积用于空间阵列。利用反卷积技术去除阵列指向性的影响，摆脱物理孔径限制。课题开展了反卷积波束形成理论建模、方法研究及应用研究工作。首先，完成了反卷积波束形成理论建模，建立空间任意阵列反卷积波束形成的统一数学模型，特别针对空域移变模型阵列（移不变模型可视为其特例）开展了理论建模工作；然后，完成了空域移变模型反卷积波束形成解算算法研究，针对移变水下阵列信号模型，结合传统反卷积算法与似然估计、稀疏字典等思想形成了多种新的算法，针对移变模型情况下算法计算量大计算缓慢的问题提出了基于空间重采样的快速算法，显著提高了运算速度。通过仿真对比分析算法的鲁棒性、分辨率、增益和计算量等性能；最后，开展了多种具体阵列形式反卷积波束形成算法应用性能海上试验研究，通过声压阵及圆弧阵水池试验、矢量线阵海试、等间距水平声压阵近场海试和垂直阵等间距线阵海试充分验证了反卷积处理算法的可行性和性能。仿真和试验数据结果皆表明在水声探测的低信噪比环境下，空域移变反卷积波束形成技术相比于常规方法能够显著提高对多目标的分辨能力，降低旁班级从而改善在强干扰下对弱目标的检测能力，另外相比于其它高分辨处理方法，具有更好的稳健性。稳健高分辨的阵处理技术一直是水声、雷达等很多领域的核心技术问题，课题的研究成果为这一问题提供了新的解决思路，研究成果具有广泛的应用前景。