Integrated precise orbit determination of Shenzhou IV unmanned spacecraft

Transcription

1 518 Scence n Chna Ser. E Engneerng & Materals Scence 24 Vol.47 No Integrated precse orbt determnaton of Shenzhou IV unmanned spacecraft LÜ Congmn 1,2, GU Ydong 3, LIN Baoun 3 & GUO Jong 3 1. Center for Space Scence and Appled Research, Chnese Academy of Scences, Beng 18, Chna; 2. Graduate School of the Chnese Academy of Scences, Beng 139, Chna; 3. General Establshment of Space Scence and Applcaton, Chnese Academy of Scences, Beng 18, Chna; Correspondence should be addressed to Lü Congmn (emal: lucongmn@nc.poac.ac.cn) Receved March 22, 24 Abstract Consderng the characterstc orbt of Shenzhou IV spacecraft and the advantages and dsadvantages of several types of domestc orbt measurements, a scheme of IPOD s determned, whch uses GPS, SLR and USB observaton data ontly plus precse onosphere correctons to GPS observaton data. IPOD system and mathematc models of OD are ntroduced. he results of dfferent ont OD are analyzed usng true observaton data, and show that radal accuracy s better than 2 m. Keywords: Shenzhou IV unmanned spacecraft, ntegrated precse orbt determnaton, GPS, SLR, USB. DOI: 1.136/ 4ye12 On Dec. 3, 22, Shenzhou IV unmanned spacecraft was launched successfully. he orbtal module of Shenzhou IV carres a radar altmeter for ocean dynamc research. In order to get vald and hgh precson sea surface topography (SS), errors ncludng altmeter, propagaton and orbt should be reduced or elmnated. he error budgets of man nternatonal oceanographc satelltes show that the root-mean-square error (RMS) of orbt error accounts for 7% of the total error. So, orbt accuracy s the key factor to the applcaton of altmetry data. Moreover, radal orbt error affects t most [1 3]. Accordng to expermental and applcaton research requrements of radar altmeter, radal accuracy of orbt determnaton (OD) should reach 2 to 3 meters n predetermned areas. It s the hghest requrement of OD accuracy n Chna. herefore, the Applcaton System of Chnese Manned Space Programme began to nvestgate Integrated Precse Orbt Determnaton (IPOD) of Shenzhou IV as early as After studyng the characterstc Shenzhou IV orbt and the advantages and dsadvantages of several types of domestc orbt measurements, a scheme of IPOD s determned, whch uses GPS, SLR and USB observaton data ontly. IPOD softwares met requrements va verfcaton usng OPEX/Posedon data. Jont OD was mplemented usng true observaton after launch. Copyrght by Scence n Chna Press 24

2 Integrated precse orbt determnaton of Shenzhou IV unmanned spacecraft 519 he scheme and system composed of IPOD are dscussed, mathematc models are presented, and the results of several OD modes are analyzed and evaluated. 1 Scheme of IPOD Compared wth nternatonal oceanographc satelltes, IPOD msson has three maor characterstcs: ( ) Orbt alttudes of nternatonal oceanographc satelltes are hgher than 6 km, but that of Shenzhou IV s ust about 35 km. Orbt perturbatons from earth gravty model and atmospherc drag are much hgher, whch ncreases the dffculty of IPOD. ( ) Internatonal oceanographc satelltes such as OPEX/Posedon and CHAMP carry dual-frequency P-code GPS recevers, but only sngle-frequency C/A-code GPS recever can be used by Shenzhou IV. Unlke dual-frequency GPS recever, snglefrequency GPS recever cannot determne onospherc delay autonomously. In addton, the precson of C/A-code s 1/1 that of P-code, so the poston accuracy s much lower. ( ) Up to now, methods of orbt measurement whch can be used n Shenzhou IV nclude: Unfed S Band (USB), Satellte Laser Rangng (SLR), and Global Postonng System (GPS). Each of them has ts own advantages and dsadvantages. USB s not nfluenced by weather, but measurement precson s much lower than DORIS. SLR may obtan observaton data wth centmeter-level precson under good condton. But t s nfluenced by weather condtons severely. So, t s dffcult to acheve all-weather trackng. GPS provdes global observaton and postonng data wth hgh precson n real-tme. On May 1, 2, SA was turned off by US Government 1), and thus the accuracy of sngle pont postonng was mproved from 1 meters to 2 4 meters [4]. If GPS precse satellte orbts and clocks provded by the Internatonal GPS Servce (IGS) and precse onospherc correctons are adopted, poston accuracy can be mproved to meter-level further. o sum up, t s dffcult to meet the requrement of IPOD usng only one method because of low orbt and low precson of space and ground observatons. Consequently, an IPOD scheme s adopted, whch uses GPS, USB, and SLR observaton data ontly plus precse onospherc correctons to GPS observaton data, and then determnes the orbt and evaluates the results. Modes of IPOD ncludes: ( ) GPS sngle pont postonng. ( ) GPS dynamc OD + SLR verfcaton. ( ) GPS + SLR ont dynamc OD. ( ) GPS + USB ont dynamc OD. 1) Offce of the Press Secretary, Statement by the Presdent Regardng the Unted States' Decson to Stop Degradng Global Postonng System Accuracy, 2,

3 52 Scence n Chna Ser. E Engneerng & Materals Scence 24 Vol.47 No ( ) GPS + USB + SLR ont dynamc OD. he scheme not only conforms to the present domestc condtons, but s the trend of nternatonal precse OD. Namely, the means of satellte OD changed from sngle ground trackng to ground trackng plus onboard GPS. Moreover, OD results of dfferent means can be verfed wth each other. 2 IPOD system IPOD system conssts of three maor segments: the space segment, the ground trackng segment, and the data processng segment. he space segment comprses Shenzhou IV unmanned spacecraft whch s equpped wth a laser retroreflector array (LRRA) and a GPS recever. he Shenzhou IV unmanned spacecraft moves n a near-crcular orbt nclned at 42.3 at an alttude of about 35 km, whose nternatonal number s 22-61A. Mounted on the orbtal module of Shenzhou IV, the LRRA s the frst one of ts knd n Chna. It conssts of nne 3 mllmeter corner cubes. he tme of a round trp of laser pulses reflected from the LRRA s measured by SLR statons, and the ranges from Shenzhou IV to SLR statons can be obtaned then. he onboard GPS recever s a 12-channel C/A code recever, whch works on L1 frequency ( MHz). Each GPS observaton data packet encompasses pseudoranges, carrer phases, recever clock offset and poston and velocty of Shenzhou IV. he ground trackng segment s composed of USB and SLR trackng networks, IGS, and a specal ground Data Acquston Staton (DAS) for recevng applcaton data. USB network tracks the Shenzhou IV orbtal module to obtan the USB observatons, and meanwhle, t provdes orbt elements for SLR observaton. SLR network provdes centmeter-level observaton data whch can be used n OD and verfcaton. IGS network provdes observaton data collected from 54 global statons and 25 domestc statons, GPS precse satellte ephemerdes and clocks. asks of the data processng segment can be dvded nto three sectons. Frst, GPS source packets are pre-processed, and then are changed nto RINEX 2. format. Second, onospherc delays of GPS observaton data are corrected precsely. Fnally, OD usng GPS, SLR, and USB data and the accuracy estmaton are accomplshed. 3 Mathematcal model of OD 3.1 Sngle pont postonng model Sngle pont GPS model s [5] V = Aδ Z L, (1) where V s an m 1 vector of observaton nose, m s the number of GPS satelltes n vew and [ d ] δz = δx δ y δz δ t s the ncrement vector of the recever poston Copyrght by Scence n Chna Press 24

4 Integrated precse orbt determnaton of Shenzhou IV unmanned spacecraft 521 and clock offset at epoch t. A s an m 4 coeffcent matrx wth th row composed of vector x x ρ y y ρ z z ρ c, (2) where c s the speed of lght n vacuum, ( x y z ) s the approxmate value of the phase center of the GPS recever's antenna, and s the poston of th GPS satellte. ρ s the computed pseudorange usng the approxmate value. L s an m 1 vector wth th ( = 1 m ) element ρ ρ cdt cdt ( x y z ), (3) where ρ s observed pseudorange corrected by onospherc correcton, t s an approxmate value of recever s clock offset, and GPS satellte. dt d s the precse clock offset of th Accordng to the lnear least-square estmate, the soluton of eq. (1) s δz = ( A A) So, the soluton of sngle pont postonng s A L. (4) Z = Z + δz, (5) where Z = x y z dt s the reference state. If the dfference between a reference state and the true one s too large, t wll result n convergng to a wrong soluton or dvergence. In ths case, an approxmate value can be got by usng drect soluton model proposed by Ilan Bton, and then the soluton can be computed teratvely 1). 3.2 Dynamc OD model [6,7] he ordnary dfferental equaton of Shenzhou IV n the nertal coordnate system may be descrbed as X = F( X, t), X ( t) = X, (6) where X s the state vector comprsng poston vector r and velocty vector r as 1) Hu Guorong, GPS-Based Orbt Determnaton for Low Earth Satelltes, Ph.D. hess, Insttute of Geodesy and Geophyscs, Chnese Academy of Scences,

5 522 Scence n Chna Ser. E Engneerng & Materals Scence 24 Vol.47 No well as the free parameter r β,.e. X = r. X s an ntal value, and F s the β force vector actng on the Shenzhou IV. he observaton equaton may be descrbed by Y = G( X, t) + ε, (7) where G( X, t) denotes the model value, and ε s the measurement error. * Lnearzng the state equaton and observaton equaton around a reference state X. Set x( t) = X ( t) X * ( t) and yt () = Yt () GX ( t). Omttng hgher order tems, the equatons are reduced to lnear system equatons *, x = Ftt (, ) x, y = Hx + ε, (8) ~ where Φ t, t ) s the state transton matrx, H = HΦ( t, ), and ( t ~ G H =. X * X Gven the pror state x and the covarance P, the general soluton of the lnear unbased mnmum varance estmaton s gven by wth the assocated covarance where W s the weghtng matrx. xˆ x = ( H WH + P ) ( H Wy + P ), (9) = ( H WH + P ) P, (1) So, the optmal estmaton of ˆX s X ˆ + * = X xˆ. (11) 4 IPOD results 4.1 GPS dynamc OD + SLR verfcaton hs mode uses solutons of GPS sngle pont postonng as observatons for dynamc OD, and then verfes the orbt by SLR range measurement data. able 1 shows the RMS of the orbt and SLR verfcaton results durng smultaneous observaton perod. Inner accordant accuracy of dynamc OD s about 5 to 6 meters. Compared wth SLR ranges as external verfcaton, mean range error s about 2 meters, and the estmated radal accuracy s better than 1.5 meters. Copyrght by Scence n Chna Press 24

6 Integrated precse orbt determnaton of Shenzhou IV unmanned spacecraft 523 able 1 Accuracy of GPS dynamc OD SLR verfcaton Accuracy of SLR verfcaton a) Accuracy of SLR verfcaton b) Observaton date Number of SLR SLR RMS/m (year-month-date) observatons ponts ponts /m /m a) No elevaton angle lmtaton; b) data elevaton less than 5 deg. lmted. 4.2 GPS + SLR ont dynamc OD he mode combnes the solutons of GPS sngle pont postonng and SLR data as observatons, and generates the orbt ontly. he RMS of the orbt durng smultaneous observaton perod s presented n table 2. Statstcs of GPS+SLR ont dynamc OD and GPS dynamc OD (see table 1) are consstent, and the statstcs of SLR observaton data shows that the precson of SLR measurements reaches to about 1 cm. able 2 Results of GPS SLR ont OD Observaton date Number of (year-month-date) observatons X/m Y/m Z/m SLR ponts RMS of SLR/m Although statstcs of OD changes slghtly, SLR data has mpact on OD notably. Fg. 1 shows a comparson between GPS dynamc OD and GPS+SLR ont dynamc OD n X, Y and Z drectons. he dfference between two orbts ncreases to several meters or even tens of meters when the orbt s near the trackng arc of SLR. However, t decreases to less than 2 meters far from the arc, whch confrms that two orbts are n accordance wth each other well, and radal error s less than 2 meters. SLR data not only affect the orbt, but optmze t. o demonstrate ths, a combnaton of GPS and SLR data of Changchun staton (Monument 7237) or Beng staton (Monument 7249) s used for OD. hen the results are verfed by SLR ranges of Beng staton or Changchun staton. able 3 shows a comparson of statstcs wth and wthout SLR data partcpatng n OD. Clearly, GPS+SLR ont OD has optmzed the orbt, and OD accuracy s mproved by SLR data. 4.3 GPS+USB+SLR ont dynamc OD Jont OD of GPS+USB and GPS+USB+SLR mode are mplemented respectvely,

7 524 Scence n Chna Ser. E Engneerng & Materals Scence 24 Vol.47 No Observaton date (year-month-date) Fg. 1. Comparson between GPS dynamc OD and GPS+SLR ont OD. able 3 Comparson of OD results wth and wthout SLR data SLR staton SLR staton GPS dynamc OD partcpatng n OD for verfcaton SLR verfcaton /m GPS+SLR dynamc OD +SLR verfcaton/m Observaton date (year-month-date) able 4 Comparson of GPS+USB+SLR ont OD OD mode Pass No. Ponts of SLR RMS/m GPS GPS+USB GPS+USB+SLR GPS GPS+USB GPS+USB+SLR GPS GPS+USB GPS GPS+USB+SLR Copyrght by Scence n Chna Press 24

8 Integrated precse orbt determnaton of Shenzhou IV unmanned spacecraft 525 and the results are compared wth GPS dynamc OD to nvestgate the functon of USB data n IPOD. able 4 s the comparson of three modes durng smultaneous observaton perod. Frst, accuracy of GPS dynamc OD s better than 2 meters. Second, USB contrbutes lttle to the IPOD because of low precson of USB data. Fnally, SLR data may reduce the effects of USB data, and mprove the OD accuracy markedly. 4.4 Overall evaluaton As the man data source of IPOD, GPS-based OD of Shenzhou IV are global, not restrcted to predetermned areas. Results of modes 2 to 5 show that radal accuracy s wthn the range of 1 to 3 meters. Because of the dstrbuton of SLR statons and weather, SLR observaton tme s very short, and t s dffcult to determne the orbt solely. However, t s effectve as a means of verfcaton of OD results. In addton, USB contrbutes lttle to the IPOD because of low precson of USB data. 5 Concluson IPOD results show that t s feasble to use GPS, SLR and USB observaton data for IPOD, and radal accuracy s better than 2 m n Shenzhou IV case, whch meets the msson requrements well. It s the hghest accuracy of domestc OD at present, and makes OD accuracy of LEO spacecraft of Chna step nto a new stage. Acknowledgements Organzng and actualzng of IPOD msson are presded over by the General Establshment of Space Scence and Applcaton, CAS. asks ncludng USB and SLR trackng, ground data acquston, and data processng are mplemented by Purple Mountan Observatory (PMO), X an Satellte Control Center (XSCC), Shangha Observatory (SHAO), Insttute of Geodesy and Geophyscs (IGG), Wuhan Insttute of Physcs and Mathematcs (WIPM), Payload Operaton and Applcaton Center (POAC), and the GPS recever proect group. Some contents of ths paper are cted from the research reports and fnal report of IPOD. he authors are grateful for the support of the nsttutes above and relevant authors. References 1. Rummel, R., Sanso, F., Satellte Altmetry n Geodesy and Oceanography, Berln: Sprnger-Verlag, Schnapf, A., Montorng Earth s Ocean, Land, and Atmosphere from Space-Sensors, Systems, and Applcatons, New York: Amercan Insttute of Aeronautcs and Astronautcs Inc., Stewart, R. H., Methods of Satellte Oceanography, Berkeley: Unversty of Calforna Press, Hofmann-Wellenhof, B., Lchtenegger, H., Collns, J., Global Postonng System: heory and Practce, New York: Sprnger-Verlag, eunssen, P. J. G., Kleusberg, A., GPS for Geodesy, Berln: Sprnger-Verlag, Lu Ln, Orbt heory of Spacecraft, Beng: Natonal Defence Industry Press, Montenbruck, O., Gll, E., Satellte Orbts: Models, Methods, and Applcatons, Berln: Sprnger, 2.