Integer Ambiguity Resolution with Nonlinear Geometrical Constraints
Integer ambiguity resolution is the key to obtain very accurate positioning solutions out of the GNSS observations. The Integer Least Squares (ILS) principle, a derivation of the least-squares principle applied to a linear system of equations in which some of the unknowns are subject to an integer constraint, was demonstrated to be optimal among the class of admissible integer estimators. In this contribution it is shown how to embed into the functional model a set of nonlinear geometrical constraints, which arise when considering a set of antennae mounted on a rigid platform. A method to solve for the new model is presented and tested: it is shown that the strengthened underlying model leads to an improved capacity of fixing the correct integer ambiguities.
KeywordsConstrained methods GNSS Integer ambiguity resolution
Professor P.J.G. Teunissen is the recipient of an Australian Research Council Federation Fellowship (project number FF0883188): this support is greatly acknowledged.
The research of S. Verhagen is supported by the Dutch Technology Foundation STW, applied science division of NWO and the Technology Program of the Ministry of Economic Affairs.
- Battin RH (1987) An introduction to the mathematics and methods of astrodynamics. AIAA Education Series, New YorkGoogle Scholar
- Buist PJ (2007) The baseline constrained LAMBDA method for single epoch, single frequency attitude determination applications. In: Proceedings of ION GPS, 2007Google Scholar
- Giorgi G, Buist PJ (2008) Single-epoch, single frequency, standalone full attitude determination: experimental results. In: 4th ESA workshop on satellite navigation user equipment technologies, NAVITEC, 2008Google Scholar
- Giorgi G, Teunissen PJG, Buist PJ (2008) A search and shrink approach for the baseline constrained LAMBDA: experimental results. In: Proceedings of the international symposium on GPS/GNSS 2008, Tokyo, Japan, 2008Google Scholar
- Goldstein H (1980) Classical mechanics. Addison-Wesley Pub. Co., MassachusettsGoogle Scholar
- Park C, Teunissen PJG (2003) A new carrier phase ambiguity estimation for GNSS attitude determination systems. In: Proceedings of international GPS/GNSS symposium, Tokyo, 2003Google Scholar
- Teunissen PJG (1993) Least squares estimation of the integer GPS ambiguities. Invited lecture, Section IV theory and methodology, IAG General Meeting, Beijing. Also in: LGR series No.6, Delft Geodetic Computing Center, Delft University of TechnologyGoogle Scholar
- Teunissen PJG (1994) A new method for fast carrier phase ambiguity estimation. In: Proceedings IEEE position location and navigation symposium, PLANS ‘94, pp 562–573Google Scholar
- Teunissen PJG (2006) The LAMBDA method for the GNSS compass. Artificial Satellites. J Planet Geodes 41(3):88–103Google Scholar
- Teunissen PJG (2008) GNSS ambiguity resolution for attitude determination: theory and method. In: Proceedings of the international symposium on GPS/GNSS 2008, Tokyo, Japan, 11–14 November, 2008Google Scholar