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Sensors 2016, 16(10), 1636; doi:10.3390/s16101636

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

1
iMinds, MOSAIC, University of Antwerp, Faculty of Applied Engineering, Antwerp 2020, Belgium
2
Engineering Management, University of Antwerp, Faculty of Applied Economics, Antwerp 2000, Belgium
*
Author to whom correspondence should be addressed.
Academic Editor: Fan Ye
Received: 15 July 2016 / Revised: 24 September 2016 / Accepted: 27 September 2016 / Published: 2 October 2016
(This article belongs to the Section Physical Sensors)
View Full-Text   |   Download PDF [1039 KB, uploaded 2 October 2016]   |  

Abstract

Localization systems are increasingly valuable, but their location estimates are only useful when the uncertainty of the estimate is known. This uncertainty is currently calculated as the location error given a ground truth, which is then used as a static measure in sometimes very different environments. In contrast, we propose the use of the conditional entropy of a posterior probability distribution as a complementary measure of uncertainty. This measure has the advantage of being dynamic, i.e., it can be calculated during localization based on individual sensor measurements, does not require a ground truth, and can be applied to discrete localization algorithms. Furthermore, for every consistent location estimation algorithm, both the location error and the conditional entropy measures must be related, i.e., a low entropy should always correspond with a small location error, while a high entropy can correspond with either a small or large location error. We validate this relationship experimentally by calculating both measures of uncertainty in three publicly available datasets using probabilistic Wi-Fi fingerprinting with eight different implementations of the sensor model. We show that the discrepancy between these measures, i.e., many location estimates having a high location error while simultaneously having a low conditional entropy, is largest for the least realistic implementations of the probabilistic sensor model. Based on the results presented in this paper, we conclude that conditional entropy, being dynamic, complementary to location error, and applicable to both continuous and discrete localization, provides an important extra means of characterizing a localization method. View Full-Text
Keywords: location error; uncertainty; conditional entropy; localization; Wi-Fi; fingerprinting; indoor; information theory location error; uncertainty; conditional entropy; localization; Wi-Fi; fingerprinting; indoor; information theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Berkvens, R.; Peremans, H.; Weyn, M. Conditional Entropy and Location Error in Indoor Localization Using Probabilistic Wi-Fi Fingerprinting. Sensors 2016, 16, 1636.

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