Proportional navigation guidance law based on process schedule

HICH TECHNOLOGY LETTERSIVol. 17 Na. 1|Mar. 2011pp 97 ~ 101doi:10. 3772/j. isn. 1006-6748. 2011.01.017Proportional navigation guidance law based on process schedule'Wu Guifang(吴桂芳)②, Yang Wenkao, Cai Yaru(Electronics & Information Engineering, Beijing Jjiaotong University, Beijing 100044 P. R. China)AbstractThis paper makes researches on multiple independently reentry vehicle ( MIRV) ballistic mis-sile interception. It breaks through traditional intercepting methods of missiles and combines comba-ting time characteritics of MIRV missiles with the principle of computer process schedule. In thispaper, a way of firstly intercepting the target missile with higher threaten grade is proposed. Thismethod determines the threaten grade of the attacking target according to computer process schedu-ling algorithms，then appljed a proportional navigation guidance law to intercept target missiles inpriority so that it achieves the efet of less damage. The simulation results indicate that it is efctive to use the proportional navigation guidance law based on the process scheduling to intercept tar-get missile. It possesses referential value in modem weapon combats.Key words: multiple independently reentry vehicle ( MIRV )，intercepting schedule propor-tional navigation guidanceproportional navigation guidance law to intercept a target0 Introductionmissile of high threaten grade firstly and control thecharges of weapons in a reasonable range.Multiple independently reentry vehicle ( MIRV )missile is one of the main threats in modem battlefield.1 The description of the intercepting scheduleWith the characteristics of high speed , more warheadsand strong penetration ability , it becomes more dificultStep 1: The results of raedar detecting are fed backto deal with'. At present, many common methods areto our combating department. Then we determineused for a single missile interception such as the purewhether target missiles have entered the our region. Iftracing method, the parallel asymptotic method, thethere are no attacking missiles, the radar continues ob-proportional navigation guidance law, the thee-pointserving.method, the straightening cofficient method, and soStep 2: Make an intercepting schedulable analysisonl2'. It's more widely to use the proportional naviga-of the target missile having entered the our area andion guidance law from the view of theoretical aspectdetermine schedulable priorities. The main principle isand technical realization. But for the MIRV missile in-that the missile which is firstly detected has higher pri-terception，the proportional navigation guidance lawority. If the warheads are detected at the same time,can' t intercept a sub-missile with high threaten gradethreaten propertiesare estimated. The high threaten tar-effectively. To solve this problem, this paper presentsan algorithm combining intercepting schedule with theget has a high priority. Under the same threaten condi-tions , the smaller the intersection angle is, the higherproportional navigation guidance law.Firstly, this paper combines combating time char-priority a target has.acteristics of MIRV missiles with computer processStep 3: Firstly intercepting a scheduled prior war-scheduling'. It properly uses the characteristics of anhead with the proportional navigation guidance law. Inattacking target missile to determine its interceptingthis way, the last intercepted are the ones with lowergrade so that it can dispatch the intercepting missile andpriority.cary out the intercepting misile schedule efltively.Step 4: The mission of interception is finished.On this basis, in order to achieve effective interceptingA flow chart of MIRV missile intercepting simula-probability and combat effectiveness, this paper uses the中国煤化工THCNMHGD Supported by the National High Technology Research and Development Pgramme of China.②To whom correspondence should be addressed. E-mail : 08120188@ bitu. edu. cnReceived on Nov. 27, 2009)8HIGH TECHNOLOGY LETTERSIVoL 17 No. 11Mar. 2011We divide schedulable implementation cycle T2 Mssile intercepting schedulable algorithmsbased on time slice i.e. each interval of time T andcarriy out a calculation of the missile parameters andIn order to improve the combating system in realschedule the intercepting order of a target missiletime and multi-task processing ability I，an algorithmagains. A schedulable model as is given as fllows:based on the computer process schedule is introducedThe intercepting order of sub-missile is the first(i. e. intercept firstly the first confirmed target; inter-detected is prior to the last detected one.ception in the shortest time has the priority; the targetG,≥G,2...G,。S6S";(1)of highest threaten level has the priorty). The missilewhere: C denotes the grade of sub-missile intercepting or-intercepting course is considered as a computer processder. t denotes detected time of the sub-missile.schedule. The intercepting course of a single sub-mis-Ascertain ballistic trajectories of all the sub-mis-sile is regarded as one intercepting process. We deter-siles. After being calculated by the combating system,mine the threaten grade of every misile interceptingis received the threaten coefficient order of sub-mis-process in sequence and apply the proportional naviga-siles. The highest threaten sub-missile has a highesttion guidance law to intercept the sub-missile with highintercepting priority.threaten grade. So it changes the missile interception ofG。≥Gi2..G;1.212..21 (2)high-speed movement into low-speed moving intercep-where : G denotes the intercepting priority of a sub-mis-tion.ile. I denotes the identifed threaten grade. The sub-missiles having the same threaten level are interceptedMIRV missile atackaccording to the detected time.Calculated by ground-based radar tracking andcommand center, under the same threaten grade, theIf entered ndarContinuesmaller intersection which is away from the sub-missileobserved arcaobservinginterception and the shorter the ground deployment fireT yesintercepting time is, the higher the intercepting gradeof a sub-missile isIntercept scbeduling analysisto a missile has priorityrC.≥G。{0m≤θ,m,nea,b.j (3)Determine the schedbulablela,I. +Qrbm =arl. +ar+nprioritya, and axrare the weighting coefficients of sub-mis-siles intercepting priority respectively.Intercept a war header withIntroducing multi-to muli intercepting scheme:proportional guidanceunder the same conditions, the priority of this intercep-ting segment is high. The intercepting priorities of theboost phase, the ascent stage, the center section andIntercpt suossallythe end-piece increase gradually.Fig.1 The flow chart of MIRV missile intercepting simulation2.2 Simulation of MIRV intercepting schedule2.1 Missile intercepting scheduling modelIn a particular MIRV missile intercepting combat,Missile interception is a complex and dynamicthe missile starts to separate after the middle phase.process, which floods a large number of random fac-The number of separated missiles is considered as 10.tors. Allocating a variety of resources in the missile in-Early waming satlites are labeled as A, ,A2,--1o re-tercepting process, especially for concurrent cluster at-spectively according to the detected time order. Tentacking interception will affect the effectiveness of de-corresponding eerial defensive conbating units B, ,B2,fensive combat directly... B1o can complete the guarding tasks. The intercep-In the missile intercepting dynamic warheadting sc中国煤化工'- missiles include:process, we should execute a combining schedule ithe attthe kill rate p ofMIRV missile intercepting process which is based onmissileYHCNMHGrsectionsieθofthe basic scheduling algorithms and assists in the bestmissile entering firing units and the entry angle w ofway to intercept schedule so 8 to improve MIRV inter-missilest6.cepting effectiveness.Set the kill rate of a single intercepting missile asHIGH TECHNOLOGY LETTERSIVol. 17 Na. 1|Mar. 201199follows:2v↑"(0.8335 0.8723 0.858 0.9435 0.803 0.9296 0.s96 0.740 0.7 0.04)Set the threaten coefficients of detected targets as|510 |Q=(0.9286 0.5696 0.400 a.7ms5 0.504 0.612 0.373 0.9 0.915 0.28)After ten schedulable cycles, ten warheads com-/1plete the whole combating proces. Through the analy-sis, the final curve is shown in Fig2. In Fig. 2, Num-ber 0 indicates that this sub-missile has completedcombating missions and hasn' t been within the schedu-lable sequence temporarily. In the simulation, we as-sume that the sub missile will be taken to interceptionwhen the sub-missile is in the first position of the se-→quence. So in the next schedule, we no longer consid-er this sub-missile , which is feasible in actual comba-Fig.3 Interception missile and target missile motion stateting process.It can be seen from Fig. 2 that ten targets are inter-the horizontal reference line;cepted in ten schedulable cycles. The order of ten targetsAm denotes the angle between the intercepting mis-destroyed is 3,7,2,8,1 ,4,9,10,6,5, where target 9 andsile speed and the horizontal reference line, which is a10 are both destroyed in the 7th schedulable cycle.variable;q denotes the angle between the intercepting mis-sile with the target connection and the horizontal refer-ence line;R denotes the sight distance between the intercep-ting missile and the target;N denotes the cofficient of proportional navigationguidance.From the third formula of integral Eq. (4), we .can obtainAm =Nq +Am - Nqo(5)where Amo , 9o denote the initial speed inclination angleof intercepting missile and sight angle.Set qn as the heading angle of the target relative toThe scheouil tinmes of wr-bea)the sight line, Ym as heading angle of the interceptingFig.2 Relation graph of most superior interceptingmissile relative to sight line, then:sequence and dispatching cycle[Ym=Am,=-(N-1)xqn +(N-1)XYm6)[qm =B,-(q+π)2.3 Proportional navigation guidance law to inter-Using Eqs. (4) and (6) to obtain the normnal ac-cept atacking missileceleration of the intercepting missile isSuppose intercepting missiles and attacking targetsmove in the same vertical planel&J , as shown in Fig. 3.A. =V.xThe relative motion equation and guidance equation=wv_ x ing. -ksin [-(N-1)9. +(N-1)9. +y.]of taking the proportional navigation guidance law areRrdR_(7)=V,xcos(B,-q) -V_xco8 (A_ -q)dtwhere:k =As can be seen from the above formula,{R a=V,xsin (B, -q) -v. xsin (A. -g)(4)Htthe.中国煤化工ories isy。and q。dA..τ=Nx出as ini;YHC N M H Gero-ros points ofA.depenas on tne humder oI Iv. s0 the biggerN is, thewhere :more the number of straight-line trajectories is. TheB, denotes the angle between the target speed andsmaller the angle between the two staight-line trajecto-100HIGH TECHNOLOCY LETTERSIVoL. 17 No. 1|Mar. 2011ries is, the smaller the ballistic curvature is. When Nchange the missile interception of high-speed movementis close to infinity, the space all around the target is ainto low-speed movement. So we can make full use ofstraight line. So it becomes a nearly parallel asymptoticthe advantages of proportional navigation guidance law.method.The simulation results which apply proportionalThere are always multiple stable straight-line traj-navigation guidance law to a target missile interceptionectories when k > 1. The angle between two straight-are shown in Fig.4, Fig.5 and Fig. 6. Taking V, =line trajectories is small. The curve trajectories are rel-400m/s,Vm = 800m/s,B, =20° , initial value Am =0,atively flat. If we can predict the hitting point positioninitial value q =0° ,initial value R = 10km.before htting targets and directly cary out proportionalnavigation guidance in this location, then we canThe motion track of an intercepting missile and a targetThe change incomalacelerationsie of itrecepingnissile0.03. target motiontrack0.025-" the motiontrack of itercept missile0.02)-0.015-0.01-0.005-of-.00555001000 1500 2000 2500 3000 3500borizontal coordinate (m)time (s)Fig. 4 The motin track of an interepting missile and a targetFig.6 The change in nommal acceleration size ofan intercepting missileThe distarce between ritenceptng missde andtanget10003 Conclusion900This paper makes simulation researches on the in-800-tercepting system of the MIRV missile. It breaks700through methods of the traditional missile interceptionand proposes a MIRV missile intercepting algorithm.With using a computer process scheduling algorithm,5o0we apply a proportional navigation guidance law to in-s 400-tercept the target missiles , and get a favorable simula-tion result.300This algorithm has some advantages as follows.200-In multi-to-multi combating, the attacking war-heads are intercepted according to different threatengrades. The one with high threaten grade is interceptedfirstly.中国煤化工0500100015002000250030003500of high-speedmovemYH. CNM H Gsoit redces theFig.5 The distance between an itereping misile and a targetdamage rate and improves the effective of combat, fur-thermore, it verifes the rationality and feasibility ofHICH TECHNOLOCY LETTERSI Vol.17 Na. 1 |Mar.2011101this algoithm.119-123[7] Meller J A, Lemke F. Self organizing Data Mining. Dres-Referencesden, Berlin: Libri Books, 2000. 11-113[1] Naveh B z, Lorber A. Theater Ballistic Missile Defense.[8] Charles A. F. National Missile Defense ( NMD). IEEEVirginia. USA : American Institute of Aeronautics and A8-AESS System magazine. 2002, 79 -85tronautics, Inc. , 2001[9] Mehra R K. Group method of data handling ( CMDH):[2] Gutman s. On optimal guidance for homing missiles. Jour-Review and experience. In: Proceedings of the IEEE Con-nal of Guidance and Control, 1979 ,3(4) :280 - 300ference on Decision and Control, New Odeans: Wiley-[3] DeyS, Borvik T, Hopperstad 0. s., et al. On the infu-IEEE Press, 1977.29 -34ence of constitutive relation in projectile impact of steel[10] Yuan Q. Proportional navigation researches and simulationplates. Intematinal Journal of lmpact Engineering, 2007,on interceplor: [ Master' s degree thesis ]. Hunan: Nation-34: 464 - 486al University of Defense Technology \Control Science and[4] Philippe L. Moris John Robustness to noise of stereo matc-Enineeing 2006. 12 -31hing. In: Proceedings of the 12th International Conferenceof Image Analysis and Processing, Mantova, Ilaly, 2003.Wu Guifang, bom in 1985. She received her606-611M. s. degrees in Communication and Information Sys-[5] Snehal K, Neeta D. Eficient CPU Scheduling: A Genetietem major of Beijing JiaoTong University in 2011. SheAlgorithm based Approach. IEE AESS System magazine,also received her B. S. from Liaoning University in2006 ,206 -2072008. Her research interests include multimedia com-[6] Wei Q Y. The infuence of using MIRV on penetration c&munication, image recognition computer network.pability and system ffctivenee for land-based strategicmissile. Missile and Space Launch Vehicles. 2004. (3):中国煤化工MYHCNMHG