基于非负最小二乘的矢量阵反卷积波束形成方法
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摘要
针对现有反卷积波束形成方法无法直接适用于矢量阵等具有移变点扩散函数阵列的问题,本文给出了一种利用非负最小二乘法进行矢量阵这种移变模型的反卷积求解方法。推导了矢量阵的广义卷积模型,并在常规矢量阵波束输出、矢量阵点扩散函数字典、目标函数之间建立差函数方程组,通过最小化差函数的原则来实现对目标函数的求解,从而实现矢量阵反卷积波束形成处理。本文方法同样适用于其他移变模型阵列反卷积求解。对本文方法与传统波束形成、最小方差无畸变响应和多重信号分类方法在主瓣宽度、旁瓣级和稳健性等方面的性能进行了对比分析。结果表明本文方法在存在阵元位置误差情况下具有更窄的主瓣宽度和更低的主旁瓣比。
Aiming at the problem that the existing deconvolved beamforming method cannot be directly applied to the vector array with a shift-variant point spread function( PSF),a deconvolution solution based on non-negative least squares( NNLS) method is proposed. A generalized convolution model of a vector-sensor array is derived. On this basis,the difference function equations are established among the conventional vector-sensor array beam output,the vector matrix point spread function dictionary,and the object function. The object function is solved based on the principle of minimizing the difference function,achieving the vector-sensor array deconvolved beamforming.The proposed method is also applicable to the deconvolution of other shift-variant arrays. The performance of the proposed method and the traditional CBF,minimum variance distortionless response( MVDR),and multiple signal classification( MUSIC) methods in terms of the main lobe width,sidelobe level,and robustness are compared and analyzed. The results show that the new method has a narrower main lobe width and a lower main sidelobe ratio in the presence of array element position errors.
Aiming at the problem that the existing deconvolved beamforming method cannot be directly applied to the vector array with a shift-variant point spread function( PSF),a deconvolution solution based on non-negative least squares( NNLS) method is proposed. A generalized convolution model of a vector-sensor array is derived. On this basis,the difference function equations are established among the conventional vector-sensor array beam output,the vector matrix point spread function dictionary,and the object function. The object function is solved based on the principle of minimizing the difference function,achieving the vector-sensor array deconvolved beamforming.The proposed method is also applicable to the deconvolution of other shift-variant arrays. The performance of the proposed method and the traditional CBF,minimum variance distortionless response( MVDR),and multiple signal classification( MUSIC) methods in terms of the main lobe width,sidelobe level,and robustness are compared and analyzed. The results show that the new method has a narrower main lobe width and a lower main sidelobe ratio in the presence of array element position errors.
引文
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[14]褚志刚,杨洋.基于非负最小二乘反卷积波束形成的发动机噪声源识别[J].振动与冲击,2013,32(23):75-81.CHU Zhigang,YANG Yang.Noise source identification for an engine based on FFT-non-negative least square(NNLS)deconvolution beamforming[J].Journal of vibration and shock,2013,32(23):75-81.
[15]张宾,孙贵青,李启虎.阵形畸变对拖曳双线阵左右舷分辨性能的影响[J].声学学报,2008,33(4):294-299.ZHANG Bin,SUN Guiqing,LI Qihu.Effects of shape distortion upon left/right discrimination of towed twin-line array[J].Acta acustica,2008,33(4):294-299.
[2]NSIRI B,CHONAVEL T,BOUCHER J M,et al.Blind submarine seismic deconvolution for long source wavelets[J].IEEE journal of oceanic engineering,2007,32(3):729-743.
[3]LYLLOFF O,FERNNDEZ-GRANDE E,AGERKVIST F,et al.Improving the efficiency of deconvolution algorithms for sound source localization[J].The journal of the acoustical society of America,2015,138(1):172-180.
[4]ZHONG Di,YANG Dong,ZHU Min.Improvement of sound source localization in a finite duct using beamforming methods[J].Applied acoustics,2016,103:37-46.
[5]VONESCH C,UNSER M.A fast thresholded landweber algorithm for wavelet-regularized multidimensional deconvolution[J].IEEE transactions on image processing,2008,17(4):539-549.
[6]SEKKO E,THOMAS G,BOUKROUCHE A.A deconvolution technique using optimal Wiener filtering and regularization[J].Signal processing,1999,72(1):23-32.
[7]DOUGHERTY R.Extensions of DAMAS and benefits and limitations of deconvolution in beamforming[C]//Proceedings of the 11th AIAA/CEAS Aeroacoustics Conference.Monterey,California,2005.
[8]EHRENFRIED K,KOOP L.Comparison of iterative deconvolution algorithms for the mapping of acoustic sources[J].AIAA journal,2012,45(7):1584-1595.
[9]BLAHUT R E.Theory of remote image formation[M].Cambridge:Cambridge University Press,2004.
[10]YANG T C.Deconvolved conventional beamforming for a horizontal line array[J].IEEE journal of oceanic engineering,2018,43(1):160-172.
[11]YANG T C.Performance analysis of superdirectivity of circular arrays and implications for sonar systems[J].IEEEjournal of oceanic engineering,2019,44(1):156-166.
[12]梁国龙,马巍,范展,等.矢量声纳高速运动目标稳健高分辨方位估计[J].物理学报,2013,62(14):144302.LIANG Guolong,MA Wei,FAN Zhan,et al.A high resolution robust localization approach of high speed target based on vector sonar[J].Acta physica sinica,2013,62(14):144302.
[13]时洁,杨德森,时胜国.基于最差性能优化的运动声源稳健聚焦定位识别方法研究[J].物理学报,2011,60(6):064301.SHI Jie,YANG Desen,SHI Shengguo.Robust localization and identification method of moving sound sources based on worst-case performance optimization[J].Acta physica sinica,2011,60(6):064301.
[14]褚志刚,杨洋.基于非负最小二乘反卷积波束形成的发动机噪声源识别[J].振动与冲击,2013,32(23):75-81.CHU Zhigang,YANG Yang.Noise source identification for an engine based on FFT-non-negative least square(NNLS)deconvolution beamforming[J].Journal of vibration and shock,2013,32(23):75-81.
[15]张宾,孙贵青,李启虎.阵形畸变对拖曳双线阵左右舷分辨性能的影响[J].声学学报,2008,33(4):294-299.ZHANG Bin,SUN Guiqing,LI Qihu.Effects of shape distortion upon left/right discrimination of towed twin-line array[J].Acta acustica,2008,33(4):294-299.
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