GNSS-Guided Guided Relative Positioning and Attitude Determination for Missions with Multiple Spacecraft

Transcription

1 GNSS-Guded Guded Relatve Postonng and Atttude Determnaton for Mssons wth Multple Spacecraft P.J. Bust, P.J.G. Teunssen, P. Joosten, (Mathematcal Geodesy and Postonng, Department of Earth Observaton and Space Systems of the Faculty of Aerospace Engneerng, Delft Unversty of Technology) 1 Introducton 1.1 Outlne of the Paper P Ths paper wll gve an overvew of what s acheved n the feld of GNSS-guded relatve navgaton for spacecraft and wll ndcate some of the new trends n ths research feld. In 1.2 bacground nformaton about the use of GNSS sensors for mssons wth multple spacecraft le formaton flght, constellaton control and rendezvous s provded, followed by a summary of prevous and future GNSS-guded relatve navgaton mssons n 1.3 and a dscusson on GNSS-based atttude determnaton n 1.4. In secton 2, relatve navgaton s dscussed n more detal. 2.1 provdes a mathematcal model for GNSS observatons at dstrbuted antennas. In the rest of the secton, the mplementaton of ths model for some of the mssons descrbed n 1.3 s dscussed. Secton 3 explores the possblty of GNSS-based atttude for dstrbuted satelltes. In secton 4 actvtes at Delft Unversty of Technology are dscussed, followed by the summary of ths paper. 1.2 Bacground GNSS-guded relatve postonng technques can be appled to a number of mssons wth multple spacecraft such as formaton flght, constellaton control and rendezvous between spacecraft. Currently there s a trend n space msson desgn towards payload dstrbuton. For strategc, economc and operatonal reasons, one satellte, ntegrally carryng all payload, s replaced by a cluster or swarm of smaller satelltes. The functon of the former ntegrated satellte s dstrbuted over the elements of the cluster. Major applcatons areas wll be telecommuncaton and Earth observaton. Dependng of the level of coordnaton between the satelltes of a cluster we refer to ths nd of system as a formaton flght or constellaton control [1]. Multple satelltes belongng to the same msson where the payload s dvded over more than one satellte are often referred to as dstrbuted satelltes. Formaton flyng n general nvolves real-tme, closed-loop control of multple satelltes n autonomous formaton. Thus, formaton flyng requres the control of one spacecraft relatve to one or many other spacecraft and therefore has very strngent requrements for the relatve navgaton and atttude determnaton sensors used. Constellaton control typcally does not requre ths level of autonomy, real-tme coordnaton of the relatve postons or orentatons of multple spacecraft - only that they mantan themselves wthn ther own Presented at GPS/GNSS Symposum, November, Toyo, Japan

2 assgned envelopes wthout collson or changng the overall coverage by the constellaton of the target. The technques requred for formaton flght and constellaton control are smlar to the technques used n rendezvous between spacecraft, where one spacecraft, typcally referred to as the chaser, has to determne ts relatve poston and orentaton towards the target satellte whle approachng ths satellte. The rendezvous s normally followed by docng/berthng between the two spacecraft. Rendezvous, constellatons control and formaton flght depend crtcally on subsystems such as ADCS, absolute and relatve navgaton, satellte cross-ln communcatons and data transfer. The ablty to determne and control the relatve postons, veloctes, and orentatons for a vehcle or fleet of vehcles s only as effectve as the sensors onboard these vehcles. GNSS recevers are potentally able to provde relatve and absolute postonng, tme and relatve and absolute atttude determnaton. 1.3 Overvew of Prevous and Future GNSS Guded Relatve Navgaton Mssons In the US, Europe and Japan, a number of mssons for relatve navgaton have been performed or are currently under development. The very frst msson to use GNSS (GPS) sgnals for relatve navgaton n space was the Japanese ETS-7 msson [2]. The ETS-7 msson conssted of 2 sub-satelltes called chaser and target, and t performed a number of rendezvous and docng experments from 1997 to For ths msson a communcaton ln between the two spacecraft was mplemented, whch transmtted the GPS observaton data from the target to the chaser spacecraft that made real-tme relatve navgaton possble. Other examples of orbtal experments are ORFEUS-SPAS, where a satellte was deployed from the space shuttle and raw GPS measurements were collected from both spacecraft and an accuracy for relatve navgaton of meters was acheved after post-processng, the SNAP-1 and Tsnghua-1 from SSTL, the DART msson whch was the frst real autonomous rendezvous and docng experment, EO-1 and Landsat-7 experment that mars a ey mlestone on the way to autonomous, mult-spacecraft, formaton flyng. Mssons planned for the near future are the ATV, and PRISMA project n Europe, and HTV n Japan. Accordng to [3], there are currently more than 25 formaton flght projects under consderaton n the US. An example of a scentfc msson usng relatve navgaton s GRACE, a LEO formaton consstng of two sub-satelltes whch s n orbt at ths moment, that operates at a separaton of 200±50m at 450m alttude. Examples of applcaton satelltes where precse relatve navgaton s a requrement for msson success are nterferometrc radar mssons such as Terrasar-X (TSX) and TanDEM-X(TDX), and cartwheel msson concepts that explot two or more satelltes to obtan a bstatc confguraton requred for geometrc estmaton of the earth s topography. The (TDX/TSX) msson has been proposed n a contest for new Earth observaton mssons wthn the German natonal space program [4]. It nvolves two almost dentcal satelltes, carryng a hgh-resoluton SAR operatng n the Xband (9.65GHz). The two spacecraft wll fly n a precsely controlled formaton to form a radar nterferometer wth typcal baselnes of 1m, and wll be operated for a perod of 5 years n a nearly constant 514m sun-synchronous orbt wth 97 nclnaton. The prmary msson objectve for ths nd of mssons requres the relatve poston to be nown wthn a 2 mm precson Presented at GPS/GNSS Symposum, November, Toyo, Japan

3 (1-dmensonal) [5]. Recent research at Delft Unversty of Technology has proved, usng orbtal data from the GRACE formaton that ths nd of accuracy s achevable [5]. Techncal detals of the developed method are descrbed n 2.4. When valdatng the GRACE relatve poston solutons from the Extended Kalman Flter (EKF) wth reference observatons, t has been shown that an actual overall relatve poston precson of 0.9 mm (1-dmensonal) s acheved. 1.4 GNSS-base based Atttude Determnaton for Mssons wth Multple Satelltes For formaton eepng, the relatve orentaton of the ndvdual satelltes s of great mportance, not only for the msson objectons such as pontng the formaton towards a specfc target but also for the operatons of the swarm. For nstance, the drag force has a dsturbng nfluence on spacecraft formatons [6]. Even f the spacecraft are dentcal, the drag force experenced by each satellte can be slghtly dfferent. The relatve atttude error causes the spacecraft to have dfferent atttudes wth respect to ther velocty vectors, whch means that the spacecraft wll experence dfferent ballstc coeffcents and therefore a dfferent drag force wll wor on the spacecraft. Hence a spacecraft formaton wth a smaller relatve atttude error s less effected by the drag force dsturbance, thereby lessenng the propulsve force requred to mantan the formaton. If the relatve poston (.e. baselne) between at least 3 GNSS antennas n a specfc confguraton s nown, t s possble to determne the full orentaton of the baselnes from the phase dfference between the observatons at the antennas. From 2003 tll 2005, ths nd of technque was demonstrated very successfully onboard the SERVIS-1 satellte wth a confguraton of 2 baselnes (.e. 3 antennas) [7]. The recently acheved accuracy for relatve postonng between dstrbuted satelltes opens new possbltes for atttude determnaton for ths nd of mssons, whch wll be dscussed n ths paper. Most lely because only lately sub-mm accuracy s acheved for relatve postonng between satelltes, there has not been a lot of research on GNSS-based atttude determnaton for multple satelltes. However for the nd of formatons where the satelltes carry pseudoltes for relatve navgaton above the GPS constellaton some wor has been done. For example [8] descrbed atttude determnaton for formaton flyng mssons n deep space. In [8] t s shown that n order for the formaton above the GPS constellaton, to ntalze autonomously from arbtrary ntal orentatons, each spacecraft would need to carry a total of 6 corner-located receve antennas and two transmt antennas mounted on opposng corners. Ths would provde full sy coverage n all drectons, assumng hemsphercal felds of vew for each antenna. 2 Relatve Navgaton Approaches 2.1 Mathematcal Model for GNSS Observatons at Multple Antennas on Multple Satelltes Fgure 1 shows a constellaton of two satelltes called chaser and target, whch could be ether two satelltes of a formaton or of a rendezvous msson. Both satelltes have a number of GNSS antennas. The fgure shows the relatve dstance between the master antenna on the target satellte and the master (X(Tm-Cm)) and slave antenna (X(Tm-Cs)) on the chaser satellte. Observatons from these antennas are used for precse relatve postonng between the two satelltes, whch provdes the precse vrtual baselne used for the relatve atttude determnaton between the two satelltes. Furthermore the two satelltes use ther own master and slave antennas to determne ther absolute atttude ndependent of the relatve navgaton solutons as the baselne vectors used for Presented at GPS/GNSS Symposum, November, Toyo, Japan

4 absolute atttude determnaton are fxed on the spacecraft. The nomenclature n the fgure related to relatve navgaton and atttude determnaton of the formaton are blue, those related to atttude determnaton of a sngle satellte are red and those related to both are blac. The master antenna s the antenna used for absolute navgaton of the spacecraft and the orgn of the baselne confguraton used for atttude determnaton. From fgure 1 t s clear that the relatve poston vector x between the master antennas of both satelltes s x+ c δ ) + η = R ( tt, C T R Wth R are the pseudorange observatons at the master antenna of the target and chaser, δt s dfference n cloc bas between the recevers at the two satelltes, c s the speed of lght and η s nose. Ths s the non-lnear equaton that s used n relatve navgaton, wth 4 unnowns: three elements of the relatve poston vector and the dfference n the recever cloc bases. For more accuracy the carrer phase observatons can be used nstead of pseudo range measurements for relatve navgaton, whch wll be dscussed next n more detal. A GNSS recever can provde a carrer phase measurement for each antenna. C Subtractng phase measurements from two antennas wll gve a fracton of the carrer phase cycle, whch s the observable for precse relatve navgaton and GNSS-based atttude determnaton. A carrer phase measurement s the dfference between the receved GNSS satellte s carrer phase φ and the locally generated carrer phase φ of the nternal oscllator of the GNSS recever [9]. The carrer phase observable for GNSS satellte can be wrtten as: φ = φ φ + K + I + T + d + D+ e + υ + ε where φ denotes the recever s phase and φ the receved satellte phase at recepton tme t. The term K denotes the ntal nteger ambguty, whch s the number of complete carrer phase cycles that have occurred pror to the sgnal s arrval at the antenna. The term I and T denote onospherc and tropospherc effects. The term d and D refer to the hardware delays n the GNSS recever and the GNSS satellte. e s the multpath error and υ denotes the random (thermal) measurement nose. ε s the satellte s ephemers error. By subtractng two measurements from two antennas, most errors related to the common GNSS satellte wll cancel out of the equaton: Phase dfference φ GNSS Satellte Integer ambguty λk Δr T Δr C l θtm-cm l θt Relatve Poston X(Tm-Cm) θc Ant m Ant s Relatve Poston X(Tm-Cs) Ant m Ant s Baselne bc Baselne bt RF Ln Target Satellte Chaser Satellte Fgure 1 GPS-based relatve postonng and atttude determnaton for dstrbuted satelltes Presented at GPS/GNSS Symposum, November, Toyo, Japan

5 the delay of the GNSS satellte, the tropospherc and onospherc delays f the relatve dstance between the two antennas s small, and the satellte s ephemers error. The measured GNSS carrer phase dfferences are perturbed by measurement nose (ncludng multpath nose) and a relatve phase offset between the two antennas whch s nown as lnebas (hardware delay) f the two antennas are connected to the same recever or a relatve cloc bas f the two antennas are connected to dfferent recevers. Combnng phase measurements from a sngle GNSS satellte s nown as a sngle dfference observaton. The sngle dfference carrer phase equaton s gven as: φ = r K + β + e + υ ms ms ms ms ms ms n whch carrer range dfference r s gven by rms =φm φs where φ m s the carrer dstance from the master antenna to the GNSS satellte and φ s the carrer dstance s from the slave antenna to the same satellte. The nteger K s the number of carrer cycles n the carrer dstance dfference between the master and slave antenna. If the baselne vector s larger than one carrer wavelength, the number of full cycles between the two antennas s unnown. Ths s generally nown as the ambguty problem. The lnebas or relatve cloc bas β ms s the dfference n hardware delays between master and slave antenna (dm-ds) f the antennas are connected to the same recever or a dfference n cloc bas n case of a dstrbuted satellte respectvely. The hardware delays n the GNSS satellte are cancelled out of ths equaton. υ ms s the random measurement nose and e ms s multpath error of the sngle dfference carrer phase measurement. As the sngle dfference equaton s the basc equaton for both precse relatve postonng and atttude determnaton, t s nterestng that the nteger ambguty problem for the atttude estmaton usng the phase dfference between the antennas s the same as for the relatve navgaton. In case a combned atttude and relatve navgaton algorthm s to be developed for dstrbuted satelltes, ths problem would have to be solved only once. It s well-nown that the dstance functon between two satelltes can be approxmated by R T R C where lj s the lne of sght vector to GNSS satellte j. From ths equaton a system of lnear equatons can be derved n whch the dstance between the two master antennas onboard the chaser and target satellte x(tm-tm) and the dfference n the cloc bas for the GNSS recevers are the unnown: δx r= G δt T, = l C Wth G generally nown as the Geometry matrx defned as: l G = 1 If the relatve dstance between the two satelltes becomes very large we wll have to mae a correcton for the dfference n lne of sght vector for the antennas. Now the relatve poston can be estmated by for example the least squares soluton: δx = G t ( δ j x(t m - C m ) -c( δtt, + ε G) G r T 1 T ) For more precse relatve postonng, flterng technques such as a Kalman flter are often appled n combnaton wth a propagaton model for state and covarance between the measurements. For the relatve navgaton between two spacecraft, the Hll equatons are frequently appled. As orgn of these equatons the target satellte s used and ts orentaton s gven by the vector trad {er, et, en}. The unt vector C ) Presented at GPS/GNSS Symposum, November, Toyo, Japan

6 er s algned wth the radal drecton, whle en s parallel to the orbt momentum vector (postve n velocty drecton). The vector et then completes the rght-hand coordnates system. Mathematcally, the trad can be expressed as: e e e R N T = = r r = e rxv rxv N where r and v are the nertal poston and velocty of the target satellte. Advantage of these coordnates s that the poston of the other satelltes s determned towards the target satellte, and therefore the control of the others poston relatve to the target s straghtforward. Next we wll dscuss n more detal how ths mathematcal model s mplemented by some of the mssons dscussed n 1.3. Key parameters for the dscussed mssons are summarzed n table ETS-7 (JAXA, ( Real-tme tme,, Post-processed processed) JAXA (formerly NASDA) has been developng rendezvous and docng technques snce the 90s, especally targetng ths technology to utlze at the nternatonal space staton for docng between the H2A Transfer Vehcle (HTV) and the space staton. The most spectacular test was ETS-7. The ETS-7 experment used 4 space qualfed L1 GPS recevers (2 redundant recevers on each sub-satellte) developed by Toshba. The orgnal goal of the experment was to use the GPS recever untl the two sub-satelltes arrved at a relatve dstance of 500 meter. The conservatve requrement for relatve poston and velocty was 21 m and 5 cm/s respectvely. Because of the relatve small dstance between the satelltes, the dfference n onospherc delay on the observatons at the two sub-satelltes were neglgble. xe R The orgnal code used for the onboard relatve navgaton experment estmated a 8-element state vector (3 elements relatve poston, 3 elements relatve velocty, dfference of cloc bas and cloc drft between the GPS recever of the chaser and target satellte). In the second part of the experment (1999), a carrer phase based relatve navgatonal experment was performed n whch the carrer phase ambgutes estmatons were added to the state vector, and therefore the EKF s state vector dmenson became 14 (8 orgnal states plus 6 carrer phase ambgutes for the 6 channel GPS recevers)[10]. The ntal ambgutes were calculated from the resdual of the sngle dfference carrer phase. ETS-7 made use of the Clohessy-Wltshre soluton of the Hll equatons. Besde GPS also data from the accelerometer was used for state propagaton of the EKF, and made t possble to eep the relatve errors small even when the thrusters were used to correct the approach of the chaser satellte. The state vector was updated every 10 seconds. An nterpolaton model was used to calculate the observatons from the 2 subsatelltes at the same epoch. The ETS-7 experment became a great success, and the experence ganed wth ETS-7 wll be very useful not only for rendezvous mssons but also for future Japanese formaton flght mssons. 2.3 PRISMA (DLR, ( Real-tme) PRISMA s a Swedsh msson and provdes a demonstraton for crtcal technologes related to formaton flyng and In-Orbt-Servcng (rendezvous) [11]. The PRISMA test bed comprses a fully maneuverable mcro-satellte as well as a smaller sub-satellte, smlar to the chaser and target sub-satelltes used for the ETS-7 Presented at GPS/GNSS Symposum, November, Toyo, Japan

7 msson. The msson schedule foresees a launch after 2008 of the two spacecraft nto a low Earth orbt wth an expected lfetme of the msson of at least eght months. Wthn PRISMA, the German DLR has assumed responsblty for provdng a GPS-based onboard navgaton system offerng absolute and relatve orbt nformaton n real-tme. An ntersatellte ln wll be appled to transmt GPS and telemetry data from the sub-satellte to the mcro-satellte and to relay telecommands through the mcro-satellte to the sub-satellte. Sngle-frequency Phoenx GPS recevers have been adopted for the msson. The recevers are commercal-off-the-shelf hardware wth dedcated software developed by DLR. For relatve navgaton, a double-dfference carrer phase dfference between the chaser and target satellte s appled [12]. As was shown n 2.1, dfferencng across recevers reduces broadcast ephemers and onospherc errors, the dfferencng across GNSS satelltes elmnates the user cloc error, but stll, the measurement equaton requres the soluton of the nteger ambguty. An extended Kalman flter wll be employed for absolute and relatve orbt determnaton. The flter estmates the spacecraft poston and velocty components, the emprcal acceleratons, cloc errors and bases along wth nteger carrer phase ambgutes as float values and, potentally, dfferental onospherc path delays. The relatve emprcal acceleratons n radal, along-trac and cross-trac drecton are used to capture any dscrepances or msmodelng of the relatve spacecraft dynamcs. Scalar measurement updates are appled to avod tme-consumng matrx-vector operatons, whch s mportant for real-tme mplementaton of such a large state dmenson of the EKF onboard a spacecraft. In addton to the GPS-based navgaton system, DLR contrbutes the Spaceborne Autonomous Formaton Flyng Experment (SAFE) to the PRISMA msson. SAFE wll demonstrate a fully autonomous, robust constellaton control of spacecraft. SAFE focuses on autonomous and fuel-optmzed formaton flyng at representatve dstances of 100 to 2000 m. SAFE ams at a poston control accuracy of 10/20/10 m (R/T/N 1σ). To ths end, gudance and control algorthms based on an eccentrcty and nclnaton vector separaton strategy wll be employed [12]. Ths ensures a maxmum operatonal safety n contngency cases and s deally suted for future radar mssons whch realze a close formaton flght. 2.4 GRACE-Formaton (TUDelft, Post-processed) The Gravty Recovery and Clmate Experment (GRACE) msson from NASA, conssts of two dentcal formaton flyng spacecraft n a near polar, near crcular orbt wth an ntal alttude of approxmately 500 m [5]. The spacecraft have a nomnal separaton of 220 m. The prmary msson objectve s to measure the tme varyng changes n the Earth s gravty feld, whch s accomplshed by the msson s ey nstruments, the Ka-Band Rangng System (KBR) and the accelerometers. As for as the authors of ths artcle nown, the GPS recever, based on the Blacjac developed by JPL, s not used for real tme relatve navgaton by the satelltes. Recent research at Delft Unversty of Technology has proved that usng orbtal data from the GRACE formaton, 1 mm level of accuracy s achevable for GNSS-based relatve navgaton between spacecraft. A processng strategy that have been developed for relatve spacecraft postonng usng an extended Kalman flter/smoother has proven to wor satsfactorly when tested wth orbtal GPS data. The EKF processes sngle dfference GPS pseudorange and carrer phase observatons and uses (pseudo) relatve spacecraft dynamcs to propagate the relatve satellte state over the observaton epochs. Presented at GPS/GNSS Symposum, November, Toyo, Japan

8 The EKF can resolve and ncorporate the nteger double dfference carrer phase ambgutes, whch s commonly regarded as the ey to precse GNSS based relatve postonng. Estmaton of the nteger ambgutes s accomplshed by the well nown Least Squares Ambguty Decorrelaton Adjustment (LAMBDA) method [13], developed at Delft Unversty. When valdatng the GRACE relatve poston solutons from the EKF wth reference observatons, t has been shown that an actual overall relatve poston precson of 0.9 mm (1-dmensonal) s acheved. There are a number of dfferences between the wor descrbed n [5] and the approaches descrbed before for real-tme, rendezvous mssons. The major dfferences are the use of dual frequency observatons, processng of the measurements n forward and bacward drecton, smoothng of the relatve poston estmates, the actual estmaton of the ambgutes, the propagaton model for the state vector descrbng the relatve poston, the much extended state vector ncludng states for the onospherc delay, and the 5-dmensonal vector of relatve force model parameters. Ths last vector contans the relatve drag and solar radaton pressure coeffcent as well as the relatve emprcal acceleratons. Resoluton of the nteger sngle or double dfference carrer phase ambgutes s commonly regarded as the ey to precse GNSS-based relatve postonng. The LAMBDA method used for nteger resoluton n [5], s an optmzed form of the nteger least-squares (ILS) method. Its effcency comes from an addtonal decorrelaton step pror to the search for the nteger soluton yeldng the smallest squared norm. One major dfference between both methods s the search tme whch s usually sgnfcantly smaller n case of the LAMBDA method. Table 1: Overvew of Sgnfcant Mssons Usng GNSS for Relatve Postonng Msson (Agency) ETS-7 (JAXA) PRISMA(SSC) GRACE(NASA) Relatve navgaton by JAXA DLR TUDelft Relatve dstance (m) Real-tme R R,P S P Post-processed (P) Scheduled (S) Observaton L1 (6) L1 (12) L1+L2 (24) (channels) Rendezvous (R) R R,F F Formaton Flght (F) Kalman flter state (dmenson) p, v, a, b, d (11) + n p,v, b, d (8) and p,v, b, d, na (float soluton) (14) A (float soluton) + potentally ni (11+2n) p, v, a, rd, s, b + 2nA (resoluton) + ni (12+3n) Observatons* L1 PR, DR, CP L1 PR, CP L1 PR, CP L2 PR, CP Integraton of Hll equatons Hll equatons Pseudo relatve Relatve poston by: dynamcs Other sensors accelerometer * PR: Pseudo range, DR: Delta Range, CP: Carrer Phase, p: poston, v: velocty, a: acceleraton, b: cloc bas, d: cloc drft, A: ambgutes, I: onospherc delay, rd: relatve drag, s: relatve solar radaton pressure coeffcent Presented at GPS/GNSS Symposum, November, Toyo, Japan

9 Accordng to [5] the lelhood of the best soluton obtaned from LAMBDA s hgher than any other nteger soluton. In [5], the ambguty resoluton s performed for each of the ndvdual transmttng frequences. Furthermore note that dfferent from the real-tme rendezvous approaches, the relatve cloc drft s not modeled n [5], but only the cloc bas. Propagaton of the EKF requres the ntegraton of the relatve poston, but for the targeted sub-mm accuraces, t was found that there s no drect model descrbng the relatve spacecraft moton wth the requred accuracy. Although the earler mentoned Clohessy-Wltshre equatons, also nown as the Hll equatons, provde a frst order framewor descrbng the moton between two spacecraft, they are not accurate enough for sub-mm applcatons. The relatve moton s thus obtaned from the dynamcal models of the ndvdual spacecraft, hence the pseudo relatve dynamcs. Here, ntegraton of the relatve state s accomplshed by ndependent ntegraton of the two absolute poston states, of the two spacecraft over the same tme nterval and subtractng them n the end. More specfcally, at the a-pror epoch, the absolute state from the reference spacecraft, s obtaned from a reduced dynamc a-pror reference orbt. The (auxlary) state of the other spacecraft s obtaned by addng the updated flter estmate of the relatve state at the a-pror epoch to the state of the reference spacecraft. The absolute force model parameters, requred for ntegraton of the ndvdual spacecraft states, are obtaned n a smlar way. The force model parameters for the master spacecraft are set to realstc predefned values and are ept constant over tme. The (auxlary) force model parameters for the chaser spacecraft are obtaned by addng the relatve force model parameters from the flter state to the ones of the master at the a-pror epoch. Integraton of the ndvdual spacecraft states, leadng to ther predcted values s accomplshed usng a 4th order Runge-Kutta numercal ntegraton method. The predcted relatve state, s constructed as the dfference of the predctons of the absolute states. Of course an EKF wth a state dmenson of 42 (=12+3n wth for n a maxmum number of 10 channels was found to pass the data chec algorthm used n [5]) s stll hard to mplement n a space qualfed CPU, but the wor shows that potentally sub-mm accuracy for GNSS-guded relatve postonng s achevable. More wor s requred before the developed method can be mplemented for space mssons. 3 GNSS-based Atttude Determnaton for Dst strbute rbuted Satelltes 3.1 Mathematcal Model In ths secton we wll ntroduce the possblty to use GNSS for atttude determnaton for dstrbuted satelltes. As can be seen n Fgure 1, the carrer range dfference between master antenna m and slave antenna s of the same satellte s the projecton of the baselne vector b between the two antennas onto the lne-of-sght vector l, whch gves r = b l = b cosθ. Ths s the basc equaton for GNSS-based atttude determnaton. In [7] t was demonstrated that the precse nowledge of the baselne vector s necessary for accurate GNSS-based atttude determnaton. If the dstance between the chaser and target satelltes, a vrtual baselne vector, s nown wth sub-mm accuracy, t could be possble to apply the same technques developed for fxed baselne confguratons on a formaton of satelltes. Ths atttude s also ndcated n fgure 1. The atttude of the baselne vectors of a sngle spacecraft defnes a transformaton from the GNSS reference frame, where the lne-of-sght vector s defned to the body frame where the baselne vector s defned. Ths s dfferent wth the case of dstrbuted spacecraft, where the atttude of the baselne vectors of a swarm Presented at GPS/GNSS Symposum, November, Toyo, Japan

10 of spacecraft defnes a transformaton from the lne-of-sght vector to the relatve poston vector, whch both could be defned n the GNSS reference frame, orgnatng n the master antenna onboard the target spacecraft. For both cases the atttude can be estmated by for example the least squares soluton for the atttude error vector: 1 T ψ = ( H H ) H r where ψ vector, r ) = r b T Al T ) s an atttude error s the dfference between the sngle dfference phase measurements and the expected sngle dfference phase measurements based on the last avalable atttude soluton,, H = l T j.. T x A B.. s the observaton equaton, lj s lne-sght-vector to GNSS satellte j, A s atttude matrx, b s baselne vector, B x s cross product matrx for baselne vector b. Theoretcally t s possble to determne the orentaton of the baselnes between a number of satelltes, even f these satelltes have a sngle antenna. However the absolute atttude of the satellte tself relatve to the antennas can not be determned precsely wth only a sngle antenna (there has been some wor on sngle antenna full atttude determnaton wth coarse accuracy, see for example [14]). If we would le to now the absolute atttude of the target satellte and the relatve orentaton of the other satelltes relatve to the target satellte we wll have to equp all satelltes wth at least 3 antennas n a specfc confguraton. An especally nterestng aspect of the relatve atttude determnaton problem for a multple satellte msson s that, f a method could be developed successfully, the atttude soluton could acheve a very hgh accuracy as ths accuracy depends on the baselne length, j and baselne lengths n satellte formatons can be much longer than the baselnes used for ndvdual satelltes. Another aspect s that the nter satellte ln between the satelltes, whch s necessary to send the GNSS observatons from one satellte to the other, could potentally be used to provde orentaton nformaton, as one vehcle could determne ts relatve atttude by usng the RF transmsson from another vehcle. In the rest of ths secton we wll dscuss the lmted wor that has been done for GNSS-based atttude determnaton for multple satelltes and ndcate future drectons. 3.2 ETS-7 For the ETS-7 msson, an experment was done to use observaton data collected from the GPS recevers onboard the chaser and target satelltes for atttude determnaton whle the 2 satelltes were doced. Results were presented n [15]. Ths experment made use of the fact that the chaser satellte had 2 antennas and the target satellte 1, and therefore ths confguraton of 3 antennas made a 2 baselne system. The baselne lengths were about 2 and 1.4 meter. The experment showed that t s possble to use observatons from dstrbuted satelltes for atttude determnaton, but no attempt was made to determne the relatve poston of the antennas by the GPS observaton. The baselne vectors were determned from the nown dmensons of the spacecraft. 3.3 ORION-EMERALD The ORION-EMERALD msson has the potental to demonstrate GPS-based atttude determnaton on dstrbuted spacecraft as all the 3 mcrosats of the constellaton (one Oron and two Emerald spacecraft) have multple GPS antennas (6 for Oron; 3 on the top face, 1 at the bottom and 2 at the opposte sde when the satellte s earth pontng, and 2 for the Presented at GPS/GNSS Symposum, November, Toyo, Japan

11 Emerald spacecraft) [16]. Unfortunately ths msson was scheduled to be launched by the space shuttle and at ths moment t s unsure f t wll be launched at all. The publcatons about the project ndcate that the researchers are consderng atttude determnaton for the Oron spacecraft tself but not for multple satelltes. 3.4 Future Drectons As descrbed above only recently the nd of accuracy for relatve postonng ( vrtual baselne vector estmaton) between dstrbuted satelltes necessary for atttude determnaton of formaton flyng satelltes became feasble. Therefore ths s stll a relatvely new research feld. Frst of all the mathematcal models for combned postonng and atttude determnaton have to be developed. Ths mples adequately accountng for a wde range of error sources n the hghly dynamc envronment of flyng objects, as well as capturng the nose characterstcs n a stochastc model. Algorthms have to be developed and demonstrated usng software smulatons. If possble also hardware-n-the-loop smulatons, as were developed for GNSS-guded relatve navgaton [17], should be used. In Europe smlar smulators have been developed by DLR and n Japan by JAXA. The next level would be demonstraton of ntegrated GNSS-guded relatve postonng and atttude determnaton by usng data collected n space. 4 Research on Formaton Flght at DEOS, Delft Unversty of Technology Whle algorthms for the GPS based relatve navgaton of two spacecraft n close proxmty have already been studed at Delft Unversty of Technology snce a decade ago [18], at ths moment GNSS guded formaton flght s one of the eystone research topcs of the DEOS group at the faculty of aerospace engneerng, Delft Unversty of Technology. Three Ph.D. students are worng n parallel on ths research. One s loong nto the mplementaton expects of the wor descrbed n [5]. The second s analyzng the performance of dfferent satellte formatons and future sensor technology to map the tme-varyng gravty feld of the Earth. It comprse nvestgatons nto the sutablty and feasblty of varous satellte formatons, the propagaton of errors nto estmated gravty feld parameters, tme and frequency doman senstvty studes, the separaton between ndvdual contrbutors to the tme-varyng gravty feld and ts relaton wth satellte msson parameters. For the thrd the purpose s, the subject of ths paper, to demonstrate the capabltes of formaton flyng usng GNSS for relatve postonng between, and atttude determnaton of, the elements of a formaton of satelltes. 5 Summary and Future Wor Ths paper descrbed prevous and planned mssons for the near future usng GNSS-guded relatve navgaton. It explaned the technques used for relatve navgaton and explored the possbltes to use GNSS-based atttude determnaton technques for dstrbuted satelltes. Some ey technology for formaton flght and rendezvous between spacecraft has been demonstrated n recent years or could be demonstrated n the near future. However, provdng sub-mm accuracy and very relable relatve navgaton between spacecraft s, wth the current technology level, stll very challengng. Especally f ths has to be done n near real tme. Resoluton of the nteger sngle or double dfference carrer phase ambgutes s commonly regarded as the ey to precse GNSS-based relatve postonng and atttude determnaton. The research currently beng performed at Delft Unversty of Technology s expected to have a large contrbuton n ths feld. References [1] J. Letner, F. Bauer, D. Folta, M. Moreau, R. Presented at GPS/GNSS Symposum, November, Toyo, Japan

12 Carpenter, J. How, Formaton Flght n Space: Dstrbuted Spacecraft Systems Develop New GPS Capabltes, February 2002, GPS World [2] I. Kawano, M. Mouno, T. Kasa, T. Suzuu, Frst Autonomous Rendezvous usng Relatve GPS Navgaton by ETS-VII, ION-GPS Conference, Nashvlle, TN, US, September 1999 [3] F.H. Bauer, K. Hartman, J.P. How, J. Brstow, D. Wedow, and F. Busse, Enablng Spacecraft Formaton Flyng through Spaceborne GPS and Enhanced Automaton Technologes, ION-GPS Conference, Nashvlle, TN, US, September 1999 [4] S.D Amco, O.Montenbruc, C.Arbnger, H.Fedler, Formaton Flyng Concept for Close Remote Sensng Satelltes, Advances n the astronautcal scences, 15th AAS/AIAA Space Flght Mechancs Conference, Copper Mountan, Colorado (USA), January 2005 [5] R. Kroes, Precse Relatve Postonng of Formaton Flyng Spacecraft usng GPS, phd-thess, Delft, the Netherlands, March 2006 [6] M. C. VanDye, Decentralzed Atttude Control of a Formaton of Spacecraft, AIAA Regonal Student Conference, Aprl 2004 [7] P.J. Bust, S. Kumaga, K.Hama, Flght Experence of the Integrated Navgaton Unt; Combnng GPS Atttude Determnaton wth Star Sensor Measurements, 2nd ESA Worshop on Satellte Navgaton User Equpment Technologes NAVITEC 2004, Noordwj, the Netherlands, October 2004 [8] K. Lau, S. Lchten, L. Young, B. Hanes, An Innovatve Deep Space Applcaton of GPS Technology for Formaton Flyng Spacecraft, Amercan Insttute of Aeronautcs and Astronautcs AIAA GN&C Conference, July 1996 [9] P. Bust, S. Kumaga, T. Ito, K. Hama, K. Mtan, Development of the Integrated Navgaton Unt; Combnng a GPS Recever wth Star Sensor Measurement, Proceedngs of the 10th Internatonal Conference of Pacfc Basn Socetes (ISCOPS), December, 2003, Toyo, Japan. [10] I. Kawano, M. Mouno, T. Myano, T. Suzu, Analyss and Evaluaton of GPS Relatve Navgaton Usng Carrer Phase for RVD Experment satellte of ETS-VII, ION, [11] Prsma/Prsma.html [12] E. Gll, O. Montenbruc, S. D Amco, S. Persson, Autonomous Satellte Formaton Flyng for the PRISMA Technology Demonstraton Msson, 16th AAS/AIAA Space Flght Mechancs Conference, Tampa, Florda January 22-26, 2006 [13] P.J.G. Teunssen, The Least-Squares Ambguty Decorrelaton Adjustment: A Method for Fast GPS Integer Ambguty Estmaton, Journal of Geodesy, Vol. 70, No. 1 2, 1995 [14] P.J.Bust, Y. Hashda, M. Unwn, and M. Schroeder, Spacecraft Full Atttude Determnaton from a Sngle Antenna; Expermentaton wth the PoSAT-1 GPS Recever, ION-GPS-1998, Nashvlle, Tennessee, Unted States [15] Y. Ishjma, T. Myano, T. Ito, P. Bust, GPS Atttude Determnaton Feld Test and Prelmnary Analyss Results usng On-orbt GPS Data of ETS-VII, Internatonal Worshop on Aerospace Applcatons of the Global Postonng System, Brecenrdge, Colorado, February, 2000 [16] P. Ferguson, F.Busse, B.Engberg, J.How, M.Tllerson, N.Pohlman, A.Rchards, R.Twggs, Formaton Flyng Experments on the Oron-Emerald Msson, AIAA 2001 [17] T. Ebnuma, Precson Spacecraft Rendezvous Usng Global Postonng System: An Integrated Hardware Approach, Dssertaton, Unversty of Texas, August 2001 [18] B.A.C. Ambrosus, E.T. Hesper, K.F. Waer, Applcaton of the Global Postonng System for Hermes Rendezvous Navgaton, Journal of Gudance, Control and Dynamcs, 16, No. 1, (1993) Presented at GPS/GNSS Symposum, November, Toyo, Japan

13 Presented at GPS/GNSS Symposum, November, Toyo, Japan