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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 1 February 2001 / Accepted: 18 July 2001
Rights and permissions
About this article
Cite this article
Gundlich, B., Koch, KR. Confidence regions for GPS baselines by Bayesian statistics. Journal of Geodesy 76, 55–62 (2002). https://doi.org/10.1007/s001900100222
Issue Date:
DOI: https://doi.org/10.1007/s001900100222