﻿ 基于矢量阵的近场小目标定位算法研究
 舰船科学技术  2018, Vol. 40 Issue (4): 105-109 PDF

Research on near field small target localization algorithm based on vector array
JI Qing, CHENG Jin-fang, XIAO Da-wei
Department of Weaponry Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: Aiming at the near field warning problem of underwater vehicle, in this paper, vector hydrophone array with arbitrary formation is used to locate the small target in near field. In this paper, firstly, the near field measurement model of plane vector array is derived detailedly. Then, introduces the conventional beamforming and MVDR algorithm based on vector array. Finally, the performance of the algorithm is verified by simulation and measured data. The results show that the vector MVDR has higher target resolution, and the error decreases with the increase of SNR. It is more suitable for underwater near field regional warning.
Key words: underwater warning     near field beamforming     MVDR     near field acoustic source     vector array
0 引　言

1 矢量阵近场测量模型

 图 1 近场目标与阵列的位置示意图 Fig. 1 Positions of near-field targets and array

 ${r_{nm}} = {\left[ {{{\left( {{r_{n1}}\cos {\theta _{n1}} - {x_m}} \right)}^2} + {{\left( {{r_{n1}}\sin {\theta _{n1}} - {y_m}} \right)}^2}} \right]^{1/2}}\text{，}$ (1)

 $\begin{split}& {p_m}(t) = \sum\limits_{n = 1}^N {\frac{{{r_{n1}}}}{{{r_{nm}}}}{s_n}\left( t \right)} {e^{(j{k_n}({r_{n1}} - {r_{nm}})}}) + {n_{mp}}(t)\text{，}\\& t = 1,2,...,{N_t}\text{。}\end{split}$ (2)

 $\left[ {\begin{array}{*{20}{c}}{{v_{mx}}}\\{{v_{my}}}\end{array}} \right] = \frac{{{p_m}}}{{{Z_{nm}}}}\left[ \begin{array}{l}\cos {\theta _{nm}}\\\sin {\theta _{nm}}\end{array} \right]{\rm{ + }}\left[ {\begin{array}{*{20}{c}}{{n_{mx}}}\\{{n_{my}}}\end{array}} \right]\text{。}$ (3)

 \left\{ {\begin{aligned} & {\cos {\theta _{nm}} = \displaystyle\frac{{{r_{n1}}\cos {\theta _{n1}} - {x_m}}}{{{r_{nm}}}}} \text{，}\\ &{\sin {\theta _{nm}} = \displaystyle\frac{{{r_{n1}}\sin {\theta _{n1}} - {y_m}}}{{{r_{nm}}}}} \text{，}\\ &{{Z_{nm}}{\rm{ = }}\displaystyle\frac{1}{{1 - j\frac{{{\lambda _n}}}{{2\pi {r_{nm}}}}}}} \text{。}\end{aligned}} \right. (4)

 $\begin{split}{{X}}(t) =& \left[ {\begin{array}{*{20}{c}}{{p}}\\{{{{v}}_{{x}}}}\\{{{{v}}_{{y}}}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{{{A}}_{{p}}}}\\{{{{A}}_{{p}}} \odot {{{u}}_{{x}}}}\\{{{{A}}_{{p}}} \odot {{{u}}_y}}\end{array}} \right]{{s}}(t) + \left[ {\begin{array}{*{20}{c}}{{{{n}}_p}(t)}\\{{{{n}}_{vx}}(t)}\\{{{{n}}_{vy}}(t)}\end{array}} \right]=\\& {{C}}({{\theta}}, {{r}}){{s}}(t) + {{n}}(t)\text{。}\end{split}$ (5)

2 矢量波束形成近场目标定位算法 2.1 近场矢量常规波束形成

 $Y(t) = {{{W}}^H}(\theta ,r){{X}}(t)\text{，}$ (6)

 $P(\theta ,r) = E\left\{ {{{\left| {Y(t)} \right|}^2}} \right\} = {{W}}{(\theta ,r)^H}{{RW}}(\theta ,r)\text{，}$ (7)

 $\begin{split}& {{W}}({\theta _s},{r_s}) = [{{{a}}^{\rm T}}({\theta _s},{r_s}),{{{a}}^{\rm T}}({\theta _s},{r_s}) \odot {{{u}}_{sx}},\\& {{{a}}^{\rm T}}({\theta _s},{r_s}) \odot {{{u}}_{sy}}{]^{\rm T}}{\rm{ = }}{{c}}({\theta _s},{r_s})\text{。}\end{split}$ (8)

 ${P_{CBF}}({\theta _s},{r_s}) = {{c}}{({\theta _s},{r_s})^H}{{Rc}}({\theta _s},{r_s})\text{。}$ (9)
2.2 近场矢量MVDR波束形成

 $\begin{split}& \min \left\{ {{{W}}{{(\theta ,r)}^H}{{RW}}(\theta ,r)} \right\}\\& {\rm{s}}{\rm{.t}}{\rm{. }}{{W}}(\theta ,r){{c}}({\theta _s},{r_s}) = 1\text{。}\end{split}$ (10)

 ${{{W}}_{opt}}({\theta _s},{r_s}) = \frac{{{{{R}}^{ - 1}}{{c}}({\theta _s},{r_s})}}{{{{{c}}^H}({\theta _s},{r_s}){{{R}}^{ - 1}}{{c}}({\theta _s},{r_s})}}\text{。}$ (11)

 $\begin{split}& {P_{MVDR}}({\theta _s},{r_s}) = {{{W}}^H}_{opt}{{{R}}^{ - 1}}{{{W}}_{opt}}=\\& 1/({{c}}{({\theta _s},{r_s})^H}{{{R}}^{ - 1}}{{c}}({\theta _s},{r_s}))\text{。}\end{split}$ (12)

3 仿真及实测数据分析

3.1 仿真分析

1）对双声源目标的定位能力分析

 图 2 双声源目标的空间分布图 Fig. 2 Positions of double targets and array

 图 3 双声源近场矢量CBF定位 Fig. 3 Double targets located by near-field vector CBF

 图 4 双声源近场矢量MVDR定位 Fig. 4 Double targets located by near-field vector MVDR

2）矢量波束形成性能分析

 $RMSE(\theta ) = \sqrt {\frac{{\sum\limits_{m = 1}^M {{{({{\hat \theta }_m} - \theta )}^2}} }}{M}}\text{。}$ (13)

 图 5 方位角估值的RMSE随信噪比变化 Fig. 5 Azimuth estimator’s RMSE vs SNR

 图 6 距离估值的RMSE随信噪比变化 Fig. 6 Range estimator′s RMSE vs SNR

 图 7 SNR=0 dB方位谱图 Fig. 7 Azimuth spectrum when SNR=0dB

 图 8 SNR=0 dB距离谱图 Fig. 8 Range spectrum when SNR=0dB

3.2 试验数据分析

 图 9 实测数据方位谱图 Fig. 9 Azimuth spectrum of measured data

 图 10 实测数据距离谱图 Fig. 10 Range spectrum of measured data

4 结　语

 [1] 陈强. 水下无人航行器[M]. 北京: 国防工业出版社, 2014. [2] NEHORAI A, PALDI E. Acoustic vector-sensor array processing[J]. IEEE Transactions on Signal Processing, 1994, 42(9): 2481–2491. [3] 时洁. 基于矢量阵的水下噪声源近场高分辨率定位识别方法研究[D]. 哈尔滨: 哈尔滨工程大学, 2009. [4] 余桐奎. 矢量声压组合基阵MVDR近场聚焦波束形成[J]. 舰船科学技术, 2012, 34(6): 60–63. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jckxjs201206014 [5] 熊鑫, 章新华, 卢海杰, 等. 基于任意阵的最小方差无失真响应聚焦波束形成的被动定位方法[J]. 应用声学, 2010, 29(6): 73–76. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yysx201006011 [6] CAPON J. High-resolution frequency-wavenumber spectrum analysis[J]. Proceedings of the IEEE, 2005, 57(8): 1408–1418. [7] 王川, 梅继丹, 孙磊, 等. 近场MVDR聚焦波束扫描声图定位方法研究[J]. 海洋技术学报, 2010, 29(2): 56–59. http://edu.wanfangdata.com.cn/Periodical/Detail/hyjs201002014