GPS RTK-Based Attitude Determination for the e-pop Platform onboard the Canadian CASSIOPE Spacecraft in Low Earth Orbit

Transcription

1 GPS RTK-Based Attitude Determiatio for the e-pop Platform ooard the Caadia CASSIOPE Spacecraft i Low Earth Orit Do Kim ad Richard B. Lagley Departmet of Geodesy ad Geomatics Egieerig, Uiversity of New Bruswick, Caada BIOGRAPHY Do Kim is a seior research associate i the Departmet of Geodesy ad Geomatics Egieerig at the Uiversity of New Bruswick (UNB). He has a achelor s degree i ura egieerig, ad M.Sc.E. ad Ph.D. degrees i geomatics, all from Seoul Natioal Uiversity. Dr. Kim has ee ivolved i GPS research sice 1991 ad active i the developmet of a ultrahigh-performace RTK system. He received the Dr. Samuel M. Burka Award for 2003 from The Istitute of Navigatio (ION). Richard B. Lagley is a professor i the Departmet of Geodesy ad Geomatics Egieerig at UNB, where he has ee teachig ad coductig research sice He has a B.Sc. i applied physics from the Uiversity of Waterloo ad a Ph.D. i experimetal space sciece from York Uiversity, Toroto. Prof. Lagley has ee active i the developmet of GPS error models sice the early 1980s ad has ee a cotriutig editor ad columist for GPS World magazie sice its iceptio. He is a fellow of the ION ad a associate fellow of the Royal Istitute of Navigatio. He shared the ION 2003 Burka Award with Do Kim. INTRODUCTION Over the last decade, GPS receivers have ee successfully used for attitude ad orit determiatio o microsatellites ad miisatellites i low Earth orit [Purivigraipog et al., 1999; Purivigraipog ad Uwi, 2001; Cross ad Zieart, 2002]. As a result, it has ee a tred i space missios to use cost-effective GPS receivers for space sciece ad egieerig experimets. The use of commercial compoets for spacecraft GPS receivers has ee experieced o some other space missios. However, it is so far restricted to low-grade sigle-frequecy receivers ad a limited rage of correlator chipsets. The use of a fully commercial, geodetic grade dual-frequecy receiver with o heritage i space applicatios has ee recetly cosidered for space missios [Lagley et al., 2004; Moteruck et al., 2006]. A rapid, precise ad reliale GPS-ased attitude determiatio system for satellites should e ale to compete with existig space-deployed attitude systems such as star sesors. The precisio of spacecraft GPS attitude determiatio is mostly at the degree level [Campaa et al., 1999; Giulicchi et al., 2000]. Ufortuately, due to the limited resources of microsatellites, most of the methods discussed i the papers would e difficult to ru effectively i real time. I terms of attitude precisio attaiale from GPS attitude determiatio system, multipath ad the aselie legth etwee the ateas will e the pricipal limitig factors. I this paper, we itroduce our approach for a real-time GPS attitude determiatio system usig commercial, geodetic grade dual-frequecy GPS receiver, developed for the Ehaced Polar Outflow Proe (e-pop) platform ooard the Caadia CASSIOPE (the CAScade Smallsat ad IOospheric Polar Explorer) spacecraft to e flow i low Earth orit. SPACECRAFT DESIGN CASSIOPE is a Caadia satellite scheduled for lauch i It is a hyrid missio desiged for a wide rage of tasks icludig space-ased commuicatio ad oservatios of the Earth s atmospheric eviromet. A dedicated suite of eight scietific istrumets, called e-pop, will ivestigate space storms i the upper atmosphere ad provide GPS-ased avigatio iformatio. GAP (GPS Attitude ad Profilig) is oe of the eight scietific istrumets. Figure 1 shows a cocept view of the CASSIOPE spacecraft.

2 Figure 1. Coceptual view of the CASSIOPE spacecraft. GAP Desig The desig of GAP is ased primarily o the use of commercial-off-the-shelf (COTS) GPS receiver techology. Early i the missio desig, it was decided to ase the GAP istrumet o a COTS dual-frequecy receiver rather tha a space qualified oe. The decisio was ased primarily o ecoomics. NovAtel s OEM4-G2L dual-frequecy receivers have ee selected as the cadidate hardware for this proect. A series of tests were carried out to help determie the viaility of usig COTS GPS receivers for a satellite missio [Lagley et al., 2004]. The GAP istrumet has ee desiged ad costructed i collaoratio with Bristol Aerospace. Figure 2 shows the fuctioal lock diagram of the GAP istrumet. The iterface card used to iterface the e-pop data hadlig uit with the receiver cards is ased o Bristol Aerospace cotroller architecture with spaceflight heritage ad a added FPGA (Field Programmale Gate Array). Some other compoets (such as patch ateas) also have spaceflight heritage. LNA LNA GPS #0 GPS #1 DATA HANDLING UNIT LNA GPS #2 INTERFACE CARD GPS #3 (SPARE) GPS #4 (GAP-O) SPACECRAFT CONTROLLER LNA LNA LNA/ SWITCH BOX Atea Cotrol GAP POWER SUPPLY CARD POWER CONTROL UNIT Figure 2. GAP istrumet fuctioal lock diagram. A total of five receivers o the satellite will e used for high precisio avigatio, attitude determiatio ad radio occultatio measuremets. The four ateas to e used for avigatio ad attitude determiatio, together with their associated equipmet called GAP-A, will e mouted o the zeith-facig side of the spacecraft ad oe atea for occultatio, together with its associated equipmet called GAP-O, o the ati-ram (i.e., ati-velocity) side of the spacecraft. GAP-A collects ad processes simultaeous oservatios from three of the GPS receivers. As illustrated i Figure 3, four receivig ateas icludig oe spare will e mouted o the spacecraft. These ateas are mouted i locatios to

3 l 2 = 1049 mm miimize multipath reflectios ad maximize the aselie legth etwee the ateas. GAP-O cosists of a dual-frequecy GPS receiver, with a switchale spare, to collect GPS occultatio data at a 20 Hz data rate sufficiet for ioospheric tomography sciece. RAM GPS0 GPS3 x γ = o l 1 = 1601 mm y GPS2 GPS1 Figure 3. GAP-A atea/aselie geometry. GAP-A Performace Requiremet The GAP-A experimet will serve a umer of purposes. It will provide a accurate asolute time referece, spacecraft positio ad velocity iformatio to the data hadlig uit. Also, it will perform real-time spacecraft 3-axis attitude determiatio. The performace requiremet of the GAP-A is summarized i Tale 1. More precise results will e achievale y post-processig the dow-liked data; e.g., 0.5 degree accuracy for post-processed attitude. Tale 1. GAP performace requiremet. Descriptio Accuracy (3σ) Remark Positio 10 m Velocity 0.25 m/s Real-time Time 1 µsec Attitude 5 deg Real-time 0.5 deg Post-processed RTK-BASED ATTITUDE DETERMINATION The DD (doule-differeced etwee satellites ad receivers) carrier-phase oservatios are used for spacecraft attitude determiatio i our approach while the DD pseudorage oservatios are used for estimatig omial aselie compoets ad float amiguities. As illustrated i Figure 3, GPS0 is cosidered as the ase statio while GPS1 ad GPS2 are cosidered as the rovers. GPS3 is the spare atea. At each epoch, the avigatio solutio of GPS0 is take as the Earthcetred Earth-fixed (ECEF) positio of the spacecraft. The system is ased o the geeral purpose UNB RTK (real-time kiematic) egie which has ee used for various scietific ad egieerig applicatios [Kim ad Lagley, 2003; Kim et al., 2003]. It icludes differetial carrier-phase amiguity resolutio ad positio/velocity estimatio. The attitude of the spacecraft is determied y estimatig the rotatio matrix etwee the ody-fixed ad ECEF frames usig two aselie vectors (i.e., GPS1-GPS0 ad GPS2-GPS0) ad oe vector orthogoal to them (i.e., the cross product of the two aselie vectors).

4 The Oservatio Model The liearized DD carrier-phase oservatio model for sigle- ad short-aselie (< 2 m) applicatios is give as: yi, = A x+ λini, + ei,, Cov ei, = Q y (1) i, ad ρ ρ ρ ρ ρ ρ x x y y z z A = at x, 0 (2) m 0 m 0 m 0 ρ ρ ρ ρ ρ ρ x x y y z z where y is the vector of DD carrier-phase oservatios i distace uits; x is the vector of ukow parameters icludig the aselie compoets (x, y ad z); A is the desig matrix correspodig to x; x 0 is the vector of omial aselie compoets; ρ is the geometric rage etwee a satellite ad a rover; superscript m ad suscript idicate a satellite ad a rover, respectively; superscript 0 idicates the referece satellite for the DD operatio; N is the vector of DD amiguities; λ is the wavelegth of the carrier-phase oservatios; e is the oise vector icludig multipath ad receiver system oise (here, the residual orit error, ad tropospheric ad ioospheric delays are egligile); Cov[ ] represets the variacecovariace operator; Q y is the variace-covariace matrix of the oservatios; ad suscript i idicates the type of carrierphase oservatios (e.g., L1, L2 or widelae). For the real-time attitude system, the widelie carrier-phase oservatios are used i our approach. O the other had, the L1 ad L2 carrier-phase oservatios will e used for post-processed attitude determiatio to attai more precise attitude results. Normally, widelae amiguity resolutio is easier ad more reliale compared with that for L1 ad L2. More detailed reasoig for this approach is discussed i the Validatio sectio elow. The Baselie Costrait Whe calculatig spacecraft attitude, the aselie legth etwee ateas (a pair cosistig of the ase ad a rover) is assumed to e costat ad kow. By liearizig the expressio for the aselie legth, we ca otai a costrait o the ukow parameters as: ad 2 l = hx + ε, Var ε = σε, (3) l l l h = at x 0 (4) x y z where l is the aselie legth; x is the vector of ukow parameters icludig the aselie compoets (x, y ad z); h is the desig matrix correspodig to x; x 0 is the vector of omial aselie compoets; ε is the error i the kow aselie legth; Var [ ] represets the variace operator; a rover (that is, a aselie associated with the rover). 2 σ ε is the ucertaity of the aselie legth; ad agai, suscript idicates Oce the aselie legth ad its ucertaity are kow, therefore, it is possile to treat the aselie costrait as a additioal measuremet availale with a certai ucertaity at every epoch. The, the augmeted oservatio model is give y

5 yi, A λii ei, ei, Q y i, = x + Ni, +, Cov =, (5) 2 l h 0 ε ε σ ε where I is a idetity matrix; ad 0 is a zero row vector. We use this augmeted oservatio model i the susequet amiguity resolutio. Amiguity Resolutio Least-squares estimatio with iteger costrait for the amiguity parameters is referred to as a iteger least-squares prolem. The oective fuctio to e miimized i the iteger least-squares prolem, Ω, is give as [Euler ad Ladau, 1992; Teuisse, 1995]: ˆ ˆ, m Ω = N N Q N N with N, (6) T -1 ( ) Nˆ ( ) i, i, i, i, i, i, i, where ˆN is the vector of float amiguity estimates; N is the vector of iteger amiguity cadidates selected i the amiguity search process; Q is the variace-covariace matrix of the float amiguity estimates; is the set of itegers; m ˆN is the umer of DD carrier-phase oservatios; ad agai, suscripts i ad idicate the type of carrier-phase oservatios ad a rover, respectively. Assumig that a search process for amiguity parameters has ee estalished, amiguity cadidates ca e selected i the process. The, we have to carry out the same procedure o each cadidate sequetially util o amiguity cadidate remais. The, our goal is to fid the amiguity cadidate that miimizes the oective fuctio i Eq. (6). Validatio The UNB RTK egie resolves carrier-phase amiguities usig sigle epoch oservatios, which meas istataeous epoch-y-epoch amiguity resolutio. Due to the limited resources of the spacecraft, maily power availale for the realtime attitude system, its operatio may take place oly over a short time period (perhaps, for a few tes miutes or so). I this case, a filterig techique requirig a log covergece time for amiguity resolutio is ot a appropriate approach. Istead, the carrier-phase amiguities eed to e resolved istataeously at the curret epoch. Compared to the covetioal filterig techiques such as a Kalma filter ad a sequetial least-squares estimator, the istataeous epoch-y-epoch amiguity resolutio may ot always provide reliale solutios. I fact, the amiguity cadidate that miimizes the oective fuctio i Eq. (6) does ot always guaratee correct amiguities if usig sigle epoch oservatios. To improve the reliaility of amiguity resolutio i our approach, the followig criteria for validatio are used: Baselie legths: l = x, = 1,2, (7) Ier agle etwee two aselie vectors: γ cos x x =, (8) x1 x2 where l ad γ are kow values. The amiguities will e cosidered as correct oes if oth criteria are satisfied with a certai ucertaity. I the real-time attitude determiatio system, the widelae carrier-phase oservatios are used for amiguity resolutio as previously metioed. This is also to improve the reliaility of amiguity resolutio. Attitude Determiatio The avigatio frame (-frame) is defied as a local geodetic frame which has its origi coicidig with that of the sesor frame, with the x-axis poitig towards geodetic orth, z-axis orthogoal to the referece ellipsoid poitig dow, ad y- axis completig a right-haded orthogoal frame (i.e., the orth-east-dow system). O the other had, the ody frame (frame) is defied as a orthogoal axis set which is aliged with the roll, pitch ad headig axes of a vehicle (i.e., forwardtrasversal-dow system). A rotatio matrix C from -frame to -frame ca e defied as:

6 cosθ cosψ cosφsiψ + siφsiθ cosψ siφsiψ + cosφsiθ cosψ C = cosθ siψ cosφcosψ siφsiθsiψ siφcosψ cosφsiθsi ψ + +, (9) siθ siφcosθ cosφsiθ where φ, θ ad ψ are the three Euler agles; i.e., roll, pitch ad yaw, respectively. The, the Euler agles ca e determied from C y the followig equatios: φ = ata2( c 32, c 33 ) c θ = ta c 31 ψ = ata2( c 21, c 11 ), where c ( 1 i, 3) i is the (i,)-th elemet of ay oe aselie i the -frame ad -frame are related y ( ) 1,,,,, (10) C ad ata2 is a four quadrat iverse taget fuctio. The coordiates of x = C x or x = C x = C x, = 1, 2. (11) As illustrated i Figure 4, if the third aselie vector is defied as the vector orthogoal to the two aselie vectors x ad x simultaeously; i.e., 1 2 x = x x ad x = x x, (12) 3, 1, 2, 3, 1, 2, the we have X = C X C = X X, (13) 1 where X = x1, x2, x3, ad X = x1, x2, x 3,. (14) x = x x 3, 1, 2, C x = x x 3, 1, 2, x 2, x 2, x 1, x 1, Figure 4. Attitude determiatio.

7 Ufortuately, the rotatio matrix prolem ca e resolved if we trasform ito C usig Eq. (9). Issues o Iitializatio C otaied y Eq. (13) may ot satisfy the orthogoality ad ormality coditio. This C ito the Euler agles usig Eq. (10), ad the trasform the Euler agles agai To otai the desig matrices i Eqs. (2) ad (4), A ad h, the vector of omial aselie compoets x 0 should e determied. As the geometric rage ρ is typically over 20,000 km, the desig matrix A is ot sesitive to the errors i the omial aselie compoets uless the errors are very large. O the other had, the desig matrix h is very sesitive to the errors i the omial aselie compoets due to the short-aselie coditio (< 2 m). This ca degrade the performace of amiguity resolutio i our approach. To improve its performace, therefore, we have to reduce the errors i the omial aselie compoets. Three situatios ca e cosidered: Ustailized mode: Whe the spacecraft is i maeuver, the pseudorage oservatios costitute the oly iformatio to determie the omial aselie compoets. As the errors i the pseudorage oservatios ca e as large as up to a few metres due to multipath ad oise, the desig matrix h may ot e correctly derived. This may result i wrog amiguity resolutio. To avoid this situatio, the aselie costrait i Eq. (5) should e de-weighted. Stailized mode: Whe the spacecraft is stailized i space, the velocity estimates at GPS0 ca e used to determie the omial aselie compoets as illustrated i Figure 5. The omial aselie compoets ca e determied y the geometry of spacecraft velocity ad aselie vectors. Full attitude mode: Whe spacecraft attitude iformatio is availale from previous epoch solutio, the omial aselie compoets ca e directly determied usig Eq. (11). N v RAM α β GPS0 x γ y GPS2 GPS1 Figure 5. Spacecraft velocity ad aselie vector geometry. For amiguity resolutio, the float amiguities ad their variace-covariace matrix should e determied i Eq. (6). Cosiderig the limited resources for the real-time attitude system, we have adopted a very simple approach to estimate them. The float amiguities ca e estimated usig the pseudorage ad carrier-phase oservatios at the curret epoch as: ön i, = 1 λ i ( P i Φ i ), (15)

8 where P ad Φ are the DD pseudorage ad carrier-phase oservatios, respectively. Also, the variace-covariace matrix of the float amiguity estimates ca e derived y propagatig the variace of the pseudorage ad carrier-phase oservatios availale from the receiver data log as: QN ö = 1 Q i, 2 λ Pi + Q Φi i ( ), (16) where Q Pi ad Q Φi are the variace-covariace matrices of the DD pseudorage ad carrier-phase oservatios, respectively. CONSIDERATIONS FOR 24-BIT PROCESSOR The desig of the GAP istrumet iterface is cetered o Bristol Aerospace cotroller architecture with spaceflight heritage; e.g., the Motorola DSP56309 ad the Actel A54SX72A FPGA. The digital sigal processor (DSP) will work i couctio with the FPGA to provide overall cotrol of the istrumet. The DSP will cotrol the istrumet data ad address us. The FPGA will act as the data iterface etwee the DSP ad most other iteral ad exteral devices. As the Motorola DSP56309 is a 24-it precisio DSP, all ANSI C data types are supported, except doule ad log doule, oth of which are evaluated as floats [Motorola, 1999; Taskig, 2002]. Uder this restrictio, we were faced with oe maor prolem i developig the real-time attitude determiatio software. To otai avigatio ad attitude solutios, raw GPS data should e read. Ufortuately, may GPS-related parameters ad oservatios eed to e represeted i douleprecisio. Therefore, we had to write software to covert doule-precisio variales ito sigle-precisio oes. To accomplish the goal, we used the followig approaches: Avoid direct use of doule-precisio variales i floatig poit operatio. If data logs associated with the satellite ad receiver positios are availale from the receiver output, we ca avoid doule-precisio computatio relevat to the satellite ad receiver positios sice these are of sufficiet precisio for our eeds. Perform it-wise operatio o the doule-precisio carrier-phase oservatios to separate them ito the iteger ad fractio parts (Figure 6). The, execute doule-differecig etwee satellites ad receivers for the iteger part as well as the fractio part. Later, comie the doule-differeced iteger ad fractio parts. This maipulatio will result i small sigle-precisio values. Sig (1 it) Biased Expoet (11 its) Matissa (52 its) s1 e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e m1 m2 m3 m4 m5 m6 m7 m8 m9 m10 m11 m12 m45 m46 m47 m48 m49 m50 m51 m iteger PRN Measuremet fractio PRN Measuremet Figure 6. Doule-precisio floatig poit format. The NovAtel OEM4 receiver group is capale of geeratig may differet types of data logs [NovAtel, 2003]. For RTK processig, we ormally use two data logs, RANGECMP (Message ID: 140) ad RAWEPHEM (Message ID: 41). RANGECMP is the compressed versio of the RANGE log (Message ID: 43) that cotais the chael measuremets for

9 the curretly tracked satellites. The RAWEPHEM log is the raw ephemeris log that cotais the raw iary iformatio for suframes oe, two ad three of the satellite avigatio message with the parity iformatio removed. Usig these data logs, we ca compute satellite ad receiver positios at a give epoch. Ufortuately, the computatio ivolves doule-precisio floatig poit operatios. To avoid direct use of doule-precisio floatig poit operatios, we use the SATXYZ log (Message ID: 270) for satellite positio i ECEF Cartesia coordiates. Also we use the PSRXYZ (Message ID: 243) ad PSRPOS (Message ID: 47) logs for receiver positio i ECEF Cartesia ad local geodetic coordiates, respectively. PERFORMANCE TEST To demostrate the capailities of the attitude software, three differet hardware systems were used as GAP software test eds, icludig a laptop computer, the Bristol SPP (System Platform Processor) cotroller, ad the GAP iterface card EM (Express Module). The Bristol SPP cotroller is a multipurpose cotroller oard developed for soudig rocket missios. It features a Motorola DSP56309, 128 KB SRAM (Static Radom Access Memory) memory, Flash Memory, ad two RS-232 serial ports. The GAP iterface card EM is ased o the Bristol STARS cotroller architecture with added FPGA. As illustrated i Figure 7, a 3-axis motio tale was uilt usig stepper motors ad stepper motor cotrollers (Potech STP100). Also, a Etheret-to-serial cotroller (Sollae EZL-400s) was itegrated i the test ed. This add-o device ealed the motio tale to e accessed ad cotrolled from a remote place. The rotatio agles measured y each stepper motor ca e used as the referece of attitude solutios computed usig the three GPS receivers. To accomplish this ed, the stepper motors ad GPS receivers should e sychroized i time. This has ot ee completed yet. GPS Atea 3 or 4 GPS ateas o the 3-axis rotatig plate Roll Axis Geared stepper motor Pitch Axis Yaw Axis Geared stepper motor Geared stepper motor Stepper Motor Cotrollers Wireless Etheret Etheret WAN/LAN Etheret Etheret-to-Serial Cotroller Figure 7. GAP software test ed cofiguratio. To test the attitude software while commuicatig with up to three GPS receivers, a real-time attitude determiatio test was performed o a laptop computer (Petium 4-M 1.8 GHz IBM T30). The experimet cofiguratio is illustrated i Figure 8. The test was performed o the roof of Gilli Hall o the Uiversity of New Bruswick Fredericto campus. Due to the pethouse of Gilli Hall ad uildigs i the viciity of the GPS ateas, we could test the attitude software i a

10 multipath-rich eviromet. This situatio was useful i aalyzig its performace uder the worst case sceario of GPS attitude determiatio. GPS Ateas GPS Receivers GPS Attitude Moitorig Statio Motio Tale Cotrol Statio Figure 8. Real-time attitude determiatio experimet cofiguratio. Figures 9 illustrates the output of the attitude software o the laptop computer. Durig the test, the motio tale was i a static mode. This situatio made it easy to evaluate overall performace of the attitude software. At each epoch, two aselie vectors were computed y the UNB RTK egie as show i the left pael. To otai the aselie solutios, the widelae oservatios were processed ad their amiguities were fixed. The right pael i Figure 9 shows that all of the attitude solutios were determied withi 5-degree accuracy. This result satisfies excessively the real-time attitude requiremet i Tale 1. Figure 9. Real-time attitude determiatio test o a laptop computer: RTK solutios for two static aselies (left) ad Matla plot of attitude solutios, iterfaced with the Microsoft Visual C compiler (right). The motio of a spacecraft was simulated y geeratig rotatios o the yaw, pitch ad roll axes. As show i Figure 10, two aselie vectors were computed epoch-y-epoch after fixig the amiguities of widelae carrier-phase oservatios. Compared with the horizotal solutios (i.e., orthig ad eastig) i Figure 10, the vertical solutios (i.e., up) seem to e oisier. Fudametally, this is due to a poor GPS geometry i the vertical directio. As a result, the pitch ad roll solutios seem to e oisier tha the yaw solutios i Figure 11. Ufortuately, we could ot compare the attitude solutios with the rotatio agles measured y each stepper motor ecause the stepper motors ad GPS receivers were ot sychroized i this test. By triggerig the stepper motors with a GPS time-stamped commad o receivig GPS data logs, we could sychroize oth agle ad attitude solutios to withi microsecod-level latecy. We pla to complete this task i the ear future.

11 Figure 10. RTK solutios for two aselies i a kiematic mode. Figure 11. Attitude solutios correspodig to the RTK solutios for two aselies. Susequetly, the PC-versio attitude software was itegrated ito the software for the Bristol STARS cotroller developed with Taskig s C compiler (versio 3.5). Actually, the Bristol STARS cotroller software provided the platform for developig the attitude software prior to istallatio o the GAP oard. To commuicate with the Bristol SPP cotroller ad the GAP iterface card EM via the Bristol DSP56309 EVM (EValuatio Module), the Taskig CrossView deugger was used. The DSP used for oth the SPP ad the EM has two data memory areas: X ad Y. The ase memory iside the processor has the same 4 KB for each X ad Y memory area. There is a exteral 128 KB SRAM chip o the SPP that is mapped to Y memory. The EM has a exteral 256 KB SRAM for Y memory. By default, the Taskig s C compiler allocates data i X memory uless specified otherwise. So, the variales ad data defied y the attitude software should e located i Y memory. Otherwise, the attitude software will e ruig out of memory. The fial versio of attitude software is desiged to fit i 256 KB memory. CONCLUDING REMARKS Out of a dedicated suite of eight scietific istrumets for the e-pop missio, GAP provides a accurate asolute time referece, spacecraft positio ad velocity iformatio to the data hadlig uit. Also, it will perform spacecraft 3-axis attitude determiatio. Due to the limited resources of the spacecraft availale for GAP real-time attitude determiatio, its operatio may take place oly over a short time period. For that reaso, our approach to resolve carrier-phase amiguities is

12 ased o epoch-y-epoch amiguity resolutio, which resolves amiguities istataeously at the curret epoch. At each epoch, two aselie vectors are computed y the UNB RTK egie, ad the they are coverted ito the attitude solutios. To satisfy the real-time attitude requiremet of 5-degree accuracy at the 3-sigma level, the widelae carrier-phase oservatios are used i our approach. The tests coducted so far provide good evidece for a proper fuctioig of the attitude software. Further testig of GAP will e carried out at the Uiversity of Calgary's Istitute for Space Research, which is leadig the developmet of e-pop, ad at Bristol Aerospace. Susequetly, additioal testig will take place durig the spacecraft assemly, itegratio ad test program for the e-pop payload at the Caadia Space Agecy s David Florida Laoratory i Ottawa. ACKNOWLEDGEMENTS The hardware system (the Bristol SPP cotroller ad the GAP iterface card EM) discussed i the paper has ee let y Bristol Aerospace for testig GAP software. The authors would like to thak Alexis Deis at Bristol Aerospace for his kid support ad may useful discussios ad the e-pop team at the Uiversity of Calgary's Istitute for Space Research for their advice ad help i maagig the developmet, costructio ad testig of GAP. The authors would also like to thak Luis Serrao i the Departmet of Geodesy ad Geomatics Egieerig at UNB (curretly workig at Leica Geosystems AG, Heerrugg, Switzerlad) for performig experimets usig the 3-axis motio tale. Special thaks to NovAtel ad Sollae Systems for providig equipmet ecessary to coduct this research. The GAP developmet work ad associated space sciece research at UNB is supported y the Caadia Space Agecy ad the Natural Scieces ad Egieerig Research Coucil of Caada. REFERENCES Campaa, R., L. Marradi ad S. Bofati (1999). GPS attitude determiatio y adaptive Kalma filterig. Proceedigs of ION GPS 1999, 12th Iteratioal Techical Meetig of the Satellite Divisio of The Istitute of Navigatio, Nashville, TN, Septemer, pp Cross, P. ad M. Zieart (2002). LEO GPS attitude determiatio algorithm desiged for real-time o-oard executio. Proceedigs of ION GPS 2002, 15th Iteratioal Techical Meetig of the Satellite Divisio of The Istitute of Navigatio, Portlad, OR, Septemer, pp Euler, H.-J. ad H. Ladau (1992). Fast GPS amiguity resolutio o-the-fly for real-time applicatio. Proceedigs of Sixth Iteratioal Geodetic Symposium o Satellite Positioig, Columus, Ohio, March, pp Giulicchi, L., L. Boccia, G. Di Massa ad G. Amedola (2000). Performace improvemet for GPS-ased attitude determiatio systems. Proceedigs of ION GPS 2000, 13th Iteratioal Techical Meetig of the Satellite Divisio of The Istitute of Navigatio, Salt Lake City, UT, Septemer, pp Kim, D. ad R. B. Lagley (2003). O ultrahigh-precisio positioig ad avigatio. Navigatio: Joural of The Istitute of Navigatio, Vol. 50, No. 2, Summer, pp Kim, D., R. B. Lagley, J. Bod ad A. Chrzaowski (2003). Local deformatio moitorig usig GPS i a ope pit mie: Iitial study. GPS Solutios, Vol. 7, No. 3, Decemer, pp Lagley, R. B., O. Moteruck, M. Markgraf ad D. Kim (2004). Qualificatio of a commercial dual-frequecy GPS receiver for the e-pop platform ooard the Caadia CASSIPOE spacecraft. Proceedigs of NAVITEC '2004, the 2d ESA Workshop o Satellite Navigatio User Equipmet Techologies, ESTEC, Noordwik, The Netherlads, 8-10 Decemer 2004, pp Moteruck O., M. Garcia-Feradez ad J. Williams (2006). Performace compariso of semicodeless GPS receivers for LEO satellites. GPS Solutios, Vol. 10, No. 4, Novemer, pp Motorola (1999). DSP56309EVM user s maual, DSP56309EVMUM/D, Rev. 1.92, 12/1999, Board Rev. 1.2, Motorola Ic., Austi, TX. NovAtel (2003). OEM4 Family of Receivers User Maual - Vol. 2 Commad ad Log Referece, OM , Rev. 12, 2003/07/31, NovAtel Ic., Alerta, Caada. Purivigraipog, S., Y. Hashida ad M. J. Uwi (1999). GPS attitude determiatio for microsatellites. Proceedigs of ION GPS 1999, 12th Iteratioal Techical Meetig of the Satellite Divisio of The Istitute of Navigatio, Nashville, TN, Septemer, pp Purivigraipog, S. ad M. J. Uwi (2001). Determiig the attitude of a miisatellite y GPS. GPS World, Vol. 12, No. 6, Jue, pp Taskig (2002). DSP56xxx v3.5 C++ compiler user s guide, MA , Doc. Ver. 1.53, Altium Ltd., Carlsad, CA.

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