How Abnormal Are the PDFs of the DIA Method: A Quality Description in the Context of GNSS

Safoora Zaminpardaz*, Peter J.G. Teunissen

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

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The DIA-method, for the detection, identification and adaptation of modeling errors, has been widely used in a broad range of applications including the quality control of geodetic networks and the integrity monitoring of GNSS models. The DIA-method combines two key statistical inference tools, estimation and testing. Through the former, one seeks estimates of the parameters of interest, whereas through the latter, one validates these estimates and corrects them for biases that may be present. As a result of this intimate link between estimation and testing, the quality of the DIA outcome x̄ must also be driven by the probabilistic characteristics of both estimation and testing. In practice however, the evaluation of the quality of x̄ is never carried out as such. Instead, use is made of the probability density function (PDF) of the estimator under the identified hypothesis, say x̂i, thereby thus neglecting the conditioning process that led to the decision to accept the ith hypothesis. In this contribution, we conduct a comparative study of the probabilistic properties of x̄ and x̂i. Our analysis will be carried out in the framework of GNSS-based positioning. We will also elaborate on the circumstances under which the distribution of the estimator x̂i provides either poor or reasonable approximations to that of the DIA-estimator x̄.

Original languageEnglish
Title of host publication9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018
EditorsPavel Novák, Mattia Crespi, Nico Sneeuw, Fernando Sansò
Place of PublicationCham
Number of pages9
ISBN (Electronic)978-3-030-54267-2
ISBN (Print)9783030542665
Publication statusPublished - 2019
Event9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018 - Rome, Italy
Duration: 18 Jun 201822 Jun 2018

Publication series

NameInternational Association of Geodesy Symposia
ISSN (Print)0939-9585
ISSN (Electronic)2197-9359


Conference9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Detection, identification and adaptation (DIA)
  • DIA-estimator
  • Global Navigation Satellite System (GNSS)
  • Probability density function (PDF)
  • Statistical testing


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