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DIA-datasnooping and identifiability.

S Zaminpardaz1, P J G Teunissen1,2

  • 11Department of Spatial Sciences, GNSS Research Centre, Curtin University, Perth, Australia.

Journal of Geodesy
|March 16, 2019
PubMed
Summary
This summary is machine-generated.

This study analyzes datasnooping within the DIA (Detection, Identification, and Adaptation) method for mismodelling errors. It clarifies how nonseparable hypotheses impact parameter adaptation in estimation and testing, offering insights into bias detection and identification.

Keywords:
DIA estimatorDatasnoopingDetection, identification and adaptation (DIA)Minimal detectable bias (MDB)Minimal identifiable bias (MIB)Misclosure space partitioningNonseparable hypothesesProbability of correct identification

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Area of Science:

  • Geodesy
  • Statistical Data Analysis
  • Metrology

Background:

  • The Detection, Identification, and Adaptation (DIA) method addresses mismodelling errors through estimation and testing.
  • Datasnooping is crucial for analyzing the combined estimation and testing procedures within the DIA framework.
  • Understanding the interplay between hypothesis nonseparability and parameter estimability is key to robust error analysis.

Purpose of the Study:

  • To present and analyze datasnooping within the context of the DIA method.
  • To investigate the conditions of hypothesis nonseparability in the identification step of the DIA estimator.
  • To explore the implications of nonseparability on parameter adaptation and the structure of the DIA estimator.

Main Methods:

  • Development and analysis of the DIA estimator, integrating estimation and testing.
  • Mathematical analysis of DIA-datasnooping decision probabilities and misclosure space partitioning.
  • Application of a theorem linking hypothesis nonseparability to parameter inestimability.

Main Results:

  • Demonstrated that nonseparable hypotheses preclude adaptation of the complete parameter vector.
  • Identified parameter functions that may still be adaptable even when the complete vector is not.
  • Analyzed the impact of measurement setup geometry on testing procedures, decision probabilities, and minimal biases.

Conclusions:

  • Nonseparability in the DIA method implies that certain parameters cannot be estimated or adapted.
  • The structure of the DIA estimator is altered when parameter functions are adaptable despite hypothesis nonseparability.
  • Geometric configurations in measurement setups significantly influence the sensitivity of the testing procedure to biases.