基于连续信任函数理论的鲁棒雷达目标检测方法

doi:10.12305/j.issn.1001-506X.2021.09.12

摘要/Abstract

摘要：

目标检测是雷达的基本功能, 其鲁棒性直接决定了雷达应用的成败。针对瑞利目标检测问题, 充分利用连续信任函数理论在不确定性信息表征和推理方面的优势, 提出一种鲁棒雷达目标检测方法, 在决策空间中可对先验模型噪声、真实目标和外来干扰的信任进行精准量化。鉴于该检测方法不存在解析解的问题, 通过随机变量的变换, 将任意瑞利目标幅度起伏模型转化为标准瑞利模型, 再利用查表方式实现信任函数的数值计算, 最后完成检测决策或用于后续融合推理。瑞利目标检测实验验证了所提方法的鲁棒性。

关键词: 雷达目标检测, 瑞利目标幅度起伏模型, 连续信任函数理论

Abstract:

Target detection is the basic function of radar, and its robustness directly determines the success or failure of radar application. Aiming at the problem of Rayleigh target detection, a robust radar target detection method is proposed by making full use of the advantages of continuous belief function theory in uncertain information representation and reasoning. The belief of prior model noise, real target and external interference can be quantified accurately in the detection decision space. In view of the fact that the proposed method does not have analytical solution, through the transformation of random variables, the arbitrary Rayleigh target amplitude fluctuation model is transformed into the standard Rayleigh model.And then, the numerical calculation of the belief function is realized by using the look-up table method. Finally, the detection decision is completed or used for subsequent fusion reasoning. Rayleigh target detection experiments verify the robustness of the proposed method.

Key words: radar target detection, Rayleigh target amplitude fluctuation model, continuous belief function theory

中图分类号:

TN951

杨威, 刘永祥, 付耀文, 黎湘. 基于连续信任函数理论的鲁棒雷达目标检测方法[J]. 系统工程与电子技术, 2021, 43(9): 2463-2469.

Wei YANG, Yongxiang LIU, Yaowen FU, Xiang LI. Robust radar target detection method based on continuous belief function theory[J]. Systems Engineering and Electronics, 2021, 43(9): 2463-2469.

图/表 7

图1

表1

表2

基于信任函数理论的鲁棒雷达目标检测算法"

步骤	操作	备注
先验信息	标准瑞利概率密度函数的等投注概率表	根据应用需求选择近似精度
步骤1	获得点观测z∈R⁺	雷达幅度观测
步骤2	当$ z\ge \sqrt{{\bar{\sigma }}}$时, 对$ \forall \theta_{c} \in \Theta$, 按照式(17)计算条件观测似然函数: $\text{p}{{\text{l}}^{\bf{R}}}\left[ {{\theta }_{c}} \right](z)\approx \sum\limits_{{{\eta }_{i}}=\frac{z}{\sqrt{{\bar{\sigma }}}}, \Delta \eta >0}^{\text{CO}{{\text{V}}_{\text{rls}}}}{2}\left[ \bar{\gamma }\left( {{\eta }_{i}} \right)-{{\eta }_{i}} \right]\left( 1-2\eta _{i}^{2} \right)\exp \left( -\eta _{i}^{2} \right)\Delta \eta $	定理1
步骤2	当$ z <\sqrt{{\bar{\sigma }}}$时, 对$ \forall \theta_{c} \in \Theta$, 按照式(17)~式(20)计算条件观测似然函数: $\text{p}{{\text{l}}^{\bf{R}}}\left[ {{\theta }_{c}} \right](z)\approx \sum\limits_{{{\eta }_{i}}={{{\bar{\gamma }}}^{-1}}\left( \frac{z}{\sqrt{{\bar{\sigma }}}} \right), \Delta \eta >0}^{\text{CO}{{\text{V}}_{\text{rls}}}}{2}\left[ \bar{\gamma }\left( {{\eta }_{i}} \right)-{{\eta }_{i}} \right]\left( 1-2\eta _{i}^{2} \right)\exp \left( -\eta _{i}^{2} \right)\Delta \eta $	定理1
步骤3	对$ \forall S \subset \Theta, m^{\Theta}[z](S)=\prod\limits_{\left\{\theta_{c} \mid \theta_{c} \in S\right\}} \mathrm{p} l^{\bf{R}}\left[\theta_{c}\right](z) \prod\limits_{\left\{\theta_{d} \mid \theta_{d} \in \bar{S}\right\}}\left\{1-\mathrm{pl}^{\bf{R}}\left[\theta_{d}\right](z)\right\}$	GBT
步骤4	对$ \forall \theta_{c} \in \Theta$, 计算投注概率值$\operatorname{BetP}[z]\left(\theta_{c}\right)=\sum\limits_{\left\{S \mid \theta_{c} \subset S\right\}} \frac{m^{\Theta}[z](S)}{\left\{1-m^{\Theta}[z](\phi)\right\}\|S\|} $	投注概率计算
步骤5	用于决策硬判决时, 选择最大投注概率假设$ \theta_{d}=\arg \max \limits_{\forall \theta_{c} \in \Theta} \operatorname{Bet} \mathrm{P}[z]\left(\theta_{c}\right)$；或将m^Θ[z](S)和BetP[z](θ_c)输出给下一级, 待进一步融合后决策。	参考文献[27]

表2

图2

图3

图4

图5

参考文献 27

1	罗鹏飞, 张文明, 刘忠, 等. 统计信号处理基础——估计与检测理论[M]. 北京: 电子工业出版社, 2011, 501
	LUO P F , ZHANG W M , LIU Z , et al. Fundamentals of statistical signal processing[M]. Beijing: Publishing House of Electronics Industry, 2011.
2	BASSEM R M . Radar signal analysis and processing using Matlab[M]. New York: Chapman and Hall CRC, 2010: 290- 292.
3	ZUO L , WANG J , WANG J P , et al. UAV detection via long-time coherent integration for passive bistatic radar[J]. Digital Signal Processing, 2021, 112, 102997. doi: 10.1016/j.dsp.2021.102997
4	CHEN X L , GUAN J , CHEN W S , et al. Sparse long-time cohe-rent integration-based detection method for radar low-observable maneuvering target[J]. IET Radar, Sonar and Navigation, 2020, 14 (4): 538- 546. doi: 10.1049/iet-rsn.2019.0313
5	LI X L , CUI G L , YI W , et al. Coherent integration for maneuvering target detection based on radon-Lv's distribution[J]. IEEE Signal Processing Letter, 2015, 22 (9): 1467- 1471. doi: 10.1109/LSP.2015.2390777
6	MARKA R, 邢孟道, 王彤, 等. 雷达信号处理基础[M]. 2版北京: 电子工业出版社, 2017.
	MARK A R , XING M D , WANG T , et al. Fundamentals of radar signal processing[M]. 2nd ed Beijing: Publishing House of Electronics Industry, 2017.
7	ZHAO Y C , SU Y . Vehicles detection in complex urban scenes using Gaussian mixture model with FMCW radar[J]. IEEE Sensors Journal, 2017, 17 (18): 5948- 5953. doi: 10.1109/JSEN.2017.2733223
8	YANG G , LI H C , YANG W , et al. Unsupervised change detection of SAR images based on variational multivariate Gaussian mixture model and Shannon entropy[J]. IEEE Geoscience and Remote Sensing Letters, 2019, 16 (5): 826- 830. doi: 10.1109/LGRS.2018.2879969
9	LIANG X , SHUI P L , SU H T . Bi-phase compound-Gaussian mixture model of sea clutter and scene-segmentation-based target detection[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2021, 14, 4661- 4674. doi: 10.1109/JSTARS.2021.3074172
10	SEABRA J C , FRANCESCO C , ORIOL P , et al. Rayleigh mixture model for plaque characterization in intravascular ultrasound[J]. IEEE Trans.on Biomedical Engineering, 2011, 58 (5): 1314- 1324. doi: 10.1109/TBME.2011.2106498
11	NAR F , OKMAN O E , OZGUR A , et al. Fast target detection in radar images using Rayleigh mixture and summed area tables[J]. Digital Signal Processing, 2018, 77, 86- 101. doi: 10.1016/j.dsp.2017.09.015
12	AKYILMAZ E . Multilogit prior-based Gamma mixture model for segmentation of SAR images[J]. IEEE Geoscience and Remote Sensing Letters, 2019, 16 (5): 741- 745. doi: 10.1109/LGRS.2018.2880819
13	LI T , LIU Z , XIE R , et al. Ship detection for polarimetric SAR images based on Gp mixture model[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2019, 12 (6): 1812- 1824. doi: 10.1109/JSTARS.2019.2912895
14	FERNANDEZ-MICHELLI J I , HURTADO M , ARETA J A , et al. Unsupervised polarimetric SAR image classification using Gp mixture model[J]. IEEE Geoscience Remote Sensing Letter, 2017, 14 (5): 754- 758. doi: 10.1109/LGRS.2017.2679103
15	KHAN S , GUIDA R . On single-look multivariate G distribution for PoISAR data[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2012, 5 (4): 1149- 1163. doi: 10.1109/JSTARS.2012.2202557
16	LIU W J , LIU J , HAO C P , et al. Multichannel adaptive signal detection: Basic theory and literature review[J]. Science China: Information Sciences, doi: 10.1007/s11432-020-3211-8
17	LIU J , HAN J , ZHANG Z J , et al. Bayesian detection for MIMO radar in Gaussian clutter[J]. IEEE Trans.on Signal Processing, 2018, 66 (24): 6549- 6559. doi: 10.1109/TSP.2018.2879038
18	BESSON O . Adaptive detection using randomly reduced dimension generalized likelihood ratio test[J]. Signal Processing, 2020, 166, 107265. doi: 10.1016/j.sigpro.2019.107265
19	田晓. 雷达有源欺骗干扰综合感知方法研究[D]. 成都: 电子科技大学, 2013.
	TIAN X. Study on the methods of radar active deception jamming integrated sensing[D]. Chengdu: University of Electronic Science and Technology of China, 2013.
20	FANG Z , LI H T , QIAN Y M . Cognitive anti-jamming receiver under phase noise in high frequency bands[J]. Journal of Systems Engineering and Electronics, 2018, 29 (1): 31- 38. doi: 10.21629/JSEE.2018.01.03
21	TIAN C , PEI Y , HOU P . Multi-target tracking algorithm based on PHD filter against multi-range-false-target jamming[J]. Journal of Systems Engineering and Electronics, 2020, 31 (5): 859- 870. doi: 10.23919/JSEE.2020.000066
22	PHILIPPE S . Belief functions on real numbers[J]. International Journal of Approximate Reasoning, 2005, 40 (3): 181- 223. doi: 10.1016/j.ijar.2005.04.001
23	CAI Q X , GAO X Z , DENG Y . Pignistic belief transform: a new method of conflict measurement[J]. IEEE Access, 2020, 8, 15265- 15272. doi: 10.1109/ACCESS.2020.2966821
24	LIU B , HUANG Q , ZHAO J B , et al. A novel belief function based framework for UOPF with multiprobability-characterized and knowledge deficient power sources[J]. IEEE Trans.on Industrial Informatics, 2021, 17 (5): 3153- 3164. doi: 10.1109/TII.2020.3006222
25	FRANCOIS C , BRANKO R , EMMANUEL D , et al. Least committed basic belief density induced by a multivariate Gaussian: formulation with applications[J]. International Journal of Approximate Reasoning, 2008, 48 (2): 419- 436. doi: 10.1016/j.ijar.2006.10.003
26	FICHE A , CEXUS J C , ARNAUD M , et al. Features modeling with an alpha-stable distribution: application to pattern recog-nition based on continuous belief functions[J]. Information Fusion, 2013, 14 (4): 504- 520. doi: 10.1016/j.inffus.2013.02.004
27	PHAN H G . Decision with dempster-shafer belief functions: decision under ignorance and sequential consitency[J]. International Journal of Approximate Reasoning, 2012, 53 (1): 38- 53. doi: 10.1016/j.ijar.2011.09.004

$\bar{\gamma }\left( {{u}_{i}} \right) $	u_i	p^rls(u_i)	$\bar{\gamma }\left( {{u}_{i}} \right) $	u_i	p^rls(u_i)
0.05	1.91	0.099 8	0.45	1.00	0.735 0
0.10	1.68	0.198 0	0.50	0.94	0.778 8
0.15	1.53	0.293 1	0.55	0.88	0.812 9
0.20	1.41	0.384 3	0.60	0.82	0.837 2
0.25	1.31	0.469 7	0.65	0.77	0.852 0
0.30	1.22	0.548 4	0.70	0.71	0.857 7
0.35	1.14	0.619 3	⋮	⋮	⋮
0.40	1.07	0.681 7

[1]	时艳玲, 林毓峰, 梁丹丹. 非平稳海杂波背景下子带分段ANMF检测器[J]. 系统工程与电子技术, 2018, 40(4): 782-789.
[2]	时艳玲. 空间非均匀海杂波的协方差矩阵估计新算法[J]. 系统工程与电子技术, 2013, 35(11): 2239-2243.
[3]	吴兆平，吴惠阳，苏涛. 距离-多普勒-时间三维雷达数据中的目标能量积累[J]. Journal of Systems Engineering and Electronics, 2013, 35(1): 68-72.
[4]	冯讯，王首勇，朱晓波. 基于SG-Alpha稳定分布模型的雷达目标Rao检测方法[J]. Journal of Systems Engineering and Electronics, 2012, 34(2): 287-291.