How Abnormal Are the PDFs of the DIA Method: A Quality Description in the Context of GNSS
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 combi
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Abstract
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 xN must also be driven by the probabilistic characteristics of both estimation and testing. In practice however, the evaluation of the quality of xN is never carried out as such. Instead, use is made of the probability density function (PDF) of the estimator under the identified hypothesis, say xO i , thereby thus neglecting the conditioning process that led to the decision to accept the i t h hypothesis. In this contribution, we conduct a comparative study of the probabilistic properties of xN and xO i . 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 xO i provides either poor or reasonable approximations to that of the DIA-estimator x. N Keywords
Detection, identification and adaptation (DIA) DIA-estimator Global Navigation Satellite System (GNSS) Probability density function (PDF) Statistical testing
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Introduction
In the DIA-method for the detection, identification and adaptation of mismodelling errors, next to estimation of S. Zaminpardaz () Geospatial Sciences, School of Science, RMIT University, Melbourne, VIC, Australia e-mail: [email protected] P. J. G. Teunissen Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, The Netherlands GNSS Research Centre, School of Earth and Planetary Sciences, Curtin University, Perth, WA, Australia e-mail: [email protected]
parameters of interest, a statistical testing is also exercised to check the validation of underlying model. The actual DIA outcome is then the one which rigorously captures this combination of estimation and testing, and was introduced as the DIA estimator in Teunissen (2017b). The DIA-method has been widely used in a variety of applications, including the quality control of geodetic networks and the integrity monitoring of GNSS models, see e.g. DGCC (1982), Teunissen (1990), Salzmann (1995), Tiberius (1998), Perfetti (2006), Khodabandeh and Teunissen (2016), Zaminpardaz et al. (2015). As a result of the combined estimation-testing scheme of the DIA-method, the DIA outcome xN must also be evaluated on the basis of characteristics of both estimation and testing. In practice however, the evaluation of the quality of xN is carried out based upon the probability density function (PDF) of the estimator under the identified hypothesis, say
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