恶意攻击下基于分布式稀疏优化的安全状态估计

张岱峰; 段海滨

doi:10.16383/j.aas.c200276

恶意攻击下基于分布式稀疏优化的安全状态估计

doi: 10.16383/j.aas.c200276

张岱峰^1,,
段海滨^{1, 2,}

1.
北京航空航天大学自动化科学与电气工程学院仿生自主飞行系统研究组北京 100083
2.
鹏城实验室深圳 518000

基金项目: 国家自然科学基金(U20B2071, 91948204, U1913602, U19B2033), 科技创新2030“新一代人工智能”重大项目(2018AAA0102303), 航空科学基金(20185851022)资助

详细信息

作者简介:
张岱峰：北京航空航天大学自动化科学与电气工程学院博士研究生. 2013年于合肥工业大学获得学士学位, 2016年于北京航空航天大学获得硕士学位. 主要研究方向为多智能体协调控制与决策. E-mail: zdfskh@163.com

段海滨：北京航空航天大学自动化科学与电气工程学院长聘教授. 2005年于南京航空航天大学获博士学位, 分别于2007年、2011年在新加坡国立大学、韩国水源大学从事访问学者研究. 主要研究方向为仿生智能, 无人机自主控制. 本文通信作者. E-mail: hbduan@buaa.edu.cn

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出版历程
- 收稿日期: 2020-05-02
- 录用日期: 2020-08-14
- 修回日期: 2020-07-03
- 刊出日期: 2021-04-23

Secure State Estimation Based on Distributed Sparse Optimization Under Malicious Attacks

ZHANG Dai-Feng^1
,,
DUAN Hai-Bin^{1, 2
,}

1.
Bio-inspired Autonomous Flight Systems Research Group, School of Automation Science and Electrical Engineering, Beihang University, Beijing 100083
2.
Peng Cheng Laboratory, Shenzhen 518000

Funds: Supported by National Natural Science Foundation of China (U20B2071, 91948204, U1913602, U19B2033), Science and Technology Innovation 2030-Key Project of “New Generation Artificial Intelligence” (2018AAA0102303), and Aeronautical Science Foundation of China (20185851022)

More Information

Author Bio:
ZHANG Dai-Feng　Ph. D. candidate at the School of Automation Science and Electrical Engineering, Beihang University. He received his bachelor degree from Hefei University of Technology in 2013, and the master degree from Beihang University in 2016. His main research interest is the cooperative control and decision of multi-agent systems

DUAN Hai-Bin　Long-term professor at the School of Automation Science and Electrical Engineering, Beihang University. He received his Ph. D. degree from Nanjing University of Aeronautics and Astronautics (NUAA) in 2005. He was an academic visitor of National University of Singapore (NUS) in 2007, a senior visiting scholar of the University of Suwon (USW) of South Korea in 2011. His research interest covers bio-inspired intelligence, and autonomous control of unmanned aerial vehicles. Corresponding author of this paper

摘要

摘要: 恶意生成的量测攻击信号是导致信息物理系统(Cyber-physical system, CPS)探测失效的主要原因, 如何有效削弱其影响是实现精准探测、跟踪与感知的关键问题. 分布式传感器网络(Distributed sensor network, DSN)依靠多传感器协作与并行处理突破单一监测节点的任务包线, 能够显著提升探测系统跟踪精度与可靠性. 首先, 依据压缩感知理论, 将单一节点的目标运动状态估计建模为一种基于l₀范数最小化的稀疏优化问题, 采用正交匹配追踪法(Orthogonal matching pursuit, OMP)重构量测攻击信号, 以克服采用凸优化算法求解易陷入局部最优的缺陷. 通过卡尔曼滤波量测更新抵消攻击信号影响, 恢复目标运动的真实状态. 其次, 针对错误注入攻击等复杂量测攻击形式, 基于势博弈理论, 提出一种分布式稀疏优化安全状态估计方法, 利用多传感器节点信息交互与协作提升探测与跟踪的稳定性. 仿真结果表明, 所提方法在分布式传感器网络协作抵抗恶意攻击方面具有优越性.
- 恶意攻击 /
- 分布式安全状态估计 /
- 稀疏优化 /
- 势博弈
Abstract: Malicious attacks against the measurements is one of the primary cause accounting for the detection failure of cyber-physical systems (CPS). Reducing the impact of measurement attack is a key problem of the accurate detection, target tracking, and sensing for CPS. Distributed sensor networks (DSN) are able to break through the task envelope of single surveillance node through coordination and parallel processing and thus remarkably improve the tracking performance and reliability of detection systems. Based on the compressive sensing theory, the state estimation for single-plant target tracking is modelled as an l₀-norm minimization problem, which is also equivalent to a sparse optimization problem. Under sparse malicious attacks, the orthogonal matching pursuit (OMP) is utilized to reconstruct the attack signals and to avoid the local optima induced by the convex optimization algorithms. A combined Kalman filter is presented to obtain the true target information where the attack signals are compensated in the measurement update. Then, a distributed secure state estimation method based on the potential game theory is proposed in view of the complex attacks such as the false data injection, where a potential game framework is established to enhance the stability of target tracking by the information exchange and coordination among neighboring sensors. Simulation results demonstrate the effectiveness of the proposed method against the sparse malicious attacks on DSNs.
- Malicious attack /
- distributed secure state estimation /
- sparse optimization /
- potential game

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图 1 分布式稀疏优化安全状态估计流程图

Fig. 1 Flowchart of secure state estimation algorithm based on distributed sparse optimizations

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图 2 DSN网络通信拓扑结构

Fig. 2 Communication topology of DSN nodes

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图 3 测试算法对目标轨迹的跟踪效果对比

Fig. 3 Comparison of trajectory tracking by the candidate algorithms

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图 4 测试算法对目标X轴位置的跟踪误差对比

Fig. 4 Comparison of X-position estimation errors by the candidate algorithms

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图 5 测试算法对目标X轴速度的跟踪误差对比

Fig. 5 Comparison of X-velocity estimation errors by the candidate algorithms

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图 6 算法A1中探测节点的融合策略选择

Fig. 6 Fusion decision making by the nodes in A1

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表 1 DSN遭受的分时段攻击列表

Table 1 Time sharing attacks of DSN detection nodes

节点	时段
节点	0 s ~ 3 s	3 s ~ 6 s	6 s ~ 9 s	9 s ~ 10 s
1	无	无	无	I类
2	I类	I类	无	无
3	无	无	II类	II类
4	II类	II类	无	无
5	无	无	I类	I类

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表 2 5种算法对X轴位置的均方估计误差比较 (m)

Table 2 Comparison of mean square errors (meters) of position estimations in X-axis by the five algorithms

	A1	A2	A3	A4	A5
节点 1	0.0724	0.0238	28.6083	0.0302	3.6060
节点 2	0.0150	7.2185	33.0688	8.3714	3.5778
节点 3	0.0724	0.2550	29.0511	0.3338	3.6056
节点 4	1.3807	40.6553	29.5093	39.4624	3.5778
节点 5	0.0054	0.4213	31.6166	0.1078	3.5785

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