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Sight Rate with a Strap-down Imaging Guidance

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Sight Rate with a Strap-down Imaging Guidancea,Sight,Rate,with,sight,rate

    Sight Rate with a Strap-down Imaging

    Guidance

    JournalofBeijingInstituteofTechnology,2009,Vo1.18,No.4

    MethodforObtainingLine--of?SightRatewitha

    Strap-downImagingGuidance

    LIYi(李遗),MAYanni(马艳妮),SONGZhenduo(宋振铎).

    (1.SchoolofAerospaceEngineering,BeijingInstituteofTechnology,Beijing100081,China;2.ChinaWeapon

    EngineeringInstitute,Beijing100089,China;3.Troop63961,Beijing100012,China) Abstract:Inthestrap-downTVguidancesystem,theline-of-sight(LOS)ratecannotbeobtainedfronIthe

    measuredinformation,themathplatformtoselectmi~ileattitudeinformationmustbesetup.TheLOSrate

    selectingmodelsbasedonthemissileattitudeangleandtherategyroaresetup,theinfluencingfactorandthe

    extractingprecisionofLOSrateareemulatedandanalyzed.

    Keywords:strapdownimagingguidance;obt~ningLOSrate;attitudecalculation CLCnumber:TJ765.4Documentcode:AArticleID:10040579(20O9)O4045706

    Mostmodernimagingterminalguidancemissiles

    usetheimagingseekerwithinertialstabilizationto

    extractthelineof-sight(LOS)rate,andusepropor

    tionalnavigationastheterminalguidancelaw.With

    thecontinuouslyhighrequirementontacticalperfor

    manceofmissiles,imagingseekerwithinertialstabi

    lizationhasbeenconfrontedwitharloutstanding

    problem,thecomplicatedmachineryelectronicdevise

    notonlyseriouslyrestrictstheweaponfunctionbut

alsogreatlyraisesthecostoftheweapon.Forresolv

    ingthisproblem,moreattentionispaidtothestrap

    downhomingguidancetechnologysince1970s[. Strap-downimagingseekerwithopticalmea

    surementsystemisdirectlyfixedtothemissile.Iner

    tialstabilizationplatformcanbeabandonedwiththe developmentofthestrapdowntechnology.Instead,

    thisseekerisolatestargettrackandmissileattitude motionbybuilding"mathematicsplatform"basedon, themeasuringLOSangleonbodyandbodyattitude angleratesensitivetoinertialdevice.Sincetheme

    chanicalplatforrnusedforinertialstabilizationiscan

    celled,systematicreliabilityandmaneuveringperfor

    mancewillbeincreasedobviously,thecostofweapon willbereducedatthesametime.Significantdeficien

    cyisthatinertialLOSratemessagecannotbeob

    taineddirectlyandneedtobecalculatedthroughalgo

    rithms[2I.

    Basedonthis,twoimplementationalgorithms usedtoextractLOSanglerateispreferred.Oneof thealgorithmsisbasedonthemissileattitude;the otheralgorithmisbasedontherategyro.Thenquali

    tativeandquantitativecomparisonsoftheextraction preeisionsofthesetwoalgorithmsarecarriedon. 1MainCoordinateSystemandTheir

    TransformationRelationship

    ToresearchtheLOSrateextractingmethod

     basedonstrapdownimagingguidancesystem,coot

    dinatesystemsshowninFig.1arebuilt.

    1?1MainDefinitionofCoordinateSystems

?Inertialcoordinatesystem(OxiYii):

    LOSanglerateiscalculatedinthiscoordinate system.Oxiaxisisadirectioninthehorizonta1plane (suchasamissileliftoffdirection).Oyiaxisisup

    wardalongplumbbobdirection.Oziaxisisinhori

    zonplaneandmakesuprighthandrectangularcoordi

    natesystemtogetherwithOxiaxisandOyiaxis.Itis brieflynotedas"icoordinate",whenneglectingthe

    09.19 Received2008

    BiographiesLIYi(1973),doctoralstudent,liyi0513@163.corn;SONGZhen

    duo(1945),professor,doctoraladviser

    457

    J0ofBeijingInstituteofTechnology,2009,Vo1.18,No.4 Fig.1Definitionofcoordinatessystem

    EarthrotationandtherevolutionaroundtheSunand assumingthatgroundsurfaceisflat.Theinertiaco

    ordinatesystemcanbesimplifiedasfloorcoordinate system.

    ?Bodycoordinatesystem(OXbYbZb):

    OXbdirectstothefrontalongmissilebodyaxis. Oybislocatedintheaxisdirectionsurfaceofmissile body,normaltoOxbaxis,directingupward.Ozb axisisinthehorizontalplaneandmakesupright handrectangularcoordinatesystemwithOxbaxisand Orbaxis.Itisbrieflynotedas"bcoordinate". ?Sightcoordinatesystem(OxsYss):

    TheoriginOisthemissilecenter.Oxsaxisisa

    longLOSdirection,andtheabscissaispositivealong thetargetdirection;Oysaxisisintheverticalsurface containingOxsaxis,norm~toOxsaxis,theordi-

    hateispositiveinupwarddirection;Ozsaxismakes uprighthandrectangularcoordinatesystemtogether withOxsaxisandOysaxis.Itisbrieflynotedas"s Sln?

    cosTslCOSe

    ——sin7slcose

    where

    R11cos~cosqsCOSesCOScosesingsinflcosy

    cosesinq~cosqssine8sinY+sinesinqssin?'

    sin~cosqssine.cos?!,

    R12cosqsCOSessingcos~sinqscos?!+

    cos~cosqssinessin?',

    R13=sin~cosqsCOSesCOS+sinesinpsinqscos?'+ sinesin~cosqssinessin?'+cosesinqssin?'

    cos~cosqssinescos?',

    R21=cos~bsinqsCOSescos~0cossincosqscos?'+

    coordinate".

    ?LOSonthebodycoordinatesystem(Ox~lyaza): TheoriginOisthemissilecenter,0slaxisis alongtheLOSdirection,0slaxisisinthelongitudi

    nalsymmetricalsurfaceofmissilebodyandnormalto Oxslaxis,itspositivedirectionistheupwarddirec

    tion;Ozaaxismakesuprighthandrectangularcoot

    dinatesystemtogetherwithOx,aaxisandOyslaxis. Itisbrieflynotedas"slcoordinate".

    1.2TramformationsofCoordinateSystems Fig.2depictedthatthetransitionmatrixfrom"i coordinate''bywayof"bcoordinate"to"slcoordi

    nate"isCil:L(q,es)L(y,0,).

    Fig.2Transformationsamongthecoordinatesystems

    Thetransitionmatrixfrom"icoordinate''by wav0f"scoordinate''to"slcoordinate"isCh= L(ys1)L(q,e).

    Then,weobtainthefollowingidenticalequation Ch=L(q.,es)L(y,0,)=L(s1)L(q,e), (1)

    namely

    458

    R12

    R22

    R32

    cosesin~sinqssinessin?'+sin~cosqssin?'+ sinesinq.sine.cos?',

    R22sinqscosessin9+cos~cosqscos?'

    eos~sinqssinessiny,

    R23sin~sinqsCOSescos+sinesingeosqscos?'

    sinesin~sinqssinessin?'+cos~cosqssin?'+ cosesinqssinescos?',

    R31cosesinescos+COS~COSessin?'sin9+ COSescos?'sin~,

    R32sinessin~oCOSessin?'cos9,

    1??????J."

    RRR

    g

    

    g

    ?q+

    

    U?(

)eta1./MethodforObtainingLine-~SightRatewithaStrap-downImagingGuidance

    R33=sinCsinescossin~cosessinysinq~+

    COSEscosrcos~,

    whereLOSaltitudeangleqistheangleincludedbe

    tweentheLOSdirection(Oxaxis)andhorizontal plane(Axzplane).WhenOxsaxisisabovetheAxz plane,qispositive,ontheotherhandqisnegative. LOSdirectionalangleeistheangleincludedbe

    tweentheprojectionofLOSdirection(Oxsaxis)in thehorizontalplane(Azzplane)andAxaxis. LookingdownfacingtheAyaxis,ifecanbeob

    tainedwhenAaxisrotatescounterclockwise.thene ispositive,ontheotherhand,eisnegative. LOSaltitudeangleonbodyqistheanglein

    cludedbetweentheprojectionofLOSdirection(Ox axis)inlongitudinalsymmetryplaneofmissilebody (OxbYbplane)andlongitudinalaxisofmissilebody (Oxbaxis).IfOxbaxisisupwardtotheprojection ofOxbaxis,thenqsispositive(productingpositive liftforce),ontheotherhand,gsisnegative. LOSdirectionalangleonbodyesistheanglein

    eludedbetweentheLOSdirection(Ox.axis)andthe longitudinalsymmetryplaneofmissilebody(OXbYb plane),observingalongtheflyingdirectionofthe missile,ifOxsaxisisontherightsideofOXbYh plane,then?sispositive,ontheotherhand,esis negative.

    2ExtractionAlgorithmofLOSAngle

    RateofTrap?downImagingGuid-

    anCe

    2.1ExtractionPrincipleofLOSAngleRate Fig.3showstheprincipleblockdiagram[,.]of mathematicalplatforrnonextractingLOSanglerate ofstrapdownimagingseeker.Theseekertransforms LOSazimuthangle?sonmissilebodyandelevation

    angleqintoinertialLOSanglecalculatingvaluee andbasedontheoutputofbodyattitudeofinertial partsofstrapdownguidancesystem.Thenthrough appropriatedifferentiatingnetworktheinertialLOS angleratesandareobtained.Theaccurateguid

    anceinformationwillbeobtainedafterfiltering. Fig.3Schematicdiagramindetermining

    Threenormalrategyroscopesfixedonthemis

    silebodyaresensitivetobody'sattitudeanglerate componentbb=[bbbby?bbTinthebody

    coordinate,byusingEulerangledifferentialequation ofbodyattitude,wehave

    sinycos0eosTeos0~

    I

    cosVsin2'I

    cosysin0sin)'sin0J

    (2)

    Bodyattitude[y]Tandstrapdownatti

    tudematrixC8canbeevaluatedbynumericalinte

    theLOSrateforstrapdownimagingseeker

    gratingEq.(2).

    StrapdownattitudematrixcEis

    CC=L(,,y)=

    

    e0sOsin0c~Z+sinCsin7

c0s&~y

    sinCsinOc~7+co#sin7

    111

    m22I

    m233

    c~0sinF

    sinCsindsiny

    .

    

    }.

    

    o0Sc0s

    Assumingthatthestrap.-downTVimagingseek. eropticssystem'sfocusisf,theCCDpixeldimen

    sionisd×d,thecenterofmasscoordinateinCCD 459--?——

    

    ?

    _l

    1?????????j

    ...

    y

    .......................................L JournalofBeijingInstituteofTechnology,2009,Vo1.18,No.4

    targetis[Ix],thentheLOSdirectioninbodyCO

    ordinatesystemcanbeexpressedas rs=[fII]T.

    VectorrepresentationofthetargetLOSangledi

    rectionininertialcoordinatesystemcanbeobtained

    throughcoordinatestransformation.

r.=[rs1rra3]T=cErb.(4)

    AndtheinertialLOSanglesaltitudearecomput-

    edasfollows

    arctan

    (

    arctan{\

    rslI

    (5)

    accordingtoEq.(5).TheLOSglerate[()()]T

    is[qs()es()ITateachsamplingmoment,then c=

    f.s.0.:in.0sine0COSek:][k;].?()=l1lI()1.L.()().JL()j TheLOSangularrateinthebodycoordinates relativetoinertialcoordinatesintheinertia1framecan

    beobtainedbythefollowingequation: ?ii

    s1:R.b()I~bl(k)=Rm()(?bb()+?bl(k)).

    (7)

    Fig.4Implementationprocedurebasedonrategyro

    Thenweabtain

    )].()IM|w()?():

    ()J

    f2

    cose(k)

    sine(k)eosq(k)

    ()

    dnq(k)

    0

    .

    _sinq(k)

?

    (8)

    ItisdepictedthatM|w()isafunctionofun

    knownparametersq(k)ande(k).Aftersubstitut- ingEq.(1),elementsofdecouplingmatrixMare calculatedbyusingbodyattitude[r(k)()()].

    Theequationis

    1

     ‰赢12.上』

    ——

    R130

    ,(9)

    whereR11,R12,R13aredescribedinEq.(1).Imple

    mentationofthismethodismorecomplicatedthan themethodbasedonbodyattitude[6]. ---——

    460?--——

    :l1

    ge

    ,????????(,?????【

    ..

    g.e

    

    LjYi()./MethodforObtainingLine-of-SightRatewithaStrap-downImagingGuidance

    3SimulationonExtractingAccuracy ofLOSRate

    3.1SimulationCurveofLOSRateExtracting SamplingfrequencyofstrapdownTVimaging

    guidancesystemis100Hz,samplingfrequencyof

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