Theoretical entropy assessment of fingerprint-based Wi-Fi localization accuracy

•The entropy is employed as a new metric to evaluate the fingerprint-based Wi-Fi location accuracy.•The relations of entropy and accuracy with variable RP densities and standard deviations are given.•The reckless increase of the number of APs cannot be an effective way to improve location accuracy.•The substantial saving of computation cost by the entropy is achieved over the existing metrics. The fingerprint-based Wi-Fi localization technology has been recognized as one of the remarkable solutions to the future ubiquitous location based services (LBSs) in indoor and underground environment. Thus, how to evaluate the performance of fingerprint-based localization has attracted significant attentions. In this paper, we propose localization entropy as a novel metric to effectively and efficiently evaluate the accuracy of fingerprint-based Wi-Fi localization. Based on a simple N×M centrosymmetric model with the logarithmic Gaussian distribution, the relations among the localization precision, entropy and expected errors in the cases of none, one, two and three hearable access points (APs) have been carefully discussed. Furthermore, we conduct a series of simulations and experiments to examine the reliability and time-efficiency of our proposed performance metric (i.e., localization entropy) in a variety of reference point (RP) densities and received signal strength (RSS) standard deviations.