基于标签多伯努利跟踪器的对手风险动态评估方法

王明阳; 刘旭旭; 李裕霖; 李溯琪; 王佰录

doi:10.12000/JR23207

基于标签多伯努利跟踪器的对手风险动态评估方法

doi: 10.12000/JR23207

1.
西南电子技术研究所成都 610036
2.
重庆大学微电子与通信工程学院重庆 400044

基金项目: 国家自然科学基金(62301091, 62371078)，中国博士后面上基金(2022M710533, 2022M710535)

详细信息

作者简介:
王明阳，博士，高级工程师，主要研究方向为目标跟踪、目标识别、信息融合、机器学习等

刘旭旭，硕士生，主要研究方向为基于随机集的多目标跟踪技术、基于随机集的目标对抗风险评估技术等

李裕霖，硕士生，主要研究方向为分布式多传感器信息融合、基于随机集的多目标跟踪

李溯琪，博士生导师，弘深青年学者教授，主要研究方向为基于随机集的多目标跟踪技术、分布式多智能体协同探测与信息融合技术、5G/6G基站感知技术等

王佰录，博士，主要研究方向为分布式多传感器信息融合、5G/6G基站定位技术、雷达微弱目标检测跟踪等

通讯作者:
李溯琪 lisuqi@cqu.edu.cn

责任主编：李天成 Corresponding Editor: LI Tiancheng
中图分类号: TN953
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出版历程
- 收稿日期: 2023-10-25
- 修回日期: 2023-12-25
- 网络出版日期: 2024-01-09
- 刊出日期: 2024-02-28

Dynamic Adversarial Risk Estimation Based on Labeled Multi-Bernoulli Tracker

1.
Southwest Institute of Electronic Technology, Chengdu 610036, China
2.
School of Micro-electronics and Communication Engineering, Chongqing University, Chongqing 400044, China

Funds: The National Natural Science Foundation of China (62301091, 62371078), China Postdoctoral Science Foundation Funded Project (2022M710533, 2022M710535)

More Information

Corresponding author: LI Suqi, lisuqi@cqu.edu.cn

摘要

摘要: 在诸多的军事和民用领域都存在对手目标蓄意入侵我方重要区域从事恶意伤害活动的场景。对手风险评估是基于我方传感器获取的量测数据，在线评估和预测对手行动对我方资产造成的潜在伤害和损失。为了评估随机且动态变化的对手风险，该文提出一种基于标签多伯努利(LMB)跟踪器的统计对手风险动态评估方法。首先，在LMB跟踪器的框架下，基于加性模型和乘性模型，分别推导了统计对手风险最小均方误差估计的表达式。其次，针对所涉及的非线性函数积分问题，结合混合高斯近似和抽样近似方法，提出统计对手风险最小均方误差估计的数值计算方法；最后，将统计对手风险估计方法与LMB跟踪器的迭代过程有机结合，可实现入侵的多目标对我方重要资产期望损失的动态在线评估。模拟多个具有杀伤能力的目标攻击我方雷达阵地的场景，利用雷达获取的实时点迹量测数据，验证了提出算法的有效性和性能优势。
- 对手风险评估 /
- 多目标跟踪 /
- 标签多伯努利跟踪器 /
- 随机集理论 /
- 威胁等级评估 /
- 态势重建
Abstract: In many military and civilian areas, there exists a scenario in which multiple intruders from an adversary attempt to enter important region of our own to carry out intentional malign activity. Adversarial Risk (AR) estimation is used to assess and predict the expected damage to our valuable assets from the actions of online adversaries based on measurements performed by sensors. To evaluate random and time-varying AR, this study proposes a stochastic AR estimation approach based on a Labeled Multi-Bernoulli (LMB) tracker. First, in the formulation of LMB filtering, expressions of the minimum mean squared error estimation of the stochastic AR are derived for the additive and multiplying model. Second, by combining the Gaussian mixture and sampling approximations, we devise a numerical calculation approach for the proposed AR estimations. Third, we achieve an online evaluation of the expected damage to our valuable assets from the adversary by embedding the proposed AR estimation and LMB filtering. The effectiveness and performance advantage of the proposed estimation algorithms are verified using measurements from radars, considering a simulated scenario wherein multiple lethal targets hit the radar positions.
- Adversarial risk estimation /
- Multiple-target tracking /
- Labeled multi-Bernoulli filter /
- Random finite set statistics /
- Threat level assessment /
- Posture reconstruction

HTML全文

图 1 对手目标打击我方资产场景示意图

Figure 1. A schematic diagram of the scenario where the opponent’s targets attack own assets

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图 2 对手风险评估算法整体流程图

Figure 2. Overall flow chart of adversarial risk assessment algorithm

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图 3 雷达监视场景-3D视图多目标真实运动轨迹

Figure 3. Radar surveillance scene-3D view multi-target real movement trajectory

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图 4 杂波率${\lambda _{{c}}} = 25$，检测概率${P_{\mathrm{D}}} = 0.8$下，资产1的PHD-AR算法和LMB-AR算法的对手风险估计值随时间变化的曲线

Figure 4. Curves of the counterparty risk estimates of asset 1’s PHD-AR algorithm and LMB-AR algorithm changing over time under the clutter rate ${\lambda _{{c}}} = 25$ and detection probability ${P_{\mathrm{D}}} = 0.8$

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图 5 LMB-AR算法的全场景对手风险估计热力图

Figure 5. Heat map of full-scenario opponent risk estimation of LMB-AR algorithm

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图 6 固定杂波率${\lambda _{{c}}} = 25$，不同检测概率下，资产1的PHD-AR和LMB-AR的对手风险估计RMSE随时间变化的曲线

Figure 6. Curve of counterparty risk estimate RMSE of asset 1’s PHD-AR and LMB-AR changing over time under fixed clutter rate ${\lambda _{{c}}} = 25$ and different detection probabilities

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图 7 检测概率${P_{\mathrm{D}}} = 0.90$，不同杂波率下，资产1的PHD-AR和LMB-AR的对手风险估计RMSE随时间变化的曲线

Figure 7. Curve of the counterparty risk estimate RMSE of asset 1’s PHD-AR and LMB-AR changing over time under detection probability ${P_{\mathrm{D}}} = 0.90$ and different clutter rates

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表 1 不同目标的出生时刻和死亡时刻

Table 1. The birth and death moments of different targets

目标	出生帧数	死亡帧数	目标初始位置 (km, km, km)	打击目的地
T₁	1	360	(34,99,6.5)	S₁
T₂	50	360	(98,80,6)	S₁
T₃	50	360	(–30,90,6.5)	S₃
T₄	100	360	(–10,80,6)	S₂
T₅	100	360	(32,60,6.5)	无

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表 2 杂波率${\boldsymbol{{\lambda _{{c}}} = 25}}$，不同检测概率下，加性模型PHD-AR算法和LMB-AR算法资产1对手风险估值的平均RMSE比较

Table 2. Comparison of average RMSE of asset 1 counterparty risk valuation of additive model PHD-AR algorithm and LMB-AR algorithm under fixed clutter rate ${\boldsymbol{{\lambda _{{c}}} = 25}}$ and different detection probabilities

平均RMSE	PHD-AR	LMB-AR
${P_{\rm D}} = 0.95$	3.5422	0.8065
${P_{\rm D}} = 0.90$	3.5789	0.6440
${P_{\rm D}} = 0.85$	4.4482	0.6436
${P_{\rm D}} = 0.80$	5.9562	0.6747

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表 3 杂波率${\boldsymbol{{\lambda _{{c}}}}} {\bf{= 25}}$，不同检测概率下，乘性模型PHD-AR算法和LMB-AR算法资产1对手风险估值的平均RMSE比较

Table 3. Comparison of average RMSE of asset 1 counterparty risk valuation of multiplicative model PHD-AR algorithm and LMB-AR algorithm under fixed clutter rate ${\boldsymbol{{\lambda _{{c}}} }}{\bf{= 25}}$ and different detection probabilities

平均RMSE	PHD-AR	LMB-AR
${P_{\rm D}} = 0.95$	2.4355	0.3405
${P_{\rm D}} = 0.90$	2.6386	0.3539
${P_{\rm D}} = 0.85$	2.9412	0.4587
${P_{\rm D}} = 0.80$	3.3243	0.5771

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表 4 检测概率${{\boldsymbol{P}}_{\bf{D}}} {\bf{= 0.90}}$，不同杂波率下，加性模型PHD-AR算法和LMB-AR算法资产1对手风险估值的平均RMSE比较

Table 4. Comparison of average RMSE of asset 1 counterparty risk valuation of additive model PHD-AR algorithm and LMB-AR algorithm under detection probability${{\boldsymbol{P}}_{\bf{D}}} {\bf{= 0.90}}$ and different clutter rates

平均RMSE	PHD-AR	LMB-AR
${\lambda _c} = 10$	3.3973	0.5588
${\lambda _c} = 25$	3.5789	0.6440
${\lambda _c} = 50$	3.9733	0.7970

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表 5 检测概率${{\boldsymbol{P}}_{\bf{D}}} {\bf{= 0.90}}$，不同杂波率下，乘性模型PHD-AR算法和LMB-AR算法资产1对手风险估值的平均RMSE比较

Table 5. Comparison of average RMSE of asset 1 counterparty risk valuation of multiplicative model PHD-AR algorithm and LMB-AR algorithm under detection probability ${\boldsymbol{{P}}_{\bf{D}}} {\bf{= 0.90}}$ and different clutter rates

平均RMSE	PHD-AR	LMB-AR
${\lambda _c} = 10$	2.6345	0.2561
${\lambda _c} = 25$	2.9412	0.3539
${\lambda _c} = 50$	3.3478	0.4985

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