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

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.

Long-Term WiFi Fingerprinting Dataset for Research on Robust Indoor Positioning

“…The table shows that, in the mean case and for contiguous samples, the difference is not as significant as suggested by Figure 7. The difference is slightly higher than the likely variation of 1 dBm assumed in some studies [41]. The sample pair 1-2 has the largest difference (1 dBm more than the others), which indicates that the first sample may be buffered measurements taken by smartphone's software before the subject arrived to the collection position.…”

“…Prob: It is the known probabilistic method first presented by Youssef and Agrawala [44], which finds the position l (x, y, floor) from the training set that maximizes the probability of P (l|s), with s being the operational fingerprint and with P (s|l) = ∏ P (s i |l), where s i is the RSS value of the ith detected AP. In our settings, we have computed P (s i |l) in a similar way as Berkvens et al [41], specifically:…”

A Survey of Enabling Technologies for Network Localization, Tracking, and Navigation

“…While some progress has been reported recently, error estimation still needs further investigation [85], [86]. Authors in [85] propose a conditional entropy metric as a dynamic measure of the uncertainty associated to each position estimate, and conclude that a low value of the conditional entropy is highly correlated with small positioning errors, while high values of the conditional entropy are associated to both small and large errors. Aiming to dynamically estimate the positioning error, an extensive analysis was performed in [86] for the causes of large errors in Wi-Fi fingerprint matching, using both simulation and realworld data.…”

“…Hence, these approaches may fail in sparse anchor scenarios. Moreover, the distance estimates to the reliable anchors may include large errors, which means their Wi-Dist uses a convex-optimization formulation and fuses noisy fingerprints Applicable to various sensors and wireless fingerprints, with uncertain mutual distances given by their bounds up to 40% better accuracy than state-of-the-art [80] Integration of human-centric collaboration to improve accuracy by positive Robust with respect to malicious feedback, quickly and negative user feedback on their estimated locations self-correcting based on subsequent helpful feedback [81] Bayesian-rule based objective function and particle swarm optimization Kalman filter updates the initial location and tracks technique combined with Kalman filter for user tracking the user, thus mitigating the estimation error [82] Non-parametric information filter for Wi-Fi RSS fingerprints and sensor Sensitive to sensor drifting readings combined with RP selection, AP selection, and outlier detection [83] Bayesian filter predicts location from motion sensors and updates it with Sensitive to sensor drifting Wi-Fi fingerprint matching formulated as a compressive sensing problem [85] Conditional entropy metric as a dynamic measure of the uncertainty Low entropy values are correlated with small errors, associated to each position estimate high values may indicate small or large errors [86] Extensive analysis for the causes of large errors in Wi-Fi fingerprint Some large errors may be due to the geometry matching with the aim to dynamically estimate the positioning error of the space and access points placement [87] Parametric pathloss model for the GP mean and a non-parametric Using 23 RPs similar accuracy was achieved with covariance function to create the RSS radiomap with a few training data over 230 RPs for an office space of 2500 m 2 [88] Empirical Regional Propagation Model to construct the RSS radiomap Better prediction of RSS values than existing models, from sparse fingerprints through affinity propagation clustering 50% workload reduction for fingerprint data collection…”

RFID 3D-LANDMARC Localization Algorithm Based on Quantum Particle Swarm Optimization

“…The indoor localization with low complexity and high accuracy is one of the main challenges in today's wireless world [2]. In order to provide positioning and navigation in the indoor environment, various methods based on different technologies such as WSN-based networks [3,4], WIFI network [5,6], and RFID localization technology [7,8] have been proposed and developed. Among various indoor localization schemes, RFID technology has obtained more and more interest in localization systems development for its low cost, easy deployment, and successful utility in harsh environments in recent years [9].…”