﻿ 基于粒子群算法的水下多元线阵阵形有源校正方法
 舰船科学技术  2017, Vol. 39 Issue (8): 151-155 PDF

Array shape calibration of underwater linearray with multiple sources based on particle swarm optimization
LI Guang-yuan, HOU Peng, CHENG Guang-fu
Dalian Scientific Test and Control Technology Institute, Dalian 116013, China
Abstract: Aiming at the sensors position errors of the underwater linear array with multiple sensors,a far-filed array shape calibration method with multiple sources is proposed.The method chooses two sources working at different time and constructs objective function with unconditional maximum likelihood.Then,it optimizes the sensors position errors with the particle swarm optimization.Computer simulation is used for the uniform linear array with the mentioned method and the result shows that the method has good robustness,high accuracy and it is promising in application.
Key words: noise sources localization     particle swarm optimization     linear array with multiple sources     calibration of array shape     unconditional maximum likelihood
0 引　言

1 信号模型
 图 1 远场阵列示意图 Fig. 1 The array-source geometry of the far-filed case

 ${\rm{A}}\left( {{{\rm{\theta }}_m},{{\rm{\delta }}_n}} \right) = {\rm{exp}}\left\{ {{\rm{j}}\frac{{2{\rm{\pi }}}}{{\rm{\lambda }}}\left[ {\left( {{x_n} + {\rm{\Delta }}{x_n}} \right)\sin {{\rm{\theta }}_m} + \left( {{y_n} + {\rm{\Delta }}{y_n}} \right)\cos {{\rm{\theta }}_m}} \right]} \right\}$ (1)

 ${X}\left( k \right) = {AS}\left( {\rm{k}} \right) + {N}\left( {\rm{k}} \right)\text{，}$ (2)

 ${{R}_{{\rm{xx}}}} = E\left[ {{X}\left( k \right){{X}^H}\left( {\rm{k}} \right)} \right] = {AS}{{A}^H} + {{\rm{\sigma }}^2}{I},$ (3)

 ${{E}_{\rm{S}}}{E}_S^H + {{E}_N}{E}_N^H = {I},$ (4)

 $\widehat {\rm{\alpha }} = {\rm{arg}}\underbrace {{\rm{max}}}_{\rm{\alpha }}\left\{ { - {\rm{lndet}}\left[ {{{P}_A}\hat{ R}{{P}_A} + \frac{{{\rm{tr}}\left[ {{P}_A^ \bot \hat{ R}} \right]{P}_A^ \bot }}{{{\rm{N}} - {\rm{M}}}}} \right]} \right\},$ (5)

 $\hat{ R} = \frac{1}{K}\mathop \sum \limits_1^K {X}\left( k \right){{X}^H}\left( k \right)\text{。}$ (6)

2 基于粒子群算法的阵形校正方法 2.1 粒子群优化算法

 $V_{id}^{k + 1} = \omega V_{id}^k + {c_1}{r_1}\left( {P_{id}^k - X_{id}^k} \right) + {c_2}{r_2}\left( {P_{gd}^k - X_{id}^k} \right)\text{，}$ (7)
 $X_{id}^{k + 1} = X_{id}^k + V_{id}^{k + 1}\text{。}$ (8)

2.2 阵形校正思路及实施过程

 ${F_n} = - det\left[ {{{P}_{An}}\widehat {{{R}_1}}{{P}_{An}} + \frac{{tr\left[ {{P}_{An}^ \bot \widehat {{{R}_2}}} \right]{P}_{An}^ \bot }}{{N - M}}} \right]\;n = 1,2\text{，}$ (9)

 $F = {\rm arg\;min}\left( {{F_1} + {F_2}} \right)\text{。}$ (10)

1）基于UML方位估计原理，利用式（9）和式（10）构建目标函数；

2）根据信号模型，设置粒子群算法的相关参数，使其兼顾校正精度和收敛速度；

3）利用粒子群算法对阵元位置进行寻优；

4）将寻优结果代入阵列流形中，利用校正过的阵列进行DOA估计，验证校正方法是否有效。

3 性能仿真结果分析 3.1 设计实例

 图 2 校正前后UML谱 Fig. 2 The DOA spectrum before and after calibration with UML

 图 3 阵形校正前后阵元位置关系 Fig. 3 The array shape before and after calibration
3.2 算法性能分析

3.2.1 信噪比对校正精度的影响

 图 4 不同信噪比条件下DOA估计的均方误差 Fig. 4 Mean square error mse of DOA with different snr

3.2.2 辅助源角度差对校正精度的影响

 图 5 不同辅助源角度差条件下DOA估计的均方误差 Fig. 5 Mean square error（MSE）of DOA with different angles

3.2.3 阵元位置对校正精度的影响

 图 6 不同阵元位置误差条件下DOA估计的均方误差 Fig. 6 Mean square error （MSE） of DOA with different error range
4 结　语

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