Joint estimation of DOA and polarization parameters based on uniform circle array with vector sensor
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摘要:
针对极化敏感阵列中非完备电磁矢量传感器多参数联合估计问题，提出一种基于三维电磁矢量传感器平面圆阵模型的波达方向(DOA)和极化参数联合估计方法。利用阵列流型矩阵的特性将四维谱函数进行解耦，严格证明DOA搜索与极化参数估计的不相关性，将四维谱搜索优化为仅与DOA相关的二维谱搜索，提出DOA谱峰搜索二级比较策略，可使雷达自动识别谱峰坐标，有效提高信号处理的实时性；提出一种基于精英反向学习和Lévy飞行的改进粒子群算法对极化参数进行估计，提高极化参数的收敛性能。通过与同类算法进行仿真对比，结果表明：所提算法在牺牲少量时间的条件下可提高估计精度。
Abstract:To address the problem of multi-parameter joint estimation of incomplete electromagnetic vector sensors in the polarization sensitive array, a joint estimation method of Direction of Arrival (DOA) and polarization parameters is proposed based on a circle array model of the three-dimensional electromagnetic vector sensor plane. Using the characteristics of the array flow pattern matrix, a four-dimensional spectral function is decoupled, and the uncorrelation between DOA search and polarization parameter estimation is rigorously proved. A four-dimensional spectral search is optimized to a two-dimensional spectral search only related to DOA. A two-level comparison strategy of the DOA spectral peak search is proposed, which enables the radar to automatically identify the spectral peak coordinates and effectively improve the real-time performance of signal processing. The improved particle swarm optimization algorithm based on elite reverse learning and Lévy flight is proposed to estimate the polarization parameters, which improves the convergence performance of polarization parameters. The simulation results show that the proposed algorithm improves the estimation accuracy at the expense of a small amount of time.
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图 1 入射波与圆阵中心的示意图
Figure 1. Schematic diagram of incident wave and center of circle array
图 2 电场的正交分解示意图
Figure 2. Schematic diagram of orthogonal decomposition of electric field
图 7 Tk(γ,η)的等高线俯视图及粒子的初始化分布(N=20)
Figure 7. Top view of Tk(γ,η) contour, and initial distribution of particles (N=20)
图 11 极化幅角γ随SNR的RMSE
Figure 11. RMSE of polarization amplitude angle φ with respect to SNR
图 12 极化相位差η随SNR的RMSE
Figure 12. RMSE of polarization phase angle η with respect to SNR
表 1 不同信源数下识别谱峰所需时间
Table 1. Time required to identify spectral peaks with different numbers of sources
s 信源数 所需时间 人为输入 采用DOA二级比较策略 1 约3 2×10 −3 2 约6 7.4×10 −3 3 约9 7.6×10 −3 4 约12 8.2×10 −3 5 约15 18.4×10 −3 
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表 2 不同粒子数的PSO算法和本文算法收敛性能
Table 2. Convergence performance between PSO algorithm and the proposed algorithm with different particle numbers
N Cinteration Ctime/s Cvalue PSO算法 本文算法 PSO算法 本文算法 PSO算法 本文算法 10 25.6 13.4 0.0059 0.0082 0.0076 0.0071 15 17.86 10.66 0.0067 0.0091 0.0066 0.0062 20 16.8 8.66 0.0085 0.0099 0.0054 0.0053 25 15.73 8.46 0.0103 0.0116 0.0054 0.0053 30 13.8 8.53 0.0108 0.0129 0.0054 0.0053
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表 3 不同数据类型进行乘、加运算产生的运算量
Table 3. Amount of computation generated by multiplication and addition of different data types
数据类型 运算类型 运算量/次 实数 复数 四元数 实数 相乘 1（乘法） 相加 1（加法） 复数 相乘 2（乘法） 4（乘法）
2（加法）8（乘法）
4（加法）相加 1（加法） 2（加法） 2（加法） 四元数 相乘 16次（乘法）
12次（加法）相加 4（加法）
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表 4 MUSIC类算法运算性能
Table 4. Computational performance among 4 MUSIC-type algorithms
算法 D $ {\widehat {\boldsymbol{R}}_{\boldsymbol{X}}} $运算量/次 $ (\theta ,\varphi ) $运算量/次 $ (\gamma ,\eta ) $搜索时间/s 总运行时间/s LV-MUSIC 6 1.4746×107（乘法）
7.3728×106（加法）7.2402×1012（乘法）
3.6200×1012（加法）46047.9 DL-MUSIC 2 1.6384×106（乘法）
8.1920×105（加法）4.7369×107（乘法）
2.6984×107（加法）0.0108 1.3044 Q-MUSIC 2 1.6384×106（乘法）
8.1920×105（加法）4.5166×107（乘法）
2.2258×107（加法）0.1604 1.5627 本文算法 3 3.6864×106（乘法）
1.8432×106（加法）1.0672×108（乘法）
5.3363×107（加法）0.0813 2.1682
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