dc.contributor.author Verhagen, S. dc.contributor.author Teunissen, Peter dc.date.accessioned 2017-01-30T13:16:40Z dc.date.available 2017-01-30T13:16:40Z dc.date.created 2012-06-11T02:32:57Z dc.date.issued 2006 dc.identifier.citation Verhagen, Sandra and Teunissen, Peter. 2006. On the probability density function of the GNSS ambiguity residuals. GPS Solutions. 10 (1): pp. 21-28. dc.identifier.uri http://hdl.handle.net/20.500.11937/30000 dc.identifier.doi 10.1007/s10291-005-0148-4 dc.description.abstract Integer GNSS ambiguity resolution involves estimation and validation of the unknown integer carrier phase ambiguities. A problem then is that the classical theory of linear estimation does not apply to the integer GPS model, and hence rigorous validation is not possible when use is made of the classical results. As with the classical theory, a first step for being able to validate the integer GPS model is to make use of the residuals and their probabilistic properties. The residuals quantify the inconsistency between data and model, while their probabilistic properties can be used to measure the significance of the inconsistency. Existing validation methods are often based on incorrect assumptions with respect to the probabilistic properties of the parameters involved. In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GPS carrier phase ambiguity residuals. The residuals and their properties depend on the integer estimation principle used. Since it is known that the integer least-squares estimator is the optimal choice from the class of admissible integer estimators, we will only focus on the PDF of the ambiguity residuals for this estimator. Unfortunately the PDF cannot be evaluated exactly. It will therefore be shown how to obtain a good approximation. The evaluation will be completed by some examples. dc.publisher John Wiley and Sons, Inc. dc.subject GNSS residuals dc.title On the probability density function of the GNSS ambiguity residuals dc.type Journal Article dcterms.source.volume 10 dcterms.source.number 1 dcterms.source.startPage 21 dcterms.source.endPage 28 dcterms.source.issn 15211886 dcterms.source.title GPS Solutions curtin.department curtin.accessStatus Open access
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