Integer variables estimation problems: the Bayesian approach
Main Article Content
Abstract
In geodesy as well as in geophysics there are a number of examples where the unknown parameters are partly constrained to be integer numbers, while other parameters have a continuous range of possible values. In all such situations the ordinary least square principle, with integer variates fixed to the most probable integer value, can lead to paradoxical results, due to the strong non-linearity of the manifold of admissible values. On the contrary an overall estimation procedure assigning the posterior distribution to all variables, discrete and continuous, conditional to the observed quantities, like the so-called Bayesian approach, has the advantage of weighting correctly the possible errors in choosing different sets of integer values, thus providing a more realistic and stable estimate even of the continuous parameters. In this paper, after a short recall of the basics of Bayesian theory in section 2, we present the natural Bayesian solution to the problem of assessing the estimable signal from noisy observations in section 3 and the Bayesian solution to cycle slips detection and repair for a stream of GPS measurements in section 4. An elementary synthetic example is discussed in section 3 to illustrate the theory presented and more elaborate, though synthetic, examples are discussed in section 4 where realistic streams of GPS observations, with cycle slips, are simulated and then back processed.
Article Details
How to Cite
Sansò, F. and Venuti, G. (1997) “Integer variables estimation problems: the Bayesian approach”, Annals of Geophysics, 40(5). doi: 10.4401/ag-3878.
Issue
Section
OLD
Open-Access License
No Permission Required
Istituto Nazionale di Geofisica e Vulcanologia applies the Creative Commons Attribution License (CCAL) to all works we publish.
Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, so long as the original authors and source are cited. No permission is required from the authors or the publishers.
In most cases, appropriate attribution can be provided by simply citing the original article.
If the item you plan to reuse is not part of a published article (e.g., a featured issue image), then please indicate the originator of the work, and the volume, issue, and date of the journal in which the item appeared. For any reuse or redistribution of a work, you must also make clear the license terms under which the work was published.
This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your own work will ensure your right to make your work freely and openly available. For queries about the license, please contact ann.geophys@ingv.it.