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1. 装备学院 研究生院, 北京 101416;
2. 北京跟踪与通信技术研究所, 北京 100094;
3. 装备学院 科研部, 北京 101416

Method of time-to-go estimation based on predicted crack point
LI Yuan1,2 , ZHAO Jiguang3 , BAI Guoyu1 , YAN Liang2
2. Institute of Tracking and Telecommunications Technology, Beijing 100094, China ;
3. Department of Scientific Research, Equipment Academy, Beijing 101416, China
Received: 2015-07-31; Accepted: 2015-09-06; Published online: 2015-09-10 17:53
Foundation item: National High-tech Research and Development Program of China
Corresponding author. ZHAO Jiguang.Tel.:010-66364196.E-mail:zjgbeijing@126.com
Abstract: Aimed at the different characters of the head-pursuit and head-on interception flight trajectory, the time-to-go (TGO) estimation methods are designed. According to the prediction of the crack point for the interceptor and target, the influence of different launch conditions on the precision of TGO estimation is decreased. At first, the linear proportional navigation motion equation is transformed, and the first order differential equation about the distance between interceptor and target is obtained. Based on the predicted crack point, the error for the integration result caused by the different initial launch angles is corrected. Then the TGO analytical expressions of two interception models are obtained. Compared with the existing three methods, the simulation result verifies the real time performance and the estimation precision of the proposed method which is able to optimize the guidance performance effectively.

1 TGO估算 1.1 基础理论

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 图 1 平面几何关系 Fig. 1 Planar interception geometry

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R=Vctgoctgo为剩余拦截时间，Vc为拦截弹接近速度，并将式(2)按时间微分后得

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1.2 逆轨拦截运动目标TGO估计

TGO估计的主要思想是通过预测出拦截弹与目标的碰撞点，然后按照拦截静态目标的时间估计方法对剩余拦截时间进行估计。拦截弹在逆轨模式下拦截目标的几何关系如图 2所示。

 Vt—目标速度；Rt—目标与预测碰撞点间的距离；Rm—拦截弹与预测碰撞点间的距离；β—预测内框角；γ—预测外框角。 图 2 逆轨拦截几何关系 Fig. 2 Head-on interception geometry

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1.3 顺轨拦截运动目标TGO估计

 图 3 顺轨拦截几何关系 Fig. 3 Head-pursuit interception geometry

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2 仿真验证

Tahk小组根据几何关系推导出TGO估计的解析式[15]

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2.1 不同框架角下的TGO仿真验证

 图 4 不同初始框架角下TGO估计误差 Fig. 4 TGO estimation error at different initial heading errors
 图 5 TGO估计所需CPU时间 Fig. 5 CPU time of TGO estimation

 图 6 不同初始框架角下拦截过程TGO估计误差 Fig. 6 TGO estimation error during interception at different initial heading errors

2.2 TGO估计对制导律性能的影响

 参数 取值 目标速度/(m·s-1) 1 500 拦截弹速度/(m·s-1) 600 初始弹目距离/m 10 000 拦截弹失效距离/m 30 初始视线角/(°) 8 目标初始路径倾角/(°) 0 导航比 3

 方案 初始路径倾角/(°) TGO估计方法 实际飞行总时间/s 初始加速度/g 控制力/(m·s-1) 1 75 预测碰撞点法 5.09 -12.45 106.464 3 2 75 解析法 4.96 -13.01 125.068 5 3 20 预测碰撞点法 4.74 22.05 201.831 3 4 20 解析法 4.79 22.21 202.419 2

 图 7 逆轨拦截仿真结果 Fig. 7 Simulation results of head-on interception

 方案 初始路径倾角/(°) TGO估计方法 实际飞行总时间/s 初始加速度/g 控制力/(m·s-1) 1 105 预测碰撞点法 10.77 5.14 94.97 2 105 经典法 10.93 4.84 111.45 3 160 预测碰撞点法 10.94 -9.43 182.59 4 160 经典法 10.75 -10.55 209.71

 图 8 顺轨拦截目标仿真结果 Fig. 8 Simulation results of head-pursuit interception

 方案 拦截模式 初始路径倾角/(°) TGO估计方法 实际飞行总时间/s 控制力/(m·s-1) 1 逆轨 20 预测碰撞点法 4.75 218.096 1 2 逆轨 20 解析法 4.80 220.716 4 3 顺轨 160 预测碰撞点法 10.99 233.670 2 4 顺轨 160 经典法 10.82 254.189 3

 图 9 拦截机动目标仿真结果 Fig. 9 Simulation results of maneuvering target interception

3 结 论

1) 针对顺/逆轨拦截模式，提出了基于预测碰撞点的剩余拦截时间估计方法。该方法基于线性的RPN/PN制导律，通过假设出的预测碰撞点，求解二阶微分方程并积分得出拦截弹路径，建立拦截弹和目标飞行时间的等式，进而得出预测碰撞点位置和剩余拦截时间。通过与3种不同TGO估计方法对比，验证了基于预测碰撞点TGO估计法的有效性，并具有精确度高、控制力小等特点。

2) 本文提出的TGO估计方法所需参数少、计算简单、实时性好，其思想对于不同制导律都易于移植和实施，尤其是算法复杂多变的最优制导律。

 [1] RYOO C, CHO H, TAHK M. Time-to-go weighted optimal guidance with impact angle constraints[J]. IEEE Transactions on Control Systems Technology, 2006, 14 (3) : 483 –492. DOI:10.1109/TCST.2006.872525 [2] KIM K B, KIM M, CHOI J W. Modified receding horizon guidance law with information on small accurate time-to-go[J]. IEEE Transactions on Aerospace and Electronic Systems, 2000, 36 (2) : 725 –729. DOI:10.1109/7.845274 [3] TANAKA A, MAEDA H. Studies on the time-to-go indexing control scheme for an automatic aircraft landing system[J]. Transactions of the Japan Society for Aeronautical and Space Sciences, 1973, 16 (31) : 1 –18. [4] WHANG I, RA W.Time-to-go estimation filter for anti-ship missile application[C]//Society of Instrument and Control Engineers (SICE).Piscataway, NJ:IEEE Press, 2008:247-250. [5] YORK R, PASTRICK H. Optimal terminal guidance with constraints at final time[J]. Journal of Spacecraft and Rockets, 1977, 14 (6) : 381 –382. DOI:10.2514/3.57212 [6] JEON I, LEE J, TAHK M. Impact-time-control guidance law for anti-ship missiles[J]. IEEE Transactions on Control Systems Technology, 2006, 14 (2) : 260 –266. DOI:10.1109/TCST.2005.863655 [7] LIU P, SUN R, LI W. Homing guidance law with falling angle and flying time control[J]. Journal of Harbin Institute of Technology, 2014, 21 (1) : 55 –61. [8] KIM T H, LEE C H, TAHK M J. Time-to-go polynomial guidance with trajectory modulation for observability enhancement[J]. IEEE Transactions on Aerospace and Electronic Systems, 2013, 49 (1) : 55 –73. DOI:10.1109/TAES.2013.6404091 [9] 马国欣, 张友安, 李君. 带导引头视场限制的多约束导引律及剩余时间估计[J]. 系统工程与电子技术, 2014, 36 (8) : 1609 –1613. MA G X, ZHANG Y A, LI J. Guidance law with multiple constraints and seeker field-of-view limit and the time-to-go estimation[J]. Systerms Engineering and Electronics, 2014, 36 (8) : 1609 –1613. (in Chinese) [10] 李辕, 闫梁, 赵继广, 等. 顺轨拦截模式剩余飞行时间估计方法研究[J]. 航空学报, 2015, 36 (9) : 3032 –3041. LI Y, YAN L, ZHAO J G, et al. Method of time-to-go estimation for head-pursuit interception mode[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36 (9) : 3032 –3041. (in Chinese) [11] 刘剑锋, 庄志洪. 利用导引头测角信息进行遭遇段剩余飞行时间估计的算法[J]. 兵工学报, 2006, 27 (1) : 27 –31. LIU J F, ZHUANG Z H. The algorithm of time-to-go using angle information provided by seeker during missile-target encounter[J]. Acta Armamentarii, 2006, 27 (1) : 27 –31. (in Chinese) [12] RIGGS J T L.Linear optimal guidance for short range air-to-air missile[C]//Proceedings of National Aerospace and Electronics Conference NAECON'79.Piscataway, NJ:IEEE Press, 1979:757-764. [13] HULL D G, RADKE J J, MACK R E. Time-to-go prediction for homing missiles based on minimum-time intercepts[J]. Journal of Guidance, Control, and Dynamics, 1991, 14 (5) : 865 –871. DOI:10.2514/3.20725 [14] DHANANJAY N, GHOSE D. Accurate time-to-go estimation for proportional navigation guidance[J]. Journal of Guidance, Control, and Dynamics, 2014, 37 (4) : 1378 –1383. DOI:10.2514/1.G000082 [15] TAHK M, RYOO C, CHO H. Recursive time-to-go estimation for homing guidance missiles[J]. IEEE Transactions on Aerospace and Electronic Systems, 2002, 38 (1) : 13 –24. DOI:10.1109/7.993225 [16] 常青, 邢超, 李言俊. 利用导弹轴向加速度估算剩余飞行时间的新方法[J]. 弹箭与制导学报, 2002, 22 (4) : 112 –114. CHANG Q, XING C, LI Y J. A new method for time-to-go using the acceleration along the axis of missile[J]. Journal of Projectiles Rockets Missiles and Guidance, 2002, 22 (4) : 112 –114. (in Chinese) [17] 张友安, 马国欣. 大前置角下比例导引律的剩余时间估计算法[J]. 哈尔滨工程大学学报, 2013, 34 (11) : 1409 –1414. ZHANG Y A, MA G X. Time-to-go estimation algorithm for the proportional navigation guidance law with a large lead angle[J]. Journal of Harbin Engineering University, 2013, 34 (11) : 1409 –1414. (in Chinese) [18] PRASANNA H M, GHOSE D. Retro-proportional-navigation:A new guidance law for interception of high-speed targets[J]. Journal of Guidance, Control, and Dynamics, 2012, 35 (2) : 377 –386. DOI:10.2514/1.54892 [19] SHIMA T. Intercept-angle guidance[J]. Journal of Guidance, Control, and Dynamics, 2011, 34 (2) : 484 –492. DOI:10.2514/1.51026 [20] TAL S, GOLAN O M. Head pursuit guidance[J]. Journal of Guidance, Control, and Dynamics, 2007, 30 (5) : 1437 –1444. DOI:10.2514/1.27737 [21] ZARCHAN P. Tactical and strategic missile guidance[M]. 3rd ed Reston: AIAA, 2002 : 15 . [22] YUAN P, CHERN J. Ideal proportional navigation[J]. Journal of Guidance, Control, and Dynamics, 1992, 15 (5) : 1161 –1165. DOI:10.2514/3.20964

#### 文章信息

LI Yuan, ZHAO Jiguang, BAI Guoyu, YAN Liang

Method of time-to-go estimation based on predicted crack point

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(8): 1667-1674
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0509