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摘要:
对战机对抗导弹的措施优化问题进行了研究，将该问题归结为不确定条件下的序贯决策问题，提出了一种基于Markov决策过程(MDP)的导弹对抗措施优化方法。首先, 该方法根据作战过程将作战阶段分为不同的状态，将电子对抗措施(ECM)和战术机动作为可供战机选择的行动；然后, 通过不同战术行动下状态之间的转移概率来反映行动的不确定性，以雷达搜索状态和导弹命中状态的期望值来表征不同策略下的飞机生存力；最后，通过建立Markov决策模型得到飞机生存力最大时各个状态对应的最佳行动。仿真结果表明:飞机生存力随着时间推移而逐渐降低；不同策略下飞机的生存力不同，基于MDP的策略可以有效提高飞机的生存力；单步优化措施不能提高战机的生存力，必须考虑长期状态转移的影响。
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关键词:
- 飞机生存力 /
- 电子对抗措施(ECM) /
- 战术机动 /
- Markov决策过程(MDP) /
- 导弹对抗 /
- 序贯决策
Abstract:Missile countermeasure optimization problem for fighter aircraft was studied. The missile countermeasure optimization was modeled as a sequential decision-making problem under uncertainty, and a Markov decision process (MDP) based approach was proposed. First, the engagement process was divided into several phases, and these phrases were marked by states. Electronic counter measures (ECM) and strategic maneuvers were treated as actions. Then, the state transition probability was used to reflect the uncertainty of each action, and average occupancy of "hit" state and "search" state was used to evaluate the aircraft survivability under different policies. Finally, the policy iteration algorithm was used to get the optimal policy, which maps the optimal action to be taken in each state. Simulation indicates that the aircraft survivability decreases as time goes on; the proposed MDP-based approach can effectively improve the aircraft survivability; one-step optimization is useless for the aircraft survivability and the influence of the state transition should be considered from the view of long-time horizon.
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图 4 最佳策略下各状态与行动的对应关系
Figure 4. Relationship between states and actions under optimal policy
图 6 有限时间内各状态的平均占有率
Figure 6. Average occupancy rate for all states in finite time steps
图 7 不同初始状态下s1和s13的平均占有率
Figure 7. Average occupancy rate of s1 and s13 under different initial states
图 10 不同策略下s13的平均占有率(γ=0.90)
Figure 10. Average occupancy rate of s13 under different policies (γ=0.90)
表 1 状态集及其元素
Table 1. State set and its elements
编号 状态名称及缩写 s1 Search s2 Acquisition (ACQ) s3 Non-Adaptive Track (NAT) s4 Range Resolution 1 (RR1) s5 Range Resolution 2 (RR2) s6 Range Resolution 3 (RR3) s7 Track Maintenance (TM) s8 Passive Track (PT) s9 Missile Launching (ML) s10 Mid-Course Guidance (MCG) s11 Terminal Guidance (TG) s12 Miss the target (Miss) s13 Hit the target (Hit) 
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表 2 行动集及其元素
Table 2. Action set and its elements
行动集 状态相关的行动 行动名称 A1 a1→s1, s2, s10 Multi False Target (MFT) a2→s1~s7, s10 Noise Jamming (NJ) a3→s4 Range False Target 1 (RFT1) a4→s5 Range False Target 2 (RFT2) a5→s6 Range False Target 3 (RFT3) a6→s3 Range-Gate Pull-Off (RGPO) a7→s7, s10 Velocity-Range-Gate Pull-Off (VRGPO) a8→s11 Flares+Chaffs a9→s8 No Jamming (NoJ) A2 a10→s1 No Maneuvering (NoM) a11→s7 Maximum Acceleration (MA) a12→s7 Maximum Deceleration (MD) a13→s10, s11 Maximum Overload Pull-Up (MOPU) a14→s10, s11 Maximum Overload Dive (MOD) a15→s10, s11 Maximum Overload Left Turn (MOLT) a16→s10, s11 Maximum Overload Right Turn (MORT) A3 a17→s2, s7 MOPU/MOD/MOLT/MORT+MFT a18→s7, s10 MOPU/MOD/MOLT/MORT+VRGPO a19→s10, s11 MA/MD+Chaffs+Flares a20→s11 MOPU/MOD/MOLT/MORT+Chaffs+Flares
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