Autonomous Nucleus Tracking for Con~Et/Asteroid Encounters: the STARDUST Example

Autonomous Nucleus Tracking for Con~et/Asteroid Encounters: The STARDUST Example

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Jet l’rol)ulsiott l,al~oratory Califorltia IIlstitu(e of ‘lkcl II Iolc)gy AIS 301- IL(I 4800 Oak Grove l)rivc l’asadclIa, Califorl~ia, 9110{1

AIIsimct S’1’ARI)US’J’ is a nlissio~t to flyl)y tlic coIIIct 4. lMA(:IN(: SYSrl’lhl Wil&2 it) early 2004 aild rcturII saln~~les of tlic COIIIEI to ~ I)artll. ])uritlg its 120-150 k[H flyby of tllc colllct llu- KAI, I’IIAN’ l~lf:l’1:1{ SII:’l’U1) cleas, a scco]ldaly science goal is to ol~taill illlagcs of 6. nlo~’rl: CA1{l,O SIAILJLAYlOAI ANI) RII;SIJI;J’S the IIUCICUS usiltg tile o]lboard tiavigatioll cal]lcra, l)UC to the 40 minute rouncl-tril) light tilllc, grouIId l)roccss- 7. ‘1’IMIN[: illg of navigation data to uIJdatc ~)oilltiag illfor]natio)l to 8. CON(:lJUSIONS ]I)ailktaitl tlic IIaclcLIs if] tlIe ca]ncra flclcl-of-view is ilm practical. ‘J’bus, a silnl)lc, rdiahlc, and fast algoritlllil was CICVCIO1)CC1 to close tile navigation loop olll)oard during ctlcouttter. ‘J’lIc algoritl]ll] uses inlages of tllc IIUCICUS 1 IN’J’I{OI)IJC’J’ION clurillg al]])roacll to ul)datc target relative shtc illforlllw tiotl. ‘J’)lis involves ccmtroiding olI tllc ilnagc to olltaill IIU- clcas cctltcr-of-fi.gurc data aIid then I)roccssiug tllc data S’1’AI{l)US’1’, tl~c fourth lnission ill NASA’s l)iscovcry tllrougll a Kaltnan filter to update tlIc sl)acccraft, I~osi- I)rogra]tl, is a Inissioll to I)c launcl}cd in early 1999, per- tion ancl attitucle. Monk Carlo sill] ulatiolw \vcrc tlICII fortn a relatively low \clocity flyby of the comet l’/Wilcl-2 Ijerformcd to test tlIc algoritl]ltl. ‘J’llesc sit[]ulatiol]s il~- ill Jailuary, 2004, and return to IIkirtll in 2006. Its ]mimary corporatcd errors ill sl)acccraft itlitial I)ositiol[ and ill at- scic]lcc goal is to collect 1000 particles of cometary clust titude kIIowlcdc to I)rcwide a ‘Irutl l’) Inodcl wllicll tlIc of greater tlla]l 15 t[licrolls durilig tile flyby and rctaru filter Itlast rccovcr froln, ‘J’IIc results of tJIP sii[Iulatiolw tllcl][ to l)artlt ill a saln~~le rcturll calwule. As secondary I)rovcd that tile algorit]lru }vas sacccssful iIl I[lailltaillillg scictlcc goals, tllc sl)acecraft will also collect. interstellar tllc lIuclcas in tllc ca~tlcra flclcl-of-vic!v assaillitlg Ilol[lillal dast ]Jar(icles a]ld ol)tai[l \\Tilcl-2 collia and nucleus iltl- valaes for tlic errol sources. II:vcn wit]l \vorst case errors, agcs during tlIc cilcountcr, l)uc to tllc size of tllc navi - tllc algoritllnl ]]crfor]ncd successfalty ill over 90[)4 of tllc gaiiol) urlccrtaitltics at tlw titoe of tl]c fil]al uplink of the cases. ctlcoarltcr scqucf Icc to tl]c spacecraft, tllc tracking of tllc IIaclc IIs duriflg tllr cllcoul]tcr usitig tllc onl)oarcl calnera catltlot l~c I)crfortilcd o~)cll-lool). 111 acldition, tile large ‘1’A 111,1:011’ CON’1’II:N’J’S (w40 IIlillatc rout, cl-trijl ligh-tilllc) }jrccludes ground in- tcrvc]ltiot] during tlIc cllcoulitcr tillic l~miod to uI)datc Ilavigatioll illfor[llatioll. ll]stcad, iiilagcs taken with tltc 1. lN’1’I{OI)lJC1’ION Calllcra start i[lg around 20 ]I]illutcs })rior to closest al]- 2. ‘1’111; hflSSION I)roacll }vill },(s used to refitle tllc coinct-relative sl)acccraft st ate, a]ld t l]crcfore tltc catncra borcsight point il]g direc- 3. F! A\~l GArl’lON tiotl to t l]e coIIIct, olll)oarcl tlkc s~lacecraft itself. ]kcause

1 of the tight turnarc)ulld IICCCM to Iilaitltaill lock, tlic oll coli)d during a])l)roach WIICII it is hiddea from view by board al&ritllm IIas to bc si]nl)lc, rcliahlc, and fasl. 1( tile \Yllipl)lc slliclcl, a periscope is lnountcd which ~wers ]Jcrforl]ls centroidillg to clcterlnillc tile ccllter of tllc co]l]ct around ttlc shield. ‘J’llis ca]ncra/Inirror/pcriscopc combi- nuc]cus, and illcorl)oraks this itlforlnatio]l into Kalt]]arl ]Iatiol] fortns tllc irtla.giag systcl]l ~vllicl~ cloublcs as both filter to update state iaformatioa. ‘1’llis pal,cr descrilm i]} tllcscicllcc al~d o]~tical ]laligatic]]li llstr~]lllcllt. detail the algorithnls used, and the rmalts of sitnula(iolls to verify tllc code. After cc,llccti]lgt lies a]lll)lcs, tl)e acrogcl isst.o}ved iatoa salnp]c rctuutl caI)sulc cqaipr)cd with at) aeroshe]l where it Ivill rclllaitl for tllc rest of tlie Inissio[l, ‘1’lic s~)acccraft tllcll rctargcts its trajectory for atl l;artl~ rcturll to oc- 2 ‘1’IJII: NJISS1ON cur 011 Jatluary 13, 2006. At 1;-1 days, tile spacecraft ])crfc)rltls its fitlal]llallclllcrt otargct tile SRCfor a land- S’l’Altl)lJSrl’ is the fourt,ll ~ilission of NASA’s l)iscovcry i[lg witllitl a 60 I)y 6.5 kIu footprint at the Air Force’s prograln, followilg hlars }’athfinder, Near lkrtll Askroid Ulall ‘J’cst aIId ‘I’rairlillg l{aIlgc (ll’J’rl’l{) facility. Several }{mdczvoas, aIld ],unar l’rospector. ‘J’l Ic ]t]issioIl is a col- IIours])ric)r toctttry, tllc SILClis jettisollecl froIiltlle It]aill lahorat iw e{fort, with J 1’1, providing the ])rojcct lnanagc- sl)acecraft ])us, }vllicll tllcll ]wrfortnsa divert mancuverto ment, I)avigat, ion, and missiolt clesig[] car)al)ilit, im, I,ock - kcclJ it fro]n also c]itcringt lie l}artl~’s atmosphere. After hecd Martin AstroI~autics ill ])cnvcr, CO I)rovidi]tg tllc lal[dillgat [J’I’’I’I{, tile aerogcl with tlIc samplesis rccov- s])acccraft and most Inissio]i olwratio]w, atId tllc U]livcr- crcd fro]n tlic SI{C and sc]lt to a facility at the Johnson sity of Wasl]ingtonj wlwrc tl}c l’ril~ci])al lilvestigator is lo- SI~acc Cclltcr for storage allcl dissclninatio]] to the sci- cated. ‘i’l Ic sl)acecraft will bc laatlclled irl ]Ili+l’’e})ruary, CIICC tealn, I’or ]Ilorc i[]forlnatio]] OH tllc S’I’AR1)US’J’ 1999 al)oard a l)elta 7436 launch vcllic]c. l)aritlg its 5 ]nissioll, scc its IIOIIIC page 011 the World Jfride JYeb at year cruise to tllc comet 1’/Jl’ild-2, it will I)crforltl OIIC lltt I)://stardust .jpl.]lasa.gov/. gravity assist using tlic I}artll to give it cnouglI etlcrgy to rcltdczvous with tlIc comet. CoIIIet flyl)y will occar olI Jarluary 1, 2004 at a colnct-relative velocity of a little over 3 NAVIGKI’1ON 6 km/s. IJuring this flyby, a unique sulmtatlcc liIIOWII as awogcl, developed at the Jet ProI)ulsioIl l,al)oratory, will be dcp]oycd to collect coma dust partic]cs. ‘1’llc vclliclc ‘1’IIc ])rilllary II~ode of]lavigation fc)r the Inission Jvill be itself Ivill t~c protechxl froln tile lly~mrvclocity iln])acts of sta]ldard ,Y-l)alid l)ol)plcr and rallgiag. Covariancc anal- tllcsc particles usiag a forward facitlg sllicld (t,erlllcd tllc ysis IIassllolvl] tliat this issafficietl( to Incet the reqaire- “\Vlli],]Jlc” sliicld, in IIonor of astro]lo]lier IIkd \Vllil)- II ICIIt S for all dccl)-sl)acc Inallcuvcrs, l;arth gravity assist, pk). ‘J’lIc I)ril]]ary science rcquirclncllt, is to c.ollcct at and I;artll return, For comet flyby IIo}vcvcr, tllc a-priori least 1000 ],articlcs of greater than 1.5 ]llicroIl size }v}licll uncertaitltics itl tlIc colnet epllclncris (arouacl 1500 ktn) irnlml tllmnsclvcs ill tllc acrogcl as tlIc sl)acecraft flies I)y froth groatlcl-l)ased observations I,rcclude usirg radio data tllc colllct. l)Llc to tile ullccrtai]lty irl tlIc Inodcls wllicll alo]ieto ]lalrig:ltet llis~)llasco ftllclllissioll, ‘J’hcrefore, the clcscribc tllc density of cfast surroulldi[lg tl~e llaclcus, tlw olllmard calncralrlust bcuscd totakcimagcso fthcco met actual flyl)y distance is still so]ncwllat ullccrtaill, alId ill- llrior to ctlcc)utltcr to improve tile co~l]ct eplwmeris k[lowl- volvcs a trade-ofl bct}vecll s])acecraft safety and Itlcctiilg cdgcsaflicicllt tol[lcct tllc 120-150 kr]lflyl)y reel LlircIllcrlt, tlw 1000 ])articlc lccluireinc]]t, With current cotna IIIOCl- Startiilg at \lJilcl-2eltcoL] lltcr (\f’)-100 days, itnagcs will CIS, tllc clistallcc is set bctwcca 120 atld 150 kIII, I)ut tllc Iw taken at tlic rate of once ])er week, ‘J’hcsc will ilk uaccrtaiaty ill tllc ]IIodcls is roughly a factor or ‘2 or 3. crease it) frcqaeIlcy to twice per }veck at W-50 days, o[lce Also duri]lg tltc flyby, coma and nuc]cas illlagcs will I)c ])er day at \\’-7 days, and OIICC pcr ]Iour at W] day. taken by tlw onhoarcl calnera tllrougll cc)lor filters atId ‘1’IIcw o])tical ]lavigation (01’NAV) images are used to downlil}kecl ill real-time to tllc groutld, cxcc~)t for a +4 su})~)ort four ‘1’rajcctory Correction Nlaneuvers (rl’Chls), Itlinutc ])criod sarrou Iidil]g Cllcouliter WIIe II tltc ittlages occurrir[g at \\’-3O days, IW1O days, \V2 clays, and M- will })c stored for later I)layback. 6 lIoLIrs. Cotlcllrretlt scicllcc images taken at tlie same frcqaellcy arc also used to refiac the co]namodc] to de- ‘1’0 ]I]ailltaitl tllc coIIlct in tllc camera field-of-view (1’OV) tcrll)ilwdast dmlsity. A final decisio]l on the actual flyby cluring al)proacllj cacc)u]ltcr, and dc-l)arturc, the l)orcsigllt distallcc }vill bc ]nade and ituple]llcatecl at the \V-2 day of the canlera must sweep through nearly 180° ia angle, ‘lCN1. 11’itll tllcco]lll)irlat ioa of radio and O1’NAV data, ltatller tl]a]l lnount the camera oIl a scan l)latforIll (aII cx- tllc delivery oftllc spacecraft to its aitnr)oiat at the fiual ])crlsil,c so]utioll both in cost, colnI,lexity, al]tl ]Ilass), this \\’il{l-2targct il}g’l’Chl will be accurate torougllly8 ktn task is acco]nl)lisllml by Incafls of a ]l]irror wllicl] is free itl tllc crosstrack direct iotl, and 150 kln (or 24 seconds) to rotate about OIIC axis SUCII that it rotates ia tile or})ital iii tile dow[ltrack, ortilne-to-go, direct iollj (all la). ])laacoftllc flyby, At 180secoIIds l)riortoc]lco~lt]ter, LIIC sl)acecraft I)crforlI]s a roll Iilalleuvcr to l)lacc tlie co]nct ‘J’llesc dclivcry accuracies arcsafIicicIlt tot[laitltai[ls~~ace- it] tllc nlirror p]allc of rotation. III addition] to scc tlIc craft safety and lnrwt tllc I)rilnary science reqairc~nellt assuming the lninimulu ellcoulltcr distallcc dots not, go below 120 km. IIowever, tlicy arc Ilot suf[iciellt to sulJ- port the secondary goal of cncounkr ]ILlclcus itnagillg. l]) particular, the crosstrack urlccrtain(y is ]Iot stt]all cllougll (0 cletcrtnille tlw exact orbital ]jlal~c to which the s])acecraft ]Ilust roll. Also, the clown tcack ut}ccrtaillty is too large (0 clckrmine which dircctioJt to ]~oiltt tl]c Jnirror ill tl]c Jllillutcs surrout]ding C1OSCS(. alllJroacll. 01’NA\7 i]tl- agcs taken l)ast ll~c fil~al targcti]lg ‘J’ch$ }}rill, of COIIIW, provide very accurate it~formatioJl wllicll call rcducc l~otll uJlcertaitlties, but tllc 40 minute round-tcil J ligll(-tilnc cf- fcctivcly rules out controllitlg tllc roll angle and mirror l)ointiJlg angle fronl the ground. ‘1’his is }vllat Jlcccssi- tates using closed-loolJ o]lboard llavigatiol) to ]ilail~taiJl visual lock oJl tlie lIuclcus by the ca[ncra to lIIcet tllc +7. ‘ Periscope i][]agitlg scicJlcc requircJtlents. ‘J’lic ])rocedurc during ct)- \ countcr }vill he to initialize the oJll~oard ]Iavigator with . Ntivig

5 KAl,h4AN 11’11:1’1:1{ S1’:’J’IJI’ ‘1’llere arc tllrec prilnary conl[)ollcnts to tile itnagiag systc]n used OJI S’1’AIU)lJS’J’: t]le caJllcra, J]~irror, artd pcriscolw. ‘J’llc catnera is mouJltcd such that the l)orc- Illirduc[loll sight poi]lts straigl~t down tllc sl)acecraft --Y axis (see IJigurc 1). ‘1’hc lnirror is thca calltcd at a 45° allglc to tlw ‘1’lIc l)ur])osc of tllc KalJnall filter is to use the onboard canlcra boresigllt and allowed to swivel arouJld tllc sl)ace- data to correct tlic nomitlal comet relative sl~acccraft po- craft 1’ axis such tl]at the effective calncra I)orcsigllt view sitioJl so that tl[c calncra will be l)oilltcd in the right il~g direction sweeps froJll tllc sl)acecrafL +X axis to tllc dircctioJl to ca~]ture tile ~lucleus it] foture images. ‘1’he – Z axis and finally to the –X axis lvitll t.lw col\veJltiol] Jlolllina] coJllct relative spacecraft eI)llemeris is l)rovided tliat 0° mirror angle is +X, 90° is –Z, aJId 180° is –X. }~y groutl&}Jasccl navigation. ‘1’hc sole clata tylw used hy I)urillg cJlcountcr, the spacecraft will t]c oriclltecl sucl I tllc olllward Ilavigator for JIuclms trackillg is the image that the slmcecraft +X axis (wllcrc tile l\]llil)])le sl~icld is of tllc coJnet. IIy dcterJnining tllc ceJltcr of tl]c JIUCICLIS locatccl) is along the co[[lct-ccutcrcd s}mcccraft velocity ill tile itllage, tile 1,0S direction of the comet, froln the vector, aJld the sl)acccraft X-Z plane is coi Jlcidc]lt witl] slmcccrafl caI\ t~e co~nputcd. I’;xl)licitly thoug]~t the 1,0S the colllct-centered ort)ital plane of tllc flyl)y. If tl]c llav- to tllr nucleus is IIot actually coltll)utecl froltl the itnage; igatioJ) delivery were ])crfcct tllcJl, t]lC COJllCt WOIJld tW il]stcad, tllc I)ixcl and line (the * and y coordinates io the located at exactly –Z at clkc.oul}ter. ‘1’lIc Ijcrisco])c is a

x Spacecraft Ilody-Fixed Frame froll] tlIc image aIId diffcrcnccd witl] I)rcdicts of tllc cctltcr locatio]l to c)l~taitl data residuals. ‘J’llcsc residuals arc . [~-z tllrlt IJroccsscd l)y the Kallnan filter to get correct, io]ls to ! tllc a-priori state. Mirror 1>’ Effective Camera Frame - N’

II] order to co]IIIJuie l)rcdicts of tllc colllct localiotl ill tllc calnera l“OV, tlie trallsforlnatioll of all iticrtial vector into camera pixel ancl liuc coordinates is IIccdcd. ‘1’llis is a three step process; tile first stq) is to rotate all itlcrtial h$ ‘ vector into a ca]ncra coorditlatc fralne (tllc Af-A’-l, fralnc r l’igurc 3: S])acccraft aud ~a]l]cra ~oordillate lramcs SIIOWJI in IJigurc 2), tile second is to ])rojcct tllcsc 3-1) coordiliatm i]lto tl]e 2-1) cal]lcra focal ])lallc, atld tllcil fiIIally scale tllc rcsu]t il]to values of I,ixcl aIId liilc. III suit that flf ’- N’-l,’ is ]Lo lollgcr a riglit-llatldcd coordinate tllc following dc]ivation, tllc ]Iotation 1{1(0), I

Wllcr’e --1 0 0 (5) 1{, := 010. (2) 1 h j 001 [1 I+ ’or a difi’erc]lt orient atioli of tllc calncra mounting) the ‘1’hc ]natrix, Itr, accounts for tlIe Inirror rcflcctioll abc)ut ]]roccdurc followccl Ivoulcl I)e tlie salncexccl)t that +90° tile X-Z I)lallc wl]ich flips Af froln 1’ to –}’, ]vitll tllc rc- or 4 180° tvou]d llccdcd to be added to the Rs rotation in l;q. (l), and a clifl’ercnt rcflcctioll ]I]atrix wOuld tv.- I)cdd. {;clttcrfiliditlg is tllc l)rocess of c)t)tai[lillg tile celltm of the Oncc I;c, a 1,0S vector in calmra A4-N-1, coorxlillatcs is target ol)ject ill Llle ilnagc for use l~y ttic filter. }listori- obtaillcd, it needs to bc trallsforltlcd itlto tllc 2-1) catllcra cally, tltis llroccss l~as bccm refined throug]l tile Voyager focal I)lal)c. A detailed description of this IJIOCCSS call IJC ctlcoutlters ~vitll hTcI)tullc and lJrarlus such that accura- found itl [1]; a brief syllol)sis will I)c givcll IIerc. l’irst, cies of Inocll less tllall a lJixel are IJossil)lc [2], [3]. ‘1’hc aIJIJly tile gllomonic ]Jrojwtioli, }Iicturcs talicl{ l)y tlw s~)acecraft of ]Jlalletary satellites ~vcrc scl It to tile groutld for ~)roccssin.g. IIerc, an analyst ((i) lvould first drtcrlnirle a rougl] ccllter by eye; com])uter algoritlll]ls wllicll llloclcl Lhc elli~woidal slla~w of tl}c tar- Wllf.m gc~ Jvitll cormt liglltil]gduc to I)hasc allglcs and albcdo variations could tllc[l refine tile cmltcr locatioll .gucss to a f = the camma focal lmlgtl)l ill ]nltl ]Iigll accuracy. l’orSrl’AI{I)lJS’I’l lo}vc~er,tl \ccci~troiclirlg ]ltust I)c doltc ollboarcl without, llaman illtcrvent, ion on an Vcl , I’cz, VC3 == the coml)oncllts of tllc line-of-sigllt, ol~jcct lvitll u])kllown size, sllapc and albedo properties, vector it) M-AT-I, coorditlatcs and kvitlt tllc additional cornplcxit,y of ranclon~ bright ar- 2’,?/ == tllr projection of tlic 1,0S vector eas aIJl~cariltg due to colnet outgassing. il~to focal l~lauc coordinates, [;urrcllt]y, tllc olily closeup itnages of a co~llct frolu a lneasurcd in lmn. sl)acecraf~ }vcrc taken by the Giotto spacecraft as it flew l,yllallcyitl 1986. ‘J’llcirllages sllo~vltlllltil) lcllargcbrigllt jctscttlalt:ltitlgfrolll thecomctallcl aclarli nuc]eus barely Next, fiIId tlIc hiss to r aIld y, AT aild Ay, caused I)y visil~lc. ‘1’0 tl]c liulnali cye at least, it aI,pcars that a oI)tical clistortions by: I,riglltllcss cctltroidi[lg algoritlll]l TVoulcl l)ick a location outside of tllc nucleus, which TVould rccluirc a much lnore co]tll)licated al.goritltlnto locate tlwlluclcus, Fortunately, \\’il&2sllould t)cconsidcrat)ly ]cssactivethatl IIalley was (7) lvitll tllc result that, whc]l tllc sI)acccraft is insiclc the coltla, tile II UCIL=US S11OUICI bc the brightest ot)jcct itl the illl:~gc. III zl{lclitioll,o~ltgassirlg activity sl(ould alsobc less frc~luciit over tl)ccl~c.oLlllter tilllcsl):ill allclovcr as[llallcr sl)atial cxtcllt around t,llc IIuclcus. with ltor tllcsc rcaso]lsj it lvasclccidml to usc asim~,lehrigllt- IIcss It Io]IlcIIt algoritlllna sthcfirst step ill tllcccntcrfincl- ittg ~lrocww,

\vllcre I’ == r2+y2, and tllc v’s arc tllc c)[)lical distort ioli N A’ cocfficierlts. ‘J’lIc corrcctcd image locatiorls, r’ at)d ?/, arc X Ej”~j tlicll

(9) l“iaally,tlle conversion fromthc rectangular coordil}atcs lvllcrc l~j is tllc l~riglltacss value at pixel i and line ~, topixc] altd lillc is: A’ is 1024, and f)c’ altd lC’ are ttlc comr)utcd brightnms cc]llcrs. ltl additiolij tllc l)~js are cllosell such that

Iv}lcre f{,,i,~ is tllc llliaittluln backgroutlcl noise value allcl I\,,a,. is tlte liluit l~cyollcl lvllich tlic brightness prok>ahly Jvllere IL’ isatrallsf<]rlll atiolllllat rixfrolll llllilto l)ixcl/litlc rcl)rcscrlts utlusua] ootgassing activity. ‘J’lIc actual val- sl)acc, atlcl ~JO at)d 10 arc t,llc center I)ixcl and litlc Of tll(’ ues for tltesc IJourldarim will dcpclld on calibrations clone ~(;l). ~llrrclltly, tllcl/’sirll;c1. (7)alld allcrosstcrlllsitl cluritlg flight and far etlcoullter wlten conlct II1OC1C1S will tllc K matrix ill l;q. (10) aresct tozcro. IJllritlgfligllt, t)c iltll)rovcd, calibration ilna.gcs of clclisc star ficlcls will be take]] aild used to accuratc]y dctcrlnine Ll)csc para]nctcrs. I{r arid ‘J’llis algoritllltl produces a ccllter-of- briglltncss cstitnatc I{Y fortlle Srl'AItl)LJYl'c alllcrai s83.8l)ixcls/1l~ll~. (~Oll); what is nwclcd is tllc ce~ltcr-of-figure (~01’). If tl]c ol).icct lvcrc spherical, a sitnl)le correction) factor colt I- ‘1’al)lc 1: 1 cr \Talucs for Gyro l;rror Model l]arametcrs puted ‘as a futlctioll c)f the sc)lar lJllasc lvould suflice to obtain tlic ~X311-~OF oflsct and lIIC resulting (;01” mti- IIlitial Attitude l;rror 0.1 deg. lnate Tvould lJC accurate to tlw pixel lCVCI. Alt.lmugli it ltalldo]tl Attitude Noise 1 .9 X1 O-4 Clcg. is highly utllikc]y that Wil&2’s lluclcus is sl)llcrical, tllc Gyro l)rift Rate 0.0033 dcg/hour, off’set is still apl~licd to rclnove gross errors it) tllc CK)l] Gyro l{alldo~u lf’alk 0.025 dcg/mm to ~OIJ oflsct. ‘J’IIc forlnula is

sillct(l + COSO) ~ = x! —. (13) 16 (7r[– – O) COSO +s itlo 1 l)ynalnics Model lvllcre tltc ofkct factor, ~ call take values l)ctwwcll 0 and ‘J’lIc tittlc fraltlc during wllicll tile onhoard navigatio]l pro- 1 to rcl)rescllt the offset as a fraction of the assutncd ol)- ccssitlg Jvill I)c active is shout tlw 20 Ininutes surrounding jcct radius, h’. ct is tile l)llasc angle, wllicl], duritlg cll- closest alJI)roacll. IIccause the flyby distance is fairly large coulltcr, will vary between during allJ)roacll to 10° at. 70° (> 100 ktll) and tile Iilass of the colnct is fairly sniallj the ‘1’0 aI)lJly tllc correction Ll)cll, first fitld tllc Cllcoulltcr. trajectory during this tilnc is cssctltially linear (pcrturba- direction of tllc sutl ill the camera cc)orditlatcs I)y rotat- tiot[s callscd l)y ittlpacts with conlct dust Ilarticlcs is also ing tllc illcrtial 1,0S vector to the SUII, A usiIlg 7}c froln llc~ligil]lc). ‘J’lius, tllc trajectory lllodcl used by tile filter al)ovc, i.e., ‘. ‘1’lIcn, coln})ute tile SUII dircc- Ac = 7~c A call safely assutned to bc a straight lillc, tion ill the itnagc, ~), lncasurccl cloclitvisc fro])] 0° ill tllc l)ositive I)ixcl dircctioli, as i< = ito + X’t(i – to) (18) it = it”. (19)

‘J’lle olmrved IIuc]eus center is tllcn: ~vllere ~t is tllc I)osition al~d Ai is the velocity, expressed ill tile co)tlet-ccntcrcd, J2000 I’:artll Nleall Ikluatorial in- e}tial Coordil}atc system. ‘1’lic initial conclitions, ~~~ and z\~~o lvIIctI olll~oard navigation is startccl arc provided by ttlc results froltl ground-based navigation. ‘1’he utlccr- WIICIC lfc is tllc size of ttlc nuc]cus trallsforttlcd itlto l)ixcl taitlties ill tllmc initial conditiol~s is largely in the posi- uliits. Givcll tile range to the nucleus, p, frolti tllc Iloltlitlal tiol] (around 8 kln ill the crosstracfi dircctiolts, 150 klo cpllclneris, I{C call be computed as it] dolvlltrack), Jvllcrcas tile velocity is well determimcl fro]]] l)c)I)I)lcr data to better than 10 cItl/s. I:or this rca- SOII, tile oII})cmrd filter o~lly IIecds to uI)datc tile l)osi- (17) tiol{; tllc velocity is assulned to I)e I)crfect and is not LIp dated. ‘J’llus, corrections to tile colnet-cetlterccl l)osition, lkcattsc tllc true size and shape of tllc ]IIICICLIS is ult- AT = [Ao AJI A2]7’, forlll tile first tlirec co~tlponents Iillowll, tllc accuracy of tllc ~OF CStillliit C is diflicult to of tllc estiltlatc wctor. cstatjlisll. l’or use ill tile Kallllan filter, tllc ~,01” data It \vas rccogtlized fairly early that tile kno}vledge of the was ~vciglltcd fairly conscrvativcly, as will be dcscrilmd slmcecraft attitude was a Illajor error source during em I)c101v. loose wciglltitlg of tllc data also rnitigatm tllc ef- counter. l)uring cruise, A~S dctcrl[lims tllc sl)acccraft fects of systelllatic Liascs introduced I)y usirlg })riglltllcss attitude using a star tracker. l)urirlg encou~lter, llolvevcrj cent roids. ttlcrc is 110 guaralltcc that stars ~vill t)c visit)lc through ‘1’0 ]Ilil]illlizc the ljossil)ility that brigllttlcss cclltroiditl.g tl)c colila, sc) gyrosco])cs are LMCd to ol)taift sIJacecraft at- Ivas I)erforttlcd 011 cllll)ty sI)ace or ratldolll ~loisc, ttlc titude. scarcli area to perforlil the Centroidillg is narroJvcd down ‘1’lic gyros arc il~itialimd with values from tile star tracker by hoxillg a rcgioll around tile a-priori guess at tllc cclltcr several lIc)urs l)rior to encounter, deI)cllding on the ob- lc)catioll. ‘1’lle I)ox size is set by l)rojcctiilg l}IC ])ositioll served co]l~a ol~acity. ‘J’llcsc initial values will have a bias uncmtaitlty ellipsoid itlto tllc catnera ~)lallc, takitlg tllc associated }vitll t,llct)l. As time passes, the gyros will also largest ditncnsion of tile ellipse and adding tile size of ] drift, a[~d Ilavc rando]u ~wrturbat ions wl]ich affect the tllc IIUCICUS (a 2..50 clliJm is used). ltl additioll, (Ilc inte- IIlcasuret[lcrlts. ‘1’lle statistical nature of the biases and grated briglitlms ill tile ccntroided rc-gio)l lnust l)C al)ovc drifts call Ilc dcterlninccl Leforellandj and are given in a certain threshold for the ilnagc to be valid. ‘l’lie value of ‘J’al)le 1 [4]. the thrcsllolcl is still to he cleterlllincd and will dclwt Id 011 tllc observed sensitivities of tllc catllera frol[l calil)ratiotl ‘J’IIc al)c)vc vallies can tw used to forill a model of sJ)ace- itnagm takcll ill flig;llt. craf{ attitude kiiolvlcdgc errors. A rallclo~ll saltlIJliilg of tl)c values are Laliell allcl tllc gyro drift is coIIIJ)utcd as :1 funct ic)u of tittlc for each of tile three sl)acecraft axes (l’igurc 4). ‘1’l]e drifts arc taken to be rotations almut each of tllc sl)acecraft axes, that is, tile true sl)acecraft attitude is a rotation about the Collll)utcd sl)acecraft X, 1’, and X (a) Rolabon about spaceccaf~ X-axis axes with tllc ~nagnituclc givcll by tllc plots in l“igurc 4. ‘J’IIc net cflict 0]1 tllc olmrvcd Ijositiolls is slIowJi itl l~i.g- urc 5. ‘I’l Ie Ijlots sllcw Ivhat tlic data residual Ivould look like if tllc tra.jcctory lillowlcdgc and ccllterfillditlg al)ility were ~Jcrfcct, allcl tllc only error is caused t)y sl)acccrafL attitude knowledge errors. It is clear that tlic effect o]t 25r r –r ..—— . , --––– ., — —., , the data clue to this error source is large and Illust I)c accoulltcd for itl the filter. ‘J’tlw, it) additio]l to corrections to tllc position, the filter cstilnatcs corrections to tllrcc coltl])ollcnts of sJJacccraft attitude: ~lIC right asccll- ’221 , ..— .,–— .- .— L._ –—L. — —–-—, ———.. J -1200 -1000 8 -60g - 4&)rj -200 0 200 sion (A) allcl clcclinatioll (6) oftllc body-fixed X-axis, atld ‘ $’)‘? Rotat!on a out spat raft Z-ax!s , -, _—— –r ___ -_ –..—- _.–—–-— -— ttvist (y), tllc rotatiol~ about this axis. ~. g,

.+;s .2 ~+ ~ @ L ,. -.. —-.. .—— ..- —L. . ––--—*. -—— ,.. .—.1 -1200 -1000 -800 -600 -400 -200 0 200 ltme to encounhr (see) ‘1’lIc filter used to l)rovidc a state update at tllc current titllc, ii is a standard extended Kalltla]l filter. l)UC to tllc fzzct that tllc translational ecluatiolis of Inotiolls arc lillcar, IPigure 4: Gyro l)rifts vs. ‘lime for 3 Spacecraft Axes altd o]Ily corrcxtic)lls to tllc llolllillal attitude arc lIccdcd, llulncrical integration is IIot nccdccl wllicll greatly sitnl)li- fics tl)c filter. First, the olEcrvatioll J)artia] derivatives with rcsl)cct to tllc state, }f~, is:

a(p, 1) ]1 = —-———-.— _____ (20) d(Ax, A~j, A2, AA, Ah, AP)

‘1’hc partials arc colllputccl IIumcrica]ly usitlg central dif- fcrenccs. };or exalnJ)lc, tllc partial of l)ixcl or lillc ~vitll 50 ~ , r r r.-, resl)cct to ollc of tllc estimated J)ara[l]ctcrs, q, is:

8]) _ p(q + C@) -- p(q - dq) , (21) fi– 215q . . wllcrc I), 1 =- j(z~, A, r$, ~, 0) atld call I)c colt II) Litcd usit]g l;qs. (1 )-(10). ‘Jo get tl]c clcl)clldcncc OII A, i?, and 9, Ilc)tc tltat 7jJ~~, ill l’;q. (4) can be collll)utcd as

wllcrc IL’] , lt~, and 1/3 arc rc)tatiolls al)out tile sJmcccrafl A’, )’, and Z axes, rcsl)cctivcly.

Sillcc tllc olily cstilllatcd ~)arameters are tllc l~ositioll and collstallt, attitudes, the state tratlsitio[l lnatrix to ]IIaI) _401 ..—. L— ,..1 -1200 -1000 -800 -600 -400 -200 0:‘ o cstirllatcs from i~_ 1 to ii is tllc idclltity ltlatrix. ‘J’llusl t,me 10 encounter (WC) tllc a-priori covariallce at fz is tllc saltic as for f~_ I, that is, l~igllrc 5: l’ixcl/l,iilc llmiduals l)UC to S1)acccraft Atti- ~’i ~ Pi-l. (23) tude Kllowledgc l}rmr

‘1’hc statldard form of tllc Kalman gain IIlatrix cat] tllcll be writtct) as: IIrw, 1<~ is a diagoual wcigl~tillg IIlatrix, ll~atrix usiug tl~c cquatious:

(’25) A = tau-l (%:W ’28)

6 = tau-l \vllc K’ and arc the lvcigllts ou I)ixcl a]ld lilic, rc- 29) 0; L7; (3*1’:’’3)) ’ slwctivcly. ‘I’lleclata }vcigllt istllcsc](larc oftllc assulncd radius of tile nucleus iu pixel space, wllicll, assuluiu,g a 30) 2klll]l[]clctisraclius, k’arics frollllllillillllllll of4 lJix&at ~=ta’’-](%%:l) ’ \f’-2O Illillutmto a Ill:ixiltl(llllofal)ollt 220 l)ixels at CIE tvllcrc courltcr, ‘J’l)c updated csti[natc of the state, i’, is tllcll givcll l)y:

2. Add tlIc I)rcviously filtcwd attitude corrcctioas, AA, AA, and AW to the ACS provicled attitude ili I’;qs. (28) tc) (30). lror tlie first illlage that is pro- CCSSCXI. t])csc corrections are assuuled to be zero.

3. Adcl l~reviously filtered correct io]ls to tl~c Tlo]uiual ],ositioll aad I)ropagate tile I)osition to tile c.urreut whrm tltc observed cetlters, IJO aud iO are ol~tai[lcd frol]l titne. ‘1’llr cormctious will bc zero for the first ittt- tllccclltroiclilJ gJ~roccss, andpc and 1, arecolllI)Lltc[lllsillg agf.’ l;qs. (1)-(10) aud tile nonlilialvaluc for ~. l~itlally, tllc uIJdated covariaucc at f~ is calculated as: 4. l’rocms tllel)icture togcttlleotmrvcd IIuclcuscem tcr locatiol], usiug the llolnillal curreut ~)ositiou to – I’i 1: (1 l{ill~)i’i. (27) start tllc scarcll aud to get tllc rauge to the Ilucleus to c.ollll)utc data weigl~ts.

(jive)] tile C(l(latic}rlsf(jrtlle Kalmallfiltcr, tlic cetltroi(l- ~ ~oltl])utca corrected sl)acecraft attitude, ~~IJF, us- illg process, aud the inertial to camera tra[lsforlnatiolw, il]g tllc updatccl attitude fro]n step (2), usiug F,q. tllc algoritlltu to do tile ul)dates call bc dmcrit)cd. l’rior (22). to starting the autonolllous tracliiilg, tllc software is itli- iiali~jccll ~itlltllecllrrcllt calllcra llloclcl, I~re(lictccl ]iucleus 6. Usiug tllc current position atid corrected attitude, size, atld tllc sljacccrafl state (~)ositiorl and velocity) as fiIId IICW cstifuates for currcut })ositioll aud correc- dctertt)iticd fro~[l groutld-based I]avigatioll at t,lie start tiollsto tlleattitudewit]l tllcfilterc cltlatiollss llo~vll titnc. ‘1’lle covari:ince ou tllc iuitial positiol[ is also JJrO ill II;qs. (20) to (27). OIIly OIIe itcratiorl is needed vialed. Ascacll imageistalml bytllccai[lcra (at allotl~illal for cc)llvergcllcc. frcquc~~cy ofomevc.ry 10secouds), tllctrackit}gs oft~~’are 7. Storctllc ul)dated l)ositiotl z~llclattitllclec orrectio~ls isrutl toll JJclatc lJoirltillgI )re(lictsfo rtllcllext itnagc. ‘J’llc for use Ivllcl] tllc next imagcisol)taiucc]. itll~uts to tllc IJrocms as it is ruauitlg arc:

● ‘1’]lr slluttcr opcl) t,it]]c for tllc currc]lt itllagc, [i h40N’]’l; CA1{l,O SIMIJI,ArJ’ION ANI) 1{1;s111:1’s ● ‘J’lle 31,3 itlertial to slmcccraft body-fixed rotation luatrix,lj~~~,, at tllc tilncthc ittlage }vassllllttcrccl. l?l{mduclic~n

● ‘1’IIc ltlirrorallglc, d, at the tiluc lIc iruagc Tvas sllut- tcred. lftllcclyllal[lic c(lllatiollsllsecl it) tllefilterl )rcciselylllocl- elrxl the true fc)rccs acti Ilg on the spacecraft, then the ● ‘1’}Ic iluage ilsclf. col’:iriaf]ccc)l)taitlcc] aftcrfiltcriug ~vou]d accuratc]y repre- sent tile statistics of the estimated values. ‘1’his is clearly ]Iot tlic case }Iolvwcr, as we llavc clclihcratcly used a re- ‘J’hc algoritlilu used tc) generate a p edict. for the ]Icxt duced set of dyllalt]ics to keep tile a]goritll]u si~llI]le aud l)ict,urc opl)ortuuit,y wheu proviclcd tllc al~ovc illforlllatiotl fast. l`ortllisr casoll, hloIlteC arlosiIllL]lati ollsareIleeclecl with each ~)icture is as follows. to assess tile al)ility of tile algorithm to maiutaiu visual lock olltlle IIUCICUS. l’ortllc silnulatol~sla “truth” model 1. C;oltiI)ute tllc currcut sl)acecraft right asce]lsioll, of tile trajectory, spacecraft attitucle, allcl obscrvatious dcclirlatio]l, a]ld twist by dccoml)osit]g tllc lj~j+, are .gc]lrrtrtcd aIId I)roviclcd to tile filter. l’or a giver] rutl, 1 Ile t rlllll ~tlodel rcpresc]its a Yaaclolll saIllI,liug of tllc er- al)ovc, ivliicll assaltlw errors ill attitucle Iillolvlecfge t)ut ror sources \vl)icll affect that II1OCICI. OIIc-li LIIIdrccl rutls I)erfcct corltrol. Once agaitl, Gaussiar) clistributiom of are IJcrformed, and t,l]c results are evaluated l)y clctcrmitl - tile itlitial I)ias aad raricloln aoise arc sampled for each of itlg wlletller or not t,llc IIuclclls was visilJIC ill t,]lc CalllCra tllC tllrcc axes, and a t,itlle history of tllC rotatiol~s abo~lt, l’O\r at all tilnes. ‘J’llc details of this l)rocess will IIOW l)c tllc axes are gcllcratecl (I~igure 4). Startitlg with tile I]oII)- dcscril)cd. illal itlcrtial to sl)acccraft body-fixed rotation Inatrix, ill- crctlle!ltal mtatiolls fro~tl tllc error salnl)le are al)pliecl at cacll irtlagc titllc ant] passecl to tile trackiag algorithm to 7kljdoly Afo(lel lnitnic A[X’S attitude kaowledgc. ‘1’hc “t,rut,h” attit, udc ill this case is sitlll)ly tile Iloluiual, tvllicll can t)e comr)arecl ‘1’hc truth trajectory is illtcgratecl forward fro)n tllc start- to tile filtered estimates from tl[e algorithln. ilig conditions using numerical intcgratio]] of tlie fall t rallslatiollal cquat ions of ~[lotion of tflc sjmcccraft. ‘1’IICSC ccluations illcludc the mitral body force frolll tllc suti, l)Ius third I)ody l)crt,url)atioIls froln tlie lliilc l)laacts atld solar radiation j)rcssurc. ‘1’lIc starting collditio]ls are OL ‘1’IIc al)ility to coltlI~utc a nucleus ccntroid from the itnage tai]led froln a ranclom salnpliag of tllc lJositioll utlcertaill- is a crucial cotllr~ollellt ofthc trackiag algorithm. 11] orclcr tics at tillle of initiation for autollomom trackitlg, wliicll to I)roIwrly test this coltlpollmlt, accurate rel)resentatiol~s is assamccl to be 20 miautcs prior to tllc ltolllirlal elI - of tlic co]tlet IIucleus allcl coma arc needed. ‘1’his is a dif- cottntcr titllc. I“roln tile latest grouncl-tmscd IIavigatio]l ficult task llo}Ycvcr, and still a work ill progress, partic- studies, it has been detmllli[lf.wl that tllc unccrt, aillties ill ularly sitlcc l)ara~[lcters wllicll descrihc the coma bright- position at this time are 8 km ill t,llc crosstrack direction tIcws atld dust dcnisities nave large uncertainties associated al)d 150 kIII in tllc dowlltrack (all la). I{’or tlic siltlalatiolt with tllc[ll. Ncvertllelcss, solne simple sirnalated images tllm, itldcI)cllclcat ralldoltl sa~llples of tllcsc values with lIave IJCCII gcllcrated atld the ccatroicliag algoritl]m does a Gaussian clistributio~l arc dra~v~l for cacll run, rotated lwrforln fairly \vell it) determinilqg tllcir ccmtcrs. itlto tile colnct-ccntcrccl cartcsiall coordinate systc[n, atld ‘J’IIC use of generated irtlagcs for Llollte ~arlo simulations added to tllc ]Ioltlinal iaitia] state. ‘J’IIc posit ion arid ve- is ltecessarily litnitcd, tllougll, due to tlic large artloullt locity arc IJrolJagated using a ILut]gc-l

‘J’lle frcque]lcy of this ltappcnirlg is UIIkIIOW,II at I)rcsetlt, A ~ ~~ + v(l:R;) Cc)S~) + (if;. ]t:)&,, (32) and IIigltly dci)ellclcrlt 011 dust density Inodcls wllicll arc l;L =: 1: -t -y(~:,}t~)sifl # + (~i.f{~)a,. (33) currently t ]Iougllt to hc accurate only tc] an order c)f l]lag- llitadc. 1:,, tllc Illultiplier to tile true raclius ill 11[]s.. .(32) . Silllalations of tflc A(3S colltro] systcln arc I)citlg pcr- atId (33) is a scale factor to obtaitl hrigllt[lcss shifts as a forltlcd at l,ocfiliecxl hfartill Astronautics; IIowevcr fall I)crcclltage c)f tlir true radius, ‘I’l IC paranlctcr can he var- integration with tllc navigation autol]oltlous trackirlg }vill ied to simulate tllc efrccts of different sllalws arid its effects Ilot be ac.colnplisllcd u])til Novell~hcr of 1997. ‘J’]ius, tllc 01) tile l)ri.glitacss celltroid. ‘J’hc third term it) (32) ar]d sIJacecraft attituclc lnodcl in our currcllt silnulation ol)ly (33) is used to add ralido~n noise tllc sitnulatccl briglltaess iucorj)orates tllc gyro drift ]Ilodcl dcscrit)cd ill ‘J’a})lc 1 cclltroid, lvitll a IIlagrlituclc oltcc again a lwrcentagc of t,llc true IIucleus radius. or is a rando]II saIIIIJlc of Gal]ssia Il noise talicu at cacll ilnagc w’it]l a lIlea]I of zero atid utli( standard deviatio])

(a) Cown,rack Reslllls 600 .,... ,,,, r ,.– —,. .— –,, , -–—– ,

\ ‘.. \ “..., 400 \ ‘J’]Ic WSU](S of a 100 sarnplc hfollte ~;arlo siitlulatior] to . . . \ 1 ““” ““- ...... \ test tlIc nucleus trackiug algorit]lln is SIIOIVII it) l’igurc 6. l“or these ruIIs, the truth state was samI~lcd frolll tllc )ioIII- iltal uuccrtaintics of 8 km crosstracli a[ld 150 k]tl dowl I- track and tllc trut]l attitude was sarnplcd frol]l !Ile gyro error Itlodcd ill ‘1’al)lc 1. ‘1’l]c observations }Ycrc o})taillcd using values of 1“S a~ld l’; of 1.0 slid 0.25, that is, tllc brightness shift was 100% and raildo~n IIoisc 25% of !Ilc radius, rcsI)cctivcly. ‘J’lic true target radius was set at 2.6 kltl, }vllereas t,hc filter assull]cxl a 2.0 kItl radius. 01)- scrvatiotls were takcll startiltg at W-20 Illillutes to \W2 -, lninutcs, with a 40 sccol)d gaIJ starting at \fT-180 scco]ids 0 to accc)ullt for the roll ~[laucuvcr. ]+’igurc G JJlots tllc differ- , –..– ence I)etwecn the true spacecraft positio]l and cstitnatcd I)ositioll at each olmrvatio~l tilllc ill tllc cloJvlltracli, out- of-plalle crosstrack, and implaue crosstrack dircctiolls, for all 100 salnl)lcs.

Qualitatively, it is clear frolu tile plots that tllc initial positiol) error is being rmtlovcd by tllc filter. Sot I]c sirw plc quantitative checks call be made also. lirst, it call Illl!l!!lllllllllllllll tkc noted that tllc c)ut-of-l)lallc crosstracli error ll~ust I)c roughly less tllall l[alf the calnera FOV (1 .75°) at tile tilue of tl)c roll lnancuver iuitiatioll so that. t}lc lIUCICUS !!!,::; .,, . . :,:. . ...;.;;.,,,.;:;.:.:.’ ,.. ,. will swwc}) by ill tllc corrcc.t IIlirror l)lallc. Givctl a ]ioIII- -15 ,,:;:...:::::.. irlal flyby distance of 150 ktu, a 3U ill-l)latlc error I)laccs ., . ...,”” ;2f2(:”1 , the Itlillil[luifl flyl)y at 125 k[n, so Inultil)lyitlg this value -Iota -802 -m -4CM -Zcm 0 tme to encounte. (SCC) by tllc tallgcllt of 1.75° gives about 3.7 ~111. ‘1’lIus, if tlic (c) In-plane Crosslrack ou-of-pla]le error at roll iuitiatioll is greater than 3.7 k[tl, 20 r –——r—. —––-!.—- -- ,– .

Illost of tile liuclcus will be lost,. ‘J’he uI)pcr aud lower 3.7 :: :.::,, 15 ..’...,, klu boundary is lllarkccl as clashed lines ill l“igurc 6(1)), [ aud it is seen that at \V-180 sccollds, tllc error ill all 100 sait II)lcs is less tllall this alnoutlt. 1 ‘1’ILc dowl~tracli crrc)r bc]lavcs slightly diffmcntly. At a far distallcc, the dowlltrack error IIas ])0 cffcc.t 011 calllera l)oitltitlg sillcc the caltlcra l]orcsigllt is eflcctivcly I)aral- lcI to !Ilc downtrack clircction. As tllc colllct al) I)roacllcs, tllc dowlltrack error rapidly rotates i[lto tllc calncra fc)- cal I)lallc until cmcoullter is reached, at wllicll tiitlc tllc ~tlaxirl]utt] error that, call be tolerated is tllc sal[lc as for tile crosstrack, 3.7 km. ‘1’he ellvelopc dcscribccl by tllc 0 I[laxiltlutll error is showli Lky tllc I)aral)olic dasllcd lillcs iu Figure 6(a) (earlier tlla]l }$’-420 SCCOIICIS, it is ofr tllc scale). Agaiu, all 100 saltll)lc errors arc l)CIOW t.llc tllrcsll- l>i~urc (i: I’ositioll l;rrors (Iktilnatccl - ‘1’ruth) for 100 Olcl. Nl;l)te (;arlo Sitllulatiolls ‘

As a final check, a circ.lc describing tllc l)rojcctioli of a spherical IIuclcus into the calnera focal l)latlc }Yas co])l - puted at cacll irllagc. If over IO% of this circle was out, of tile caltlcra 10\T, tile illlage was flagged I)ad and it was assu IIId tlie nucleus }vas lost. Given tl)c llolnillal values for’ (IIC’ Cr’r’or’ sources, oIlly two of the 100 Salllp]cs rut) lost tlIc IIUCICUS acccllding to this crikrio]l.

‘J’llis test assolnd that all illlages wvxc availat)]c aIId cc)uld (a) Nominal (b) Degraded Atbtude 3or I ,, 30 T –. ],C J)I’O1)CI]J’ 1)1’OCCSSCd fOr CCll(I’C,id illfOI’IllatiOll. ]t iS ]ikC’ly 1 tllc)ugll, that itnagcs will bc lost, eitllcr due to tllc sJ)acc- 25 [I’ ! I craft attitude lwiug knockecl ofl”by particle iltlI)acts, noise ill tllc itnages which throw off tllc cclltroidillg, or otllcr factors. ‘J’]lus, a second silnulatioll was l~erforlnml where al)l)roxitnately 40(70 of tl]c itnagm were dclctcd, wllcre tl]c deleted ilnages wcm distrihukd ralldolnly tllroogll t,lIc :5 0 5 :5 0 5 run. ‘1’lIc results slIo\vccJ that even ill this case, tllc al- error (km) error (km) goritl)lo I)erforlnecl successfully, wit II o])ly 3 out of 100 (c) Degraded Navigation 30 , failures as dctcrminecl by tllc circle critcrio]l. [1” :1

A third variatic)ll to test tile sys~clll was to doul)lc tile utlcertainties 011 tile gyro IIlodcl given ill ‘J’al)lc 1. It] this case, tile alnoul[t of of loss duc to tllc circle criteria ~vas 12 out of 100. lloJvcver, tile I)rol)al)ility of .gct~itlg at least solne l)art of tl)e IIucleus is still fairly IIigll. ‘J’llis

can be sem graphically by cxamilling tile llistograln l~lots error (km) in l~igure 7 slid Figure 8. ‘1’hcsc show tile sl)rcad of tllc

cstilnatcd errors in tllc out-of-plane cross track direction I’igurc 7: 1 I istograln of Out-of -l)lalic ~rosstrack l}rrors at tllc itlitiatioll of tllc roll matlcuvcr (W180 see), aI]d (Iktil,iatd - ‘] ’rutl,) at 1{011 Mal,cuver initiation ‘lime error sj)rcad of the dowl]track dircctic]n at tllc ]tomitlal etlcoutlt,er time, for tile IIolninal case ill (a) and degraded attitude ktIolvlcdgc ill (b). ‘1’llc vertical daslied lines sliow tllc tllrcsllold error at wllicll tllc ]Iuclcos is Iilore tllall IIalf out of tl)e camera l“OV. IT] F’igure 6(L)), it call I)e sccti that o]ily one saml)lc was greater tllall tllc tliresllold, itidicat- illg that tile correct orl]ital I)lalle \vas deterlllirled 99% of tile tilllc. III tllc dowlltrack dircctioll, 4 or 5 saltll)lcs were

al)ove tllc tllrcsllold which nlealls that in tllcse cases, tile (a) Nominal (b) Degraded Anwde cllcou]ltcr itllages were lost. ‘1’bus, for al)out $)4%] cases, ,. . ,.–—–. .r––-––, . 1 1 1 l)art of tile lIuclem Jvas still ill tllc l“O\r. 1 1 1 1 1 1 1 A final variatio]l ~vas to douhlc tl]c initial ]lavigat ion {)o- 1 I sitio]l ut]ccrtaitlties. ‘J’lIc results frolll this rLIII arc Plot(ed 1 1 in the histograms ill ~~igure 7(c) and l’igure 8(c). lt) this 1 1 case, tllc roll IIlallcuvrr was accurately detcrltlitled fc)r all .h N .h n; .mi‘rl –1‘ -..rl ___ cases, I)ut tl)c clowlltrack distallcc }vas IIlisscd ill al)out 8 -5 o 5 -5 0 5 1 error (km) UIJerror (km) ~ of tllelll. ‘J’l)is is reflected itl tile circle test., ~vitll 8 out, (c) Degraded Navigation 100 10SSCS. If, tllc grouncl-l)asccl IIavigatioll utlcer(ait]ties .,, .,. -–– –––. arc really this IIigh, llowcver, it is likely that tllc flyby distance lvill he itlcrcascd, lnaJiillg it easier for tile algoritllrll to tort cct the downtrack erlor.

‘i’ ‘J’IMING -5 0 5 10 error (km) IIt addition to being accurate, a I,ritlle collsiclmatioll it] tllc algoritl]lll dcveloI)ltlcllt is tllc ti[ilitlg ltccdcd to j)crforlll l’igurc 8: ]Iistograln of l)o~vlltrack l;rrors (Iktimatcd - all tlie tasks. ‘1’he cc)mputcr ol]hoard S’J’AI{l)US’1’ is a ra- dial ion Ilardctlclld li6000 ~)roccssor caI)al)lc of rull]lillg at sI)ccds of 5, 10, and 20 hfllz (20 h!llz will l)e used duritlg cllcoutlter for the tracking COCIC). ‘1’llis processor is sitlli- lar to tllc l’owcrl’~ ~jloccssor atld uses lIIllclI of tile saillc .

arcllitccturw and code set. ‘1’itlli]lg tests have lJccIi doac at flyl)y of all asteroid ancl colnet [7]. Siacc hotll these fly- I,ockhccd hlartill 011 a 1’1’(3 603 ruallitlg at 66 h!llz to sw I)ys occur ivcll I)cfore S’J’AILI)I-JS’1’ reaches its target, they how fast the algorithm pcrfor[ns. ‘J’hcsc tcs~s SIIOW that Jvill I)rovidc a good realistic test of the systclll. the cllt.irc tracking code colnlJlctcs in aI)l)roximately 2.7 sccoIlds, Ivith the lnajority of tllc time is takcll UI) it] tllc brigllttlcss centroidilkg l)or~iotl [6]. Altlloagll tlic 1t6000 rails at a slolver clock speed, it pcrforlns faster oli floating IJoiat oI)erations, sc) overall tllc tilllitlg degradation frolll l’P~ 603 to H,6000 SIIOUIC1 IIOt be very II IUCII. ‘1’IIc 2.7 sccollcl time meets the requircmcllt, but furtllcr s1)cccI-u1) ‘1’IIC }vorli dcscrit)cd ill this pa~)er was carried out, at the is still l)cirlg looked into. OIlc sitnljle way to do this is Jet l)rol)ulsion l,ahoratory, California lmtituteofrl’ecll- to cmtroid usiag every otllcr, or cwry third IJixel, ill tllc ]lo]ogy,~lllclcrcolltract” witlitllc National Aeronautics aad I)rightllcss lIIomeI)t algorithm. ‘1’llis should ]Iot aflcct tllc Sl)acc Adtnil)istratio]l. cclitroid location at close distances wllrll tllc nucleus will fill up a sul~stantial portion of tile camera frattlc, l)ut will at far distances, so a range Check woulcl ]Iccd to l)C lnadc l)cforc sal)samplill,g.

8 CONCI,lJSIONS [1] l!’. hf. OtYctI a]ld 1{. ill. Vaugllall, “OI)tical Navigation l’rogralll hfatllcll]at icalhlodels” JI’l, internal I)ocatllent ‘1’llc sitlllllatiollst lcscril)ccl arc a good first test of tllc algo- J1’1,-l;hl 314-513, August 9, 1991. rithm to assess its l)erformancc. IIy tllclnsclvcsj llowcvcr, they arc Ilot sufficient to completely lJrovc its rclial)lity. ‘1’hc tlvo lnajor areas where further work IIccds tc] l~c clone [2] J. l{iedel, \f’. Otven, J. Stuw, S. Synnott, and It. are ill colnct visllalizatioll ll~odclitig and sljacccraft atti- Vau.gllaflj ‘K)[)tica] Navigation l)uriag the Voyager iYcp- tude ]Ilodeling. l’or tllc forlncr, work is co]ltilluillg 011 tu]lc lhlcour]tcr” AI AA/AAS Astroclynamics Specialist

devclo])itlg a realistic model of a colnct, co]n])lete wit]i (k)llfcrc]ice, AI AA-90-2877, l’ortlal~d Oregon, Augustl irregularly shaI)ccl nuclei and a coma, ‘1’l)csc ]Icw iinagcs 1900. will tllc]l IN ])rovidcd to tllc ccmtroidcr. Assutnit)g dif- fcrc]lt paralllclers for tile dust clcnsity and otllcr ol)tical l)roI)ertics, the ability of tllc cc[]troidcr to accurakly find [3] S. 1’. Sy]l[lott, A. J. l)onegan, J. I;. l{icdcl, J. A. Stuvc, the nuc]eus can bc tested unclcr diffcrcrlt collditiolls. If “ltlterI)la]lctary OI)tical N’avigatio]l: Voyager Uranus 1;11- tllc silnplc brightness celltroiding is IIot rol)ust cllougll Coulltcl’” , AlAA [;ol~fcrcncc, J1’illiall]s})urg, Virginia, ALI- for tl,r Illajority of cases, more col]ll)licatcd cclltcrfitldillg gust, 1986. algoritlllns need to bc dcvcloI)ed.

hlartiIl Astronautics l)c]lver, ‘J’lie sl)acccraft attitude moclcliag issue is itrlI)ortalit llc- [4] 1;. 1’. IJalldcr, l,ockl)ccd l cause it is yet ullcert.aia lIOW l)article ilnJ)acts will afrect CO, ])crsollal coltlrtl(lliicatio]}. tllc tracking l)erformancc. “J’llis aslmct was crudely sitll- ulated Ly ralldolr~ly deleting some percctltagc of tllc itll- [5] 1;. l). l,a]ldcr ancl S. 1;. Ilolli*r, “Attitucle control ancl ages. I)urillg flight however, tllc losses will I,robal)ly ]iot Survival of tllc S’l’AltI)lJSrl’ Spacecraft l)uring the [;oma l)eclllitca srallclc)lllallcl ltlayl~c collcclltratccl itltllclllitl- l’assagc c)f \f’il&2°, AAS 97-005, AAS Guidance aad utcs surrounding ctlcoulltcr wl]cn tllc dust dctwity will ~olltrol (k~llfcre]lcc, llrcckellridgc, CO, lcbruary, 1997. lje greatest. ‘J’lie ollhoard A(;S will attc)tll)t to returtl tl]c attitude to the correct oricntatio]l atlcr irnl)acts, })ut without couplil)g all attitude control silillllatiolllvitll tllc nucleus tracking algoritllln, it is dif[icalt to detcrlninc if [6] 1). Gingcric]l, I,ockliccd hfartill Astronautics, Ikavcrj tile illlpacts will result ii) loss of tracking, and if so, at CO, ]mrsoaa] collltll(l[]icatioll. what level c) fimr)actstllis llaI)pcns. ‘1’llis test iscurrc]lt]y scl)edulrcl to I)c performed solllctinlc late ill 1997. [71 J. 14;. Ricdcl, S. Illlaskarall, S. 1’. Ss’nuott, S. l). l)c- l’ilially, it slIoLIlcl bc noted that, altllougl] tllc ]iucleus ~:~, \l’. 1;. IIollttlall, 1’. J. l)ultlollt, ~. A. }Iak]l, 1). tracki[lg algoritlltn was developed for tile S’1’AI{I)lJS’1’ IIal], 11. h!. Kcnlledy, (;. J$’. Null, M’. Nf. Owen, R. A. {, missioa, it call be easily applied to ally Inissioll that itlcor- \\rcrtlcr, and 11. G. \f’illiams, “Navigation for the Neiv( /’ , poraks small body flyby. Current plans call for usitlg a hlillclltliuttl: Autol]o~nous Navigation for lkel)-Sl)ace-1”, ]Icarly idc]]tical version of the trackitlg code for tllc h’cw l’rocmxlitlgs 12t11 lliterllatiollal Symposia[u olk lrlight I)y- hlillc]]tlium l’rop;raln’s I)ccl) S1)acc 1 ]nissio]l duritlg its ]Ialtlics, l)arlnstadt, (;cr[nally, Juac, 1997. Sllymn ~l~askara~] is a Scaior II;llgit,ecri]lg Staff IllcItl- bcr of the Optical Navigation Group at tl)c Jet l’rolJul- sion I,at,oratory. IIis current tasks itlcludc LILC dcsigll, clevclo})lllcnt, and tcstillg of the autollolnous Ilavi.gatioll systeIIl for tlIe N’cw Millcnlniut[l l)ccl) Sl)acc 1 IIlissioll. l]} addition, llc is also ml)omiblc for clcvclol)in.g and tcstillg tllc autollolnous nucleus tracking systctll for tllc Srl’Alt- 1)11S’1’ Inission. III tlIe past six years at, J]’],, IIc ~vas also a navigation tcalu ]neml)cr of tile Galileo IIlissioll, and IIas ]mrticil)atcd ill several adva]]ccd studies for radio and ol)tical Ilavigation systcltls for futuw IIlissiolls. l)r. IIhaskarall received his 11. S. and ill. S. at tlic lJlli- vcrsity ofrJ’exas at Austilt, and a I’11. 1). at tllc lJllivcmity of Colorado ill IIoulder, all it) Acrosl)acc II;rlgiaccrillg.

Josq)l] ~. Ilimlcl received a 11.S.in J)llysics a~ld as- trol)llysics frolt~ the IJniversit,y of ~;alifortlia, lr~rillc ill 1978. ltlll[lecliatl:lyjoitlillg tile Voyager Navigation ‘J’cal]l at J])],, l]e lJarticipaicd in all planclary cl)coutltcrs of l)otll spacecraft, and was tile lead c)ptical llavigatiotl cmgitlccr for the Ncptullc flyl~y. After lcadillg tllc op]lav efforts for tltc Ga]ilco asteroicl flybys alId early Galilcall tour, lJc bc- caltlc tllc N’ew hlillcnnium Na~rigatioll ‘lkatn cllicf, direct- ing tile dcwclopmc]lt of a completely autollolllous ol)tical llavigatioll system to guide tllc a~)l)roacll and flyl)y of 1)S1 l,ast ail asteroid, Mars and a colnct. IIe is at] aut]lor of nutl!crous papers oll navigation, ol)tical Iiavigatioll atld ll:i~rigat ioll-rclatccl illlagc proccssitlg tccllllOlogy.

Stc:l)llcll Syllllott rcccivcd a 1’111) dcgrcc fronl tllc Acro- Ilau(ics and Astro][autics departlnmtt at N1l’1’ ill 1974 and Ilas I)CCII in tllc Navigation %ctiou at J]’], ever sitlcc. lIc is currcllt]y suI)crvisor of tllc ol)tical Ilavigatioll grou I) ill that scctioll. lie was ]cadcr of oljtical Ilavigatioll o~ma- tiol~s for both tllc Voyager and Galileo ll~issio]ls, atld IIas hccm involved ia ~nally stuclics of future ])lanctary lnis- siolls and the usc of radio tracking data for Ilavigatioll and I)lallctary scicncc purposes. hlost rccctltly IIc has su- l)crviscd tl]e dcvclo~)mcllt of all autollotnous ol)tical IIaw igatioa systctll for itlterplailctary lllissiolls to be flOWII for tllc first tilnc 01( tllc New Tllillellriiuln l)ccl) Space 1 lllis- sion. l)r. Synaott has discovcmd 13 l)reviously UIIkIIOWIi satellites of the outer l)lancts usiag Voyager iltlagitl.g data. Ilc is a lt~elnbcr of tile Amcricali Astro]iolnical Society aad tllc Itltcraational Astronolnical Ullio]l.