TY - GEN
T1 - How Abnormal Are the PDFs of the DIA Method
T2 - 9th Hotine-Marussi Symposium on Mathematical Geodesy, 2018
AU - Zaminpardaz, Safoora
AU - Teunissen, Peter J.G.
N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care 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.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Detection, identification and adaptation (DIA)
KW - DIA-estimator
KW - Global Navigation Satellite System (GNSS)
KW - Probability density function (PDF)
KW - Statistical testing
UR - http://www.scopus.com/inward/record.url?scp=85092142046&partnerID=8YFLogxK
U2 - 10.1007/1345_2019_57
DO - 10.1007/1345_2019_57
M3 - Conference contribution
AN - SCOPUS:85092142046
SN - 9783030542665
T3 - International Association of Geodesy Symposia
SP - 89
EP - 97
BT - 9th Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium in Rome, 2018
A2 - Novák, Pavel
A2 - Crespi, Mattia
A2 - Sneeuw, Nico
A2 - Sansò, Fernando
PB - Springer
CY - Cham
Y2 - 18 June 2018 through 22 June 2018
ER -