Abstract
In this work we analyze the integrity properties of an affine-constrained estimator applied to arrays of GNSS antennas. GNSS pseudorange and carrier phase measurements from multiple antennas whose relative positions are known are cast in a linearly-constrained observation model. The linear constraints are inherent to an affine transformation that is applied to the baseline coordinates. The affine transformation yields enhanced redundancy, thus improving the model integrity properties with respect to the unconstrained model. The extent of the improvement is measured in terms of internal and external reliability.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Baarda W (1968) A testing procedure for use in geodetic networks. Netherlands Geodetic Commission Publications on Geodesy, vol. 2, issue 5, 97 p
Bar-Itzhack IY, Montgomery P, Garrick J (1998) Algorithm for attitude determination using global positioning system. J Guid Control Dyn 21(6):846–852
Cohen CE (1992) Attitude determination using GPS. Ph.D. Thesis, Stanford University, Palo Alto, CA
Giorgi G (2011) GNSS carrier phase-based attitude determination. Estimation and applications. Delft University of Technology
Giorgi G, Teunissen PJG (2013) Low-complexity instantaneous ambiguity resolution with the affine-constrained GNSS attitude model. IEEE Trans Aerosp Electron Syst 49(3):1745–1759
Giorgi G, Teunissen PJG, Verhagen S, Buist PJ (2011) Instantaneous ambiguity resolution in GNSS-based attitude determination applications: the MC-LAMBDA method. J Guid Control Dyn 35(1):51–67
Giorgi G, Teunissen PJG, Verhagen S, Buist PJ (2012) Integer ambiguity resolution with nonlinear geometrical constraints. IAG Symp 137:39–45
Shuster MD (1993) A survey of attitude representations. J Astronaut Sci 41(4):439–517
Strang G, Borre K (1997) Linear algebra, geodesy, and GP. Wellesley-Cambridge Press, Welleseley
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 Technology
Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593
Teunissen PJG (2006) Testing theory: an introduction. Series on mathematical geodesy and positioning, 2nd edn. Delft Academic Press, Orlando
Teunissen PJG (2007) A general multivariate formulation of the multi-antenna GNSS attitude determination problem. Artif Satell 42(2):97–111
Teunissen PJG (2012) The affine constrained GNSS attitude model and its multivariate integer least-squares solution. J Geod 86:547–563
Teunissen PJG, Kleusberg A (1998) GPS for geodesy, 2nd edn. Springer/Heidelberg, Berlin/New York
Acknowledgements
The research of Peter J.G. Teunissen has been supported by an Australian Research Council Federation Fellowship (project number FF0883188).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Giorgi, G., Teunissen, P.J.G. (2015). Multivariate GNSS Attitude Integrity: The Role of Affine Constraints. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VIII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 142. Springer, Cham. https://doi.org/10.1007/1345_2015_1
Download citation
DOI: https://doi.org/10.1007/1345_2015_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24548-5
Online ISBN: 978-3-319-30530-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)