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DIA-Estimator and Multidimensional Model Misspecifications: GNSS-based Positioning Safety Analysis for UAV.

Sebastian Ciuban1, Peter J G Teunissen1,2,3, Christian C J M Tiberius1

  • 1Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, The Netherlands.

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Summary
This summary is machine-generated.

This study introduces a positioning safety analysis using the Detection, Identification, and Adaptation (DIA)-estimator to assess multidimensional model errors. It quantifies positioning failure probability, crucial for safety-critical systems like automotive and aviation.

Keywords:
DIA-EstimatorMultidimensional model misspecificationsPositioning safetyProbability of positioning failure

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Area of Science:

  • Navigation Systems
  • Statistical Signal Processing
  • Aerospace Engineering

Background:

  • Model misspecifications, particularly multidimensional ones like simultaneous outliers, pose challenges in parameter estimation and hypothesis testing.
  • Existing research often focuses on detecting and identifying these misspecifications, with less attention paid to their impact on positioning safety.
  • Safety-critical applications (automotive, aviation, rail, maritime) require robust positioning with quantifiable failure probabilities.

Purpose of the Study:

  • To present a positioning safety analysis framework based on the Detection, Identification, and Adaptation (DIA)-estimator.
  • To investigate the effect of multidimensional model misspecifications on the DIA-estimator's probability density function (PDF).
  • To formulate and quantify the probability of positioning failure for safety-critical navigation systems.

Main Methods:

  • Utilized the DIA-estimator framework to analyze positioning safety under multidimensional model misspecifications.
  • Developed methods to formulate and quantify the probability of positioning failure and its conditional components.
  • Conducted a simulation-based study using a UAV with a GPS receiver, analyzing fixed and varying satellite geometries over a 24-hour period in the Netherlands.

Main Results:

  • The study quantifies the probability of positioning failure, a key safety indicator for navigation systems.
  • Analysis revealed insights into the DIA-estimator's PDF structure, including multimodality and orientation relative to safety regions.
  • The simulation demonstrated the impact of GPS satellite geometry on positioning safety evaluation.

Conclusions:

  • The DIA-estimator framework provides a robust approach for positioning safety analysis, especially concerning multidimensional model misspecifications.
  • Quantifying positioning failure probability is essential for ensuring the safety of life-critical navigation applications.
  • The presented methodology is generalizable to multisensor configurations, other GNSS constellations, and diverse safety-critical applications.