臺灣博碩士論文加值系統

福爾摩沙衛星三號(FORMOSAT-3/COSMIC, F3/C)發射於2006年4月15日，為台美合作的衛星任務。此任務共有6顆微衛星被發射升空，每顆衛星均裝載2個POD GPS天線。本研究使用GPS 無差分觀測量與利用減動力法與動態法進行LEO軌道的解算，並且將F3/C與GRACE衛星進行GPS觀測量品質分析比較。對於F3/C 與GRACE衛星，其電碼觀測量之多路徑效應的影響分別為P1 (MP1)，0.77 m和0.35 m; P2 (MP2) 1.06 m 和0.57 m; 週波脫落發生的頻率分別為1/29 和 1/84; 後驗單位權標準偏差分別為4 cm 和 1 cm; 動力軌道與動態軌道之差異分別為，10 cm 和2 cm。
本文進行F3/C衛星質量中心(COM)的變化、衛星姿態、GPS天線相位中心的變化和纜線延遲影響之相關性的研究。在本研究中，nominal 姿態給定出的F3/C軌道優於observed 姿態給定的軌道。數值的測試顯示出，為了不破壞軌道的求定，F3/C的COM必須精準地被率定。 兩條不同的30小時軌道弧長被使用於5小時和6小時之軌道重疊分析，而動力軌道與動態軌道之精度幾近相同，且落於2-3 cm的精度。本研究的軌道與UCAR(near real-time)和WHU (post-processed)比較，差異大約為10 cm，其原因為力模式、GPS軌道與GPS時錶改正之不同所致。而本研究的F3/C動態軌道將被使用於地球時變重力場之反衍。利用F3/C GPS資料進行重力場的求定，仔細的選擇GPS資料是必須的。然而由於F3/C共有6顆衛星，其大量的軌道資料量將可以補足GPS資料品質的缺陷。
而另一個評估定位品質的方法，就是利用量化姿態誤差。姿態轉換矩陣主要用於座標框架之間的轉換，而當中之間的軌道精度損失可能發生於不穩定的姿態控制時段。使用時間段DOY 118 to 336, 2008的GPS資料進行評估， 可得F3/C定位精度依序為FM1 (2.72 cm), FM2 (2.62 cm), FM3 (2.37 cm), FM4 (1.90 cm), FM5 (1.70 cm), and FM6 (1.99 cm).

The joint Taiwan-US mission FORMOSAT-3/COSMIC (F3/C) was launched on April 15, 2006. Each of the six satellites is equipped with two precise orbit determination (POD) antennas. The POD antennas of F3/C and GRACE-A satellites are from the same manufacturer, but are installed in different configurations. The LEO satellites are determined from GPS data using undifference carrier-phase measurements by the reduced dynamic and kinematic methods. This study compares the qualities of GPS observables from F3/C and GRACE. Using selected satellites and time spans, the following average values for the satellite F3/C and satellite A of GRACE are obtained: multipath effect on the pseudorange P1 (MP1), 0.77 m and 0.35 m; multipath effect on the pseudorange P2 (MP2), 1.06 m and 0.57 m; occurrence frequency of cycle slip, 1/29 and 1/84; standard error of unit weight, 4 cm and 1 cm; dynamic-kinematic orbit difference, 10 cm and 2 cm.
The effects of satellite center of mass (COM) variation, satellite attitude, GPS antenna phase center variation (PCV), and cable delay difference on the F3/C orbit determination are studied. Nominal attitudes estimated from satellite state vectors deliver a better orbit accuracy when compared to observed attitude. Numerical tests show that the F3/C COM must be precisely calibrated in order not to corrupt orbit determination. Based on the analyses of the 5-h and 6-h orbit overlaps of two 30-h arcs, orbit accuracies from the reduced dynamic and kinematic solutions are nearly identical and are at the 2-3 cm level. The mean RMS difference between the orbits from this study and those from UCAR (near real-time) and WHU (post-processed) is about 10 cm, which is largely due to different uses of GPS ephemerides, high-rate GPS clocks and force models. The kinematic orbits of F3/C are expected to be used for recovery of temporal variations in the gravity field. For gravity determination using F3/C GPS data, a careful selection of GPS data is critical. With six satellites in orbit, F3/C’s large amount of GPS data will make up the deficiency in data quality
An alternative assessment of the positioning quality is made by propagating attitude error to orbit error. The attitude transformation matrix is responsible for coordinate frame conversions, and a degraded orbit accuracy in the F3/C satellites might occur under an unstable attitude control. This assessment, using GPS data of DOY 118 to 336, 2008, leads to the following 3-D positioning accuracies: 2.72, 2.62, 2.37, 1.90, 1.70, and 1.99 cm for FM1, …, and FM6.

Abstract (in Chinese)………………………………………………………………….………I
Abstract………………………………………………………………………………………III
Table of Contents……………………………………………………………………………..V
List of Tables……………………………………………………………………………….VIII
List of Figures………………………………………………………………………………...X
Acronyms…………………………………………………………………………………XIII
Chapter 1 Introduction……………………………………………………………………….1
1.1 Motivation………………………………………………………………………………….1
1.2 Review of recent LEO missions……………………………………………………………3
1.2.1 CHAMP mission…………………………………………………………………………3
1.2.2 GRACE mission………………………………………………………………………….5
1.2.3 GOCE mission…………………………………………………………………………...7
1.3 Literature review…………………………………………………………………………...9
1.4 Outline of thesis…………………………………………………………………………..10
Chapter 2 GPS observables for orbit determination……………………………………...12
2.1 Observation types………………………………………………………………………....12
2.1.1 Code pseudorange………………………………………………………………………12
2.1.2 Phase pseudorange……………………………………………………………………...14
2.2 Linear combination of observations………………………………………………………16
2.2.1 Ionosphere-free linear combination…………………………………………………….16
2.2.2 Geometry-free linear combination……………………………………………………...17
2.2.3 Multipath equation……………………………………………………………………...17
Chapter 3 F3/C spacecraft and GPS payload……………………………………………...19
3.1 Spacecraft geometry………………………………………………………………………19
3.2 Satellite center of mass and variation…………………………………………………….22
3.3 Gain pattern, phase center offset and variation of antenna……………………………….24
3.3.1 Gain pattern……………………………………………………………………………..25
3.3.2 Phase center offset and variation……………………………………………………….27
3.4 Cable delay difference between two GPS antennas………………………………………29
Chapter 4 Quality analysis of GPS data for orbit determination………………………...31
4.1 Status and acquisition of F3/C GPS POD data…………………………………………...31
4.2 Code multipath……………………………………………………………………………35
4.3 Ionospheric delay and cycle slip………………………………………………………….46
Chapter 5 Attitude determination and control system for F3/C…………………………54
5.1 Spacecraft attitude definition……………………………………………………………..54
5.2 Attitude determination and control system……………………………………………….58
5.3 Stabilize/Safehold mode in ARS…………………………………………………………62
5.4 Nadir mode in ARS………………………………………………………………………65
5.5 Nadir-Yaw mode in ARS…………………………………………………………………66
5.5.1 Nadir Yaw-Fixed………………………………………………………………………..66
5.5.2 Nadir Yaw-Steering…………………………………………………………………….67
5.5.2.1 Optimal Yaw-Steering………………………………………………………………..68
5.5.2.2 Inverse Yaw-Steering…………………………………………………………………70
5.6 Analysis of attitude control based on ground test………………………………………...72
Chapter 6 Precise orbit determination for FORMOSAT-3/COSMIC…………………..80
6.1 GPS ephemeris and clock correction products…………………………………………...80
6.2 Reduce-dynamic orbit determination…………………………………………………….84
6.3 Kinematic orbit determination……………………………………………………………89
6.4 Effect of PCV and COM on F3/C orbit…………………………………………………..92
6.4.1 Effect of satellite COM on orbit……………………………………………………….92
6.4.2 Effect of PCV on orbit…………………………………………………………………94
6.5 Analysis of phase residuals……………………………………………………………...95
6.6 Quality assessment for differences between kinematic and reduce-dynamic orbits…………………………………………………………………………………………99
6.7 Assessment of orbit accuracy……………………………………………………………101
6.7.1 Assessment based on orbit overlaps…………………………………………………...101
6.7.2 Comparison with UCAR and WHU orbits……………………………………………103
Chapter 7 Attitude control effect on orbit determination and quantification of attitude error…………………………………………………………………………………………105
7.1 Effect of attitude error and choice of attitude data………………………………………105
7.2 Data size and β angle……………………………………………………………………108
7.3 Residuals in the eclipse and sun acquisition…………………………………………….109
7.4 Quantification of attitude error based on kinematic orbit determination………………..112
7.4.1 Procedure of estimated baseline between POD antenna phase center and satellite COM…………………………………………………………………………………………112
7.4.2 Quantification of attitude error………………………………………………………..113
7.4.3 Assessment of positioning accuracy ………………………………………………….115
Chapter 8 Conclusions and outlook………………………………………………………117
8.1 Conclusions……………………………………………………………………………117
8.2 Future work……………………………………………………………………………...118
Reference……………………………………………………………………………………120
Curriculum Vitae…………………………………………………………………………..128

Balmino G (1994) Orbit choice and the theory of radial orbit error for altimetry. In: Sansó F and Rummel R (eds) Satellite Altimetry in Geodesy and Oceanography. Lecture Notes in earth sciences, Vol. 50, Springer, Berlin, pp. 244-317
Bar-Server YE (1996) A new model for GPS yaw-attitude. J Geod 70: 714-723
Beutler G, Brockmann E, Gurtner W, Hugentobler U, Mervart L, Rothacher M, Verdun A (1994) Extended orbit modeling techniques at the CODE processing center of the international GPS service for geodynamics (IGS): theory and initial results. Manuscr Geod 19: 367-386
Beutler G, Jäggi A, Hugentobler U, Mervart L (2006) Efficient satellite orbit modeling using pseudo-stochastic parameters. J Geod 80: 353-372, doi 10.1007/s00190-006-0072-6
Bock H (2003) Efficient Methods for Determining Precise Orbits of Low Earth Orbiters Using the Global Positioning System. Geodätisch-geophysikalische Arbeiten in der Schweiz, Band 65, Schweizerische Geodätische Kommission, Institut für Geodäsie und Photogrammetrie, Eidg. Technische Hochschule Zürich, Zürich
Bock H, Dach R, Hugentobler U, Schaer S, Beutler G (2004) CODE High-rate GPS Satellite Clock Corrections. IGS Workshop, Bern, Switzerland, March 1-5
Bock H, Dach R, Jäggi A, Beutler G (2009a) High-rate GPS clock correction from CODE: support of 1Hz applications. J Geod, doi 10.1007/s00190-009-0326-1
Bock H, Dach R, Yoon Y, Montenbruck O (2009b) GPS clock correction estimation for near real-time orbit determination applications. Aerosp Sci Technol 13: 415-422, doi: 10.1016/j.ast.2009.08.003
Bock H, Hugentobler U, Springer TA, Beulter G (2002) Efficient precise orbit determination of LEO satellites using GPS. Adv Space Res 30:295-300, doi: 10.1016/S0273-1177(02)00298-3
Bock H, Jäggi A, Švehla D, Beutler G, Hugentobler U, Visser P (2007) Precise orbit determination for the GOCE satellite using GPS. Adv Space Res, doi:10.1016/j.asr.2007.02.053
Chao BF, Pavlis EC, Hwang C, Liu CC, Shum CK, Tseng CL, Yang M (2000) COSMIC: geodetic applications in improving earth's gravity model. Terr Atm Ocean Sci 11: 365-378
Coker C, Dymond KF, Budzien SA, (2002) Using the Tiny Ionospheric Photometer (TIP) on the COSMIC Satellites to Characterize the Ionosphere. American Geophysical Union, Fall Meeting, abstract #SA52A-0389
Colombo O (1984) Altimetry, Orbits and Tides. NASA TM 86180, Greenbelt, Maryland
Comp CJ, Axelrad P (1998) Adaptive SNR-Based Carrier Phase Multipath Mitigation Technique. IEEE Trans. Aerosp Electron Syst 34: 264-276
Dach R, Hugentobler U, Fridez P, Meindl M (2007) Bernese GPS Software - Version 5.0. Astronomical Institute. University of Bern, Switzerland
Dickman J, Zhu Z, Bartone C (2009) Carrier phase multipath error characterization and reduction in signal aircraft relative positioning. GPS Solut 14: 141-152, doi: 10.1007/s10291-009-0126-3
Ditmar P, Kuznetsov V, van der Sluijs AAV, Schrama E, Klees R (2006) DEOS_CHAMP-01C_70: a model of the Earth's gravity field computed from accelerations of the CHAMP satellite. J Geod 79: 586-601
Estey LH, Meerten CM (1999) TEQC: the multi-purpose toolkit for GPS/GLONASS data. GPS Solut 3(1): 42-49
Fong CJ, Yang SK, Chu CH, Huang CY, Yeh JJ, Lin CT, Kuo TC, Liu TY, Yen NL, Chen SS, Kuo YH, Liou YA, Chi S (2008) FORMOSAT-3/COSMIC Constellation Spacecraft System Performance: After One Year in Orbit. IEEE Trans Geosci Remote Sens 46: 3380-3394
Gerlach Ch, Földvary L, Švehla D, Gruber Th, Wermuth M, Sneeuw N, Frommknecht B, Oberndorfer H, Peters Th, Rothacher M, Rummel R, Steigenberger P (2003) A CHAMP-only gravity field model from kinematic orbits using the energy integral. Geophys. Res. Lett. 30 (20) 10.1029/2003GL018025.
Gurtner W, (1994) RINEX: The receiver-independent exchange format. GPS World 4: 48-52
Hauschild A, Montenbruck O (2009) Kalman-filter-based GPS clock estimation for near real-time positioning. GPS Solut 13: 173-182, doi: 10.1007/s10291-008-0110-3
Hofmann-Wellenhof B, Lichtenegger H, Collins J (2001) Global Positioning System: Theory and Practice. Springer Wien New York, ISBN 3-211-83472-9
Hughes PC (1986) Spacecraft attitude dynamics. John Wiley & Sons, Singapore
Hwang C (2001) Gravity recovery using COSMIC GPS data: application of orbital perturbation theory. J Geod 75:117-136
Hwang C, Lin TJ, Tseng TP, Chao BF (2008) Modeling orbit dynamics of FORMOSAT-3/COSMIC satellites for recovery of temporal gravity variations. IEEE Trans. Geosci Remote Sens 46: 3412-3423
Hwang C, Tseng TP, Lin T, Švehla D, Schreiner B (2009) Precise orbit determination for the FORMOSAT-3/COSMIC satellite mission GPS. J Geod 83: 477-489, DOI 10.1007/s00190-008-0256-3
Hwang C, Tseng TP, Lin T, Švehla D, Hugentobler U, Chao BF (2010) Quality assessment of FORMOSAT-3/COSMIC and GRACE GPS observables: analysis of multipath, ionospheric delay and phase residual in orbit determination. GPS Solut 14 (1): 121-131, doi 10.1007/s10291-009-0145-0
IGSCB (2004) IGS products; URL http://igscb.jpl.nasa.gov/components/prods.html
Jäggi A, Dach R, Montenbruck O, Hugentobler U, Bock H, Beulter G (2009) Phase center modeling for LEO GPS receiver antenna and its impact on preceise orbit determination. J Geod 83:1145-1162, doi 10.1007/s00190-009-0333-2
Jäggi A, Hugentobler U, Beutler G (2006) Pseudo-stochastic orbit modeling techniques for low Earth orbiters. J Geod 80: 47-60, DOI 10.1007/s00190-006-0029-9
Jäggi A, Hugentobler U, Bock H, Beutler G (2007) Precise orbit determination for GRACE using undifference or doubly differenced GPS data. Adv Space Res 39 (10): 1612-1619, doi 10.1016/j.asr.2007.03.012
Jan YW (2003) Attitude Determination and Control System Design for Micro/Small Satellite. Ph.D. dissertation for Department of Electrical and Control Engineering, National Chiao Tung University, Taiwan
Jan YW, Tsai JR (2005) Active control for initial attitude acquisition using magnetic torquers. Acta Astronaut 57: 754-759, doi: 10.1016/j.actaastro.2005.03.067
Kang Z, Tapley B, Bettadpur S, Ries J, Nagel P, Pastor R, (2006) Precise orbit determination for the GRACE mission using only GPS data, J Geod 80: 322–331, DOI 10.1007/s00190-006-0073-5
König R, Michalak G, Neymayer KH, Zhu SY (2006) Remarks on CHAMP orbit products. In: Flury J, Rummel R, Reigber C, Rothacher M, Boedecker G, Schreiber U (eds), Observation of the Earth System From Space, pp. 17-26, Springer, Berlin
Koch KR (1987) Parameter Estimation and Hypothesis testing in Linear Models, Springer, Berlin
Kouba J (2002) A guide to using international GPS service (IGS) products. URL http://igscb.jpl.nasa.gov/components/IGSProducts_user_v17.pdf
Kouba J (2009) A simplified yaw-attitude model for eclipsing GPS satellites, GPS Solut 13:1-12, doi 10.1007/s10291-008-0092-1
Lee LC, Rocken C, and Kursinki ER (2000) Special issue for applications of the Constellation Observing System for Meterology, Ionosphere and Climate (COSMIC). Terr Atmos Ocean Sci 11 (1)
Leick A, (2004) GPS satellite surveying. Third edition, John Wiley & Sons, Inc., Hoboken, New Jersey
Liu JN, Ge MR (2003) PANDA software and its preliminary result for positioning and orbit determination. The fourth international symposium on GPS/GNSS, Nov. 6-8, 2002, WHU, P.R. China
Long AC, Cappellari JO, Velex CE, Fuchs AJ (eds) (1989) Goddard Trajectory Determination System Mathematical Theory. Revision 1, FDD/552-89/001
Mayer-Gürr, T, Ilk, KH, Eicker, A, Feuchtinger, M (2005) ITG-CHAMP01: A CHAMP Gravity Field Model from Short Kinematical Arcs of a One-Year Observation Period, J Geod 78: 462-480, Springer-Verlag
Montenbruck O, Garcia-Fernandez M, Williams J (2006) Performance comparison of semicodeless GPS receivers for LEO satellites. GPS Solut 10: 249–261,doi 10.1007/s10291-006-0025-9
Montenbruck O, Garcia-Fernandez M, Yoon Y, Schön S, Jäggi A (2009) Antenna phase center calibration for precise positioning of LEO satellites. GPS Solut 13:23-34, doi 10.1007/s10291-008-0094-z
Montenbruck O, Gill E, Kroes R (2005) Rapid orbit determination of LEO satellites using IGS clock and ephemeris products. GPS Solut 9: 226-235, doi 10.1007/s10291-005-0131-0
Montenbruck O, Kroes R (2003) In-flight performance analysis of the CHAMP BlackJack GPS Receiver. GPS Solut 7: 74-86, doi: 10.1007/s10291-003-0055-5
Neumayer K-H, Michalak G, König R (2005) On calibrating the CHAMP on-board accelerometer and attitude quaternion processing - In: Reigber Ch, Lühr H, Schwintzer P, Wickert J, (Eds.), Earth observation with CHAMP: Results from Three Years in Orbit, pp. 71-76, Springer, Germany
Ogaja C, Hedfors J, (2007) TEQC multipath metrics in MATLAB. GPS Solut 11: 215-222, DOI 10.1007/s10291-006-0052-6
Reigber C, Bock R, Förste C, Grunwaldt L, Jakowski N, Lühr H, Schwintzer P, Tilgner C (1996) CHAMP phase B-executive summary; Scientific technical report STR96/13, GeoForschungsZentrum Potsdam
Reubelt T, Austen G, Grafarend EW (2004) Harmonic analysis of the Earth's gravitational field by means of semi-continuous ephemerides of a low Earth orbiting GPS-tracked satellite. Case study: CHAMP. J Geod 77(5-6), 257-278, DOI10.1007/s00190-003-0322-9
Schmid R, Rothacher M, Thaller D, Steigenberger P (2005) Absolute phase center corrections of satellite and receiver antennas impact on global GPS solutions and estimation of azimuthal phase center variations of the satellite antenna. GPS Solut 9(4):283–293, doi: 10.1007/s10291-005-0134-x
Schmid R, Steigenberger P, Gendt G, Ge M, Rothacher M (2007) generation of a consistent absolute phase center correction model for GPS receiver and satellite antennas. J Geod 81(12):781–798, doi: 10.1007/s00190-007-0148-y
Schreiner B, (2005) COSMIC GPS POD and Limb Antenna Test Report. Internal report of UCAR
Schreiner W, Rocken C, Sokolovskiy S, Hunt D (2010) Quality assessment of COSMIC/FORMOSAT-3 GPS radio occultation data derived from single- and double-differnece atmospheric excess phase processing. GPS Solut 14 (1): 13- 22, doi: 10.1007/s10291-009-0132-5
Seeber G (2003) Satellite Geodesy. 2nd ed, de Gruyter, Berlin
Švehla D, Rothacher M (2005a) Kinematic Precise Orbit Determination for Gravity Field Determination. IUGG General Assembly 2003, June 30 – July 11 2003, Sapporo, Japan. The Proceedings of the International Association of Geodesy: A Window on the Future of Geodesy. Eds. F. Sanso. Spriger Verlag, IAG Vol 128. pp 181-188
Švehla D, Rothacher M (2005b) Kinematic positioning of LEO and GPS satellites and IGS stations on the ground. Adv Space Res 36: 376-381. doi:10.1016/j.asr.2005.04.066
Švehla D, Rothacher M (2006) Can the reference system be defined based on the LEO/GPS bi-constellation? Paper presented at the 36th COSPAR Scientific Assembly, 16-23 July 2006, Beijing, China
Švehla D, Rothacher M, (2004) CHAMP and GRACE in Tandem: POD with GPS and K-Band Measurements. Joint CHAMP/GRACE Science Meeting, 6–8 July 2004, GeoForschungsCentrum Potsdam, Germany
Švehla D, Rothacher M (2003) Kinematic and Reduced–Dynamic Precise Orbit Determination of Low Earth Orbiters. Adv Geosci 1: 47-56
Syndergaard S, Schreiner WS, Rocken C, Hunt DC, Dymond KF, (2006) Preparing for COSMIC: Inversion and Analysis of Ionospheric Data Products. Atmosphere and Climate, doi 10.1007/3-540-34121-8_12
Tapley B, Ries J, Bettapur S, Chamber D, Cheng M, Condi F, Guenter B, Kang Z, Nagel P, Pastor R, Pekker T, Poole, Wang F (2005) GGM02-An improved Earth gravity field model from GRACE. J Geod 79:467-478
Visser PNAM, Van den IJssel J (2000) GPS-based precise orbit determination for the very low Earth-orbiting gravity mission GOCE. J Geod 74: 590-602
Warren DLM, Raquet JF (2003) Broadcast vs. Precise GPS ephemerides: a historical perspective. GPS Solut 7: 151-156, doi:10.1007/s10291-003-0065-3
Wertz JR (1991) Spacecraft Determination and Control. Kluwer Academic Publishers, Boston
Wu BH, Fu CL, Liou YA, Chen WJ, Pan HP (2005) Quantitative analysis of the errors associated with orbit uncertainty for FORMOSAT-3. Proc. of Int. Sym Remote Sensing (ISRS), October 12-14, 2005, Korea, pp. 87-90
Wu JT, Wu SC, Hajj GA, Bertiger WI, Lichten SM (1993) Effect of antenna orientation on GPS carrier phase. Manuscr Geod 18: 91-98
Zumberge, JF, Gendt G (2001), The demise of selective availability and implications for the International GPS Service. Phys Chem Earth Part A 26(6–8): 637–644