基于背景插值的空空导弹攻击区在线模拟方法
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摘要
针对空战态势迅速变化对空空导弹攻击区模拟实时性的需求,提出基于背景插值的攻击区在线模拟方法。首先预测下一采样时刻态势,并针对预测态势模拟解算攻击区信息;当下一采样时刻到来时,利用攻击区预测值和先前两次攻击区模拟信息及相应的态势记录插值估计攻击区真实值。背景插值方法将攻击区模拟解算放到先前计算周期中,实时性高。理论分析证明了背景插值误差随着采样时间的减小收敛于零。仿真结果表明,背景插值模拟方法的误差与传统攻击区模拟方法相当,而前者平均可在7.16×10-6 s内给出结果,后者平均计算耗时为0.290s。
Capture zone simulation requires several time-consuming trajectory integrations.However,the change of situation is very fast and demands the information of capture zone in real time.In order to compute the information of capture zone in real time,this paper suggests a background interpolation strategy for capture zone on-line simulation.Firstly,the value of the state variables at the next sample time is predicted according to the state equations.And the capture zone at the predicted state is simulated.Secondly,when the next sample time arrives,the predicted values of capture zone in the current cycle and the previous two cycles,as well as the corresponding state values,are used to interpolate the true capture zone value in current cycle.In this manner,the time-consuming processes of trajectory integration is removed into the background.Thus,the interpolation is the only operation that delays the capture zone information.The theoritical analysis proves that the error of interpolation converges to zero as the sample interval decreases.Simulation results show that the errors of the background interpolation method and the traditional capture zone simulation are almost the same,and the average time delays are 7.16×10-6 and 0.290 second,respectively.
Capture zone simulation requires several time-consuming trajectory integrations.However,the change of situation is very fast and demands the information of capture zone in real time.In order to compute the information of capture zone in real time,this paper suggests a background interpolation strategy for capture zone on-line simulation.Firstly,the value of the state variables at the next sample time is predicted according to the state equations.And the capture zone at the predicted state is simulated.Secondly,when the next sample time arrives,the predicted values of capture zone in the current cycle and the previous two cycles,as well as the corresponding state values,are used to interpolate the true capture zone value in current cycle.In this manner,the time-consuming processes of trajectory integration is removed into the background.Thus,the interpolation is the only operation that delays the capture zone information.The theoritical analysis proves that the error of interpolation converges to zero as the sample interval decreases.Simulation results show that the errors of the background interpolation method and the traditional capture zone simulation are almost the same,and the average time delays are 7.16×10-6 and 0.290 second,respectively.
引文
[1]HUI Y L,NAN Y,CHEN S D,et al.Dynamic attack zone of air-to-air missile after being launched in random wind field[J].Chinese Journal of Aeronautics,2015,28(5):1519-1528.
[2]MENG G L,PAN H B,LIANG X,et al.Allowable missile launch zone calculation for multi-fighter coordination attack under network targeting environment[C]∥Proc.of the Chinese Control and Decision Conference,2016:2143-2146.
[3]SCHARL J,MAVRIS D N,BURDUN I Y.Use of flight simulation in early design:formulation and application of the virtual testing and evaluation methodology[C]∥Proc.of the World Aviation Conference,2000:1-11.
[4]WANG H J,LEI H M,YE J K,et al.A novel capture region of retro proportional navigation guidance law for intercepting high-speed nonmaneuvering targets[C]∥Proc.of the Institution of Mechanical Engineers:Part G-Journal of Aerospace Engineering,2017,232(6):1186-1198.
[5]汪丽珍.空对空导弹允许发射区算法[J].战术导弹技术,1992(2):1-7.WANG L Z.Air-to-air missile allowable launch zone algorithm[J].Tactical Missile Technology,1992(2):1-7.
[6]梁红年,白文林.空对空导弹全向攻击区计算研究[J].北京航空航天大学学报,1989(1):135-144.LIANG H N,BAI W L.Research on calculation of air-to-air missile omnidirectional attack zone[J].Journal of Beijing University of Aeronautics and Astronautics,1989(1):135-144.
[7]KUNG C C,CHIANG F L.A study of missile maximum capture area and fighter minimum evasive range for negotiation team air combat[C]∥Proc.of the 15th International Conference on Control,Automation and Systems,2015:207-212.
[8]CHO N,KIM Y.Optimality of augmented ideal proportional navigation for maneuvering target interception[J].IEEE Trans.on Aerospace&Electronic Systems,2016,52(2):948-954.
[9]刘代军,董秉印.超视距空-空导弹允许攻击区快速模拟算法[J].战术导弹技术,1998(4):10-14.LIU D J,DONG B Y.Fast simulation algorithm of over-thehorizon air-to-air missile allowable attack area[J].Tactical Missile Technology,1998(4):10-14.
[10]王志刚,张宁,李伟.一种空空导弹攻击区的快速解算方法[J].固体火箭技术,2014(4):448-452.WANG Z G,ZHANG N,LI W.A fast solving method for attacking area of air-to-air missile[J].Journal of Solid Rocket Technology,2014(4):448-452.
[11]崔晓宝,姚伟,王明志.弹道计算格斗导弹攻击区的一种快速模拟计算法[J].火力与指挥控制,2014.39(11):133-136.CUI X B,YAO W,WANG M Z.A fast simulation algorithm of short-range missile’s launch acceptance zone based on the missile’s trajectory calculation[J].Fire Control&Command Control,2014,39(11):133-136.
[12]付书堂,章惠君.空空导弹攻击区高精度快速计算方法[J].科学技术与工程,2012,12(27):7074-7077.FU S T,ZHANG H J.High-precision and fast calculation method for air-to-air missile attack area[J].Science Technology and Engineering,2012,12(27):7074-7077.
[13]惠耀洛,南英,陈哨东,等.空空导弹动态攻击区的高精度快速算法研究[J].弹道学报,2015,27(2):39-45.HUI Y L,NAN Y,CHEN S D,et al.Research on rapid and high-precision calculation of dynamic attack zone for air-toair missile[J].Journal of Ballistics,2015,27(2):39-45.
[14]张平,方洋旺,金冲,等.空空导弹攻击区实时解算的新方法[J].弹道学报,2010,22(4):11-14.ZHANG P,FANG Y S,JIN C,et al.A new method of real-time calculation for attack area of air-to-air missile[J].Journal of Ballistics,2010,22(4):11-14.
[15]PARK S S,KIM D W,HONG J H,et al.Computation algorithm for dynamic launch zone of air-to-air missiles[J].Journal of the Korean Society for Aeronautical&Space Sciences,2014,42(9):762-772.
[16]孙兆雨,张安柯.中远距空空导弹射后效能动态评估[J].弹箭与制导学报,2016,36(4):29-32.SUN Z Y,ZHANG A K.Dynamic effectiveness evaluation of intermediate-long-range air-to-air missile after being launched[J].Journal of Projectiles,Rockets,Missiles and Guidance,2016,36(4):29-32.
[17]方学毅,周德云.空空导弹攻击区在线模拟的背景计算策略[C]∥航空学会青年科技论坛会议,2018:534-540.FANG X Y,ZHOU D Y.Background calculation method for online simulation of air-to-air missile capture zone[C]∥Proc.of the Aviation Society Youth Technology Forum,2018:534-540.
[18]CHEN L,LI K B,LIANG Y G.Dimension-reduction method of three-dimensional guidance laws[C]∥Proc.of the AIAAGuidance,Navigation,and Control Conference,2012:1-13.
[19]PELED-EITAN L,RUSNAK I.Three dimensional guidance against helix maneuver with unknown turning rate[J].World Congress of of the International Federation of Automatic Control(IFAC)-PapersOnLine,2017,50(1):2726-2731.
[20]ZHANG Z,MAN C,LI S,et al.Finite-time guidance laws for three-dimensional missile-target interception[C]∥Proc.of the Institution of Mechanical Engineers Part G:Journal of Aerospace Engineering,2016,230(2):392-403.
[21]CHANG L,LIU Z H,ZONG X X.Design of 3-D discrete sliding mode variable structure guidance law for air missile[C]∥Proc.of the Intelligent Control and Automation,2012:2204-2208.
[22]HE S M,LIN D F.Three-dimensional optimal impact time guidance for antiship missiles[J].Journal of Guidance,Control,and Dynamics,2018.DOI:https:∥doi.org/10.2514/1.G003971.
[23]PANDIT S,PANCHAL B,TALOLE S E.Design of three-dimensional guidance law for tactical missiles[C]∥Proc.of the AIAAGuidance,Navigation,and Control Conference.Kissimmee,2018:1-25.
[24]WEISS G,RUSNAK I.All-aspect three-dimensional guidance law based on feedback linearization[J].Journal of Guidance,Control,and Dynamics,2015,38(12):2421-2428.
[25]HU X,YANG S X,XIONG F F,et al.Stability of spinning missile with homing proportional guidance law[J].Aerospace Science and Technology,2017,71:546-555.
[26]SONAWANE H R,MAHULIKAR S P.Effect of missile turn rate on aircraft susceptibility to infrared-guided missile[J].Journal of Aircraft,2013,50(2):663-667.
[27]张安柯,孔繁峨,贺建良.目标强机动对中远程空空导弹可攻击区的影响[J].弹箭与制导学报,2016,36(2):21-25.ZHANG A K,KONG F E,HE J L.Effect of strong maneuver target on attacking area of long-range air-to-air missile[J].Journal of Projectiles,Rockets,Missiles and Guidance,2016,36(2):21-25.
[28]张安柯,孔繁峨.空空导弹射后动态攻击区的计算及信息提示[J].电光与控制,2016,23(1):75-79.ZHANG A K,KONG F E.Calculation and function of attack zone of air-to-air missile after launching[J].Electronics Optics&Control,2016,23(1):75-79.
[29]顾佼佼,刘卫华,姜文志.基于攻击区和杀伤概率的视距内空战态势评估.系统工程与电子技术[J].2015,37(6):1306-1312.GU J J,LIU W H,JIANG W Z.WVR air combat situation assessment model based on weapon engagement zone and kill probability[J].Systems Engineering and Electronics,2015,37(6):1306-1312.
[30]吴胜亮,南英.空空导弹射后动态可攻击区计算[J].弹道与制导学,2013,33(5):49-54.WU S L,NAN Y.The calculation of dynamical attack zone of air-to-airmissile after being launched[J].Journal of Projectiles,Rockets,Missiles and Guidance,2013,33(5):49-54.
[31]IMADO F,KURODA T.Engagement tactics for two missiles against an optimally maneuvering aircraft[J].Journal of Guidance Control&Dynamics,2015,34(2):574-582.
[32]IMADO F,KURODA T,ICHIKAWA A.A trade-off study between conventional and augmented proportional navigation[C]∥Proc.of the Guidance,Navigation,&Control Conference,1996:1-8.
[33]ZARCHAN P.Tactical and strategic missile guidance[M].6th ed.Reston,Virginia:AIAA,Inc.,2012.
[34]HELLER C,YAESH I,ASHER B J.Optimal setting of the proportional-navigation gain[J].Journal of Guidance,Control,and Dynamics,2013,36(3):887-890.
[35]李枭扬,周德云,冯琦,等.基于遗传规划的空空导弹攻击区拟合[J].弹箭与制导学报,2015,35(3):16-18.LI X Y,ZHOU D Y,FENG Q,et al.Air-to-air missile launch envelops fitting based on genetic programming[J].Journal of Projectiles,Rockets,Missiles and Guidance,2015,35(3):16-18.
[36]王宏伦,张安,张海,等.空-空导弹攻击区的高精度快速拟合[J].航空学报,1997,18(5):631-632.WANG H L,ZHANG A,ZHANG H,et al.Accurate and fast approximation of air-to-air missile launch envelopes[J].Acta Aeronautica et Astronautica Sinica,1997,18(5):631-632.
[37]陆启韶,彭临平,杨卓琴.常微分方程与动力系统[M].北京:北京航空航天大学出版社,2010.LU Q S,PENG L P,YANG Z Q.Ordinary differential equations and dynamic systems[M].Beijing:Beihang University Press,2010.
[38]周灿辉,周德云,聂志强,等.中程空空导弹可攻击区解算的新方法[J].火力与指挥控制,2012,37(7):54-56.ZHOU C H,ZHOU D Y,NIE Z Q,et al.A new method for calculating the allowable attack area of air-to-air missile[J].Fire Control&Command Control,2012,37(7):54-56.
[2]MENG G L,PAN H B,LIANG X,et al.Allowable missile launch zone calculation for multi-fighter coordination attack under network targeting environment[C]∥Proc.of the Chinese Control and Decision Conference,2016:2143-2146.
[3]SCHARL J,MAVRIS D N,BURDUN I Y.Use of flight simulation in early design:formulation and application of the virtual testing and evaluation methodology[C]∥Proc.of the World Aviation Conference,2000:1-11.
[4]WANG H J,LEI H M,YE J K,et al.A novel capture region of retro proportional navigation guidance law for intercepting high-speed nonmaneuvering targets[C]∥Proc.of the Institution of Mechanical Engineers:Part G-Journal of Aerospace Engineering,2017,232(6):1186-1198.
[5]汪丽珍.空对空导弹允许发射区算法[J].战术导弹技术,1992(2):1-7.WANG L Z.Air-to-air missile allowable launch zone algorithm[J].Tactical Missile Technology,1992(2):1-7.
[6]梁红年,白文林.空对空导弹全向攻击区计算研究[J].北京航空航天大学学报,1989(1):135-144.LIANG H N,BAI W L.Research on calculation of air-to-air missile omnidirectional attack zone[J].Journal of Beijing University of Aeronautics and Astronautics,1989(1):135-144.
[7]KUNG C C,CHIANG F L.A study of missile maximum capture area and fighter minimum evasive range for negotiation team air combat[C]∥Proc.of the 15th International Conference on Control,Automation and Systems,2015:207-212.
[8]CHO N,KIM Y.Optimality of augmented ideal proportional navigation for maneuvering target interception[J].IEEE Trans.on Aerospace&Electronic Systems,2016,52(2):948-954.
[9]刘代军,董秉印.超视距空-空导弹允许攻击区快速模拟算法[J].战术导弹技术,1998(4):10-14.LIU D J,DONG B Y.Fast simulation algorithm of over-thehorizon air-to-air missile allowable attack area[J].Tactical Missile Technology,1998(4):10-14.
[10]王志刚,张宁,李伟.一种空空导弹攻击区的快速解算方法[J].固体火箭技术,2014(4):448-452.WANG Z G,ZHANG N,LI W.A fast solving method for attacking area of air-to-air missile[J].Journal of Solid Rocket Technology,2014(4):448-452.
[11]崔晓宝,姚伟,王明志.弹道计算格斗导弹攻击区的一种快速模拟计算法[J].火力与指挥控制,2014.39(11):133-136.CUI X B,YAO W,WANG M Z.A fast simulation algorithm of short-range missile’s launch acceptance zone based on the missile’s trajectory calculation[J].Fire Control&Command Control,2014,39(11):133-136.
[12]付书堂,章惠君.空空导弹攻击区高精度快速计算方法[J].科学技术与工程,2012,12(27):7074-7077.FU S T,ZHANG H J.High-precision and fast calculation method for air-to-air missile attack area[J].Science Technology and Engineering,2012,12(27):7074-7077.
[13]惠耀洛,南英,陈哨东,等.空空导弹动态攻击区的高精度快速算法研究[J].弹道学报,2015,27(2):39-45.HUI Y L,NAN Y,CHEN S D,et al.Research on rapid and high-precision calculation of dynamic attack zone for air-toair missile[J].Journal of Ballistics,2015,27(2):39-45.
[14]张平,方洋旺,金冲,等.空空导弹攻击区实时解算的新方法[J].弹道学报,2010,22(4):11-14.ZHANG P,FANG Y S,JIN C,et al.A new method of real-time calculation for attack area of air-to-air missile[J].Journal of Ballistics,2010,22(4):11-14.
[15]PARK S S,KIM D W,HONG J H,et al.Computation algorithm for dynamic launch zone of air-to-air missiles[J].Journal of the Korean Society for Aeronautical&Space Sciences,2014,42(9):762-772.
[16]孙兆雨,张安柯.中远距空空导弹射后效能动态评估[J].弹箭与制导学报,2016,36(4):29-32.SUN Z Y,ZHANG A K.Dynamic effectiveness evaluation of intermediate-long-range air-to-air missile after being launched[J].Journal of Projectiles,Rockets,Missiles and Guidance,2016,36(4):29-32.
[17]方学毅,周德云.空空导弹攻击区在线模拟的背景计算策略[C]∥航空学会青年科技论坛会议,2018:534-540.FANG X Y,ZHOU D Y.Background calculation method for online simulation of air-to-air missile capture zone[C]∥Proc.of the Aviation Society Youth Technology Forum,2018:534-540.
[18]CHEN L,LI K B,LIANG Y G.Dimension-reduction method of three-dimensional guidance laws[C]∥Proc.of the AIAAGuidance,Navigation,and Control Conference,2012:1-13.
[19]PELED-EITAN L,RUSNAK I.Three dimensional guidance against helix maneuver with unknown turning rate[J].World Congress of of the International Federation of Automatic Control(IFAC)-PapersOnLine,2017,50(1):2726-2731.
[20]ZHANG Z,MAN C,LI S,et al.Finite-time guidance laws for three-dimensional missile-target interception[C]∥Proc.of the Institution of Mechanical Engineers Part G:Journal of Aerospace Engineering,2016,230(2):392-403.
[21]CHANG L,LIU Z H,ZONG X X.Design of 3-D discrete sliding mode variable structure guidance law for air missile[C]∥Proc.of the Intelligent Control and Automation,2012:2204-2208.
[22]HE S M,LIN D F.Three-dimensional optimal impact time guidance for antiship missiles[J].Journal of Guidance,Control,and Dynamics,2018.DOI:https:∥doi.org/10.2514/1.G003971.
[23]PANDIT S,PANCHAL B,TALOLE S E.Design of three-dimensional guidance law for tactical missiles[C]∥Proc.of the AIAAGuidance,Navigation,and Control Conference.Kissimmee,2018:1-25.
[24]WEISS G,RUSNAK I.All-aspect three-dimensional guidance law based on feedback linearization[J].Journal of Guidance,Control,and Dynamics,2015,38(12):2421-2428.
[25]HU X,YANG S X,XIONG F F,et al.Stability of spinning missile with homing proportional guidance law[J].Aerospace Science and Technology,2017,71:546-555.
[26]SONAWANE H R,MAHULIKAR S P.Effect of missile turn rate on aircraft susceptibility to infrared-guided missile[J].Journal of Aircraft,2013,50(2):663-667.
[27]张安柯,孔繁峨,贺建良.目标强机动对中远程空空导弹可攻击区的影响[J].弹箭与制导学报,2016,36(2):21-25.ZHANG A K,KONG F E,HE J L.Effect of strong maneuver target on attacking area of long-range air-to-air missile[J].Journal of Projectiles,Rockets,Missiles and Guidance,2016,36(2):21-25.
[28]张安柯,孔繁峨.空空导弹射后动态攻击区的计算及信息提示[J].电光与控制,2016,23(1):75-79.ZHANG A K,KONG F E.Calculation and function of attack zone of air-to-air missile after launching[J].Electronics Optics&Control,2016,23(1):75-79.
[29]顾佼佼,刘卫华,姜文志.基于攻击区和杀伤概率的视距内空战态势评估.系统工程与电子技术[J].2015,37(6):1306-1312.GU J J,LIU W H,JIANG W Z.WVR air combat situation assessment model based on weapon engagement zone and kill probability[J].Systems Engineering and Electronics,2015,37(6):1306-1312.
[30]吴胜亮,南英.空空导弹射后动态可攻击区计算[J].弹道与制导学,2013,33(5):49-54.WU S L,NAN Y.The calculation of dynamical attack zone of air-to-airmissile after being launched[J].Journal of Projectiles,Rockets,Missiles and Guidance,2013,33(5):49-54.
[31]IMADO F,KURODA T.Engagement tactics for two missiles against an optimally maneuvering aircraft[J].Journal of Guidance Control&Dynamics,2015,34(2):574-582.
[32]IMADO F,KURODA T,ICHIKAWA A.A trade-off study between conventional and augmented proportional navigation[C]∥Proc.of the Guidance,Navigation,&Control Conference,1996:1-8.
[33]ZARCHAN P.Tactical and strategic missile guidance[M].6th ed.Reston,Virginia:AIAA,Inc.,2012.
[34]HELLER C,YAESH I,ASHER B J.Optimal setting of the proportional-navigation gain[J].Journal of Guidance,Control,and Dynamics,2013,36(3):887-890.
[35]李枭扬,周德云,冯琦,等.基于遗传规划的空空导弹攻击区拟合[J].弹箭与制导学报,2015,35(3):16-18.LI X Y,ZHOU D Y,FENG Q,et al.Air-to-air missile launch envelops fitting based on genetic programming[J].Journal of Projectiles,Rockets,Missiles and Guidance,2015,35(3):16-18.
[36]王宏伦,张安,张海,等.空-空导弹攻击区的高精度快速拟合[J].航空学报,1997,18(5):631-632.WANG H L,ZHANG A,ZHANG H,et al.Accurate and fast approximation of air-to-air missile launch envelopes[J].Acta Aeronautica et Astronautica Sinica,1997,18(5):631-632.
[37]陆启韶,彭临平,杨卓琴.常微分方程与动力系统[M].北京:北京航空航天大学出版社,2010.LU Q S,PENG L P,YANG Z Q.Ordinary differential equations and dynamic systems[M].Beijing:Beihang University Press,2010.
[38]周灿辉,周德云,聂志强,等.中程空空导弹可攻击区解算的新方法[J].火力与指挥控制,2012,37(7):54-56.ZHOU C H,ZHOU D Y,NIE Z Q,et al.A new method for calculating the allowable attack area of air-to-air missile[J].Fire Control&Command Control,2012,37(7):54-56.