﻿ 矢量圆阵时域解析 MVDR 算法研究
 舰船科学技术  2017, Vol. 39 Issue (3): 131-134 PDF

1. 海军潜艇学院，山东 青岛 266042;
2. 海军青岛雷达声呐修理厂，山东 青岛 266000

Studying of circular vector sensor array time-domain analysis mvdr algorithm
WANG Yi-chuan1, LI Hai-tao1, GAO Xin1, CHEN Peng2
1. Navy Submarine Academy, Qingdao 266042, China;
2. Navy Qingdao Radar and Sonar Repair Factory, Qingdao 266000, China
Abstract: To improve the resolution of direction estimation of circular vector sensor array, a new algorithm based on VTAMVDR is used in circular vector sensor array signal processing. Circular vector sensor array time-domain analysis MVDR algorithm is proposed. Studied the principle and process flow of circular vector sensor array time-domain analysis MVDR algorithm. Compared the beam width and resolution capability of circular vector sensor array time-domain analysis MVDR with circular vector sensor conventional beamforming algorithm. Theoretical analysis and computer simulations show that the proposed algorithm is more effective in improving resolution of multiple targets than the traditional algorithm．
Key words: circular vector sensor array     time-domain analysis     beamforming
0 引　言

1 矢量圆阵时域解析 MVDR 算法原理

 $\left\{ \begin{array}{l}P = S{}_p + {V_p}\text{，}\\{V_x} = S{}_x + {V_x}\text{，}\\{V_y} = S{}_y + {V_y}\text{。}\end{array} \right.$ (1)

 图 1 均匀分布离散圆阵工作扇面 Fig. 1 Sketch map of circular vector sensor array

 $\left\{ \begin{array}{l}{Y_P} = P + j \cdot H(P)\text{，}\\{Y_{{V_x}}} = {V_x} + j \cdot H({V_x})\text{，}\\{Y_{{V_y}}} = {V_y} + j \cdot H({V_y})\text{。}\end{array} \right.$ (2)

 $P = E[{ Y}{{ Y}^{H}}] = {{w}^{H}}{{R}_c}{w} \text{，}$ (3)

 ${ Y} = \left[ \begin{array}{l}{Y_P}\\{Y_{{V_x}}}\\{Y_{{V_y}}}\end{array} \right]\text{。}$

 $\left\{ \begin{array}{l}\arg \underbrace {\min }_w({{w}^H}{{R}_c}{w})\text{，}\\{\rm s}.{\rm t}. {{w}^H}\left[ {{A} \otimes a\left( \theta \right)} \right] = 1\text{。}\end{array} \right.$ (4)

 $L(w) = \frac{1}{2}{{w}^{H}}{{R}_c}{w} - \lambda \left\{ {{{w}^{H}}\left[ {{A} \otimes a\left( \theta \right)} \right] - 1} \right\} \text{，}$ (5)

 ${w} = \lambda \left[ {{A} \otimes a\left( \theta \right)} \right]{{R}_c}^{^{ - 1}}\text{。}$ (6)

 ${w} = \frac{{{{\left[ {{A} \otimes a\left( \theta \right)} \right]}^{H}}{{R}_c}^{ - 1}}}{{{{\left[ {{A} \otimes a\left( \theta \right)} \right]}^{H}}{{R}_c}^{ - 1}\left[ {{A} \otimes a\left( \theta \right)} \right]}} \text{，}$ (7)

 $P(\theta ) = \frac{1}{{{{\left[ {{A} \otimes a\left( \theta \right)} \right]}^H}{{R}_c}^{ - 1}\left[ {{A} \otimes a\left( \theta \right)} \right]}}\text{。}$ (8)

 图 2 矢量圆阵时域解析 MVDR 算法流程图 Fig. 2 Schematic diagram of circular vector sensor array time-domain analysis MVDR algorithm

2 数值仿真分析

 $\sqrt {\frac{1}{N}\sum\limits_{j = 1}^N {\left( {{{\bar \theta }_{ij}} - {\theta _{ij}}} \right)} {}^2} \text{。}$ (9)

 图 3 单目标矢量圆阵常规波束形成和矢量圆阵时域解析 MVDR 算法的波束输出 Fig. 3 Beamforming cure of the two algorithm with single target

 图 4 不同信噪比下的方位估计均方根偏差 Fig. 4 Direction of arrival estimation under diffetrent SNR

 $\left| {{{\bar \theta }_1} - {\theta _1}} \right| - \left| {{{\bar \theta }_2} - {\theta _2}} \right| < \left| {{{\bar \theta }_1} - {{\bar \theta }_2}} \right|\text{。}$ (10)

 图 5 双目标时矢量圆阵常规波束形成和矢量圆阵时域解析 MVDR 算法的波束输出 Fig. 5 Beamforming cure of the two algorithm with two targets

 图 6 不同角度间隔下矢量圆阵常规波束形成与矢量圆阵时域解析 MVDR 算法双目标分辨成功概率比较 Fig. 6 Success resolution probabilityof two targets under different angle
3 结　语

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