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    On the probability density function of the GNSS ambiguity residuals

    186114_186114.pdf (399.2Kb)
    Access Status
    Open access
    Authors
    Verhagen, S.
    Teunissen, Peter
    Date
    2006
    Type
    Journal Article
    
    Metadata
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    Citation
    Verhagen, Sandra and Teunissen, Peter. 2006. On the probability density function of the GNSS ambiguity residuals. GPS Solutions. 10 (1): pp. 21-28.
    Source Title
    GPS Solutions
    DOI
    10.1007/s10291-005-0148-4
    ISSN
    15211886
    URI
    http://hdl.handle.net/20.500.11937/30000
    Collection
    • Curtin Research Publications
    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.

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