文章快速检索 高级检索

Theoretical research of decision-making point in air combat based on hidden Markov model
FENG Chao, JING Xiaoning, LI Qiuni, YAO Peng
College of Aeronautics and Astronautics Engineering, Air Force Engineering University, Xi'an 710038, China
Received: 2016-03-21; Accepted: 2016-09-09; Published online: 2016-11-18
Foundation item: National Science Fund for Distinguished Young Scholars (71501184); Aeronautical Science Foundation of China (20155196022)
Corresponding author. JING Xiaoning, E-mail:1216682261@qq.com
Abstract: From geometric air combat to energy air combat, till angle air combat theory, the process of air combat is analyzed more from the fighter performance point of view, the effect of the operational pilot in decision-making is neglected. This paper analyzes the variation characteristics of observation data in air combat, and an analysis method for close-range air combat process based on hidden Markov model is proposed. Viterbi algorithm is used to judge the pilot state sequence in air combat, and then the decision-making point is acquired in theory. Through theoretical analysis, the decision-making point in air combat is proposed to judge the pilot's flight quality. Through simulation, the feasibility of discussion of close-range air combat based on Markov model is verified, and when the pilot's decision-making point is in the tendency of surrounding, the pilot has a higher probability of winning.
Key words: evaluation of close-range air combat     OODA loop     hidden Markov model     Viterbi algorithm     dynamic programming

1 近距空战理论与作战流程

1.1 能量机动理论

 (1)

1.2 角度机动理论

 图 1 角度位置关系示意图 Fig. 1 Schematic diagram of relation of angle and position

 (2)

 编号 攻击机位置 目标机位置 ATA/(°) AOT/(°) AGC 1 0 0 1.00 2 0 45 0.75 3 0 90 0.75 4 0 180 0.50 5 45 135 0 6 90 90 0 7 90 180 -0.50 8 135 180 -0.75 9 180 180 -1.00

 (3)

1.3 空战流程

 图 2 OODA环图 Fig. 2 Diagram for OODA loop

OODA决策环模型是从飞行员角度对近距空战的一种简洁的描述。由于该过程是在一种动态的、复杂的环境中进行，且易受到不确定性因素的影响，所以OODA决策环具有循环特性、时效性、嵌套性等特点。传统上一般认为，如果敌我双方有一方的OODA决策环比对手的操作周期短，就容易获得优势，并且这种优势是可以积累的。一般而言，经验丰富的飞行员OODA决策过程比新手的决策过程所用时间更短、更高效。在同等条件下，经验丰富的飞行员更具有优势。

2 基于隐马尔可夫模型的空战分析

2.1 近距空战的隐马尔可夫模型

Q={q1, q2, …, qN}为飞行员可能的状态的集合 (OODA决策环的状态)，V={v1, v2, …, vM}为所有可能观测的集合 (过载的大小)。其中N为可能的状态数，M为可能的观测数。在本文中，飞行员状态数N=4，飞行员状态集合为{观察，判断，决策，行动}；所有可能观测集合数M=3，观测集合为{小过载，中过载，大过载}。

I=(i1, i2, …, iT) 为长度为T的状态序列，O=(o1, o2, …, oT) 为对应的观测序列。A为状态转移概率矩阵:

 (4)

 (5)

π为初始状态概率向量

 (6)

 (7)

 (8)

 (9)

 (10)

2.2 Baum-Welch算法

 (11)

 (12)

1) 数据预处理。在使用算法处理数据之前，对数据进行清洗，并采用合适方法进行采样。本文建议对数据首先进行归一化处理，并且估计数据可能存在的最高频率fs，根据采样定理，按照最高频率的4~5倍进行间隔采样，减少数据点。并且最好使用足够多的样本来形成对比。对于训练模型参数趋于0的问题，本文建议对某些序列做出适当修正。

2) 这里给出一种序列分类方法。假设将需要处理的序列过程为{Xn, n=0, 1, 2, …}。通过分析序列的变化曲线，首先计算序列的平均值，然后根据平均值划定一条基准线，然后在此基准线基础上，确定所有的波峰值x1, x2, …, xk，以波峰值为样本，分析其众数，然后根据需要对序列划定不同的区间范围。本文给出一种划分3个区间范围 (即大过载、中等过载和小过载) 的经验方案：第1区间范围在0到平均值之间，第2区间范围在平均值到众数乘以1.5之间，第3区间范围在众数乘以1.5到最大值之间。

2.3 维特比算法求解隐马尔可夫模型

 (13)

 (14)

 (15)

3 决策点理论分析方法

3.1 决策点包络分析理论

 图 3 空战中能量-AGC序列 Fig. 3 Energy-AGC sequence in air combat

 图 4 决策点的能量-AGC序列 Fig. 4 Energy-AGC sequence for decision-making point

3.2 决策点包含能量理论

 图 5 包含能量变化过程 Fig. 5 Changing process of inherent energy

4 实验仿真及分析

 图 6 典型的逃逸战术 Fig. 6 Typical escape tactical maneuver

 编号 目标机状态 1 观察点 2 观察点 3 观察点 4 观察点 5 观察点 6 观察点 7 判断点 8 判断点 9 判断点 10 决策点 11 行动点 12 观察点 13 观察点 14 观察点 15 观察点 16 观察点 17 观察点 18 观察点 19 观察点 20 观察点 21 观察点 22 观察点 23 观察点 24 观察点

 图 7 目标机轨迹图 Fig. 7 Trochoid of target plane

 图 8 预先转弯轨迹图 Fig. 8 Trochoid of pre turn

 图 9 典型预先转弯仿真图 Fig. 9 Simulation diagram of typical "pre turn"

 图 10 对抗双方的关键决策点集合[11] Fig. 10 Key decision-making set of two sides[11]

 编号 文献[11]给出的决策点时刻 使用隐马尔可夫模型得到的决策点时刻 对应的判断点时刻 判断过程所用的时间 1 K+18 K+19 K+18 1 2 K+25 K+25 K+24 1 3 K+30 K+30 K+29 1 4 K+34 K+36 K+34 2 5 K+49 K+48 K+47 1 6 K+51 K+52 K+51 1 7 K+57 K+57 K+57 0 8 K+64 K+65 K+64 1 9 K+71 K+71 K+70 1 10 K+75 K+73 K+72 1 11 K+92 K+92 K+91 1 12 K+99 K+98 K+98 0

 编号 文献[11]给出的决策点时刻 使用隐马尔可夫模型得到的决策点时刻 对应的判断点时刻 判断过程所用的时间 1 K+19 K+19 K+17 2 2 K+45 K+44 K+40 4 3 K+62 K+61 K+59 2 4 K+79 K+79 K+77 2 5 K+107 K+108 K+107 1 6 K+112 K+112 K+111 1

 图 11 空战实例决策点的能量-AGC序列 Fig. 11 Energy-AGC sequence for decision-making of two sides in air combat

 图 12 双方包含能量变化过程 Fig. 12 Changing process of inherent energy of two sides

5 结论

1) 本文从飞行员决策过程角度回答飞行员决策对于空战结果的影响，使用隐马尔可夫模型分析近距空战，使用维特比算法预测飞行员状态序列，得到飞行员在空战过程中的决策点。

2) 通过实验分析，发现在双方武器装备处于同等条件下，决定空战结果的关键因素在于飞行员判断过程所用的时间。飞行员从判断到决策所用时间越少，飞行员优势越大。经验丰富的飞行员相较于新手而言，决策更为果断，所用时间更少，几乎是下意识就做出决定，所以经验丰富的飞行员在空战中更具有优势。

3) 本文也发现，空战双方如果对手不跟我方的OODA环走，依旧我行我素，那么我方的OODA环对敌方的影响是有限的。

4) 空战决策点理论作为一个新的空战理论，仍有许多研究空白：对于观测序列状态区间范围的选择仍然依靠人为经验给定。对于决策点分析方法仍然缺少理论支撑。战机飞行时数据量巨大，如何利用算法高效处理这些数据，仍然是个问题。这些将在下一步的研究工作中加以考虑。

 [1] 傅莉, 王晓光. 无人战机近距空战微分对策建模研究[J]. 兵工学报, 2012, 10 (10): 1210–1216. FU L, WANG X G. Research on close air combat modeling of differential games for unmanned combat air vehicles[J]. Acta Armamentarii, 2012, 10 (10): 1210–1216. (in Chinese) [2] KRISHNA K K, KANESHIGE J.Artificial immune system approach for air combat maneuvering[C]//Proceedings of SPIE-The International Society for Optical Engineering.Bellingham:SPIE, 2007:274-299. [3] ROGER W S, ALAN E B.Neural network models of air combat maneuvering[D].Las Cruces:New Mexico State University, 1992:125-131.. [4] 张立鹏, 魏瑞轩, 李霞. 无人作战战斗机空战自主战术决策方法研究[J]. 电光与控制, 2012, 19 (2): 92–96. ZHANG L P, WEI R X, LI X. Autonomous tactical decision-making of UCAVs in air combat[J]. Electronics Optics & Control, 2012, 19 (2): 92–96. (in Chinese) [5] NUSYIRWAN I F, BIL C.Factorial analysis of a real time optimization for pursuit-evasion problem[C]//Proceedings of the 46th AIAA Aerospace Science Meeting and Exhibit.Reston:AIAA, 2008:195-198. [6] 杨俊, 谢寿生. 基于模糊支持向量机的飞机动作识别[J]. 航空学报, 2005, 26 (6): 738–742. YANG J, XIE S S. Fuzzy support vector machines based recognition for aeroplane flight action[J]. Acta Aeronautica et Astronautica Sinica, 2005, 26 (6): 738–742. (in Chinese) [7] KAI V, JANNE K, TUOMAS R. Modeling air combat by a moving horizon influence diagram game[J]. Journal of Guidance, Control, and Dynamics, 2006, 29 (5): 1080–1091. [8] 钟友武, 柳嘉润, 申功璋. 自主近距空战中敌机的战术动作识别方法[J]. 北京航空航天大学学报, 2007, 33 (9): 1056–1059. ZHONG Y W, LIU J R, SHEN G Z. Recognition method for tactical maneuver of target in autonomous close-in air combat[J]. Journal of Beijing University of Aeronautics and Astronautics, 2007, 33 (9): 1056–1059. (in Chinese) [9] 张涛, 于雷, 周中良, 等. 基于混合算法的空战机动决策[J]. 系统工程与电子技术, 2013, 35 (7): 1445–1450. ZHANG T, YU L, ZHOU Z L, et al. Decision-making for air combat maneuvering based on hybrid algorithm[J]. Systems Engineering and Electronics, 2013, 35 (7): 1445–1450. (in Chinese) [10] 刘波, 覃征, 邵利平, 等. 基于群集智能的协同多目标攻击空战决策[J]. 航空学报, 2009, 30 (9): 1727–1739. LIU B, QIN Z, SHAO L P, et al. Air combat decision making for coordinated multiple target attack using collective intelligence[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30 (9): 1727–1739. (in Chinese) [11] 左家亮, 杨任农, 张滢. 基于模糊聚类的近距空战决策过程重构与评估[J]. 航空学报, 2015, 36 (5): 1650–1660. ZUO J L, YANG R N, ZHANG Y, et al. Reconstruction and evaluation of close air combat decision-making process based on fuzzy clustering[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36 (5): 1650–1660. (in Chinese) [12] VEERASAMY N.A high-level mapping of cyberter-rorism to the OODA loop[C]//Proceedings of 5th European Conference on Information Management and Evaluation.Red Hook, NY:Curren Associates Inc., 2011:352-360. [13] 黄建明, 高大鹏. 基于OODA环的作战对抗系统动力学模型[J]. 系统仿真学报, 2012, 24 (3): 561–574. HUANG J M, GAO D P. Combat systems dynamics model with OODA loop[J]. Journal of System Simulation, 2012, 24 (3): 561–574. (in Chinese) [14] RABINER L, JUANG B. An introduction to hidden Markov models[J]. IEEE ASSP Magazine, 1986, 28 (7): 6–10. [15] RABINER L. A tutorial on hidden Markov models and selected applications in speech recognition[J]. Proceedings of the IEEE, 1989, 77 (2): 257–286. DOI:10.1109/5.18626 [16] BAUM L, PETRIE T, SOULES G, et al. A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains[J]. Annals of Mathematical Statistics, 1970, 41 (3): 164–171. [17] BILIMES J A.A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models[EB/OL].(1997-06-15)[2016-03-21].http://ssli.ee.washington.edu/~bilmes/mypubs/bilmes1997-em.pdf. [18] LARI K, YOUNG S J. Applications of stochastic context-free grammars using the inside-outside algorithm[J]. Computer Speech & Language, 1991, 5 (3): 237–257. [19] GHAHRAMANI Z. Learning dynamic Bayesian networks[J]. Lecture Notes in Computer Science, 1997, 45 (2): 168–197. [20] RADFORO N, GEOFFREY H, JORDAN M.A view of the EM algorithm that justifies incremental, sparse, and other variants[M]//JORDAN M I.Learning in graphical models.Cambridge, MA:MIT Press, 1999:355-368. [21] ROBERT S. Fighter combat:Tactics and maneuvering[M]. Annapolis, MD: Naval Institute Press, 1985: 84-86.

#### 文章信息

FENG Chao, JING Xiaoning, LI Qiuni, YAO Peng

Theoretical research of decision-making point in air combat based on hidden Markov model

Journal of Beijing University of Aeronautics and Astronsutics, 2017, 43(3): 615-626
http://dx.doi.org/10.13700/j.bh.1001-5965.2016.0220