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Conditional Entropy and Location Error in Indoor Localization Using Probabilistic Wi-Fi Fingerprinting.

Rafael Berkvens1, Herbert Peremans2, Maarten Weyn3

  • 1iMinds, MOSAIC, University of Antwerp, Faculty of Applied Engineering, Antwerp 2020, Belgium. rafael.berkvens@uantwerpen.be.

Sensors (Basel, Switzerland)
|October 6, 2016
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Summary

This study introduces conditional entropy as a dynamic measure of localization uncertainty, complementing traditional location error. This new method offers a more accurate assessment of localization system performance without needing ground truth data.

Keywords:
Wi-Ficonditional entropyfingerprintingindoorinformation theorylocalizationlocation erroruncertainty

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Area of Science:

  • Computer Science
  • Electrical Engineering
  • Robotics

Background:

  • Localization systems are crucial, but their utility depends on knowing the uncertainty of location estimates.
  • Current methods use location error against ground truth, a static measure unsuitable for dynamic environments.
  • This static approach fails to capture real-time uncertainty variations during localization.

Purpose of the Study:

  • To propose conditional entropy as a dynamic and complementary measure of localization uncertainty.
  • To demonstrate that conditional entropy can be calculated during localization using sensor measurements.
  • To validate the relationship between conditional entropy and location error across different sensor model implementations.

Main Methods:

  • Conditional entropy of posterior probability distribution was calculated as a measure of uncertainty.
  • This dynamic measure was compared against traditional location error using three public datasets.
  • Probabilistic Wi-Fi fingerprinting with eight sensor model implementations was employed for validation.

Main Results:

  • Conditional entropy provides a dynamic uncertainty measure, independent of ground truth.
  • A relationship exists: low entropy correlates with small location error; high entropy can indicate small or large errors.
  • Discrepancies between measures were largest for unrealistic sensor models, highlighting conditional entropy's sensitivity.

Conclusions:

  • Conditional entropy is a valuable, dynamic, and complementary uncertainty measure for localization.
  • It is applicable to both continuous and discrete localization algorithms.
  • This measure offers an essential, extra dimension for characterizing localization method performance.