Abstract
In this contribution we determine the first two moments of the ‘fixed’ GPS baseline. The first two moments of the ‘float’ solution are well-known. They follow from standard adjustment theory. In order to determine the corresponding moments of the ’fixed’ solution, the probabilistic characteristics of the integer least-squares ambiguities need to be taken into account. It is shown that the ‘fixed’ GPS baseline estimator is unbiased in case the probability density function of the real-valued least-squares ambiguity vector is symmetric about its integer mean. We also determine the variance matrix of the ‘fixed’ GPS baseline. This matrix differs from the one which is usually used in practice. The difference between the two matrices is made up of the precision contribution of the integer least-squares ambiguities.
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Hofmann-Wellenhof B, Lichtenegger H, Collins J 1997: Global Positioning System: Theory and practice. 4th edition. Springer Verlag
Kleusberg A, Teunissen P J G eds 1996: GPS for geodesy. Lecture notes in Earth sciences. Vol. 60, Springer Verlag
Leick A 1995: GPS satellite surveying. 2nd edition, John Wiley, New York
Strang G, Borre K 1997: Linear algebra, geodesy, and GPS. Wellesley-Cambridge Press
Teunissen P J G 1990: In: Een halve eeuw in de goede richting, Lustrumboek Snellius. 215–233.
Teunissen P J G 1993: Least-squares estimation of the integer GPS ambiguities. Invited Lecture, Section IV Theory and Methodology, IAG General Meeting, Beijing, China, 1993. Also in: LGR Series, No. 6, Delft Geodetic Computing Centre
Teunissen, P J G 1997: Artificial Satellites, 32, No. 3, 119–130.
Teunissen, P J G 1998: On the integer normal distribution of the GPS ambiguities. Artificial Satellites (in press)
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Teunissen, P.J.G. The Mean and the Variance Matrix of the ‘Fixed’ GPS Baseline. Acta Geod. Geoph. Hung 34, 33–40 (1999). https://doi.org/10.1007/BF03325555
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DOI: https://doi.org/10.1007/BF03325555