Integer least squares with quadratic equality constraints and its application to GNSS attitude determination systems
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In this paper we introduce the quadratically constrained integer least-squares problem and show how the LAMBDA method can be used to solve it for the purpose of GNSS attitude determination. The integer least-squares principle with quadratic equality constraints (ILSQE) is used to formulate our cost function. The solution of the ILSQE problem is derived and it is shown how the solution can be computed efficiently and rigorously with a novel LAMBDA based method. Experimental results with various single frequency GPS receivers are given to show the effectiveness of the proposed method. The method is also compared with some current methods of GNSS attitude determination. Apart from its efficiency, the proposed method is shown to dramatically improve the success rates of integer ambiguity GNSS attitude resolution.
KeywordsAttitude determination GNSS ILSQE integer ambiguity BC-LAMBDA
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- Ashtech, “ADU5: GNSS sensors and marine survey solutions,” http://products.thalesnavigation.com/en/products/index.asp, 2003.
- I. Y. Bar-Itzhack, P. Montgomery, and J. Garrick, “Algorithm for attitude determination using GPS,” Proc. of AIAA Guidance, Navigation and Control Conf., New Orleans, LA, USA Paper no. AIAA 97-3616, Aug. 1997.Google Scholar
- C. E. Cohen, Attitude Determination Using GPS, Ph.D. Thesis, Stanford University, 1992.Google Scholar
- Furuno Electric Co., “Model SC-120: Satellite compass,” http://www.furuno.co.jp/english/index.html, 2003.
- G. H. Golub and C. F. van Loan, Matrix Computations, 2nd edition, The Johns Hopkins University Press, Baltimore, Maryland, USA, 1998.Google Scholar
- R. R. Hatch and H. J. Euler, “Comparison of several kinematic techniques,” Proc. of ION GPS-94, Salt Lake City, Utah, USA pp. 363–370, September 20–23, 1994.Google Scholar
- P. J. Jong de and C. C. J. M. Tiberius, The LAMBDA Method For Integer Ambiguity Estimation: Implementation Aspects, Delft Geodetic Computing Centre LGR series, no. 12, 1996.Google Scholar
- P. Joosten, The LAMBDA-Method: Matlab™ Implementation. Matlab Toolbox and Manual, Mathematical Geodesy and Positioning, TU Delft, 2001.Google Scholar
- G. Lu, “Development of a GPS multi-antenna system for attitude determination,” UCGE Reports 20073, Dept. of Geomatics Eng., University of Calgary, 1995.Google Scholar
- C. Park, I. Kim, G. I. Jee, and J. G. Lee, “Efficient ambiguity search using constraints equation,” Proc. of IEEE Position, Location and Navigation Symposium PLANS’96, Atlanta, Georgia, USA, 1996.Google Scholar
- C. Park and I. Kim, “An error analysis of 2-dimensional attitude determination using global positioning system,” IEICE Transaction on Communications, vol. E83-B, no. 6, pp. 1370–1373, 2000.Google Scholar
- C. Park and P. J. G. Teunissen, “A baseline constrained LAMBDA method for an integer ambiguity resolution of GNSS attitude determination system,” Journal of Institute of Control, Robotics and Systems (in Korean), vol. 14, no. 6, pp. 587–594, June 2008.Google Scholar
- P. J. G. Teunissen, Least-squares Estimation of the Integer Ambiguities, Delft Geodetic Computing Centre LGR series, no. 6, 1993.Google Scholar
- P. J. G. Teunissen, “A new method for fast carrier phase ambiguity estimation,” Proc. of IEEE Position, Location and Navigation Symposium PLANS’94, Las Vegas, NV, USA, pp. 562–573, April 11–15, 1994.Google Scholar
- P. J. G. Teunissen and A. Kleusberg editors, GPS for Geodesy, 2nd edition, Springer-Verlag, Berlin, Germany, 1998.Google Scholar
- P. J. G. Teunissen, “GNSS ambiguity bootstrapping: theory and application,” Proc. of International Symposium on Kinematic Systems in Geodesy, Geomatics and Navigation, Banff, Canada, pp. 246–254, 2001.Google Scholar
- P. J. G. Teunissen, “Theory of carrier phase ambiguity resolution,” Proc. of the 9th GNSS workshop-2002 International Symposium on GPS/GNSS, November 6–8, Wuhan, China, 2002.Google Scholar
- C. C. J. M. Tiberius, Recursive Data Processing for Kinematic GPS Surveying, Ph.D. Thesis, Mathematical Geodesy and Positioning, TU Delft, 1998.Google Scholar
- C. H. Tu, K. Y. Wang, and W. C. Melton, “GPS compass: a novel navigation equipment,” Proc. of ION National Technical Meeting, Santa Monica, CA, USA, 1996.Google Scholar
- S. Verhagen, Visualization of GNSS-related design parameters. Manual for Matlab User Interface Visual, Mathematical Geodesy and Positioning, TU Delft, 2002.Google Scholar
- M. Ziebart and P. Cross, “LEO GPS attitude determination algorithm for a macro-satellite using boom-arm deployed antennas,” GPS Solutions, vol. 6, pp. 242–256, 2003.Google Scholar