PRECISION ON-BOARD ORBIT MODEL FOR ATTITUDE CONTROL OF THE ADVANCED LAND OBSERVING SATELLITE (ALOS)

Transcription

1 PRECISION ON-BOARD ORBIT MODEL FOR ATTITUDE CONTROL OF THE ADVANCED LAND OBSERVIN SATELLITE (ALOS) Tknor Iwt Jpn Aerospce Explorton Agency (JAXA), -- Sengen, Tsukub, Ibrk JAPAN, Abstrct: Str-sensor-bsed tttude determnton system estmtes spcecrft tttude wth respect to the nertl coordnte system. When stellte hvng the str-sensor-bsed tttude determnton system mplements geocentrc pontng, t requres stellte s poston nformton reltve to the geocenter. Conventonl Erth pontng stelltes hd crred only low-order onbord orbt models, becuse of ther Erth-sensor-bsed tttude determnton systems nd moderte tttude ccurcy requrements. The Advnced Lnd Observng Stellte (ALOS) tht hd strngent tttude control ccurcy nd tttude stblty requrements nd therefore str-sensorbsed tttude determnton system crred hgh-order precson on-bord orbt model hvng 5 prmeters nd ccomplshed the requred ccurcy by frequent updtes of those prmeters. Ths pper presents the desgn of the on-bord orbt model nd ts flght results. In ddton, the tttude control errors nd tttude stblty performnce tht were nduced by the tttude control reference generted by the orbt model were ssessed. eywords: Orbt Model, Orbt Propgtor, Atttude Control, Atttude Stblty, ALOS, Flght Experence.. Introducton Advnces n msson requrements result n the pursut of more precse tttude determnton nd control. Becuse of ths trend, supported by str sensors dvnces, str-sensor-bsed tttude determnton nd control becomes stndrd, n prtculr, for recent Erth observton stelltes whose reference tttude s geocentrc pontng. Str-sensor-bsed tttude determnton system estmtes spcecrft tttude wth respect to the nertl frme. When stellte hvng the strsensor-bsed tttude determnton system seeks geocentrc pontng, t requres stellte s poston nformton reltve to the geocenter for genertng n tttude control reference frme. And, ccurcy nd stblty of the stellte poston nformton cn be mjor fctor for stellte s tttude control ccurcy nd tttude stblty. On-bord orbt models re one of the pproches for gvng the stellte poston nformton. Conventonl Erth pontng stelltes hd crred only low-order nd therefore low-ccurcy onbord orbt models, becuse of ther Erth-sensor-bsed tttude determnton systems nd moderte tttude ccurcy requrements. Recent Erth observton stelltes hvng str-sensorbsed tttude determnton systems, such s SPOT nd Envst, crred hgher-order on-bord orbt models (typclly th order) thn those of conventonl stelltes nd generted tttude control reference frmes bsed on the orbt models [][]. However, s further mprovement n tttude control ccurcy nd tttude stblty s requred, more precse poston nformton s needed. The Advnced Lnd Observng Stellte (ALOS) developed by the Jpn Aerospce Explorton Agency (JAXA) ws lunched on Jnury, 6 nto sun-synchronous sub-recurrent orbt of pergee lttude of 69 km, nd hs been operted successfully for 5 yers snce then (Fg. ). Ths hgh-resoluton stellte, whose msson ncludes crtogrphy nd dsster montorng by mens of globl collecton of hgh-resoluton Erth mges, hd strngent tttude control ccurcy nd tttude stblty requrements. Therefore, t crred nd mplemented str-sensor-bsed tttude determnton system to ts flght softwre. It propgtes hgh-order precson on-bord orbt

2 model hvng 5 prmeters nd updtes t frequently, for genertng precse tttude control reference frme, nsted of usng ts on-bord PS recever s nvgton results or low-order onbord orbt model. Presented n ths pper re the desgn of the ALOS hgh-order on-bord orbt model nd ts flght dt nlyss. The flght dt nlyss ncludes the ssessment of tttude control ccurcy nd tttude stblty due to the on-bord orbt model. Str Trcker Dt Rely Communcton Antenn 9m PS Antenn mss: kg power: 7 kw Phsed Arry type L-bnd Synthetc Aperture Rdr (PALSAR) Pnchromtc Remote-sensng Instrument for Stereo Mppng (PRISM). On-Bord Orbt Model Advnced Vsble nd Ner Infrred Rdometer type (AVNIR-) m Solr Arry Pddle Fgure. Advnced Lnd Observng Stellte (ALOS) (Left: On-Orbt Confgurton, Rght: Dys before Lunch).. Atttude Control Reference Frme nd Atttude Control Error Erth pontng stelltes requre stelltes poston (nd velocty) nformton reltve to the geocenter n order to generte the tttude control reference frme (.e. orbt frme) to whch the tttude s controlled. If the estmted poston nd velocty nformton hve n error wth respect to true poston nd velocty, the generted tttude control reference frme wll hve n orentton error wth respect to true (.e. del) tttude control reference frme to whch the tttude s supposed to be controlled, s Fg. shows. Ths orentton error, whch ths pper clls the tttude control reference frme error, cuses the tttude control error. Ths tttude control reference frme error often becomes mjor error source for the tttude control error. Note tht the tttude control error conssts of the tttude control reference frme error nd n tttude control error wth respect to the generted tttude control reference frme, nd the ltter conssts of n tttude determnton error nd n tttude control resdul, whch s the dynmcs error tht tttude control could not compenste. Correct Atttude Control Reference Frme True Stellte Poston Estmted Stellte Poston enerted Atttude Control Reference Frme Atttude Control Reference Frme Error Fgure. Stellte Poston nd Erth Pontng Atttude Control Reference Frme

3 .. ALOS Atttude nd Orbt Control System s Approch The ALOS Atttude nd Orbt Control System (AOCS) [] s key subsystem n chevng the precson pontng requrement gven by conflctng msson requrements: globl dt collecton of hgh-resoluton mges, nd therefore, s desgned for precson. In order to ccomplsh precson tttude requrement broken down from the precson pontng requrement, AOCS hs newlydeveloped three-hed precson str trcker nd newly-developed 6-bt-MPU-bsed hghperformnce tttude control computer, mplements n extended-lmn-flter-bsed precson tttude determnton system usng the str trcker nd n nertl reference unt for the frst tme s Jpnese Erth pontng stelltes, nd controls ts tttude usng ths tttude estmte. Fgure shows closed-loop block dgrm of ALOS AOCS. As Fg. shows, AOCS clcultes tttude quternon estmtes wth respect to the nertl frme by n extended lmn flter usng mesurement dt of the str trcker nd the nertl reference unt. Becuse the msson tttude s geocenter pontng, AOCS hs to defne n orbt frme representng the stellte s current poston nd velocty nd control dfference between the stellte tttude nd the orbt frme. In order to defne the orbt frme, the correspondng coordnte trnsformton mtrx (coordnte rotton) from the nertl frme to the orbt frme s necessry. To derve the coordnte trnsformton mtrx, the stellte s current orbt nformton s needed. There re two mjor pproches for estmtng the stellte s rel-tme orbt nformton. One s n pproch bsed on the propgton of on-bord orbt models whch re used n tttude nd orbt control systems of conventonl Erth observton stelltes such s ADEOS nd ADEOS-II. The other s n pproch n whch the stellte crres PS recever nd uses on-bord nvgton results provded by the on-bord PS recever. The pproch bsed on the propgton of on-bord orbt models requres the ground-bsed estmton of prmeters of the on-bord orbt model nd the perodc uplod of them to the stellte. Despte ths opertonl lod, the on-bord orbt model pproch hs benefts n ts smplcty, stblty, nd robustness. Snce ADEOS nd ADEOS-II crred only Erth-sensor-bsed tttude determnton systems, the generton of precse tttude control reference tht ALOS requres ws not necessry. Therefore, lthough ADEOS nd ADEOS-II s low-order on-bord orbt model provded only low ccurcy, the generton of orbt nformton by on-bord orbt models tself s ttrctve becuse of ts smplcty nd flght hertges. On the other hnd, the generton of orbt nformton by PS recever s rel-tme nvgton hs benefts n ccurcy nd reducton of opertonl lod. However, t hs rsk n terms of stble contnuton of the recever s nvgton. If the rel-tme nvgton s nterrupted by externl cuses such s nterference sgnls or recever s problems, the tttude control system hs to suspend ts tttude control nd chnge ts control mode. ALOS crres newly-developed dulfrequency crrer-phse mesurng PS recever. If we ntroduced the PS recever s nvgton results nto the ALOS tttude control loop, t would ncrese complexty of the tttude control loop nd dd rsk tht two newly developed tems of the PS recever nd the str-trcker-bsed precson tttude determnton system re requred to relze specfed functon nd performnce of the tttude control system. In ddton, f we used the orbt frme bsed on the PS recever s stnd-lone nvgton results, t would degrde tttude stblty becuse of rndom errors of the nvgton results. Therefore, we dopted the pproch n whch we do not ntroduced the PS recever s nvgton results to the tttude control loop but mplemented more precse on-bord orbt model by whch AOCS genertes the tttude control reference frme to obtn requred tttude control ccurcy nd stblty. Ths functon corresponds to the block denoted by Reference Atttude enerton n Fg..

4 DRC AVNIR- DRC Coopertve Control AVNIR- Coopertve Control Momentum Mngment - Wheel Speed Est. - Unlodng Lw Note: n Norml Control Mode Roll Control Lw Ptch Control Lw Yw Control Lw Actutor Mngement - Skew Dstrbuton Lw - Wheel Speed Servo Drve Elec.+ Recton Wheel Drve Elec. + Mgnet Torquer Atttude Dynmcs Atttude Det. Mngement - Prec. Att. Det. FDIR - Auto/Cmd. Chnge Ref. Atttude enerton - Control Ref. - Yw Steerng Precson Atttude Determnton System - Str Identfcton - Att. Mesurement - Extended lmn Flter Stndrd Atttude Determnton System - Roll/Yw Att. Det. - Ptch Att. Det. Str Trcker Inertl Reference Unt Erth Sensor Sun Sensor Fgure. Closed-Loop Block Dgrm of ALOS Atttude nd Orbt Control System.. Hgh-Order On-Bord Orbt Model The ALOS Atttude nd Orbt Control Flght Softwre (ACFS) hs n on-bord orbt model tht lwys clcultes the stellte orbt on-bord bsed on prmeters trnsmtted from the ground nd cn derve the Erth center from the clculted orbt elements. The on-bord orbt model conssts of orbt elements to be estmted, constnt coeffcent prmeters determned bsed on nomnl orbt, nd vrble prmeters P to be updted wthn specfc ntervls. In order to obtn more precse stellte orbt elements (.e. stellte poston nd velocty) tht the orbt model estmtes nd to reduce the tttude control reference frme s error contrbuton out of tttude control error, we modeled ALOS orbt moton t 5-th order for both nd P, nd propgtes t on-bord. Perturbton fctors tken nto ccount re seculr nd short-perod perturbtons by the J term, n tmospherc drg perturbton, long-perod perturbtons by the non-zonl terms, nd eccentrcty vector rotton by the J nd J terms. The ALOS on-bord orbt model s gven by ( t) P cos P5t ex ( t) P cos cos Pt cos( P7 ) t P e ( t) P sn sn P t sn ( P ) t P y ( t) P ( t) P 5 ( t) P 6 5 ( t) cos P t 9 6 sn P t P t 8 9 cos sn sn 5 7 ( P7 ) t P sn( P7 ) t P sn( P7 ) t P cos( P7 ) t P ( P ) t P cos( P ) t P 7 e ( t) e( t)cos ( t) e ( t) e( t)sn( t) ( t) ( t) M ( t) x y, where t s n elpsed tme from n epoch t. Usng these equtons, the orbt elements (the semmjor xs, the eccentrcty vector e, e, the nclnton, the rght scenson of scendng node x, nd the rgument of lttude ) re clculted t every control cycle ( ms). y The constnt coeffcent prmeters of the on-bord orbt model represent perturbtons cused by the Erth s grvttonl potentl, s descrbed below, nd re pre-determned by the nomnl orbt elements of the stellte: 7

5 () Short-perod perturbton by J term e 7 J sn J 8 e J ( 5sn ) J 8 8 e 5 J sn cos 6 J e 7 J ( 5cos ) 8 () Long-perod perturbton by non-zonl (, ) term n e r 8 sn 9 n r e n e r () Long-perod perturbton by non-zonl (, ) term 5 n e r 7 cos 5 n e r cos e ( cos cos 9 sn sn e e sn ( 7 sn cos 5 n e r sn 7 sn cos sn () Long-perod perturbton by non-zonl (, ) term n e r 5 cos sn sn ) 9 sn cos n e r 5 5 sn Physcl menng of ech prmeter s summrzed n Tble.,, 7 represent the short-perod perturbton cused by the J term. 8,, represent the long-perod perturbton cused by the non-zonl (,) term,,, represent the long-perod perturbton cused by the non-zonl (,) term, nd nd 5 represent the long-perod perturbton cused by the non-zonl (,) term. On the other hnd, the vrble prmeters P gven below re updted t the regulr ntervls (once per few dys) correspondng to n cceptble orbt estmton error. Physcl menng of ech prmeter P s summrzed n Tble. () Men orbt elements t the epoch P ( t ) P e ( t ) P P 5 e ( t ) y ( t ) P P 6 x ( t ( t ) ) ( t ) M ( t ) )

6 Tble. Constnt Coeffcent Prmeters Perturbton Fctor Short-Perod Perturbton of by J term (Perod: ) Short-Perod Perturbton of e by J term (Perod: ) Short-Perod Perturbton of e x by J term (Perod: ) Short-Perod Perturbton of e y by J term (Perod: ) 5 Short-Perod Perturbton of by J term (Perod: ) 6 Short-Perod Perturbton of by J term (Perod: ) 7 Short-Perod Perturbton of by J term (Perod: ) 8 Long-Perod Perturbton of by (, S) 9 Long-Perod Perturbton of by (, S) Long-Perod Perturbton of by (, S) Long-Perod Perturbton of by (, S) Long-Perod Perturbton of by (, S) Long-Perod Perturbton of by (, S) Long-Perod Perturbton of e x by (, S) 5 Long-Perod Perturbton of e y by (, S) P Fctor C term (Perod: ( ) ) C term (Perod: ( ) ) C term (Perod: ( ) ) C term (Perod: ) C term (Perod: ) C term (Perod: ) C term (Perod: ) C term (Perod: ) Tble. Vrble Prmeters P P Sem-Mjor Axs of Men Orbt Elements t Epoch, P Eccentrcty Vector of Men Orbt Elements t Epoch, e x P Eccentrcty Vector of Men Orbt Elements t Epoch, e y P Inclnton of Men Orbt Elements t Epoch, P 5 Rght Ascenson of Ascendng Node of Men Orbt Elements t Epoch, P 6 Argument of Lttude of Men Orbt Elements t Epoch, P 7 Rte of Chnge of Rght Ascenson of Ascendng Node, d / dt P 8 Rte of Chnge of Argument of Lttude, d / dt P 9 Rte of Chnge of Rte of Chnge of Argument of Lttude, d / dt P t Epoch P t Epoch P t Epoch P Rte of Chnge of Men Eccentrcty Vector, de x / dt P Rte of Chnge of Men Eccentrcty Vector, de y / dt P Reducton Rte of Sem-Mjor Axs, d / dt 5 () Rte of chnge n rght scenson of scendng node nd rgument of lttude by Jterm seculr perturbton d d P7 P8 dt dt () Rte of chnge n rte of chnge of rgument of lttude by tmospherc drg d P9 dt () Argument of non-zonl (, ), (, ), nd (, ) terms t the epoch P ( t ) ( t ) ( t ) ( t ) ( t ) ( t ) P ( t ) ( t ) ( t ) (5) Rte of chnge n eccentrcty vector by J nd J terms de de x P P dt dt P y

7 (6) Rte of chnge n sem-mjor xs by tmospherc drg d P5 dt P,, P6 re men orbt elements t the epoch. P 7 nd P 8 represent the seculr perturbton cused by the J term, P 9 nd P 5 represent the tmospherc drg perturbton, nd P nd P represent the chnge of the men eccentrcty vector. The orgnl model s defned for the true-of-dte nertl frme. However, becuse the on-bord tttude control system performs the tttude determnton nd control wth respect to the J. nertl frme, we use the model nd prmeters for the J. nertl frme n opertons... Bckground The bsc concept of on-bord orbt models les on nlytcl solutons of the generl perturbton technque. Erly works on the nlytcl solutons re found n oz s method bsed on Lgrnge plnetry equtons [] nd n Brouwer s method bsed on Hmltonn plnetry equtons [5] wth the form [6]: e e e LP LP LP e M M nt M LP M SP The orgnl works dd not tke nto ccount tmospherc drg, but lter, vrous extensons to ther methods hve been publshed [6]. The nlytcl solutons re lso extended to opertonl pplctons under the nmes: orbt propgtors, orbt propgton models, or orbt models. Typcl nd sophstcted exmples for ground-bsed orbt propgton nclude the Smplfed enerl Perturbtons (SP) [7][8] tht U. S. Ar Force nd NORAD use nd the Poston Prtls nd Tme (PPT) [9] tht U. S. Nvy uses. SP SP SP t t LP LP SP Orbt models bsed on nlytcl solutons re lso used n spcecrft s on-bord softwre. Jpnese Erth observton stelltes ADEOS nd ADEOS-II used low-order on-bord orbt model of form x( t) x x t, x, e,,,, M, for djustng sun nd Erth sensors mesurements nd for countng n orbt tmer. French Erth observton stelltes SPOT used n on-bord orbt model wth,, 5 n the on-bord orbt model descrbed n Secton. nd updted P,, P for pontng Erth center []. Another Europen Erth observton stellte Evnst used smlr th order model hvng dfferent form []. The full-order (.e. 5th-order) model presented n Secton. ws orgnlly developed nd used for Jpnese optcl nterstellte communcton stellte OICETS to computte ts optcl ntenn s pontng drecton for nterstellte communcton. The sme fullorder orbt model n Secton. ws mplemented from ts development stge to Jpnese hghresoluton Erth observton stellte ALOS. But, the th order settng wth,, 5 SP

8 nd vrble P,, P n the frst 9 months fter the lunch. Then, on October, 6, the fullorder (.e. 5th-order) operton wth non-zero vlues for ll 5 constnt coeffcent prmeters nd ll 5 vrble prmeters ws strted nd hs been contnued..5. Prmeter Estmton nd Updte Frequency The JAXA s orbt dynmcs system clcultes orbt determnton vlues t regulr bss from mesurements of rnge nd rnge-rte, nd obtns orbt predcton vlues by propgtng the orbt determnton vlues nto the future. The updte prmeters of the on-bord orbt model re estmted by lest-squre-method-bsed model-fttng of the orbt predcton vlues for the perod to whch the prmeters re ppled (.e., the perod untl the next updte). Error sources (cll on-bord orbt model estmton error) between orbt (poston nd velocty) estmted by the on-bord orbt model nd true stellte orbt (poston nd velocty) re the followng three: Orbt model error, Orbt determnton error, nd Orbt predcton error. Upon the ALOS development, trde-off of orbt model, model order, nd prmeter updte frequency ws performed n the pont of vew whether estmton error (tttude control reference frme error) of the on-bord orbt model would meet the llocted budget of the tttude control error requrement. As result, the orbt model errors re.7 km for long-trck poston,. km for cross-trck poston,.6 km for rdl poston,. km/s for long-trck velocty,.7 km/s for cross-trck velocty, nd.5 m/s for rdl velocty (Tble ), for the condton of dy ntervl updte, nomnl solr ctvty, nd the orgnl on-bord orbt model t the lunch (.e.,,, 5 nd P,, P5 equvlent to tht of SPOT). These re equvlent to the tttude control error of.8 deg (roll),.57 deg (ptch), nd. deg (yw), whch ndcte suffcent ccurcy s n on-bord orbt model. Further, the on-bord orbt model estmton error tht ncludes the orbt determnton error nd the orbt predcton error s.78 km for the poston error of the long-trck drecton (Tble ) n whch the orbt predcton error s domnntly lrge, compred wth other errors. Ths s equvlent to the ptch-xs tttude control error of. deg, whch gves suffcent mrgn to the tttude control error budget of.95 deg (). The ccurcy study reveled tht the tttude control ccurcy requrement would be fully stsfed f the updte perod of the vrble prmeters ws less thn dys nd the mxmum orbt propgton tme on-bord (elpsed tme snce n epoch) ws less thn 8 hours. Therefore, the orbt determnton s performed on Mondy, Tuesdy, nd Thursdy, nd the updte prmeters of the orbt model whose epochs re Tuesdy UT, Thursdy UT, nd Sturdy UT re trnsmtted to the stellte on Tuesdy, Thursdy, nd Sturdy, respectvely. Ths updte cycle s summrzed n Tble 5. If the solr ctvty becomes mxmum, however, the updte frequency my hve to be ncresed to one dy ntervl t mxmum. Tble. On-Bord Orbt Model Error Orbt Model Error Orbt Model Error Poston Error Velocty Error Atttude Control Error Along Trck.7km.m/s Roll.8deg Cross Trck.km.7m/s Ptch.57deg Rdl.6km.5m/s Yw.deg Tble. Orbt Model Estmton Error nd Atttude Control Reference Frme Error

9 Along Trck Ptch Ech Error Orbt Model Atttude Control Requrement Estmton Error Error Orbt Model Error.7km.78km.deg <.95deg Orbt Determnton Error.69km Orbt Predcton Error Frme Trnsformton Error.km Tble 5. On-Bord Orbt Model Updte Cycle Orbt Determnton Orbt Model Epoch Trnsmsson to Stellte Mondy Tuesdy UT Tuesdy Tuesdy Thursdy UT Thursdy Thursdy Sturdy UT Sturdy.6. enerton of Atttude Control Reference Frme The tttude control reference frme s generted by the followng process. Frst, we convert orbt elements e f of n on-bord orbt model nto n equvlent poston nd velocty vectors n the J. nertl frme. r cos f sn f e r pf r sn f v pf e cos f r e ecos f g g r T r v T v o pf pf coscos sn sn cos cossn sn cos cos sn sn T g pf sn cos cossn cos sn sn coscos cos cossn sn sn cos sn cos Then, drecton cosne mtrx s derved from the poston nd velocty vectors s follows: r o vo ro e T z, ey, ex ey ez, To ex ey ez. ro vo ro Ths drecton cosne mtrx s converted nto quternon q o representng tttude rotton from the nertl frme to the estmted orbt frme specfed by the on-bord orbt model. To T T qo trt o,. ven n tttude estmte quternon q b representng stellte tttude wth respect to the nertl frme, we obtn n tttude error quternon q ob representng tttude rotton from the estmted orbt frme to the stellte body frme by the followng quternon mnpulton: qb, qb, qb, qb, qb qb qb q b q,,,, ob qo, qb qb qb q,,, b, qb, qb, qb, qb, where T q T o qo, qo, qo, qo,, qb qb, qb, qb, qb,. Euler ngles re clculted from ths tttude error quternon s follows (n ths pper, -- rottons re used): o pf pf

10 sn tn q q qob,qob, qob,qob, tn. q ob, qob, For these Euler ngles, ALOS executes -xs ndependent tttude control. q ob, q q ob, q ob, ob, ob, q ob, q q ob, ob, ob, qob, The sme process descrbed bove ws ppled to the clculton of the tttude control reference error (one fctor of tttude control error) nduced by n on-bord orbt model. It ws ppled not only to the trnsformton of orbt elements obtned from n on-bord orbt model telemetry but lso to the trnsformton of quternon correspondng to precson orbt estmte used s true vlue. The tttude control reference error nduced by the on-bord orbt model ws obtned by clcultng the error quternon between the quternon derved from the on-bord orbt model telemetry nd the quternon derved from the precson orbt estmte nd then trnsformng t to the Euler ngles.. Flght Dt Anlyss.. Behvor of On-Bord Orbt Model ALOS AOCS downlnks to the ground -hour-length -sec-ntervl orbt elements out of full-rte ( Hz) on-bord computton results of the on-bord orbt model s prt of low-speed msson dt. Ths secton compres the on-bord orbt model telemetres tht AOCS ctully propgted on-bord wth the precson orbt estmtes tht the ground-bsed precson orbt determnton system (UTS) computed from dul-frequency mesurements of the ALOS PS recever. The ccurcy of the UTS-generted ALOS precson orbt estmtes s.7 m () for dstnce error [] nd s fr better thn the estmton ccurcy of the on-bord orbt model. Therefore, the succeedng nlyss of the on-bord orbt model s propgton results ssumes tht the UTS precson orbt estmtes represent true vlues. A typcl one-dy propgton result (sold lne) of the on-bord orbt model s shown wth correspondng orbt elements derved from the UTS precson orbt estmtes, n Fg.. Ths shows the behvor of the modeled perturbton terms nd verfes tht they represent mjorty of the ctul orbt moton. In Fg., the dfference between the orbt model s orbt elements nd the true orbt elements s very smll nd hrdly dstngushble. Therefore, the dfference of ech orbt element s clculted nd shown n Fg. 5. Ths ssessment ndctes tht the ccurcy of the onbord orbt model s less thn m for sem-mjor xs, e-5 for eccentrcty vector,. deg for nclnton,. deg for rght scenson of scendng node, nd.5 deg for rgument of lttude. In opertons, the vrble prmeters of the on-bord orbt model were updted t bout UT8 hour. Therefore, the frst one thrd of the profles represents dt fter nerly three dy propgton. However, the estmton error of the on-bord orbt model dd not show sgnfcnt chnge before nd fter the updte. Ths s mnly due to very quet solr ctvty of those dys.,,

11 (km) x x e x e y (deg) (deg) + f (deg) Fgure. On-Bord Orbt Model Flght Dt nd True Orbt Elements (UT: to :, November 7, 6, Sold Lne: On-Bord Orbt Model, Broken Lne: True Orbt Elements) (km) e x e y x x Fgure 5. Orbt Element Error Profle of On-Bord Orbt Model Flght Dt (UT: to :, November 7, 6).. Assessment of Atttude Control Accurcy nd Atttude Stblty x - The sme on-bord orbt model flght dt nd UTS precson orbt estmtes ssessed n Secton. re converted to the orbt frmes they defne nd the rottonl component error between the two orbt frmes s trnsformed to Euler ngles. Ths set of Euler ngles represents the tttude control reference frme error cused by the on-bord orbt model estmton error nd consttutes prt of the tttude control error. The result s shown n Fg. 6. Roll nd yw ngle errors of. deg, nd ptch ngle error of. deg re obtned. Further, the obtned tttude error profles re used to clculte tttude stblty. As Fg. 7 shows, the tttude stblty degrdton nduced by 5 the on-bord orbt model stys wthn deg/5sec. (deg) + f (deg) (deg)

12 Ptch Angle (deg) Roll Angle (deg) 5 x x x - x 7 Yw Angle (deg) Tme (sec) x 7 Fgure 6. Atttude Control Reference Frme Error: Atttude Control Error due to On-Bord Orbt Model (UT: to :, November 7, 6) Yw Stblty (deg/5s) Ptch Stblty (deg/5s) Roll Stblty (deg/5s) x x -5 x x -5 x Tme (sec) x 7 Fgure 7. Atttude Control Reference Frme Stblty: Atttude Stblty due to On-Bord Orbt Model (UT: to :, November 7, 6).. 5th-Order On-Bord Orbt Model On October, 6, we uploded set of vlues hvng full degrees-of-freedom (.e. 5th order) for both constnt coeffcent prmeters nd vrble prmeters of the on-bord orbt model nd strted the operton tht would explot full-cpblty of the on-bord softwre to whch the 5thorder orbt model hd been mplemented from the begnnng. The on-bord orbt model error before nd fter the 5th-order settng s shown n Fg. 8, whle the tttude control error due to the onbord orbt model error (.e. the tttude control reference frme error) nd the tttude stblty due to the on-bord orbt model error re shown n Fgs. 9 nd. Spkes slghtly before.5 dys n the plots represent the executon of the 5th-order settng. Fgure 8 suggests tht the 5th-order operton reduced mpltudes of the perodc terms expressed by the prmeters of th nd hgher. The tttude control error profle nd the tttude stblty profle demonstrtes even more sgnfcnt mprovements. More quntttve nlyss ws performed to ssess the mprovements of the tttude control error nd the tttude stblty upon the 5th-order settng, nd the results were summrzed n Tble 6. For three dy dt before nd fter the 5th-order settng, the tttude control error nd the tttude stblty due to the on-bord orbt model were clculted nd stochstclly processed. As Tble 6 shows, the tttude control error ws reduced nd the tttude stblty ws mproved by to 5 %.

13 (km) e x e y x x (deg) + f (deg) x - (deg) Fgure 8. On-Bord Orbt Model Error before nd fter 5th-Order Settng (October 9 to November, 6) Ptch Angle (deg) Roll Angle (deg) 5 x x x - x 7 Yw Angle (deg) Tme (sec) x 7 Fgure 9. Atttude Control Error due to On-Bord Orbt Model Error before nd fter 5th- Order Settng (October 9 to November, 6) Yw Stblty (deg/5s) Ptch Stblty (deg/5s) Roll Stblty (deg/5s) x x -5 x x -5 x Tme (sec) x 7 Fgure. Atttude Stblty due to On-Bord Orbt Model Error before nd fter 5th-Order Settng (October 9 to November, 6)

14 Tble 6. Summry of Atttude Control Error nd Atttude Stblty before nd fter 5th- Order Settng (October 9 to November, 6) Before 5th-Order Settng After 5th-Order Settng Evluted Dt October to 6, 6 November to 6, 6 Atttude Control Roll.5. Error Ptch..75 (deg, ) Yw... Conclusons Atttude Stblty (deg/5s, ) Roll.7e-5.756e-5 Ptch 6.88e-5.e-5 Yw.568e-5.985e-5 The stelltes tht perform precse Erth-pontng control by precson tttude determnton system usng str trcker requre the generton of precse tttude control reference frme. As the Advnced Lnd Observng Stellte (ALOS) msson requres more precse tttude control ccurcy nd tttude stblty, we mplemented 5th-order precson on-bord orbt model nd updted the model reltvely frequently nd met the ccurcy requrement. Flght dt nlyss showed tht the 5th-order orbt model estmted most prt of the ALOS orbt moton nd obtned the mprovement of to 5 % over the ntl th-order settng. 5. References [] rc-juln,. nd Merno, M., EPS/METOP Techncl Note on Orbt Predcton, MV- EPSFDS-TN-, MV S.A., Spn, 997. [] Rnt, P., Vl Serr, S., Frgnol, D., nd Desre, P. A Str Sensor Bsed AOCS for Envst, Proceedngs of nd ESA Interntonl Conference on NC, ESA ESTEC, Noordwjk, Netherlnd, 99. [] Iwt, T., et l., Precson Atttude nd Orbt Control System for the Advnced Lnd Observng Stellte (ALOS), AIAA udnce, Nvgton, nd Control Conference, AIAA--578, Austn, U.S.A.,. [] oz, Y., The Moton of Close Erth Stellte, The Astronomcl Journl, Vol. 6, No. 7, pp , 959. [5] Brouwer, D., Soluton of the Problem of Artfcl Stellte Theory wthout Drg, The Astronomcl Journl, Vol. 6, No. 7, pp , 959. [6] Vlldo, D., Fundmentls of Astrodynmcs, rd Edton, Mcrocosm Press, 7. [7] Hoots, F. R., Roehrch, R. L., nd elso, T. S., Models for Propgton of NORAD Element Sets, Spcetrck Report No., 988. [8] Fonte, D. J., et l., Comprson of Orbt Propgtors n the Reserch nd Development oddrd Trjectory Determnton System, Proceedngs of the AAS/AIAA Astrodynmcs Conference, AAS 95-, pp , 995. [9] Schumcher, P. W. Jr., nd lover, R. A., Anlytc Orbt Model for U. S. Nvl Spce Survellnce: n Overvew, Proceedngs of the AAS/AIAA Astrodynmcs Conference, AAS 95-7, pp , 9.