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2015 | Online First | Chapter

Multivariate GNSS Attitude Integrity: The Role of Affine Constraints

Authors : Gabriele Giorgi, Peter J. G. Teunissen

Published in: International Association of Geodesy Symposia

Publisher: Springer International Publishing

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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.
Literature
go back to reference Baarda W (1968) A testing procedure for use in geodetic networks. Netherlands Geodetic Commission Publications on Geodesy, vol. 2, issue 5, 97 p Baarda W (1968) A testing procedure for use in geodetic networks. Netherlands Geodetic Commission Publications on Geodesy, vol. 2, issue 5, 97 p
go back to reference Bar-Itzhack IY, Montgomery P, Garrick J (1998) Algorithm for attitude determination using global positioning system. J Guid Control Dyn 21(6):846–852CrossRef Bar-Itzhack IY, Montgomery P, Garrick J (1998) Algorithm for attitude determination using global positioning system. J Guid Control Dyn 21(6):846–852CrossRef
go back to reference Cohen CE (1992) Attitude determination using GPS. Ph.D. Thesis, Stanford University, Palo Alto, CA Cohen CE (1992) Attitude determination using GPS. Ph.D. Thesis, Stanford University, Palo Alto, CA
go back to reference Giorgi G (2011) GNSS carrier phase-based attitude determination. Estimation and applications. Delft University of Technology Giorgi G (2011) GNSS carrier phase-based attitude determination. Estimation and applications. Delft University of Technology
go back to reference Giorgi G, Teunissen PJG (2013) Low-complexity instantaneous ambiguity resolution with the affine-constrained GNSS attitude model. IEEE Trans Aerosp Electron Syst 49(3):1745–1759CrossRef Giorgi G, Teunissen PJG (2013) Low-complexity instantaneous ambiguity resolution with the affine-constrained GNSS attitude model. IEEE Trans Aerosp Electron Syst 49(3):1745–1759CrossRef
go back to reference 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):51–67CrossRef 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):51–67CrossRef
go back to reference Giorgi G, Teunissen PJG, Verhagen S, Buist PJ (2012) Integer ambiguity resolution with nonlinear geometrical constraints. IAG Symp 137:39–45 Giorgi G, Teunissen PJG, Verhagen S, Buist PJ (2012) Integer ambiguity resolution with nonlinear geometrical constraints. IAG Symp 137:39–45
go back to reference Shuster MD (1993) A survey of attitude representations. J Astronaut Sci 41(4):439–517 Shuster MD (1993) A survey of attitude representations. J Astronaut Sci 41(4):439–517
go back to reference Strang G, Borre K (1997) Linear algebra, geodesy, and GP. Wellesley-Cambridge Press, Welleseley Strang G, Borre K (1997) Linear algebra, geodesy, and GP. Wellesley-Cambridge Press, Welleseley
go back to reference 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 (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
go back to reference Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593CrossRef Teunissen PJG (1999) An optimality property of the integer least-squares estimator. J Geod 73(11):587–593CrossRef
go back to reference Teunissen PJG (2006) Testing theory: an introduction. Series on mathematical geodesy and positioning, 2nd edn. Delft Academic Press, Orlando Teunissen PJG (2006) Testing theory: an introduction. Series on mathematical geodesy and positioning, 2nd edn. Delft Academic Press, Orlando
go back to reference Teunissen PJG (2007) A general multivariate formulation of the multi-antenna GNSS attitude determination problem. Artif Satell 42(2):97–111CrossRef Teunissen PJG (2007) A general multivariate formulation of the multi-antenna GNSS attitude determination problem. Artif Satell 42(2):97–111CrossRef
go back to reference Teunissen PJG (2012) The affine constrained GNSS attitude model and its multivariate integer least-squares solution. J Geod 86:547–563CrossRef Teunissen PJG (2012) The affine constrained GNSS attitude model and its multivariate integer least-squares solution. J Geod 86:547–563CrossRef
go back to reference Teunissen PJG, Kleusberg A (1998) GPS for geodesy, 2nd edn. Springer/Heidelberg, Berlin/New YorkCrossRef Teunissen PJG, Kleusberg A (1998) GPS for geodesy, 2nd edn. Springer/Heidelberg, Berlin/New YorkCrossRef
Metadata
Title
Multivariate GNSS Attitude Integrity: The Role of Affine Constraints
Authors
Gabriele Giorgi
Peter J. G. Teunissen
Copyright Year
2015
DOI
https://doi.org/10.1007/1345_2015_1