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.
Highlights
The location of the user is increasingly important information for context-aware applications.Examples are home automation [1], where heating and lighting automatically switches off when residents are away; smart cities that provide services to visitors and inhabitants through smart devices [2]; or a user at a shopping mall who wishes to know how to navigate to a particular shop [3]
We propose that a high quality sensor model is one for which validation samples that produce a posterior probability distribution with low conditional entropy have a low location error
We have studied the uncertainty of a Wi-Fi fingerprinting localization system by relating the location error with the conditional entropy in the location posterior probability distribution
Summary
The location of the user is increasingly important information for context-aware applications.Examples are home automation [1], where heating and lighting automatically switches off when residents are away; smart cities that provide services to visitors and inhabitants through smart devices [2]; or a user at a shopping mall who wishes to know how to navigate to a particular shop [3]. Apart from the location estimate itself, the uncertainty of this location estimate is provided, so that applications can choose between obtaining a higher certainty or using the current location estimate, improving other factors, such as interaction speed or energy efficiency. The uncertainty of this location estimate is often expressed as the expected location error, that is the difference between the location estimate and the actual location [4]. A static measure such as the Sensors 2016, 16, 1636; doi:10.3390/s16101636 www.mdpi.com/journal/sensors
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
