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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。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.
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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
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
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
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${P_{\mathrm{D}}} = 0.8$ 
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
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
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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