Maxlifd: Joint Maximum Likelihood Localization Fusing ...gchan/papers/TMC19_Maxlifd.pdf · of using...

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Maxlifd: Joint Maximum Likelihood Localization Fusing Fingerprints and Mutual Distances Suining He , Member, IEEE, S.-H. Gary Chan , Senior Member, IEEE, Lei Yu, and Ning Liu Abstract—Fusing mutual distance information with fingerprints can substantially improve indoor localization accuracy. Such distance information may be spatial (e.g., measurement among users or from installed beaconing devices) or temporal (e.g., via dead-reckoning). Previous approaches on distance-fusion often require deterministic distance measurement, consider fingerprints and distances separately, or are narrowly applicable to some specific sensing technology or scenario. Given the fact that fingerprint and distance measurements are intrinsically random, we propose Maxlifd, an accurate indoor localization framework fusing fingerprints and distances of arbitrary distributions via joint maximum likelihood. Maxlifd is a generic statistical/probabilistic framework applicable to a wide range of sensors (peer-assisted, INS, iBeacon, etc.) and fingerprints (Wi-Fi, RFID, etc.). It achieves low localization errors by a novel optimization formulation jointly considering mutual distances and fingerprint signals. Using generic probabilistic formulation, we further derive the lower bound on localization error for comprehensive performance analysis. We have implemented Maxlifd, and conducted extensive simulation and experimental trials in an international airport and our university campus. Our results show that Maxlifd achieves significantly lower errors than other state-of-the-art schemes (often by more than 30 percent). We experimentally verify that its performance does not depend sensitively on the exact knowledge of the underlying distributions beyond simple Gaussian. Index Terms—Indoor localization, fusion, joint maximum likelihood, convex optimization, semi-definite programming, noisy fingerprints, mutual distances, measurement uncertainty Ç 1 INTRODUCTION I NDOOR location-based service has attracted much atten- tion in recent years due to its commercial potentials. The quality of such service largely depends on the accuracy of localization algorithm. Among all the explored techniques, fingerprint-based approach emerges as a promising one. Fingerprint-based indoor localization is usually con- ducted in two phases [1]. In the offline (survey) phase, a site survey is conducted to collect the vectors of received signal strength indicator (RSSI) at known locations, the so-called reference points (RPs). The vectors of these RSSIs form the fingerprints of the site and are stored in a database. In the online (query) phase, a user (also known as target) samples an RSSI vector at his location and reports it to the server, which estimates and returns the user location. (Another possibility is to compute the location locally at mobiles, if the fingerprints have been downloaded.) Error in location estimation is inevitable. This is due to random signal fluctuation in both offline and online meas- urements. It has been observed that localization error can be quite high (more than 10 m [1], [2], [3]) under large open indoor environment such as malls, train stations or airports. This is unsatisfactory for many applications. In order to sub- stantially enhance accuracy, one may embed, or fuse, finger- printing with mutual distance information. Mutual distance information can be spatial, where the target estimates the distance to other users or beaconing devices in its neighborhood. This can be done using differ- ent sensing techniques: Bluetooth [4], Wi-Fi direct [5], sound [6], etc. While there have been impressive works on using spatial distance for localization, they often assume accurate distance measurements, resulting in rigid con- straints over the fingerprints. These approaches cannot be easily extended or applied to the more realistic scenarios when distance estimation is random. Besides spatial, the distance information can also be tem- poral, where the target estimates its displacement over time (e.g., by the step counter or inertial navigation system (INS) provided in one’s mobile phone). Previous approaches (like particle filter [3], [7] or Hidden Markov Model [8], [9]) in this setting often treat Wi-Fi fingerprints and pedestrian distance measurements as separate, and hence sequentially consider them. This consideration of independence may be hardly satisfactory for accurate localization, as measured fingerprints and distances are inherently correlated (cou- pled) and better jointly optimized. Given noisy/random sen- sor measurement, prior works may not fully address the issue of large positioning error. Due to signal fluctuations, wireless fingerprint is inher- ently noisy, and estimated distance is random. In this paper, we propose Maxlifd, a novel maximum likelihood framework fusing noisy wireless fingerprints and random mutual distan- ces to achieve highly accurate indoor localization. Maxlifd jointly considers fingerprints and distances, both of arbitrary S. He and S.-H. G. Chan are with the Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China. E-mail: {sheaa, gchan}@cse.ust.hk. L. Yu and N. Liu are with the School of Software, Sun Yat-sen University, Guangzhou, Guangdong 510275, China. E-mail: [email protected], [email protected]. Manuscript received 25 Apr. 2016; revised 5 Feb. 2018; accepted 16 May 2018. Date of publication 29 May 2018; date of current version 4 Feb. 2019. (Corresponding author: Ning Liu.) For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference the Digital Object Identifier below. Digital Object Identifier no. 10.1109/TMC.2018.2841842 602 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 18, NO. 3, MARCH 2019 1536-1233 ß 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See ht_tp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Transcript of Maxlifd: Joint Maximum Likelihood Localization Fusing ...gchan/papers/TMC19_Maxlifd.pdf · of using...

Page 1: Maxlifd: Joint Maximum Likelihood Localization Fusing ...gchan/papers/TMC19_Maxlifd.pdf · of using iBeacons for indoor localization. The work in [27] investigates the performance

Maxlifd: Joint Maximum Likelihood LocalizationFusing Fingerprints and Mutual DistancesSuining He ,Member, IEEE, S.-H. Gary Chan , Senior Member, IEEE, Lei Yu, and Ning Liu

Abstract—Fusing mutual distance information with fingerprints can substantially improve indoor localization accuracy. Such distance

information may be spatial (e.g., measurement among users or from installed beaconing devices) or temporal (e.g., via

dead-reckoning). Previous approaches on distance-fusion often require deterministic distance measurement, consider fingerprints and

distances separately, or are narrowly applicable to some specific sensing technology or scenario. Given the fact that fingerprint and

distance measurements are intrinsically random, we proposeMaxlifd, an accurate indoor localization framework fusing fingerprints

and distances of arbitrary distributions via joint maximum likelihood. Maxlifd is a generic statistical/probabilistic framework applicable

to a wide range of sensors (peer-assisted, INS, iBeacon, etc.) and fingerprints (Wi-Fi, RFID, etc.). It achieves low localization errors by

a novel optimization formulation jointly considering mutual distances and fingerprint signals. Using generic probabilistic formulation, we

further derive the lower bound on localization error for comprehensive performance analysis. We have implemented Maxlifd, and

conducted extensive simulation and experimental trials in an international airport and our university campus. Our results show that

Maxlifd achieves significantly lower errors than other state-of-the-art schemes (often by more than 30 percent). We experimentally

verify that its performance does not depend sensitively on the exact knowledge of the underlying distributions beyond simple Gaussian.

Index Terms—Indoor localization, fusion, joint maximum likelihood, convex optimization, semi-definite programming, noisy fingerprints,

mutual distances, measurement uncertainty

Ç

1 INTRODUCTION

INDOOR location-based service has attracted much atten-tion in recent years due to its commercial potentials.

The quality of such service largely depends on the accuracyof localization algorithm. Among all the explored techniques,fingerprint-based approach emerges as a promising one.

Fingerprint-based indoor localization is usually con-ducted in two phases [1]. In the offline (survey) phase, a sitesurvey is conducted to collect the vectors of received signalstrength indicator (RSSI) at known locations, the so-calledreference points (RPs). The vectors of these RSSIs form thefingerprints of the site and are stored in a database. In theonline (query) phase, a user (also known as target) samplesan RSSI vector at his location and reports it to the server,which estimates and returns the user location. (Anotherpossibility is to compute the location locally at mobiles,if the fingerprints have been downloaded.)

Error in location estimation is inevitable. This is due torandom signal fluctuation in both offline and online meas-urements. It has been observed that localization error can bequite high (more than 10 m [1], [2], [3]) under large open

indoor environment such as malls, train stations or airports.This is unsatisfactory for many applications. In order to sub-stantially enhance accuracy, one may embed, or fuse, finger-printing with mutual distance information.

Mutual distance information can be spatial, where thetarget estimates the distance to other users or beaconingdevices in its neighborhood. This can be done using differ-ent sensing techniques: Bluetooth [4], Wi-Fi direct [5],sound [6], etc. While there have been impressive works onusing spatial distance for localization, they often assumeaccurate distance measurements, resulting in rigid con-straints over the fingerprints. These approaches cannot beeasily extended or applied to the more realistic scenarioswhen distance estimation is random.

Besides spatial, the distance information can also be tem-poral, where the target estimates its displacement over time(e.g., by the step counter or inertial navigation system (INS)provided in one’s mobile phone). Previous approaches (likeparticle filter [3], [7] or Hidden Markov Model [8], [9])in this setting often treat Wi-Fi fingerprints and pedestriandistance measurements as separate, and hence sequentiallyconsider them. This consideration of independence may behardly satisfactory for accurate localization, as measuredfingerprints and distances are inherently correlated (cou-pled) and better jointly optimized. Given noisy/random sen-sor measurement, prior works may not fully address theissue of large positioning error.

Due to signal fluctuations, wireless fingerprint is inher-ently noisy, and estimated distance is random. In this paper,we proposeMaxlifd, a novelmaximum likelihood frameworkfusing noisywireless fingerprints and randommutual distan-ces to achieve highly accurate indoor localization. Maxlifdjointly considers fingerprints and distances, both of arbitrary

� S. He and S.-H. G. Chan are with the Department of Computer Scienceand Engineering, The Hong Kong University of Science and Technology,Clear Water Bay, Kowloon, Hong Kong, China.E-mail: {sheaa, gchan}@cse.ust.hk.

� L. Yu and N. Liu are with the School of Software, Sun Yat-sen University,Guangzhou, Guangdong 510275, China.E-mail: [email protected], [email protected].

Manuscript received 25 Apr. 2016; revised 5 Feb. 2018; accepted 16 May 2018.Date of publication 29 May 2018; date of current version 4 Feb. 2019.(Corresponding author: Ning Liu.)For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier no. 10.1109/TMC.2018.2841842

602 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 18, NO. 3, MARCH 2019

1536-1233� 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See ht _tp://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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distributions. After formulating the location estimation in ajoint likelihood problem, Maxlifd solves it using novel semide-finite programming (SDP), achieving excellent accuracy.

Unlike previous works, Maxlifd is a generic statistical orprobabilistic framework applicable to a wide range of sens-ing techniques and scenarios. As a framework, it enablesindoor localization combining both spatial and temporalmobile sensing independent of how distance is measured.For example, a target may employ opportunistic peer-to-peer spatial distances in a crowded region. For an unpopu-lated area, it may switch to dead reckoning (INS) for distancemeasurement. Meanwhile, the target may also estimate itsdistances to some fixed beaconing devices (if any).

Based on the joint maximum likelihood framework of Max-lifd, we have derived the lower bound on the localizationerror using Cram�er Rao Lower Bound (CRLB) [10]. Such deri-vation enables us to understand the impact of various systemparameters over the localization error, and sheds insights onthe system design. For example, we show that increasing thenumber of collaborative users in peer-assisted localization ordeploying more iBeacons beyond a certain point would notsignificantly improve the localization accuracy. We alsoshow effects of other factors like signal noise and distancemisestimation over the localization error.

We show in Fig. 1 the overall architecture of Maxlifdbased on wireless fingerprints. The fingerprint database isinitialized by a site survey, storing the couplets < location,RSSI vector> for each RP. In addition to the RSSI vectors, atarget measures the mutual distances (spatial or temporal)and reports them to the localization server. Based on that,the server constructs an SDP-based convex-optimizationframework and solves a joint maximum likelihood problem.It then returns the absolute location result to the target.

Maxlifd is applicable to any wireless fingerprint. Thoughmost of our discussion in this paper is on Wi-Fi fingerprints(due to its ease of deployment without extra infrastructurebeyond the existing one) for prototype studies, Maxlifd isgeneral enough to be extended to many other existing oremerging fingerprint signals [11], such as RFID and channelstate information (CSI), to achieve higher accuracy.

The contributions of our paper are as follows:

� We present a novel and general joint maximum-likelihood-based framework to fuse fingerprintsand distances of arbitrary distributions. Beyondthe previous fusion systems, Maxlifd generalizesvariant distance sensing scenarios, laying a more

comprehensive foundation for theoretical and exper-imental performance analysis.

� We formulate a novel SDP-based optimization prob-lem to fuse fingerprints and distances for indoorlocation estimation. Using the novel localizationframework, we conduct extensive CRLB analysis onthe lower bound of localization error;

� We have implemented Maxlifd based onWi-Fi finger-prints on Android platforms. We have performedlarge-scale simulation, and conducted testbed experi-ments in Hong Kong International Airport (HKIA)and our university campus. Using the commonlyavailable indoor sensors of dead reckoning, peer-assisted and beacon-based measurement, we showthat Maxlifd achieves much higher accuracy thanother state-of-the-art approaches. Furthermore, theperformance does not depend sensitively on the exactknowledge of signal or distance distribution, andGaussian distributionmay be applied for simplicity.

The rest of this paper is organized as follows. Afterreviewing related work in Section 2, we present in Section 2the framework of Maxlifd based on noisy fingerprint andrandom distance estimation, followed by an SDP-basedlocalization formulation for the example of Gaussian distri-bution in Section 4. Given the formulation, we present inSection 5 the CRLB of Maxlifd for Gaussian measurement.Illustrative results based on experimental trials and furthersimulation studies are discussed in Sections 6 and 7, respec-tively. We discuss some important implementation issues inSection 8, and conclude in Section 9.

2 RELATED WORK

Fingerprinting techniques [12], pioneered by Radar [1],have been widely studied in recent years. The work byHorus [13] estimates the target location using a probabilisticmodel, which reflects the signal distribution in the site. Ker-nel method [14], [15] and compressive sensing [16] havebeen implemented for fingerprint-based indoor localization.The techniques above solely address Wi-Fi fingerprintissues. We study here fusing distance information with fin-gerprinting to achieve much better accuracy. Fingerprintsprovide coarse location information, while mutual relativedistances help fine-grain the final results. Furthermore, mostrecent works only analyze the statistical performance of tra-ditional Wi-Fi fingerprinting localization [17] or distance-based sensor network positioning [18], [19], [20], while fus-ing noisy fingerprints with variants of statistical sensor dis-tance measurements into a single but generic probabilisticformulationwith error bound analysis, has not been compre-hensively studied before. Filling such a gap would help thefollowing researchers and practictioners to better under-stand, interpret and design such fusion systems.

Combining dead reckoning with RF signals has beendiscussed in some literature. Some of the works, like particlefilter, treat multiple temporal Wi-Fi estimations as indepen-dent, and have not jointly considered their estimation errorsfor better localization [3]. Some works [21] require extensivemotion, trajectory and map information for sophisticatedclassification model training. Some others treat the outputsfrom dead reckoning and Wi-Fi fingerprints sequentiallythrough particle filter [3], [7] or Markov model [8], [22]rather than jointly, at the cost of lessened useful informa-tion. Maxlifd, on the other hand, formulates the localization

Fig. 1. System architecture of Maxlifd.

HE ETAL.: MAXLIFD: JOINT MAXIMUM LIKELIHOOD LOCALIZATION FUSING FINGERPRINTS AND MUTUAL DISTANCES 603

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problem as a single joint convex-optimization problem givendistribution of temporal walking distance. This formulationgreatly reduces the impact of measurement noise andachieves much higher accuracy.

Our study here is orthogonal to simultaneous localizationandmapping (SLAM). InWiFi-SLAMalgorithm [23], the statespace is modeled by a Gaussian Process (Latent Variable)model. Different from WiFi-SLAM, our Maxlifd considersfusion of fingerprints and distances into one single probabilis-tic framework, and solves it efficiently through semidefiniteprogramming. Furthermore, SLAM approaches are consid-ered as orthogonal to our work, as Maxlifd considers a novelsensor fusion given a basic floor and signal map. On the otherhand, SLAM-based approaches, such asUnLoc [24], can serveas an initial provider of indoormap and fingerprint signals.

There has been some work making use of Wi-Fi direct [5]and high-pitch sound [6], [25] to measure spatial distancesbetween devices and improve localization. Some considerusing a rigid graph [5] constructed through rotation andtranslation [6], while others consider using Bayesianapproach to infer the device location [25]. Assuming staticdevices in office environment, Centaur [25] utilizes thesound to estimate device positions. In contrast, Maxlifdjointly considers distance uncertainty and fingerprint noise,and formulates the joint maximum likelihood problem toestimate the target location. Maxlifd is a much more versa-tile and generic framework accommodating measurementnoises and different application scenarios.

Some beacon-based techniques, pioneered by iBeacon,have recently been proposed for site monitoring and indoorlocalization [26], [27]. The work in [26] studies the advantagesof using iBeacons for indoor localization. The work in [27]investigates the performance of iBeacon fingerprinting. Wepropose here a new joint optimization framework combiningboth wireless fingerprints and different emerging beacontechniques (say, iBeacons, AoA [28], [29], ToA [30], Wi-Fisniffers, sound anchors [31], etc.). Our prototyping with iBea-con has further shown that such formulation achieves muchhigher accuracywith general applicability.

Based on our deployment practice, we consider spaciousand commercial application scenarios (like airport or shop-ping mall) where acts of adding many new anchor nodes ormodifying existing WLAN APs belonging to many differentparties of the site are more or less regulated. Thus, we lever-age the fingerprint-based technique (where low-cost finger-prints can be collected via crowdsourcing [32]), and beyondthis we further embrace any extra information of distances.Specifically, coarse but pervasive fingerprints anchor therough location of the user, while variant accurate ranginginformation (e.g., pedometer, phone-to-phone ranging orbeacon) is encountered opportunistically to constrain orrefine the estimation.

In our joint optimization, we consider the mutual Euclid-ean distance and have a quadratic objective function. Toreduce the computation complexity from the quadraticform, we apply semi-definite relaxation [33] to relax the dis-tances. Semi-definite programing has been applied in wire-less communication [34] and sensor networks [33]. In thispaper, we implement SDP to fuse the noisy fingerprints anddistance distributions for indoor localization. Note that,unlike multidimensional scaling (MDS) and spectral graphdrawing (SGD) [35], Maxlifd formulation considers finger-print matching with distances, and relies less on high sensor

connectivity [36], [37]. Hence Maxlifd is more applicable tocomplex signal measurements in indoor localization.

A preliminary version of this work, Wi-Dist, has beenreported in [38], which estimates location by fusing finger-prints and distance bounds. In this paper, we advance fromWi-Dist in several major ways: 1) Maxlifd jointly accountsfor the measurement noise in both fingerprints and distanceestimation, given any arbitrary distribution. As distancebound is a special case of our formulation, Maxlifd is moregeneral; 2)Maxlifd uses jointmaximum likelihood to localizethe target, which is much more robust to signal noise andhence more accurate; 3) We reformulate Maxlifd throughSDP relaxation, and solve it efficiently; 4) We further analyzethe lower bound of localization error based on CRLB; (5) Weconductmore simulation and experimental studies.

3 PRELIMINARIES & STATISTICAL FRAMEWORK

In this section, we show the preliminaries and statisticalframework on howMaxlifd estimates user locations. For con-creteness, our discussion is in the context of Wi-Fi fingerprintsignal (extension to other signals is clear and straightforward).We first present the preliminaries of Maxlifd in Section 3.1.Then in Section 3.2, we present the statistical or probabilisticframework of Maxlifd. Table 1 shows some of the importantsymbols used in our formulation.

3.1 Preliminaries of Fingerprint-Based LocalizationIn the offline phase, a site survey is conducted with a total ofQ RPs. Let rq be the 2-D position of RP q, and R be a 2�Qmatrix indicating the RP positions, i.e.,

R ¼ ½r1; r2; . . . ; rQ�: (1)

Let L be the index set of the Wi-Fi access points (APs) thatcover the site, i.e., L ¼ f1; . . . ; Lg.

At each RP, time samples of Wi-Fi RSSI readings are col-lected. Due to the random nature of radio signal, multiple

TABLE 1Major Symbols in the Maxlifd Formulation

Notations Definitions

M, V Number of spatial/temporal targets andtheir index set

Q Number of reference points (RPs) infingerprint databasebxm Estimated 2-D coordinate of targetm

X M � 2matrix of all target locationsY M �M matrix for transformation in SDPrq 2-D coordinate of reference point (RP) qR 2�Q coordinate matrix of RPsvmq Weight of RP q to estimate targetmW M �Qmatrix of weights at RPsLLm Index set of targets to be estimated in V

with distance measurements from targetmVm Set of distances (spatial or temporal) from targetmL Number of Wi-Fi APs in the site of interestCq RSSI vector received at RP q�clq Average RSSI of AP l at RP q (dBm)

slq RSSI standard deviation of AP l at RP q (dB)

Fm RSSI vector received at targetmflm RSSI of AP l at targetm (dBm)

dmn Distance measurement between targetm and n (m)Imn Indicator on existence of dmn betweenm and n

604 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 18, NO. 3, MARCH 2019

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samples are collected in order to reduce the uncertainty inthe signal measurements.

Denote the RSSI at RP q from AP l at time t asfcl

qðtÞ; t ¼ 1; . . . ; Slq; S

lq > 1g, with Sl

q being the total numberof samples collected. Denote the average RSS readings fromAP l, l 2 L, at RP q as �cl

q, and the unbiased estimate of thevariance of the RSS time samples for AP l at RP q as ðsl

qÞ2.Then for each RP, the unbiased estimates for the mean RSSIand its corresponding standard deviation at RP q are

�clq ¼

1

Slq

XSlqt¼1

clqðtÞ

0@ 1A; slq ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

Slq � 1

XSlqt¼1

clqðtÞ � �cl

q

� �20@ 1Avuuut :

(2)

Then the Wi-Fi RSSI vector at rq is

Cq ¼ �c1q ;�c2q ; . . . ;

�cLq

h i; q 2 f1; 2; . . . ; Qg; (3)

where, by definition, �clq ¼ 0 if AP l is not detected at RP q.

In the online phase, let V be the set consisting of theindexes of theM target nodes (or simply targets) to be local-ized in the site, i.e., V ¼ f1; 2; . . . ;Mg, and each of their 2-Dlocations to be estimated is denoted as bxm;m 2 V. Note thatthese targets to be estimated can be either spatial or tempo-ral. Let X be an M � 2 matrix of locations of all these points,i.e.,

X ¼ ½bx1;bx2; . . . ;bxM �T : (4)

For each of the targets (spatial or temporal), let flm be the

RSSI value at target location bxm for Wi-Fi AP l, l 2 L. Similarto the RP RSSI vector, we define the target m’s sampledRSSI vector as

Fm ¼ f1m;f

2m; . . . ;f

Lm

� �;m 2 V; (5)

where, by definition, flm ¼ 0 if AP l is not detected at target

m. Given a target m, let Lm be the set of its neighbors thathave distance measurement with. Let dmn be the distance(spatial or temporal) between targets bxm and bxn for anym;n 2 V, i.e.,

kbxm � bxnk2 ¼ d2mn; 8n 2 Lm; n 6¼ m: (6)

As the measurements of mutual distances often containnoise, we may evaluate the difference (or relationship)between kbxm � bxnk2 and dmn according to a certain distribu-tion. Then we obtain the likelihood of dmn given bxm and bxn,denoted as pðdmnjxm; xnÞ. pðdmnjxm; xnÞ can be given by a cer-tain distribution formulation. Note that for the temporalpedestrian localization, dmn exists if m and n are two conse-cutive targets (i.e., walking distance between two successiveWi-Fi RSSI measurements). For spatial scenarios, we con-sider dmn exists if two devices (sensors) are within a certaindetection range.

Based on statistical analysis of distance (spatial or tempo-ral), we can obtain the standard deviation of the distancemeasurement, i.e., smn to generalize the inherent uncer-tainty. Therefore, for each target m, we store the corre-sponding standard deviation in its distance measurementas Vm ¼ fsmng; 8n 2 Lm.

To summarize, given the M targets (temporal or spatial)to be localized in V, each of them contains the following

information in the Maxlifd problem:

Pm , fm;bxm;Fm;Lm;Vmg; m 2 V: (7)

3.2 Statistical Localization FrameworkThe RP positions R are used to estimate the locations of thetargets. Similar to traditional weighted average estimationin K-NN [1], [2], let vmq be the weight assigned to RP q tolocate targetm, so that

bxm ¼XQq¼1

vmqrq; m 2 V; (8)

where the weights vmq; 8m, satisfyXQq¼1

vmq ¼ 1; vmq � 0; 8q 2 f1; 2; . . . ; Qg: (9)

Note that in reality the target may not always be locatedwithin the convex hull due to the random indoor layout(say, corner at a corridor). This issue can be addressed byaugmenting map constraints such that the finally returnedlocations fall within the accessible area. Let W be an M �Qmatrix of vmq, rq 2 R, i.e.,

W ¼v11 . . . v1Q

..

. . .. ..

.

vM1 . . . vMQ

264375: (10)

Then the positions of all the targets in V givenW are

X ¼ WRT : (11)

Given the above, we present in the following the generallocalization framework for Maxlifd problem. Denote theindex set of APs received by target m as Lm, i.e., f

lm 6¼ 0 if

l 2 Lm. Let pðflmjrqÞ be the likelihood that signal fl

m appearsat RP q. Then the joint likelihood (considered as indepen-dent [13]) that FFm appears at RP q is

pðFFmjrqÞ ¼Yl2Lml¼1

pðflmjrqÞ: (12)

Note that we only consider the uncorrelated APs in Maxlifd,while the virtual or correlated APs and those tethered bymobiles can be easily removed via existing MAC address fil-tering [39] or correlation computation [16].

In practice, each target (temporal or spatial) may detectdifferent number of APs. Therefore, for each target m,pðFFmjrqÞ is normalized, i.e.,

pðFFmjrqÞ0 ¼ pðFFmjrqÞPQq¼1 pðFFmjrqÞ

: (13)

In summary, the probability of each target estimatedin the survey region of Q RPs is defined as the mixture oflikelihood (joint probabilistic distribution), i.e.,

pðFFmÞ ¼XQq¼1

vmqpðFFmjrqÞ0: (14)

When estimating target m based on above mixture of likeli-hood, the RPs with higher potential to be target position,i.e., with larger pðFFmjrqÞ0, tend to get larger weight vmq in

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order to maximize pðFFmÞ, whose intuition is inspired by thespirits of Gaussian mixture model (GMM) and expectationmaximization (EM) [40].

For ease of distance formulation, we denote Imn ¼ 1 ifdmn exists, and Imn ¼ 0 vice versa. Based on Equations (6)and (14), we formulate in Maxlifd a joint maximum likeli-hood problem for localization. Specifically, we are to find amatrixW for theM targets (temporal or spatial) such that

argmaxW

YMm¼1

pðFFmÞYMm¼1

YMn¼1

Imnpðdmnjxm; xnÞ;

subject to: Constraints (8), (9), (10) and (11):

(15)

In other words, we are to find the weights of RPs in order tofind the target locations which jointly maximize the likeli-hood of signals and mutual distances. The RPs which satisfyabove objective get high weights in final estimation.

4 AN EXAMPLE: LOCATION ESTIMATION WITH

GAUSSIAN FINGERPRINT & DISTANCE

Given the above statistical framework, we consider here thespecial case that both signals and mutual distances areGaussian distributed (Section 4.1). The objective function ofMaxlifd has quadratic elements (mutual distances), whichlead to high computation overhead. To reduce its hardness,we further implement Semi-Definite Programming relaxa-tion [41] to solve it (Section 4.2). Finally we discuss theapplication scenarios and complexity analysis (Section 4.3).

4.1 Gaussian Distribution for Fingerprints &Distances

In Section 3.2, the probability distribution, or likelihood, canbe calculated through several measures. The selection ofdistribution forms or likelihood functions may depend onthe signal samples and experimental environments. Wire-less fingerprint signals have been reported to follow Gauss-ian distribution [13]. We further conduct extensive datacollection in HKUST campus to evaluate the distancemeasurement randomness and error. 200 mutual distancesamples and walking distances are collected. As shown inFigs. 2a and 2b, the pair-wise distance measurementsbetween smartphones and walking distances with stepcounter may also follow the Gaussian (normal) distribu-tion [4], [6], [42]. Note that other distributions (for example,log-normal or exponential) may be considered in Maxlifd,while here we use Gaussian distribution for illustration andprototyping.

In the derivation of this section, for concreteness and easeof prototyping, we derive the maximum likelihood based on

Gaussian distribution. Therefore, in this section, for modelderivation and prototyping, we consider Gaussian distribu-tion within the wireless signal noise and distance measure-

ment, i.e., flq � Nð�fl

q; ðslqÞ2Þ and kxm � xnk2 � Nðdmn; ðsdÞ2Þ.

Note that our work is also general enough to be applied invarious distributions or statistical measures, including log-normal distribution, histogram-based [13] or kernel-based [14]methods.

Specifically, when comparing the signal vectors at RP qwith target signals FFm, we first compute the probability dis-tribution of signal value fl

m at RP q, i.e.,

pðflmjrqÞ ¼

1ffiffiffiffiffiffi2p

pslq

exp �flm � cl

q

� �22ðsl

qÞ2

0B@1CA: (16)

By definition, if AP l 2 Lm is not detected at RP q, pðflmjrqÞ is

assigned with a nonzero value pmin (in our evaluation,pmin ¼ 0:01). Device heterogeneity in RSSI can be furtheraddressed through existing approaches like offset calibra-tion by crowdsourcing [7] or online RSSI offset learning [15].For example, we can conduct regression over the RSSIscrowdsourced by many users to find the offset [15], [43].

Then the likelihood that estimated locations xm and xnmatch the measured distance dmn is given by

pðdmnjxm; xnÞ ¼ 1ffiffiffiffiffiffi2p

psd

exp � dmn � kbxm � bxnk2ð Þ22ðsdÞ2

!; (17)

where sd represents the uncertainty of mutual distance mea-surement. By definition, if there is no distance measurementbetween m and n, pðdmnjxm; xnÞ ¼ 0. The joint probabilitydistribution of the distance matching is then given by

pðddÞ ¼YMm¼1

YMn¼1

Imnpðdmnjxm; xnÞ; (18)

where indicator Imn ¼ 1 if dmn exists, and 0 otherwise.Using Equations (18) and (14), we present in the following

the objective function forMaxlifd. Let fFFmg and fdmng be theset of RSSI vectors and mutual distances. To measure thematching of all targets (spatial or temporal) with the storedsignal map and measured distances, we find the weights inW which maximize the joint likelihood [40], denoted asL fFFmg; fdmngjWð Þ, as the following distribution format [44]:

L fFFmg; fdmngjWð Þ ¼YMm¼1

pðFFmÞ !

pðddÞ

¼YMm¼1

XQq¼1

vmqpðFFmjrqÞ0 ! !YM

m¼1

YMn¼1

Imnpðdmnjxm; xnÞ:

(19)

By taking logarithm on both sides, we get rid of the exponen-tial terms in Equation (17), and transform Equation (19) intoa joint maximum likelihood formulation, i.e., the log likelihood

logL fFFmg; fdmngjWð Þ ¼XMm¼1

logXQq¼1

vmqpðFFmjrqÞ !

�XMm¼1

XMn¼1

Imn kxm � xnk2 � dmnð Þ22s2

d

� const:

(20)

Fig. 2. CDF and normal fit of (a) sound-based distance measurement(5 m between smartphones). (b) Walking distance obtained frompedometer (4 m walking distance).

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Note that the logarithm function is convex and therefore ourobjective function logL fFFmg; fdmngjWð Þ is convex, whichcan be solved through the convex optimization. In our opti-mization, we can simply leave out the constant term, whichis const ¼PM

m¼1

PMn¼1 Imn log

ffiffiffiffiffiffi2p

psd.

Our objective function finally becomes

argmaxW

logL fFFmg; fdmngjWð Þ; (21)

which jointly considers the probability of detected signalsand the physical distance constraints.

4.2 Semidefinite Programming (SDP)To relax the quadratic objective, we describe as follows solv-ing the optimization using SDP. Note that SDP approach inMaxlifd can be applied to other probability distributions bysimply replacing the probability distribution in fingerprintRSSI (Equation (16)) and distance (Equation (17)).

Let emn be an M � 1 column vector where the mth ele-ment is 1 and nth element is �1. The physical distancebetween nodem and n can be therefore represented as

d2mn ¼ eTmnXXTemn; ½dmn; dmn� 2 Vm: (22)

Denote anM �M matrix Y for internal transformation, i.e.,

Y ¼ XXT : (23)

Finally, the distance constraint can be rewritten as

eTmnYemn ¼ d2mn: (24)

Based on the transformation of Equation (24), we canrewrite Formulation (15) into

Objective: Equation (21),

subject to: Constraints (9), (11), (23) and (24):(25)

Given a symmetric matrix A, let A � 0 represent that A isa positive semidefinite matrix [41], [45]. We can then relaxthis problem into a convex one by replacing the nonconvexequality constraint, Y� XXT ¼ 0 in Constraint (23), with aconvex positive semi-definite constraint, i.e.,

Y� XXT � 0: (26)

Constraint (26) is a nonlinear constraint, which can be fur-ther transformed into linear matrix inequality (LMI) [39].Through LMI, the quadratic elements within the objectivefunction can be relaxed. Then it can be solved efficiently bya convex optimization solver [41], [45]. The extent of therelaxation can be controlled through the solver. The trans-formation is through a Schur complement:

Definition 1. Let H be a matrix partitioned in four blocks, con-sisting of four matrices B;E;C andD, i.e.,

H ¼ B EC D

� �; (27)

where B and D are symmetric and nonsingular. The Schurcomplement ofD inH, denoted as S, is defined as

S ¼ B� ED�1C: (28)

If S � 0, then H � 0 [41]. Let I2 be a 2� 2 identity matrix.Thus, by using Schur complement, we can rewrite Con-straint (26) as a matrix form for LMI, i.e.,

Y XXT I2

� �� 0: (29)

Formulation (25) is finally transformed into an SDP prob-lem [41]

Objective: Equation ð21Þ;subject to Constraints (9), (11), (23), (24) and (29):

(30)

4.3 Localization Applications & ComplexityAnalysis

The formulation above can be directly applied in peer-assisted localization. For dead-reckoning based localizationusing inertial navigation system, we may take m as the timestamp (M becomes the number of temporal targets). Infusion with dead reckoning, the device also collects theWi-Fi RSSI vectors as the user walks. Then using the nota-tion in Equation (7), the index m represents the time stampduring walking. Each target location bxm now corresponds toa temporal measurement of a single target. The most recentM temporal targets and M � 1 distances between themform a sliding window in time domain, and the estimation oftheMth target is returned as the current position. Given edmn

at time m from its predecessor, LLm ¼ ½m� 1�. Based onEquation (7), a Wi-Fi temporal target Pm is defined as

Pm , fm;bxm;Fm; ½m� 1�;Vmg: (31)

Each temporal target m has distance from its predecessor,m� 1, and by definition the first target in the sliding win-dow has no distance and predecessor. For beacon-assistedlocalization, we may let M ¼ 1, and a target measures dis-tances from those neighboring beacons with known loca-tions. In practical deployment, at a time only one of aboveapplications is triggered opportunistically given corre-sponding spatial or temporal distance measurements.

We end by analyzing the computational complexity ofthe solution. Given Q RPs and L APs, signal likelihood cal-culation takes OðQLÞ. Given M temporal or spatial targetmeasurements (usuallyM is small), the computation of SDPrelaxation is bounded by OðM3Q3Þ [46]. Some commercialSDP solver can solve this problem efficiently [41]. Furthercomputational reduction can be achieved by AP filteringand RP cluster mapping [16]. Specifically, unimportant APscan be first filtered before signal likelihood calculation, andthe target can be first mapped to a small area (namely RPcluster) before final Maxlifd calculation [16].

5 CRLB FOR LOCALIZATION ERROR

This section presents the Cram�er-Rao lower bound (CRLB) oftheMaxlifd problem discussed in Section 4.1. CRLB has beenwidely used to evaluate the fundamental hardness of an esti-mation problem [17], [47]. Here we utilize CRLB to evaluatethe localization error bound of Maxlifd, showing the optimalityof the formulated problem. Specifically, in Section 5.1, pre-liminary of CRLB is first introduced. Then, the CRLB ofMax-lifd for Gaussian distribution is derived in Section 5.2.

5.1 CRLB PreliminaryCRLB sets a lower limit for the covariance of the unbiased esti-mates of the unknown parameters [17]. In our formulation,

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the location coordinates of the targets (temporal or spatial),denoted as uu ¼ ½x1; y1; x2; y2; . . . ; xM; yM �T , are the corre-sponding parameters of the estimator. Each target corre-sponds to a 2-D location, i.e., xm ¼ ðxm; ymÞT . Let s2

xabe the

variance of coordinate xa, and sxayb be the covariance betweencoordinate xa and yb. Therefore, the covariance matrix of allthe targets should be a 2M � 2M matrix, i.e.,

CovðuuÞ ¼

s2x1

sx1y1 . . . sx1xM sx1yM

sy1x1 s2y1

. . . sy1xM sy1yM

..

. ... . .

. ... ..

.

sxMx1 sxMy1 . . . s2xM

sxMyM

syMx1 syMy1 . . . syMxM s2yM

26666664

37777775: (32)

Here the diagonal elements in Equation (32) represent themean squared errors, and the off-diagonal elements are thecovariances between the coordinates of theM targets.

The observation in our formulation, denoted as Q,consists of the received signal strength from APs and themeasured pairwise distances between targets, i.e., Q ¼f11;f12; . . . ;f1L; . . . ;fML; d12; . . . ; d1M; . . . ; dMðM�1Þ� �

. LetfuuðQÞ be the joint probability density function of the obser-vations Q conditioned on uu. Fisher information matrix (FIM),denoted as JðuuÞ (a 2M � 2M matrix), is given by

JðuuÞ ¼ �E@2 log fuu Qð Þ

@uu2

� �: (33)

CRLB is the inverse of FIM and the covariance of the esti-mated locations (Equation (32)) is bounded as

CovðuuÞ � fJðuuÞg�1: (34)

Let JmðuuÞ be the corresponding square block in FIM for tar-get m, Jxm;xn

be the element at the ð2m� 1Þth row and

ð2n� 1Þth column of FIM JðuuÞ (odd row/column), and Jym;yn

be that at the 2mth row and 2nth column (even row/

column). Then the mean squared error of each target m,

denoted as varðuumÞ, is then bounded by its local geometric

relationship fJmðuuÞg�1 [10], [18], i.e., varðuumÞ orE uum � �uumð ÞT uum � �uumð Þ� �

� fJmðuuÞg�1

¼ Jxm;xmJxm;ym

Jym;xmJym;ym

" #�1

¼ 1

jJmðuuÞjJym;ym

�Jxm;ym

�Jym;xmJxm;xm

" #;

(35)

where jJmðuuÞj ¼ Jxm;xmJym;ym

� Jxm;ymJym;xm

.

5.2 CRLB for Gaussian Signal MeasurementIn the following, we derive the CRLB of Maxlifd underGaussian distributed signal measurements.

We first derive the joint probability density functionfuuðQÞ. Based on the formulation in Equation (21) of Section4.1, we can formulate the measured signal strength betweentargetm andAP l as

fml ¼ Pl � 10g0 log dml

d0

þ Xml; (36)

where g0 ¼ glog 10 is introduced for later derivation, and

Xml � Nð0; s2mlÞ. Similarly, we formulate the probability

density function of estimated distance between m and n asnormal distribution, i.e.,

dmn � N kxm � xnk2; s2mn

� �: (37)

Given above, let �fml ¼ Pl � 10g0 log ðdmld0Þ, and �dmn ¼

kxm � xnk2. The objective in Section 4 jointly maximizes thelikelihood of wireless signals and mutual distances. Thusfor ease of analysis in CRLB, we equivalently transform theobjective function in Equation (21) [10], [17], and the jointprobability density function fuuðQÞ is then given by

fuuðQÞ ¼YMm¼1

YLl¼1

1ffiffiffiffiffiffi2p

psml

exp �ðfml � �fmlÞ22s2

ml

! !

�YMm¼1

YMn¼1

1ffiffiffiffiffiffi2p

psmn

exp �ðdmn � �dmnÞ22s2

mn

! !;

(38)

which is equivalent to the joint maximum likelihood formu-lation presented in Equation (20).

Therefore, the first derivatives of the objective function inEquation (38), are given by

@ log fuuðQÞ@xm

¼XLl¼1

1

s2mn

fml � �fmlð Þ @�fml

@xm

þXM�1

n¼1

1

s2mn

dmn � �dmnð Þ @�dmn

@xm;

(39)

@ log fuuðQÞ@ym

¼XLl¼1

1

s2mn

fml � �fmlð Þ @�fml

@ym

þXM�1

n¼1

1

s2mn

dmn � �dmnð Þ @�dmn

@ym;

(40)

where the partial derivatives with respect to coordinate xm

or ym are given by

@�fml

@xm¼ � 10g0d0

d2ml

ðxm � xlÞ; @�fml

@ym¼ � 10g0d0

d2ml

ðym � ylÞ;

@�dmn

@xm¼ xm � xn

dmn;

@�dmn

@ym¼ ym � yn

dmn:

(41)

Considering aml 2 ½0; 2pÞ as the relative angle that targetmmakes with respect to AP l, and bmn 2 ½0; 2pÞ ðbnm ¼ 2p�bmnÞ as that the target m makes w.r.t. target n. Therefore,we have

cosaml ¼ xm � xl

dml; sinaml ¼ ym � yl

dml;

cos bmn ¼ xm � xn

dmn; sinbmn ¼ ym � yn

dmn:

(42)

Given above elements, we calculate expectation of the sec-ond derivatives in Equation (33) [10], [20], and find theentries within the FIM JðuuÞ, which are given as follows:

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Jxm;xm¼ �E

@2 log fuuðQÞ@x2

m

� �¼XLl¼1

1

s2ml

10g0d0d2ml

2

ðxm � xlÞ2 þXM�1

n¼1

1

s2mn

ðxm � xnÞ2d2mn

¼XLl¼1

10g0d0ð Þ2s2ml

cosamlð Þ2d2ml

þXM�1

n¼1

ð cos bmnÞ2s2mn

;

(43)

Jym;ym¼ �E

@2 log fuuðQÞ@y2m

� �¼XLl¼1

1

s2ml

10g0d0d2ml

2

ðym � ylÞ2 þXM�1

n¼1

1

s2mn

ðym � ynÞ2d2mn

¼XLl¼1

10g0d0ð Þ2s2ml

sinamlð Þ2d2ml

þXM�1

n¼1

ð sin bmnÞ2s2mn

;

(44)

Jxm;ym¼ Jym;xm

¼ �E@2 log fuuðQÞ@xm@ym

� �¼XLl¼1

1

s2ml

10g0d0d2ml

2

ðxm � xlÞðym � ylÞ

þXM�1

n¼1

1

s2mn

ðxm � xnÞðym � ynÞd2mn

¼XLl¼1

10g0d0ð Þ2s2ml

sin 2aml

2d2ml

þXM�1

n¼1

sin 2bmn

2s2mn

;

(45)

and

Jxm;xn¼ Jxn;xm ¼ Jym;yn

¼ Jyn;ym ¼ 1

s2mn

; (46)

and

Jxm;yn¼ �E

@2 log fuuðQÞ@xm@yn

� �¼ 1

s2mn

ðxm � xnÞðym � ynÞd2mn

¼ 1

s2mn

sin 2bmn

2; (47)

while Jxn;ym ¼ Jxm;yn¼ Jym;xn

¼ Jyn;xm . To summarize, with

Equation (35) and the above components, we can obtain the

corresponding lower bound for estimation variance (mean

squared errors) of each involved targetm in Maxlifd.

6 EXPERIMENTAL EVALUATION

We have developed Maxlifd on Android platforms basedon Wi-Fi fingerprints, and conducted extensive experi-ments. In this section, we first discuss the experimentalsettings and performance metrics in Section 6.1. Then wepresent illustrative experimental results for dead reckon-ing fusion (fusing with inertial navigation system, orINS), peer-assisted (PA, i.e., fusing with mutual distan-ces of peers) and beacon-assisted (BC, i.e., fusing Wi-Fiwith sensor beacons) localization in Sections 6.1. Thoughpractically only one distance type is likely operating at atime, our framework is general enough to include all thedistance information mentioned.

6.1 Experimental Settings & Performance MetricsWe compare Maxlifd with the following typical and state-of-the-art localization schemes in our experiment:

1) Fingerprint-based localization (FL) [1], [2], which evalu-ates the Euclidean distance of target RSSI vector witheach RP fingerprint, and finds interpolation of the topk nearest neighbors for location estimation (k ¼ 15).

2) Sequential Monte Carlo (SMC) localization [3], [7], thestate-of-the-art fusion algorithm based on SequentialMonte Carlo method (particle filter) using INS dataand Wi-Fi fingerprinting (FL). Via the propagationalong the temporal walking path, the particles movefrom one location to the next. With map constraints,the spatial distribution of these particles is correctedand resampled. The final estimation is based on theweighted average of particle locations.

3) Hidden Markov Model (HMM) localization [8], [9],which fuses INS with Wi-Fi fingerprints (FL), andconducts location positioning based on a traditionalprobabilistic framework, hidden Markov models.

4) Localization with Social Interaction (SocialLoc) [4], whichfixes the Wi-Fi fingerprint-based location estimations(FL) via Bluetooth-based interaction of users (encoun-ter/nonencounter information).

5) Graph-based & fingerprint localization scheme (GB +FL) [6], which uses graph construction and Wi-Fi fin-gerprinting (similar to FL) for peer-assisted localiza-tion. With the pairwise spatial distances of peertargets, GB+FL constructs the rigid graph consistingof all targets [5], [48]. Then GP+FL searches againstthe Wi-Fi signal map and finds a set of fingerprintsto minimize the objective function S

Mm¼1kFm �Cqk2

via graph rotation and translation [6].6) MMSE [49]: For indoor beacon-based positioning

scenarios, we compare the performance of Maxlifdwith minimum mean squared error (MMSE) algo-rithm [49], which has been applied in many existingiBeacon-based systems. 3 iBeacons with the strongestRSSIs are used for MMSE.

Corresponding state-of-arts are compared in each applica-tion scenario. Specifically, in experimental comparison ofdead reckoning fusion (INS), we compare Maxlifd with SMCand HMM. In peer-assisted (PA) application, we compareMaxlifd with Social-Loc and GB+FL. In beacon-based locali-zation (BC), we compare Maxlifd withMMSE. Note that FL iscompared in all scenarios as the base comparisonwithout sen-sor fusion. In iBeacon-based localization scenario (BC), weimplement FL using Bluetooth fingerprints [26].

Let xm be targetm’s true location and bxm be the estimatedlocation. The performance metrics used are the mean locali-zation error (unit:m) of the estimated target in set V:ME ¼ P

m2V kxm � bxmk2� �=jVj.

We evaluate Maxlifd in the Hong Kong International Air-port (HKIA) boarding area and HKUST campus atrium. Inthe airport, we collect overall 1; 400 RPs in 8,000m2 area. Onthe campus we collect 394 RPs in 5,000 m2 area. Figs. 3aand 3b show the corresponding floor plans of HKIA andHKUST campus. Note that the black triangles in the mapcorrespond to the deployed iBeacons. In the HKIA and theHKUST campus, at each RP we take overall 80 Wi-Fi RSSIvectors using HTC One X+ (total 5 are used).

A quarter of these samples are collected when we are fac-ing north, south, west and east, respectively. Note that thetarget signals are collected at least one month after the fin-gerprinting. For all the application scenarios, unless other-wise stated we use the following parameters as baseline: 5m survey grid size (i.e., width between two neighboring

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RPs, which represents the density); 1 Wi-Fi RSSI sample(which takes around 1 second for sampling on our Androidplatform) is used for each target; no Wi-Fi AP reduction isconducted over the target RSSI vectors. Note that HTC OneX takes around 1 second to scan one Wi-Fi RSSI vector asthe OS needs to scan all possible channels (2.4 and 5 GHz).Bluetooth fingerprinting is conducted in the same processas the Wi-Fi fingerprinting.

Note that the ranging test is conducted in the noisy envi-ronment (including campus and airport). The sound rang-ing is working at different frequencies from the audiblesound, which is overall robust against the environmentaldynamics [6], [50].

The signal studies are illustrated as follows. In Fig. 4, weshow the CDF of detected AP number at each target and RSSIstandard deviation (STD) at RPs (Equation (2)) in HKUST andHKIA. Though in HKIA the number of detected APs at eachRP is larger, most of their detected signals are weak (less than�80 dBm). As a larger spectrum of signal variation is observedin HKIA, we expect a larger localization error there. Prepro-cessing of AP importance, virtual and correlated AP filter hasbeen conducted here, and the implementation details are simi-lar to [14], [37]. Note that we conduct the experiment duringworking hours with crowds nearby (each collection takesaround 6 hours). The sites where we conduct experiments arewith marked RSSI noise and low fingerprint differentiation,leading to accuracy degrade of state-of-the-art algorithms.

In fusing with dead reckoning (INS), sliding window sizeM ¼ 7 for Maxlifd, and the influence of different M’s is alsoevaluated in the experiment. 200 particles are used in the par-ticle filter (SMC). A step counter at the smartphone measuresuser steps and temporal distances. Each step detection isbased on the periodic changes in the gravity direction of accel-erometer [7]. The walking traces range from 8 to 15 meters.We label the ground truth based on the landmarks nearby(say, the door, hall gate or a pillar). Based on the number ofsteps, the distance travelled, or motion offset, can be esti-mated by multiplying the average stride length of the target(which is related to walking frequency as in [42]). Step lengthcalibration can be referred toworks like [21] or [51] for relatedapproaches.

For some areas visited by many users, peer-assisted locali-zation may be used [6]. Peer ranging can be based on eitherRSS-distance mapping or sound ranging. Wi-Fi direct is notconsidered as it may cause extra overhead and interference toongoing Wi-Fi transmission. Time synchronization betweentransceivers makes obtaining accurate distance informationfrom Wi-Fi direct difficult. Sound-based distance estimationis easier for time synchronization and implementation. Forease of prototyping, in the experiment we implement and testsmartphone-based sound ranging like [6] under quiet andnoisy campus environment. The mean peer ranging errorsunder these two conditions are 0.8 m and 2 m respectively.Since the distance constraint between two peers is asymmetric

due to measurement uncertainty, we use their average valueof the measurements as mean in Gaussian likelihood estima-tion. By default, 5 targets (users) are involved in sound-baseddistance measurement. We do not exclude the cases whenwalls may partition some of the peers during localization(with none-line-of-sight orNLoSmeasurements).

In beacon-assisted localization (BC), we implementMaxlifdupon Bluetooth iBeacons (Fig. 3) with TI CC2540. BesidesWi-Fi fingerprinting, we also measure the distance betweenthe beacon and the target based on the path loss model. Thecalibration of the iBeacons on RSSI-distancemodel and hetero-geneous devices can be achieved through online learning [15]and crowdsourcing-basedmethods [7]. To furthermitigate thesignal noise, we empirically implement a mean filter over asliding window of three consecutive RSSI samples. After that,a distance estimation result is returned to Maxlifd. Furtherimportance differentiation of spatial distances in both PA andBC applications is outside the scope of Maxlifd and interestedreadersmay refer to establishedprior arts like [6].

6.2 Illustrative Experimental ResultsWe evaluate the fusion with dead reckoning (INS) as follows.Fig. 5 shows the cumulative probability of localization errorsin the HKIA. We can observe at least 30 percent error reduc-tion using Maxlifd compared with other state-of-the-arts. Asthe sensor readings are jointly considered in one single formu-lation,Maxlifdmitigates the influence inwalking distance andhence achievesmuch lower errors than SMC andHMM. Fig. 6shows the computation time using SMC, HMM and Maxlifdrunning on a PC with i7 3610QM. We may observe slightlyhigher computation in Maxlifd than traditional HMM, whileMaxlifd achieves better efficiency than the particle filter inSMC. Traditional SMC often suffers from computation underlarge number of particles in order to locate the target.

Fig. 7 shows theME of Maxlifd (INS) againstM, the num-ber of Wi-Fi temporal target measurements (size of slidingwindow) in HKIA. We can see that the accuracy improves aswe utilize more temporal samples, as joint consideration ofmore periods further constrains the location estimations.When we further increase the number of measurements, thelocalization accuracy gradually converges, indicating thatgiven distances already provide sufficient constraints. Thus,to balance between localization accuracy and computationalcomplexity we choose several temporal measurements (like7 in our experiment) inMaxlifd (INS).

Fig. 8 plots the real-time localization error for Maxlifd(INS), HMM and SMC in HKIA. The estimation error fluctu-ates as the user walks in the airport. Changes in wall

Fig. 3. (a) Boarding area at HKIA. (b) HKUST campus atrium (blacktriangles: locations of iBeacons).

Fig. 4. (a) CDF of detected AP number at each target and (b) CDF ofRSSI STD (dB) at RPs in two sites.

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partitions, crowded people, user walking direction andsmartphone holding gesture introduce measurement noisein Wi-Fi and INS signals. SMC sequentially considers thefingerprints and INS measurements. It does not jointly con-sider the Wi-Fi fingerprints and the distances from themultiple time periods. Therefore, large error in location esti-mation happens. In contrast, Maxlifd constrains its estima-tions through the single optimization over the jointmaximum likelihood. Therefore, Maxlifd can achieve lowerlocalization errors and smaller estimation fluctuation.

Further evaluation of Maxlifd in peer-assisted andbeacon-based localization (BC) is presented as follows.Fig. 9 shows the mean localization errors versus differentsurvey grid size. As grid size increases, the localizationaccuracy decreases, while a diminishing return is observedwe use 5 m as the grid size. Fig. 10 shows the mean localiza-tion errors against the proportion of APs removed at targetsin HKIA. We randomly remove some received APs of eachtarget to evaluate the influence of AP reduction due to wallpartitioning or crowds of people. We can see that peer-assisted localization systems marginally rely on the numberof received APs. It is because the Wi-Fi samples at multipleusers reduce the effect of sparse AP deployment. To the con-trary, FL relies on the APs to differentiate the RPs and there-fore its estimation error increases as more APs are pruned.

Compared with GB+FL and SocialLoc, Maxlifd uses jointoptimization of fingerprints and distances which reducesnoise influence and suffers less from AP loss.

We show the CDF of location errors for different algo-rithms at two sites as follows. Figs. 11 and 12 show the loca-tion error CDF ofMaxlifd at different scenarios (PA and BC atbaseline parameters) in HKIA. Large indoor open space oftenleads to high uncertainty in Wi-Fi signals [2] and hence thedisperse nearest neighbors in signal space. Furthermore, thetemporal and spatial distance measurement also containslarge signal noise under the crowded scenarios. Therefore,we expect the signals collected (Wi-Fi and mutual distancemeasurements) contains strong NLoS elements. Comparedwith other state-of-the-art algorithms, Maxlifd significantlyreduces the errors often by around 30 percent in the noisyenvironment of HKIA. With distance constraints and jointoptimization, Maxlifd mitigates the influence of dispersednearest neighbors in locationmapping.

Compared with HKIA, the campus atrium in HKUST issmaller in size with more building partitions, which mayinfluence the peer-distance measurement accuracy. We showthe accuracy ofMaxlifd (INS, PA and BC) on HKUST campusin Figs. 13, 14 and 15, respectively. Maxlifd achieves muchhigher localization accuracy (often about 30 percent error

Fig. 5. Cumulative distribution function (CDF) of localization errors (INS)in HKIA.

Fig. 6. CDF of running time in fusing with INS (HKIA).

Fig. 7.ME versus number of Wi-Fi temporal targets (HKIA).

Fig. 8. Real-time position errors versus time in HKIA (INS).

Fig. 9.ME versus survey grid size (HKIA).

Fig. 10.ME versus reduced ratio of detected APs in HKIA.

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reduction) than the other state-of-the-art algorithms. To sum-marize, for PA scenarios, several users (say, 4 to 5) collectmul-tiple fingerprints and more mutual distances, which is likelyto provide more constraints than a single user (INS). Simi-larly, for BC scenarios, given knowledge of detected beaconlocations, the user is also unlikely to be mapped to distantlocations. In both cases, the tail of localization error is henceshorter than that in the single-user case. As the results inHKUST are qualitatively similar to those in HKIA, for brevitywe do not repeat other experimental results here.

7 SIMULATION EVALUATION

Many environmental parameters are not re-configurable ortunable for a complete experimental studies. Tomore compre-hensively evaluateMaxlifd in large-scale environments underdifferent factors (for example, signal noise, distribution, APnumber and survey grid size are limited in the experiment),we simulate a site in the Hong Kong International Airport(HKIA). In this section, we first discuss the simulation setupin Section 7.1. Then we present the illustrative results in deadreckoning fusion (INS), peer-assisted and beacon-assistedlocalization (BC) in Sections 7.2, 7.3 and 7.4, respectively.

7.1 Simulation SetupWe simulate the Wi-Fi RSSI following the work in [49]. Inthe signal model, the RSSI f (dBm) from Wi-Fi AP at a dis-tanceD can be simulated as

f ¼ fTX � L0 � 10g log10D

D0

þ �; (48)

where measurement noise is distributed as � � Nð0; s2dbÞ.

Unless otherwise stated, we use the following settings inour baseline parameters: the transmission power fTX ¼ 25dBm; the path loss exponent g ¼ 4:0; reference path lossL0 ¼ 37:7 dB; reference distance D0 ¼ 1 m; 215 m � 40 msurvey site with 5 m grid size; Wi-Fi signal noisesdB ¼ 6 dB; 10 APs are uniformly distributed in the survey

area; a target takes a Wi-Fi sample every 2 seconds duringwalking.

We also evaluate the CRLB on location errors of Maxlifdgiven these simulation environment factors. As a result, weevaluate the root mean square error (RMSE) in order tocompare with CRLB of Maxlifd, i.e.,

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

jVjXm2V

kxm � bxmk22s

; (49)

which is the root of mean square error. We also evaluate themean localization error (ME) in our simulation.

We also compare our Maxlifd with the state-of-the-artalgorithms discussed in Section 6.1. We also evaluate theperformance difference between Maxlifd and Wi-Dist insome simulations. Detailed settings for each of localizationscenarios (INS, PA and BC) are presented as follows.

In INS cases, by default 7 most recent Wi-Fi temporal tar-gets (records) are used. The step count error rate is distrib-uted as Nð0; s2

rÞ, where sr ¼ 25%, and the stride length

error follows N 0; s2l

� �, where sl ¼ 0:2 m. Additional walk-

ing displacement error is assumed to follow Nð0; s2wÞ,

where sw ¼ 3:5 m. Each user starts walking towards a ran-domly selected destination point in the site. Based on therandom waypoint model, once the user reaches the final

Fig. 11. CDF of localization errors (PA) in HKIA.

Fig. 12. CDF of localization errors (BC) in HKIA.

Fig. 13. CDF of localization errors (INS) in HKUST.

Fig. 14. CDF of localization errors (PA) in HKUST.

Fig. 15. CDF of localization errors (BC) in HKUST.

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location, he or she stops for some random time and startswalking again to another randomly selected destination [4].

In peer-assisted localization, we consider by defaultnoisy mutual distance error �m � Nð0; s2

mÞ, sm = 3.5 m; 90users are randomly distributed in the survey site. If twousers are within a certain neighborhood detection range(15 m in our simulation), a pairwise link is constructed anda distance constraint is posed upon them. Given Wi-Fi sig-nals collected at each target, by default four peer userstogether conduct a peer-assisted localization, and furtherevaluation over peer number is also conducted. k is also setas 15 for FL, SocialLoc and GB+FL.

In the beacon-based localization (BC), we utilize the log-distance path loss model for iBeacon RSSI-distance measure-ment. The basic approach is to measure the distance basedon path loss signal model. In such application, M ¼ 1 inEquation (7). For a single target, the corresponding distancedn from beacon n, given detected RSSI fn, can hence be repre-sented as dn ¼ d010

Pl�fnð Þ=g . Given a normally distributed fn,the measured distance dn follows a log-normal distribu-tion [49]. Hence in Equations (20) and (38), we replace thenormal distribution, with the logarithm of themutual distan-ces in the final formulation (note that linear signal model [15]may be also applied, and the distance measurement may bemodeled as normally distributed). CRLB derivation for theBC case is similar to that using Gaussian distribution, and forbrevity we do not repeat here. In our simulation, by default atarget can detect an iBeacon if their distance is within 12 m;80 beacons are deployed.

7.2 Fusing with Dead ReckoningFig. 16 plots the RMSE versus the signal variation in Wi-Fifingerprint (sdb in Equation (48)). We can observe that theaccuracy of SMC and HMM degrades when sdB increases. Itis because larger signal noisemakes it more difficult to differ-entiate the fingerprints. For CRLB, the fingerprint signalnoise sml (coming from sdB in Equation (48)) decreases thediagonal elements, Jxm;xm

and Jym;ym, hence increasing the

inverse of the FIM. CRLB for Maxlifd estimation enlarges.Besides, the difference betweenMaxlifd and CRLB decreasesas the noise increases. It is because under small fingerprintnoise, the distance errors become the dominant source offinal localization errors. As sdB further increases, the finger-print noise becomes dominant in CRLB. Different from SMCandHMM,Maxlifd considers signal uncertainty through thejoint maximum likelihood. By jointly maximizing the overalllikelihood in signal measurement and mutual distances,Maxlifd reduces the effect of disperse nearest neighbors insignal space and obtains better estimation results.

Fig. 17 shows the RMSE against the step count errors.Clearly, the accuracy of SMC, HMM and Maxlifd degradeswith larger step count error. SMC locates the user based onthe particle filter and HMM considers conditional indepen-dence. They have not jointly combined fingerprints and stepcount information into one formulation. From CRLB, we canobserve that the measurement errors smn in Equations (43)and (44) decrease as distance noise increases, leading toincrease of fJðuuÞg�1. Therefore, the CRLB increases with thestep count errors. When step count accuracy degrades, thedisplacement error increases and the particles become spa-tially sparse, making it difficult for SMC to converge to thecorrect location. Similarly, HMM considers conditional inde-pendence without joint consideration of measurements, andinformation loss in sensor fusion happens. Therefore, weobserve higher errors in their performance.

To the contrary, Wi-Dist and Maxlifd both localize the tar-get more accurately because the joint consideration of Wi-Fifingerprints and distances of multiple periods (temporal tar-gets) reduces the influence of measurement uncertainty.ComparedwithWi-Dist, Maxlifd constructs a joint maximumlikelihood formulation, which is more general and robust tosignal noise than using bounds. Under large distance errors,such a flexible formulation reduces the misestimation if thebounds do not properly cover the correct location.

Fig. 18 shows the RMSE against the walking displace-ment errors. We can see that as the displacement errorincreases, the overall location accuracy decreases. Similarly,from CRLB we can observe that the measurement errorssmn within temporal distances in Equations (43) and (44)decrease as distance noise increases, leading to the increaseof fJðuuÞg�1. Therefore, the CRLB increases as the step counterror becomes larger. Localization error in SMC increasesbecause the particles converge slowly given large distanceerrors and noisy Wi-Fi fingerprints. Unlike SMC, Maxlifdachieves more accurate results as it utilizes the joint maxi-mum likelihood instead of actual distance measurement. Bymaximizing the joint likelihood in fingerprints and mutualdistances, Maxlifd is more robust to distance uncertainty.As Maxlifd also outperforms Wi-Dist for fusion estimationaccuracy and robustness, in the following we focus on com-paring Maxlifd with other state-of-the-art algorithms.

7.3 Peer-Assisted FusionFig. 19 shows the RMSE versus the number of users.Clearly, more peer assistance provides more distance con-straints over the involved users and improves the localiza-tion accuracy. For CRLB, more peer assistance increases thediagonal elements in FIM JðuuÞ. As more users participate inthe localization, we can observe that CRLB decreases,and better localization accuracy is expected. Compared

Fig. 16. RMSE versus Wi-Fi signal noise (INS). Fig. 17. INS RMSE versus step counts error rate.

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with GB+FL, Maxlifd shows less dependency on the userconnectivity. It is because Maxlifd considers the measure-ment uncertainty in the optimization and jointly constrainsall the users. Therefore, it does not have to involve manyusers to achieve high localization accuracy. SocialLoc consid-ers dynamic encounters and nonencounters among users,and hence is not sensitive to user number. Maxlifd jointlyoptimizes the target estimations and achieves better resultsthan SocialLoc. Accuracy gain from number of involvedusers for Maxlifd becomes smaller as more users participatein location estimation. It is mainly because interactionbetween distant users contributes for all users in each loca-tion estimation, which is also reflected from a stabler CRLB.

Fig. 20 shows the RMSE against peer distance errors.We assume a zero-mean Gaussian noise is added to themutual distance measurement. When the distance error issmall, all algorithms achieve high accuracy given onlyWi-Fi fingerprint noise. As distance error further increases,all algorithms suffer from lower accuracy. GB+FL constructsa rigid graph to constrain relative positions of differentusers. The graph shape deforms under large distance mea-surement errors and lead to misestimation. SocialLoc con-siders independently over the pairwise distance constraintsbetween users who encounter. Without joint consideration,their accuracy still degrades with large signal noise. Max-lifd, in contrast, leverages a more flexible probabilistic local-ization based on fingerprints and distance likelihood.Without assuming a rigid graph, Maxlifd can achieve morerobust localization estimation. For CRLB, as more distancenoises, smn, are introduced to the Fisher information matrix,the diagonal elements in the FIM become smaller, leadingto higher CRLB. Therefore, we can observe the increasewithin the lower bound of estimation errors.

Fig. 21 showsME versus site survey grid size. As the gridsize increases, all algorithms degrade in accuracy. FLdegrades due to ambiguity of fingerprints under large gridsize. Without joint consideration of distances and finger-prints, GB+FL and Social-Loc cannot achieve high accuracywith low site survey density. Different from above schemes,

Maxlifd jointly considers both the distance and fingerprintuncertainty and relies less on fingerprint density. HenceMaxlifd can achieve better localization accuracy. Fig. 21 alsoshows saturation in accuracy improvement under smallgrid size due to noise and measurement uncertainty.

7.4 Beacon-Assisted FusionIn the simulation with iBeacon, we assume that when the tar-get is within the range of the beacons, the target can detectand measure the distances from them. Fig. 22 shows theRMSE versus the iBeacon detection range. It shows the locali-zation error decreases when the iBeacon detection rangeincreases. It is mainly because larger iBeacon coverageincreases the connectivity of each target, leading to more con-straints over the final location estimation. Larger range intro-duces more distance intersections and more constraints.Therefore, the diagonal elements in JðuuÞ increase and CRLBcorrespondingly decreases. Then the trend of decrease slowsdown because each target point has obtained sufficient con-straints. Similarly in CRLB, as more distance constraints areincluded, the influence over final target estimation decreases.

Fig. 23 shows the RMSE versus the iBeacon deploymentdensity. It shows that the RMSE of both MMSE and Maxlifddecreases proportionally with the iBeacon deployment den-sity. Then the trend of decrease diminishes after a certainnumber of beacons. However, dense deployment may intro-duce large survey efforts, and thus in real application wedeploy beacons at area with sparser Wi-Fi coverage. Whenthe density of iBeacon increases, the connectivity for eachtarget increases. The diagonal elements of JðuuÞ also increase,leading to a lower CRLB in location estimation.

Fig. 24 shows the ME under different probability dis-tributions in fingerprints and distances for Maxlifd (BC).We consider a uniform signal noise (i.e., � � Uð�sdb; sdbÞin Equation (48)), and the log-normal signal noise (i.e.,F � logNðFTX � L0 � 10g log10ðDD0Þ; s2

dbÞ) exists within theWi-Fi RSSIs, respectively (similar forms are applied in themutual distance measurements). We compare Maxlifd

Fig. 18. INS RMSE versus additional walking displacement errors.

Fig. 19. RMSE versus peer user number (PA).

Fig. 20. RMSE versus peer distance errors (PA).

Fig. 21.ME versus site survey grid size (PA).

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under the corresponding distribution formulations and thatconsidering Gaussian distribution (see Section 4). From themarginal sacrifice of accuracy and estimation fluctuation,we can see Maxlifd does not depend sensitively on knowingexactly the underlying signal or distance distribution, wherethe simple Gaussian representation suffices to offer reason-able accuracy. In practice, the calculation in probability dis-tribution is also similar (the overall computation is boundedby the optimization process), and the small difference inpositioning error indicates that the influence over the opti-mality is also marginal.

8 DISCUSSION

We further discuss some important deployment issuesrelated to Maxlifd as follows.

� Reducing fingerprinting cost: How to learn and reducethe fingerprints has been an important topic forindoor localization. Various mechanisms have beenproposed recently, including crowdsourcing/boot-strapping [32] and signal map reconstruction [52], inorder to get rid of detailed, costly and labor-intensivesurvey. Given context of ubiquitous crowdsourcingand appropriate preprocessing [53], fingerprints canbe collected or updated at much lower expenses [54].Despite our focus here in locating target given sensorfusion, these studies can be integrated with Maxlifdto further reduce deployment costs, achieving moreubiquitous localization.

� Adapting to power adjustment and environmental change:Signal dynamics due to power adjustment [52]and environmental alternation [55] have attractedresearch attention recently. Maxlifd is evaluated inpractical environments of strong signal dynamics(including power alteration and multi-path effects),and shown to outperform other schemes due to its

joint optimization. To make Maxlifd more robust,one may further integrate altered AP detection/fil-tering [51], and adapts the fingerprint map to thespatial-temporal dynamics [32], [55]. Interested read-ers may refer to these works, and for brevity we donot explore deeper here.

� Enhancing ranging performance: None-line-of-sight(NLoS) ranging may affect the mutual distance con-straints. Take the sound-ranging as an example.Inside narrow and NLoS environment (like smallrooms), the accuracy of PA may be compromiseddue to imperfection of their ranging models. Wemay adopt some effective schemes (see [56]) todetect strong multi-path effect within the soundreflection, thus foreseeing potential degradation insound ranging accuracy. As a general framework,Maxlifd may also switch to other more applicablesensors (say, inertial pedometer) to conduct fusion-based localization.

9 CONCLUSION

We have proposed Maxlifd, a novel joint maximum likeli-hood framework fusing wireless fingerprints with mutualdistances for indoor localization. The mutual distancescan be temporal or spatial (as obtained from dead reckon-ing, beacon-based, peer-assisted manner, etc.). Due torandom signal fluctuation, both fingerprints and distancemeasurements are noisy in nature. Given the probabilitydistributions in distances and fingerprints, Maxlifd for-mulates a single semi-definite programming problem,fusing the noisy fingerprints with uncertain distance mea-surement to localize the target based on the joint likeli-hood maximization. Maxlifd is generic, and hence isapplicable to a wide range of sensing devices and wire-less fingerprint signals.

We have implemented Maxlifd using INS (temporal),peer-assisted and beacon-assisted distance measurement(spatial), validating its accuracy and robustness. We havealso evaluated its CRLB of localization errors, which pro-vides theoretical insights for deployment.

Fig. 22. RMSE versus iBeacon detection range (BC).

Fig. 23. RMSE versus iBeacon deployment density (BC).

Fig. 24. ME and error standard deviations of Maxlifd (BC) under differentdistributions: (1)Wi-Fi RSSI distribution and (2)mutual distance distribution.

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ACKNOWLEDGMENTS

This work was supported, in part, by the National NaturalScience Foundation of China under Grant (61472455),and the Guangzhou Science Technology and InnovationCommission (GZSTI16EG14/201704030079).

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Suining He received the PhD degree from theDepartment of Computer Science and Engineer-ing, The Hong Kong University of Science andTechnology (HKUST), in 2016. He was selected asa Google PhD fellow in Mobile Computing (Chinaand East Asia), in 2015. He is currently working asa postdoctoral research fellow with the Real-TimeComputing Laboratory, The University of Michigan,Ann Arbor. His research interest includes indoorlocalization, smartphone sensing, and mobilecomputing. He is amember of the IEEE.

S.-H. Gary Chan (S’89-M’98-SM’03) received theBSE degree (highest honor), in electrical engineer-ing from Princeton University, Princeton, NJ, in1993, with certificates in applied and computationalmathematics, engineering physics, and engineer-ing and management systems, and the MSE andPhD degrees in electrical engineering from Stan-ford University, Stanford, CA, in 1994 and 1999,respectively, with a minor in business administra-tion. He is currently professor with the Departmentof Computer Science and Engineering, The Hong

Kong University of Science and Technology (HKUST), Hong Kong. He isalso the director of the Entrepreneurship Center, and chair of the Commit-tee on Entrepreneurship Education Program, Center for Education Innova-tion, HKUST. His research interest includes multimedia networking, mobilecomputing, data/user analytics, and IT entrepreneurship. He has been anassociate editor of the IEEE Transactions on Multimedia (2006-2011), anda vice-chair of thePeer-to-PeerNetworking andCommunications TechnicalSub-Committee of the IEEE Comsoc Emerging Technologies Committee(2006-2013). He is and has been guest editor of Elsevier Computer Net-works (2017), theACMTransactions onMultimedia Computing, Communi-cations, and Applications (2016), the IEEE Transactions on Multimedia(2011), the IEEE Signal ProcessingMagazine (2011), the IEEECommuni-cation Magazine (2007), and Springer Multimedia Tools and Applications(2007). He was the TPC chair of the IEEEConsumer Communications andNetworking Conference (IEEE CCNC) 2010, Multimedia Symposium ofIEEE Globecom (2007 and 2006), IEEE ICC (2007 and 2005), and theWorkshop onAdvances inPeer-to-PeerMultimediaStreaming inACMMul-timedia Conference (2005). He has co-founded several startups deployinghis research results. Due to their innovations and commercial impacts, hisprojects have received local and international awards (2012-2018). He isthe recipient of theGoogleMobile 2014Award (2010 and 2011) and the Sil-ver Award of BoeingResearch and Technology (2009). He has been a visit-ing professor and researcher in Microsoft Research (2000-2011),Princeton University (2009), Stanford University (2008-2009), and the Uni-versity of California, Davis (1998-1999). He was undergraduate programscoordinator with the Department of Computer Science and Engineering(2013-2015), director of the Sino Software Research Institute (2012-2015),co-director of the Risk Management and Business Intelligence Program(2011-2013), and director of the Computer Engineering Program (2006-2008) with HKUST. He was aWilliam and Leila fellow with Stanford Univer-sity (1993-94), and the recipient of the Charles Ira Young Memorial Tabletand Medal, and the POEM Newport Award of Excellence at Princeton(1993). He is a chartered fellow of The Chartered Institute of Logistics andTransport (FCILT), and amember of honor societies TauBeta Pi, SigmaXi,and Phi Beta Kappa. He is a senior member of the IEEE.

Lei Yu received the bachelor’s degree in softwareengineering from Sun Yat-sen University, and thedouble master’s degree in electrical and com-puter engineering from Carnegie Mellon Univer-sity and Sun Yat-sen University. He receivedmany prizes during his undergraduate period,such as the National Scholarship of China,Google Excellence Scholarship, etc.

Ning Liu received the BS degree in computa-tional mathematics from Northwest University,Xian, China, and the PhD degree in computerscience from Sun Yat-sen University (SYSU),Guangzhou, China, in 1996 and 2004, respec-tively. He is currently an associate professor withSun Yat-sen University. He has served as areviewer for several important conferences andjournals. His current research interests includecomputer vision, peer-to-peer networks, andmachine learning algorithms.

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HE ETAL.: MAXLIFD: JOINT MAXIMUM LIKELIHOOD LOCALIZATION FUSING FINGERPRINTS AND MUTUAL DISTANCES 617