加权广义逆高斯杂波下距离扩展目标的自适应检测

徐震宇; 刘维建; 陈小龙; 陈辉; 杜庆磊; 李槟槟; 周必雷

doi:10.12000/JR25072

加权广义逆高斯杂波下距离扩展目标的自适应检测

DOI: 10.12000/JR25072 CSTR: 32380.14.JR25072

1.
空军预警学院武汉 430019
2.
海军航空大学烟台 264001

基金项目: 国家自然科学基金(62471485, 62071482, 62222120)，湖北省自然科学基金(2025AFB873)

详细信息

作者简介:
徐震宇，硕士生，主要研究方向为多通道信号检测、空时自适应处理

刘维建，博士，副教授，主要研究方向为多通道信号检测、统计和阵列信号处理

陈小龙，博士，教授，主要研究方向为雷达低慢小目标检测、海杂波抑制、雷达智能信号处理等

陈　辉，博士，教授，主要研究方向为阵列信号处理、雷达抗干扰技术和新体制雷达

杜庆磊，博士，副教授，主要研究方向为雷达目标探测、识别和数字图像处理

李槟槟，博士，副教授，主要研究方向为极化敏感阵列信号处理和雷达抗干扰技术

周必雷，博士，讲师，主要研究方向为雷达信号处理和阵列信号处理

通讯作者:
刘维建 liuvjian@163.com

责任主编：许述文 Corresponding Editor: XU Shuwen
1¹⁾ 在理论推导部分，本文假设加权广义逆高斯分布的参数已知，并在仿真数据实验中基于已知参数生成杂波数据。然而，在实测数据实验中，杂波所对应的加权广义逆高斯分布参数是未知的。针对这一问题，4.2节提出了一种加权广义逆高斯分布参数估计方法。
中图分类号: TN957.51
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出版历程
- 收稿日期: 2025-04-17
- 修回日期: 2025-07-03
- 网络出版日期: 2025-09-08

Adaptive Detection of Range-distributed Targets in Weighted Generalized Inverse Gaussian Clutter

1.
Air Force Early Warning Academy, Wuhan 430019, China
2.
Naval Aviation University, Yantai 264001, China

Funds: The National Natural Science Foundation of China (62471485, 62071482, 62222120), National Natural Science Foundation of Hubei Province (2025AFB873)

More Information

Corresponding author: LIU Weijian, liuvjian@163.com

摘要

摘要: 该文研究了复合高斯杂波中距离扩展目标的自适应检测问题，其中杂波纹理分量服从加权广义逆高斯(WGIG)分布。该文基于两步Rao, Wald, Durbin和Gradient检验分别设计加权广义逆高斯杂波下的自适应检测器。针对未知协方差矩阵，分别采用近似最大似然(AML)和归一化采样协方差矩阵(NSCM)两种方法进行估计。由于纹理分量的最大后验(MAP)估计难以解析求解，因此在Rao, Wald和Durbin检验的检测器设计中，采用纹理分量的倒数期望的MAP进行替代；而在Gradient检验的检测器设计中，则基于后验概率密度函数推导检验统计量。理论分析表明，基于Rao, Durbin和Gradient检验所得到的检测器具有一致性。在性能评估方面，通过仿真数据和实测数据，分别对无信号失配和存在信号失配两种情况下的检测性能进行了系统评估。实验结果表明：(1)该文提出的基于AML的检测器均具有恒虚警率(CFAR)特性；(2)在无信号失配情况下，基于Rao准则和Wald准则的检测器在两种实测数据集上分别表现出最优的检测性能，并且相较于两步GLRT检测器的检测性能分别提升0.1～0.5 dB和0.7～0.8 dB；(3)在信号失配情况下，基于Rao准则与AML估计的检测器具有最佳的稳健性，而基于Wald准则的检测器对失配信号表现出最强的抑制能力。
- 自适应检测 /
- 加权广义逆高斯 /
- 扩展目标 /
- 恒虚警 /
- 近似最大似然
Abstract: In this paper, we investigate the adaptive detection of range-distributed targets in compound-Gaussian clutter, where the texture component follows a Weighted Generalized Inverse Gaussian (WGIG) distribution. We propose adaptive detectors for WGIG-distributed clutter based on two-step Rao, Wald, Durbin, and Gradient tests. The unknown covariance matrix is estimated using Approximate Maximum Likelihood (AML) and the Normalized Sample Covariance Matrix (NSCM). To address the analytical intractability of Maximum A Posteriori (MAP) estimation for the texture component, we adopt an alternative approach: The MAP estimator of the reciprocal expectation of the texture component, which is used in designing adaptive detectors based on the Rao, Wald, and Durbin tests. For the Gradient test-based detector, the test statistic is derived directly from the posterior probability density function. Our theoretical analysis confirms the consistency of the detectors derived from the Rao, Durbin, and Gradient tests. Extensive evaluations on both simulated and real data yield three key findings: (1) the proposed AML-based detectors maintain the constant false alarm rate property; (2) under matched signal conditions, the detectors based on the Rao and Wald tests achieve the best performance on both the IPIX radar dataset and the Journal of Radar’s maritime surveillance dataset—specifically, they outperform the two-step generalized likelihood ratio test-based detector, requiring 0.1～0.5 dB and 0.7～0.8 dB lower Signal-to-Clutter Ratio (SCR) to achieve the same detection probability, respectively; and (3) under mismatched signal conditions, the Rao test-based detector with AML estimation exhibits superior robustness, while the Wald test-based detector demonstrates the strongest suppression capability against mismatched signals.
- Adaptive detection /
- Weighted Generalized Inverse Gaussian (WGIG) /
- Distributed target /
- Constant False Alarm Rate (CFAR) /
- Approximate Maximum Likelihood (AML)

HTML全文

图 1 R已知基于仿真数据时各检测器的检测概率随信杂比变化曲线(N=4, 8)

Figure 1. PDs of the detectors based on simulated data under different SCRs for known R (N=4, 8)

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图 2 R未知基于仿真数据及AML和NSCM估计器时各检测器的检测概率随信杂比变化曲线

Figure 2. PDs of the detectors based on simulated data under different SCRs for unknown R using AML and NSCM estimators

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图 3 R未知基于仿真数据及AML和NSCM估计器时各检测器的检测概率随$ {\cos ^2}\phi $变化曲线

Figure 3. PDs of the detectors based on simulated data under different $ {\cos ^2}\phi $ for unknown R using AML and NSCM estimators

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图 4 R未知时基于仿真数据及AML和NSCM估计器时各检测器的CFAR特性

Figure 4. CFAR characteristics of the detectors based on simulated data for unknown R using AML and NSCM estimators

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图 5 $M = 2$时20221112175025_stare_VV海杂波概率密度函数曲线拟合结果

Figure 5. Fitting results of 20221112175025_stare_VV sea clutter PDF at $M = 2$

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图 6 $M = 2$时20221112175025_stare_VV海杂波累积分布函数曲线拟合结果

Figure 6. Fitting results of 20221112175025_stare_VV sea clutter CCDF at $M = 2$

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图 7 $M = 2$时IPIX_19980223_170435海杂波概率密度曲线拟合结果

Figure 7. Fitting results of IPIX_19980223_170435 sea clutter PDF at $M = 2$

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图 8 $M = 2$时IPIX_19980223_170435海杂波累积分布函数拟合结果

Figure 8. Fitting results of IPIX_19980223_170435 sea clutter CCDF at $M = 2$

下载: 全尺寸图片幻灯片

图 9 R未知基于20221112175025_stare_VV及AML和NSCM估计器时各检测器的检测概率随信杂比变化曲线

Figure 9. PDs of the detectors based on 20221112175025_stare_VV data under different SCRs for unknown R using AML and NSCM estimators

下载: 全尺寸图片幻灯片

图 10 R未知基于IPIX_19980223_170435及AML和NSCM估计器时各检测器的检测概率随信杂比变化曲线

Figure 10. PDs of the detectors based on IPIX_19980223_170435 data under different SCRs for unknown R using AML and NSCM estimators

下载: 全尺寸图片幻灯片

图 11 R未知基于20221112175025_stare_VV及AML和NSCM估计器时各检测器的检测概率随$ {\cos ^2}\phi $变化曲线(SCR=10 dB)

Figure 11. PDs of the detectors based on 20221112175025_stare_VV data under different $ {\cos ^2}\phi $ for unknown R using AML and NSCM estimators (SCR=10 dB)

下载: 全尺寸图片幻灯片

图 12 R未知基于IPIX_19980223_170435及AML和NSCM估计器时各检测器的检测概率随$ {\cos ^2}\phi $变化曲线(SCR=30 dB)

Figure 12. PDs of the detectors based on IPIX_19980223_170435 data under different $ {\cos ^2}\phi $ for unknown R using AML and NSCM estimators (SCR=30 dB)

下载: 全尺寸图片幻灯片

表 1 M = 2时各个分布模型拟合20221112175025_stare_VV海杂波数据结果

Table 1. When M = 2, the fitting results of various distribution models to 20221112175025_stre_VV sea clutter

模型	参数	MSE
WGIG	$ {\boldsymbol{w}} = \left[ \begin{gathered} 0.5514 \\ 0.4486 \\ \end{gathered} \right] $, $ a = \left[ \begin{gathered} 1.0905{\text{E}}-6 \\ 1.0434{\text{E}}-8 \\ \end{gathered} \right] $, $ {\boldsymbol{b}} = \left[ \begin{gathered} {\text{1}}{\text{.1835E8}} \\ 1.6943{\text{E}}8 \\ \end{gathered} \right] $, $ {\boldsymbol{v}} = \left[ \begin{gathered} 18.0474 \\ 0.9568 \\ \end{gathered} \right] $	3.4592E-06
GIG	$a = 2.0837{\text{E}} - 9$，$b = 7.4187{\text{E}}7$, $ v = - 0.6409 $	2.2676E–05
Inverse Gamma	$\lambda = 1.5807$, $\beta = 9.8920{\text{E7}}$	1.2227E–04
K	$\lambda = - 0.2396$, $\beta = 7.0049{\text{E3}}$	3.9341E–04

下载: 导出CSV

表 2 M = 2时各个分布模型拟合IPIX_19980223_170435海杂波数据结果

Table 2. When M = 2, the fitting results of various distribution models to IPIX_19980223_170435 sea clutter

模型	参数	MSE
WGIG	$ w = \left[ \begin{gathered} 0.9631 \\ 0.0369 \\ \end{gathered} \right] $, $ a = \left[ \begin{gathered} 2.7812 \\ 0.4670 \\ \end{gathered} \right] $, $ b = \left[ \begin{gathered} 0.5408 \\ 0.0014 \\ \end{gathered} \right] $, $ v = \left[ \begin{gathered} 0.0077 \\ 0.0446 \\ \end{gathered} \right] $	4.0693E–07
GIG	$a = 3.4697$, $b = 0.2546$, $ v = 0.5968 $	2.6538E–06
Inverse Gamma	$\lambda = 2.3372$, $\beta = 0.8660$	1.4781E–05
K	$\lambda = 0.2602$, $\beta = 0.3532$	1.4312E–04

下载: 导出CSV

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