A Survey of Maneuvering Target Tracking_Part II_Ba

ASurveyofManeuveringTargetTracking—PartII:BallisticTargetModelsX.RongLiandVesselinP.JilkovDepartmentofElectricalEngineeringUniversityofNewOrleansNewOrleans,LA70148,USA504-280-7416,-3950(fax),[e-mail],[e-mail]esecondpartinaseriesthatprovidesacomprehensivesurveyoftheproblemsandtechniquesoftrackingmaneuveringtargetsintheabsenceoftheso-calledmeasurement-originuncertainty.Itsurveysmotionmodelsofballistictargetsusedfortargettracking.Modelsforallthreephases(i.e.,boost,coast,andreentry)ofmotionarecovered.KeyWords:TargetTracking,ManeuveringTarget,DynamicsModel,BallisticTarget,Survey1IntroductionAsurveyofdynamicsmodelsusedinmaneuveringtargettrackinghasbeenreportedin[1].It,however,doesnotcovermotionmodelsusedfortrackingballistictargets(BT),thatis,ballisticmissiles,decoys,debris,andsatellites.Theprimaryreasonforthisomissionisthatthesemodelspossessmanydistinctivefeaturesthatdiffervastlyfromthosecoveredin[1].Tosupplement[1],asurveyofthesemodelsispresentedinthispaper.Toourknowledge,suchasurveyisnotavailableintheliterature.MeasurementmodelsaresurveyedinPartIII[2].TheentiretrajectoryofaBT,fromlaunchtoimpact,iscommonlydividedintothreebasicphases[3,4]:boost1,ballistic(alsoknownascoast),andreentry.Theboostphaseofmotionisthepowered,endo-atmosphericflight,whichlastsfromlaunchtothrustcutofforburnout.Itisfollowedbytheballisticphase,whichisanexo-atmospheric,free-flightmotion,continuinguntiltheEarth’satmosphereisreachedagain.Theatmosphericreentrybeginswhentheatmosphericdragbecomesconsiderableandenduresuntilimpact.Targetdynamicsduringthedifferentphasesaresubstantiallydifferent.Asuccinctoulineofthemaindynamicphasesisgivenin[5].Theboostphaseischaracterizedbyalarge(primarilyaxial)thrustacceleration,whichinthecaseofrocketstagingissubjecttoabrupt,jump-wisechanges.TheeffectsoftheatmosphericdragandtheEarth’sgravityarealsoessentialinthisphase.Aftertheboost(i.e.,duringthepost-boost),dragisnolongerpresentandthelevelofthrustbecomesloworvanishes.Duringtheexo-atmosphericballisticphasethemotionisgovernedessentiallybytheEarth’sgravityonly—thetrajectoryismorepredictable,still,smallre-targetingmaneuversarepossible.Thereentryphasefeaturesarapiddragdecelerationwithpossiblelateralaccelerations.Overall,aballistictargethasalessuncertainmotionthanmanyothertypesofpoweredvehicles,suchasmaneuveringair-craftoragilemissiles:MostBTsfollowaflightpaththatistoalargeextentpredeterminedbytheperformancecharacteristics,specificforatargettype,hencethenameballistictargets.Onlysomemoreadvancedmissilescanundergosmallmaneuvers,usuallyforre-targeting.However,thisdoesnotmeanthatthemotionofaforeigntargetcanbedeterminedaccurately.Infact,asvividlyexpressedin[4],trackingaforeignBTislikelytobe“plagued”withavarietyofuncertainties,includingthoseconcerningtrajectoryloftordepression,thrustprofilemanagement,targetweight,propellantspecificimpulse,sensorbias,andatmosphericparameters.Manyoftheseuncertaintiesstemfromtheuncertaintyinthetarget/missiletype,theprincipaluncertaintyinmodelingthemotionofaforeignBTforthetrackingpurpose.Comparedwith[1],thissurveyisslightlymoretutorialinnatureforthebenefitofthereaderslessfamiliarwiththeballisticsoraerodynamics.ThesamedisclaimersasmadeintheIntroductionsectionof[1]applytothissurvey,includingthoseontherestrictiontopointtargetsfortemporalbehaviorsandtheinterrelationshipbetweendynamicsmodelsandtrackingalgorithms.ThereadershouldkeepinmindthatwhiletherehavebeenmanyextensivestudiesofBTtracking,notmanyResearchsupportedbyONRGrantN00014-00-1-0677andNSFGrantECS-9734285.1Andpossiblyapost-boostphase,whichinvolvessmallmaneuvers.SignalandDataProcessingofSmallTargets2001,OliverE.Drummond,Editor,ProceedingsofSPIEVol.4473(2001)©2001SPIE·0277-786X/01/$15.00559resultshavebeenpublishedintheopenliterature.Inotherwords,muchoftheBTinformation,particularlytarget-typespecificinformation,suchasmotionprofiles(ortemplates),isclassifiedandnotopentothegeneralpublic.Asaresult,thissurveycoversonlythosedynamicsmodelsusedforBTtrackingintheopenliteratureavailabletous.Whilesomemodelscoveredareapplicabletosatellitetracking,theemphasisofthesurveyisonmissiletracking.Therestofthepaperisorganizedasfollows.Sec.2providesbackgroundknowledgeinballisticsandaerodynamicsthatisnecessarytounderstandtheBTmotionmodelspresentedlater.Motionmodelsforthesimplestphase,theballisticflight,arecoveredinSec.3.ThisisfollowedinSec.4byasurveyofthemodelsforreentryvehicles.Sec.5thendescribesmodelsfortheboostphase,themostsophisticatedphase.2PreliminariesInthissection,weprovidenecessary,rudimentarybackgroundinformationinaerodynamicsandballisticstohelpthereaderunderstandtheBTmotionmodelspresentedinthesubsequentsections.Wehopethiswillmakethetextmoresystem-aticandself-contained.2.1CoordinateSystemsThecoordinatesystems(CS)commonlyusedinBTtrackingareillustratedinFig.1.Muchmoredetailedinformationoncoordinatesystemscanbefoundine.g.[4,6,7,8,9,10].OxFyFzF=zIOSxSySzSNyIxI-rPpKFig.1:CoordinateSystemsTheEarth-centeredinertial(ECI)CSOxIyIzIisfixedinaninertialspace(i.e.,fixedrelativetothe“fixedstars”).Itisarigh