Exploring the Ambiguity Resolution in Spacecraft Attitude Determination Using GNSS Phase Measurement
Attitude Determination (AD) of a spacecraft using the phase measurements of the Global Navigation Satellite System (GNSS) is an active area of research. Various attitude determination algorithms have been developed in yester years for spacecrafts using different sensors but the last two decades have witnessed a phenomenal increase in research related with GPS receivers as a stand-alone sensor for determining the attitude of satellite using the phase measurements of the signals from GNSS. The GNSS-based Attitude determination algorithms have been experimented in many real missions. The problem of AD algorithms using GNSS phase measurements has two important parts; the ambiguity resolution and the determining of attitude. Ambiguity resolution is the widely addressed topic in literature for implementing the AD algorithm using GNSS phase measurements for achieving the accuracy of millimeter level. This paper broadly overviews the different techniques for resolving the integer ambiguities encountered in AD using GNSS phase measurements.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087089Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2138
 Wertz, J.R., ed., “Spacecraft Attitude Determination and Control,” D. Reidel Publishing Company, Library in Astrophysics and Space Sciences, 1978.
 M.D.Shuster,“Survey of Attitude Representations”, Journal of Astronautical Sciences, vol.4, pp 439-517, Oct-Dec 1983.
 S.K.Shrivastava and V.J.Modi, “Satellite Attitude Dynamics and Control in the Presence of Environmental Torques — A Brief Survey,” Journal of Guidance, Control, and Dynamics, vol. 6, Nov.-Dec. 1983.
 Wahba, G., "A Least Squares Estimate of Spacecraft Attitude," SUM Review, vol. 7, No. 3, p. 409. July 1965.
 Shuster, M.D. and Oh, S.D., "Three-Axis Attitude Determination from Vector Observations." J. of Guidance and Control, vol. 4, No. 1, pp. 70- 77. Jan.-Feb. 1981.
 Markley, F. L., "Attitude Determination Using Vector Observations and Singular Value Decomposition", Journal of the Astronautical Sciences, No. 36, pp. 245-258, July-Sep. 1988.
 Markley, F. L., "Attitude Determination Using Vector Observations: A Fast Optimal Matrix Algorithm,” Journal of the Astronautical Sciences, vol. 41, No. 2, pp. 261-280, 1993.
 Crassidis, Markley and Cheng, “Survey of Nonlinear Attitude Estimation Methods,” Journal of Guidance, Control and Dynamics, vol. 30, No. 1, 2007.
 Bar-Itzhack, I.Y., "REQUEST- A Recursive QUEST Algorithm for Sequential Attitude Determination," J. Guidance, Control, and Dynamics, vol. 19, No. 5, pp. 1034-1038, Sept.- Oct., 1996.
 D. Choukroun, I. Y. Bar-Itzhack and Y. Oshman, “Optimal-REQUEST Algorithm for Attitude Determination,” Journal of Guidance, Control, and Dynamics, Vol. 27, No. 3, May–June 2004.
 Crassidis, J. L., & Markley, F. L., “Minimum Model Error Approach for Attitude Estimation,” Journal of Guidance, Control, and Dynamics, vol. 20, No.6, 1241-1247, 1997.
 Mortari, D. “Euler-q Algorithm for Attitude Determination from Vector Observations,” Journal of Guidance, Control, and Dynamics, vol. 21, pp. 328-334, 1998.
 D. Choukroun, I. Y. Bar-Itzhack, and Y. Oshman, “Optimal-REQUEST Algorithm for Attitude Determination,” Journal of Guidance, Control, and Dynamics, vol. 27, No. 3, May–June 2004.
 Choukroun, D. “Adaptive Optimal-REQUEST Algorithm for Attitude Determination,” AIAA Guidance, Navigation and Control Conference and Exhibit. 20-23 August 2007, Hilton Head, South Carolina.
 Lefferts, Markley and Shuster, “Kalman Filtering For Spacecraft Attitude Estimation,” AIAA, 20th Aerospace Science Meeting, Orlando Florida, January, 11 -14, 1982.
 Martel F., Pal P. K. and Psiaki M. L., "Three- Axis Attitude Determination via Kalman Filtering of Magnetometer Data," Journal of Guidance, Control and Dynamics, vol. 13, No. 3, pp. 506-514, 1989.
 W.Parkinson, “Origins, Evolution and Future of satellite Navigation,” Journal of Guidance, Control, and Dynamics, vol.20, 1997.
 Garrick, J, “Investigation of Models and Estimation Techniques for GPS Attitude Determination,” NASA Report, 1992.
 Gabriele Giorgi and Peter J. Buist, “single-epoch, single-frequency, standalone full attitude determination: experimental results” NAVITECH 2008.
 Giorgi, G., Teunissen, P. J., Verhagen, S., Buist, P. J., G, “Testing a New Multivariate GNSS Carrier Phase Attitude Determination Method for Remote Sensing Platforms,” Advances in Space Research, Accepted Manuscript, 2010.
 SungPil Yoon, “Real Time Attitude Determination Using GPS,” PhD Thesis, Auburn University, 1999.
 Bauer, F. H., Hartman, K., & Lightsey, “Spaceborne GPS Current Status and Future Visions,” AIAA, 1998.
 F.H. Bauer, E.G. Lightsey, J. O' Donmfll and R. Sdmurr, “GADACS: A GPS Attitude Determination and Control Experiment on a Spartan Spacecraft,” Control Eng. Practice, vol. 3, No. 8, pp. 1125-1130, 1995.
 C.E.Cohen, Lightsey and Parkinson, “Space Flight Tests Of Attitude Determination Using GPS,” International Journal of Satellite Communications, vol. 12, 427-433, 1994.
 Axelrad, P., & Ward, L. M. “Spacecraft Attitude Estimation Using the Global Positioning System: Methodology and Results for RADCAL,” Journal of Guidance, Control, and Dynamics, vol. 19, No. 6, November- December 1996.
 Lightsey, E. G. “Flight Results of GPS Based Attitude Control on the REX II Spacecraft”.
 H. Uematsu, L. Ward, B. W. Parkinson, “Use Of GPS For Gravity Probe B Relativity Experiment and Co-Experiment,” Advances in Space Research, vol. 25, No.6, pp. 1199-1203,2000.
 Tortora, P. “A GPS Based Attitude Determination Algorithm for the Spin-Stabilized Microsatellite UNISAT”. Acta Astronautica, vol. 47, Nos. 2-9, pp. 139-146. 2000.
 Jinlu Kuan and Soonhie Tan, “GPS-Based Attitude Determination of Gyrostat Satellite by Quaternion Estimation Algorithms,” Acta Astronautica, vol. 51, No. 11, pp. 743–759, 2002.
 Dr Martin Unwin, P.Purivigraipong, Alex da Silva Curiel and Prof. Martin Sweeting, “Stand-alone Spacecraft Attitude Determination Using Real Flight GPS Data from UOSAT-12,”Acta Astronautica, vol. 51, No. 1-9, pp. 261-268, 2002.
 Elizabeth Rooney, Martin Unwin, Scott Gleason “Demonstration of GPS on the ALSAT-1 Disaster Monitoring Satellite,” AIAA Guidance, Navigation, and Control Conference and Exhibit 11-14 August 2003, Austin, Texas.
 Q.P. Chu and P.Th.LM. van Woaicom, “GPS for Low Cost Attitude Determination - A Review of Concepts, In-Flight Experiences, and Current Developments,” Acta Astronautica, vol. 41, No. 4-10, pp. 421- 433. 1997.
 Clark Emerson Cohen, “Attitude Determination Using GPS,” PhD Thesis, Stanford University, 1992.
 Kruczynski, L.R., P.C. Li, A.G. Evans, and B.R.Hermann, "Using GPS to Determine Vehicle Attitude: U.S.S. Yorktown Test Results," ION GPS 89, Colorado Springs, September, 1989.
 J. Rath and P. Ward, "Attitude Estimation using GPS," National Technical Meeting, ION, San Mateo, CA, January 1989.
 K.A. Brown and A.G. Evans, "GPS Pointing System Performance," ION GPS-90, Colorado Springs, CO, September 1990.
 K. Ferguson, et al., "Three-Dimensional Attitude Determination with the Ashtech 3DF 24-Channel GPS Measurement System," Proceedings of the ION National Technical Meeting, Phoenix, ,Jan. 1991.
 F. van Graas and M. Braasch, "GPS Interferometric Attitude and Heading Determination: Initial Flight Test Results," Navigation, Vol. 38, winter 1991-92.
 Gang Lu, et al., "Attitude Determination in a Survey Launch Using Multi-Antenna GPS Technologies." National Technical Meeting of the ION, San Francisco, Jan. 1993.
 R.D. Jurgens and C.E. Rodgers. "Advances in GPS Attitude Determining Technologies as Developed for the Strategic Defense Command," IONGPS 9 1, Albuquerque, Sept. 1991.
 Bar-Itzhack, I. Y., Montgomery, P. Y., & G, J. C., “Algorithms for Attitude Determination Using the Global Positioning System,” Journal of Guidance, Control, and Dynamics, vol. 21, No. 6, November– December 1998.
 Stephen J. Fujikawa, “Spacecraft Attitude Determination by Kalman Filtering of Global Positioning System Signals,” Journal of Guidance, Control, and Dynamics, vol. 18, No. 6, November-December 1995.
 Crassidis, J. L., Lightsey, E. G., & Markley, F. L., “Efficient and Optimal Attitude Determination Using Recursive Global Positioning System Signal Operations,” Journal of Guidance, Control, and Dynamics, vol. 22, No. 2, March–April 1999.
 Park, F. C. Kim, J. & K, C., “Geometric Descent Algorithms for Attitude Determination Using the Global Positioning System,” Journal of Guidance, Control, and Dynamics, vol. 23, No. 1, January–February 2000.
 Jared Madsen and E. Glenn Lightsey, “Attitude Determination Using GPS Signal to Noise Ratio and Carrier Phase Measurements,” AIAA Guidance, Navigation, and Control Conference and Exhibit, 11-14 August 2003, Austin, Texas.
 Nadler, A. Bar-Itzhack, I. Y. & Weiss, H., “Iterative Algorithms for Attitude Estimation Using Global Positioning System Phase Measurements,” Journal of Guidance, Control, and Dynamics, vol. 24, No. 5, September–October 2001.
 Chun, C., & Park, F. C., “Dynamics-Based Attitude Determination Using the Global Positioning System,” Journal of Guidance, Control, and Dynamics, vol. 24, No. 3, May–June 2001.
 Li, Y., & Yuan, J., “Attitude Determination Using GPS Vector Observations”.
 Kuang, J., & Tan, S. “GPS-Based Attitude Determination of Gyrostat Satellite by Quaternion Estimation Algorithms,” Acta Astronautica, vol. 51, No. 11, pp. 743–759, 2002.
 Y. Li , K. Zhang , C. Roberts & M. Murata, “On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements,” GPS Solutions, vol.8,pp.93–102, 2004.
 Chin-Lang Tsai, Wei-Wen Kao, “Constrained total least-square solution for GPS compass attitude determination,” Applied Mathematics and Computation, vol.183, pp.106–118, 2006.
 Parkinson and Spilker, Global Positioning System: Theory & Applications”, Progress in Astronautics and Aeronautics, AIAA (American Institute of Aeronautics & Ast), 1st edition, 1996.
 Strang and Borre, “Linear Algebra, Geodesy, and GPS”, Wellesley College, 1997.
 P.J.G. Teunissen and A Kleusberg, “GPS for Geodesy”, Springer, Berlin Heidelberg ,New York, 1998.
 Leick, “GPS Satellite Surveying”, Wiley, 3rd edition, 2004.
 Misra and Enge, “Global Positioning System: Signals, Measurements and Performance”, Ganga-Jamuna Pr , 2001.
 Hofmann-Wellenhof et al., “Global Positioning System: Theory and Practice”, Springer; 5th edition 2001.
 Peter Buist ,“ The baseline constrained LAMBDA method for single Epoch, single Frequency Attitude Determination Applications”,
 Y. Li , K. Zhang , C. Roberts and M. Murata, “On-The-Fly GPS-Based Attitude Determination Using Single- And Double-Differenced Carrier Phase Measurements,”GPS Solutions, 2004.
 P.J. Buist, P.J.G. Teunissen, G. Giorgi, S. Verhagen, “Instantaneous GNSS-based Kinematic Relative Positioning and Attitude Determination using Multi-Antenna Configurations”.
 P.J.G. Teunissen, “GNSS Ambiguity Resolution for Attitude Determination: Theory and Method”.
 Gabriele Giorgi and Peter J. Buist, “ Single-epoch, single-frequency, standalone full attitude determination: experimental results” , NAVITECH 2008.
 Verhagen, Sandra, “The GNSS integer ambiguities: estimation and validation”, PhD Thesis, Delft Institute of Earth Observation and Space Systems, Delft University of Technology, Netherlands.
 Hatch R, “Instantaneous ambiguity resolution”. Proc. of KIS'90, Ban, Canada, 1990.
 Frei E, Beutler G, “Rapid static positioning based on the fast ambiguity resolution approach FARA: theory and first results”. Manuscripta Geodaetica, 15: 325-356, 1990.
 Euler HJ, Landau H “Fast GPS ambiguity resolution on-the-fly for realtime application”, Proc. of sixth International Geodetic Symposium on Satellite Positioning, 1992.
 Teunissen PJG, “Least squares estimation of the integer GPS ambiguities. Invited lecture, Section IV Theory and Methodology”, IAG General Meeting, Beijing, 1992.
 Martfin-Neira M, Toledo M, Pelaez A “The null space method for GPS integer ambiguity resolution”. Proc. of DSNS'95, Bergen, Norway, paper no.31. 1995.
 Chen D, Lachapelle G “A comparison of the FASF and least-squares search algorithms for on-the-fly ambiguity resolution”, Navigation, 42(2): 371-390., 1995.
 Harris RA “Direct resolution of carrier-phase ambiguity by 'Bridging the wavelength gap'. ESA publication "TST/60107/RAH/Word", 1997.
 Vollath U, Birnbach S, Landau H, Fraile-Ordofnez JM, Martfin-Neira M “ Analysis of Three-Carrier Ambiguity Resolution (TCAR) Technique for precise relative positioning in GNSS-2” Proc. of ION GPS-1998, Nashville TN: 417- 426.
 Kim D, Langley RB “An optimized least-squares technique for improving ambiguity resolution performance and computational efficiency”, Proc. of ION GPS-1999, Nashville TN: 1579-1588.
 Jung J, Enge P, Pervan B “Optimization of Cascade Integer Resolution with three civil GPS frequencies”. Proc. of ION GPS-2000, Salt Lake City UT: 2191-2200.
 Joosten P, Verhagen S “Analysis of ambiguity resolution algorithms and quality control parameters for Global Navigations Satellite Systems” ESA publication, contract no. "16793/02/NL/LvH".2003.
 Verhagen S, Joosten P “Analysis of ambiguity resolution algorithms”. Proc. of the European Navigation Conference GNSS Rotterdam NL, 2004.
 P.J.G. Teunissen and S. Verhagen, “Challenges and Open Problems”,
 Teunissen PJG “An optimality property of the integer least-squares estimator”, Journal of Geodesy, 73: 587-593, 1999.
 Teunissen PJG, “A class of unbiased integer GPS ambiguity estimators”. Artificial Satellites, 33(1): 4-10, 1998.
 Buist, P. J. Teunissen, “The Baseline Constrained LAMBDA Method for Single Epoch, Single Frequency Attitude Determination Applications”. Proceedings of ION GPS, Fort Worth, TX, US, 2962-2973. 2007.
 Gabriele, Peter J. G. Teunissen , “Single-frequency, Single-epoch, Carrier Phase GNSS Attitude Determination with the Multivariate Constrained LAMBDA Method”
 Teunissen, P. J. G. “A General Multivariate Formulation of the Multi- Antenna GNSS Attitude Determination Problem”, Artificial Satellites 42 (2), 97-111,2007.