Confidence regions for GPS baselines by Bayesian statistics |
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| Authors: | B Gundlich K-R Koch |
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| Institution: | (1) Institute for Theoretical Geodesy, University of Bonn, Nussallee 17, 53115 Bonn, Germany e-mail: koch@theor.geod.uni-bonn.de; Tel.: +49-228-73-3395; Fax: +49-228-73-3029, DE |
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| Abstract: | The global positioning system (GPS) model is distinctive in the way that the unknown parameters are not only real-valued,
the baseline coordinates, but also integers, the phase ambiguities. The GPS model therefore leads to a mixed integer–real-valued
estimation problem. Common solutions are the float solution, which ignores the ambiguities being integers, or the fixed solution,
where the ambiguities are estimated as integers and then are fixed. Confidence regions, so-called HPD (highest posterior density)
regions, for the GPS baselines are derived by Bayesian statistics. They take care of the integer character of the phase ambiguities
but still consider them as unknown parameters. Estimating these confidence regions leads to a numerical integration problem
which is solved by Monte Carlo methods. This is computationally expensive so that approximations of the confidence regions
are also developed. In an example it is shown that for a high confidence level the confidence region consists of more than
one region.
Received: 1 February 2001 / Accepted: 18 July 2001 |
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| Keywords: | : GPS Ambiguities – Mixed Integer– real-valued Estimation Problem – Bayesian Statistics – HPD Confidence Region – Monte Carlo Integration |
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