Employing Spatial Analysis in Indoor Positioning andTracking Using Wi-Fi Access Points

Song GaoDepartment of Geography

University of California, Santa BarbaraCA 93106, USA

sgao@geog.ucsb.edu

Sathya PrasadApplications Prototype Lab

Esri Inc., RedlandsCA 92373, USA

sprasad@esri.com

ABSTRACTA practical WiFi-based positioning system has to be adapt-able to the variations of indoor environmental dynamic fac-tors. In this work, we propose a novel Wi-Fi indoor posi-tioning and tracking framework which employs the spatialanalysis and image processing techniques. The Wi-Fi sur-faces can be dynamically constructed and updated and thushelp to address the challenges of signal spatial heterogene-ity and environmental variations. A mobile app for indoorpositioning application has been developed as a proof of con-cept. Based on the experiments we conducted at the Esricampus, this method can achieve about 2-meter positioningaccuracy. The proposed methodology and theoretical frame-work can guide engineers to implement cost-effective indoorpositioning infrastructure, and thus offer insights on futuresmart campus applications. The introduced spatial analy-sis and geoprocessing workflow may also bring the attentionof GIScientists to make more efforts to conquer the indoorpositioning and tracking challenges.

CCS Concepts•Information systems → Mobile information pro-cessing systems; Spatial-temporal systems; Loca-tion based services; Geographic information sys-tems; Global positioning systems;

KeywordsIndoor positioning; Spatial analysis; WiFi fingerprinting

1. INTRODUCTIONIn the era of mobile age, location-based systems and ser-

vices become more and more popular in people’s daily life,such as searching nearby points of interest (POI), way find-ing and navigation. There has been growing interest amongresearchers in studying human mobility patterns based onthe data collected from location-awareness devices, e.g.,GPS-enabled devices [45, 39], cellular phones [13, 18], and

Permission to make digital or hard copies of all or part of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for components of this work owned by others than theauthor(s) must be honored. Abstracting with credit is permitted. To copy otherwise, orrepublish, to post on servers or to redistribute to lists, requires prior specific permissionand/or a fee. Request permissions from permissions@acm.org.

ISA 16, October 31-November 03 2016, Burlingame, CA, USAc© 2016 Copyright held by the owner/author(s). Publication rights licensed to ACM.

ISBN 978-1-4503-4585-9/16/10. . . $15.00

DOI: http://dx.doi.org/10.1145/3005422.3005425

Bluetooth sensors [29, 33]. Positioning is the key compo-nent to support smart mobility studies, trajectory data min-ing and travel related applications [43, 36, 40]. It is wellknown that GPS-enabled devices work well for positioningin outdoor environments but not in indoor environments be-cause of the signal obstructions and attenuation[26]. How-ever, as reported in a national human activity pattern survey(NHAPS), people spend an average of 87% of their time inenclosed buildings and about 6% of their time in enclosedvehicles [19]. There is a high-demand for indoor positioningtechnologies. In [44] the researcher systematically comparethree dominant positioning technologies: Assisted-GPS, Wi-Fi, and Cellular positioning. Their pros and cons are dis-cussed in terms of coverage, accuracy and reliability. It re-ports that Assisted-GPS obtains an average median error of8m outdoors while Wi-Fi positioning only gets 74m of thatand cellular positioning has about 600m median error in av-erage and is least accurate. However, high-resolution GPS orAssisted-GPS positioning chipsets don’t work well in indoorenvironments due to limited satellite visibility; and thus avariety of indoor positioning technologies and systems havebeen designed and developed to increase the indoor posi-tioning accuracy.

The widely use of Wi-Fi access points for Internet connec-tion in hotels, offices, coffee shops, airports and many otherfixed places makes Wi-Fi become an attractive technologyfor the positioning purpose. Location positioning systemsusing wireless area local network (WLAN) infrastructureare considered as cost-effective and practical solutions forindoor location estimation and tracking [7]. There is almostno extra hardware or other infrastructure investment, whichis different from other indoor positioning technologies suchas low-energy Bluetooth sensor networks or radio-frequencyidentification (RFID) systems. Conventional methods forindoor positioning are based on time of arrival, time differ-ence of arrival and angle of arrival of radio signals transmit-ted by mobile stations [30]. Another type of WLAN posi-tioning method unitizes the fingerprinting idea to determinea receiver’s location via clustering and probabilistic distri-butions [42]. The accuracy of localization is dependent onthe separation distance between two-adjacent Wi-Fi refer-ence points and the transmission range of these referencepoints [5]. One challenge that WLAN indoor positioningtechniques face is the spatial heterogeneity of Wi-Fi signalsurfaces caused by the signal path loss because of absorp-tion, reflection and refraction by the surrounding environ-ment. Thus the physical radiation models need complexparameter estimation and empirical fitting. Spatial analysis

techniques can be employed in dealing with geometric, topo-logical, and geographic properties which can help to capturebetter indoor environment and to construct more accurateWi-Fi surfaces for indoor positioning and tracking purpose.

In this research, we propose a novel geoprocessing-basedframework and develop a mobile application for real-timeindoor positioning and tracking using Wi-Fi access points.The goal of this study is to explore how accurate Wi-Fi in-door positioning with the support of spatial analysis canachieve. The following of this paper is organized as follows.In Section 2, we review some related work and discuss thestate of the art in indoor positioning technologies. Our pro-posed theoretical framework towards indoor positioning andtracking, and detailed methods are introduced in Section 3.The system implementation and experiments are describedin Section 4, which is followed by discussions in Section 5.We conclude and give a vision for future work in Section 6.

2. LITERATURE REVIEW

2.1 Indoor Positioning TechnologiesIn general, indoor positioning technologies can be classi-

fied into two broad categories: radio-frequency-based (RF)and non-radio-frequency-based (NRF) technologies. The RFgroup includes but not limited to WLAN, Bluetooth, andRFID systems, while the NRF group contains ultrasound,magnetic fields, and vision-based systems. Researchers havemade great efforts in the field of indoor positioning usingthese sensors and technologies [17, 11, 23, 15, 21, 24, 20].The spatial coverage area and positioning accuracy of thosedifferent technologies have been reviewed by [26]. Here, weonly briefly discuss the RF technologies that are most popu-lar in the current market share and face several challengingissues to investigate.

Wi-Fi: The Institute of Electrical and Electronics Engi-neers (IEEE) 802.11 work group [14] documents the stan-dard use of Wi-Fi technology to enable wireless networkconnections in five distinct frequency ranges: 2.4 GHz, 3.6GHz, 4.9 GHz, 5 GHz, and 5.9 GHz bands. The wirelessnetworks are widely implemented in many types of indoorbuildings in which wireless access points are usually fixedat certain positions. Those access points allow wireless de-vices (e.g., mobile phones, laptops and tablets) to connectto a wired network using Wi-Fi technology. And the relativedistance between wireless devices and access points can beroughly estimated based on Wi-Fi signal strength using sig-nal propagation models [28]. It is also well known that theaccuracy of indoor position estimation based on Wi-Fi signalstrength is affected by many environmental and behaviourfactors, such as walls, doors, settings of access points, orien-tation of human body, etc.[11, 37]. In practical applications,a good approximation of heterogeneous environmental sig-nal surfaces could help to improve the indoor positioningaccuracy. Spatial regression which is a widely used spatial-analysis method in finding spatial patterns and modelingtrend surface [8] could potentially be a good candidate.

Bluetooth: is designed for low power consumption andallows multiple electronic devices to communicate with eachother without cables by using the same 2.4 GHz radio-frequency band as Wi-Fi. The distance range within whichBluetooth positioning can work is about 10 meters. In thebeaconing mode, Bluetooth permitted messages can be usedto detect the physical proximity between two devices [10].

In an indoor environment equipped with equal to or largethan three Bluetooth low energy (BLE) beacons, the loca-tion of a target mobile device with Bluetooth can be de-termined using classic positioning approaches (see Section2.2 in detail). In this way, location-dependent triggers, no-tifications and tracking activities can be enabled by em-ploying multiple BLE beacons. There are several popularBLE beacon-positioning protocols and technology availableonline, including Apple iBeacon1, Google Eddystone2 andGualcomm Gimbal3, which guide developers to implementup-to-date indoor positioning and tracking applications.

Radio-frequency Identification (RFID): is a generalterm used for a system that communicates using radio wavesbetween a reader and an electronic tag attached to an ob-ject. Comparing with Bluetooth technology, RFID systemsusually comprise of readers and tags that store relativelylimited information about the object such as location andattribute information. Those tags can be activated and sendout stored information if they receive the signal from RFIDreaders within certain distance thresholds, which can beused to estimate the reader’s location and to show relevantinformation. Currently RFID positioning and tracking sys-tems are widely used for asset tracking, shipments trackingin supply chains, and object positioning in retailing placesand shopping malls.

Because of sensor diversity and positioning challenges invarious indoor environments, there is also an increasingtrend towards combining and integrating different sensornetworks to get a better spatial coverage and position ac-curacy than using single data source. In [9] researchers in-tegrate Wi-Fi and inertial navigation systems to get perfor-mance close to meter by fusing pedestrian dead reckoningand Wi-Fi signal strength measurements.

2.2 Indoor Positioning MethodsThe following methods usually work for both outdoor and

indoor environments, but we emphasize the indoor case here.Note that those methods can be applied in most radio-frequency-based sensors, such as Wi-Fi and Bluetooth.

2.2.1 Geometric ApproachesIn geometry, trilateration is a method to determine the

target location of a point by measurement of distances tothree points at known locations using the geometry of cir-cles, triangles, or spheres [6]. This method has been widelyused not only in positioning systems [16], but also in robotlocalization, computer graphics, aeronautics, and so on [34].For the positioning purpose, if already knowing the coor-dinate (lat,lon) information of three fixed access points, itneeds to convert the latitude and longitude of these loca-tions from the Earth reference system to axis values (x,y,z)in the Cartesian coordinate system as follows:

x = R ∗ cos(lat) ∗ cos(lon)

y = R ∗ cos(lat) ∗ sin(lon)

z = R ∗ sin(lat)

(1)

Where R is the approximate radius of earth (e.g.,6371km). Then we can try to find the solutions to trilat-eration equations to approximate the location of the target

1https://developer.apple.com/ibeacon/2https://developers.google.com/beacons/3http://www.gimbal.com/

Figure 1: Determine the location of an object usingtrilateration method.

object by referring to three points with known locations [16](See Figure 1). The equations are nonlinear and it is notso easy to obtain an exact solution. Several iterative arith-metic methods have been proposed to find efficient solutionsfor trilateration-based localization [25, 41].

It is obvious that the distance between a wireless deviceand an access point is the key for Wi-Fi positioning using thetrilateration method. The received signal strength doesn’tdirectly lead to an estimated distance to an access point. Ingeneral, it does follow a trend that the signal strength de-creases with an increase of distance as is expected, but it isnot a simple linear path loss model. The log-distance pathloss model is one of the most simplistic radio-propagationmodels [28, 32] that predict the received signal strength ata certain distance inside a building or densely populated ar-eas. However, in many practical situations, many factors un-derlying radio propagation can contribute to the reflection,refraction, absorption and scattering of signals. It is diffi-cult to predict the received signal strength with a simplisticlog-distance pass-loss model. Rather than creating a newpass-loss model, some researchers try to re-parameterize theclassic log-distance model. For example, researchers foundthat at closer ranges (e.g., smaller than 5 meters) the expo-nent factor of propagation model would take a higher value,and thus a dual-distance model has been proposed to adjustthe propagation model at larger distances for achieving abetter positioning accuracy [3].

2.2.2 Fingerprinting ApproachesAlthough most Wi-Fi access points are located at the fixed

locations of buildings, it is very hard to get their accurate co-ordinates and detailed digital floor maps because of privacyconcerns. Fingerprinting approach is a popular wireless-network positioning technology in metropolitan areas sinceit doesn’t need the exact position information of Wi-Fi ac-cess points. Instead, it needs to construct an offline databasethat contains the signal strength distribution of Wi-Fi ac-cess points at known locations, i.e., the “radiomap”. For agiven location, it receives varying signal values from equal toor less than the maximum number of available Wi-Fi access

points. The set of access points and their signal strengthsare distinctive and present a “fingerprint” to a unique loca-tion on the “radiomap”. Thus, we can employ searching andcomparison processes in the online positioning phase to findthe most probable location.

Several fingerprinting matching and calculation methodshave been developed to estimate the location of a user basedon received Wi-Fi signal strength (SS) values at known ref-erence point (RP) locations [17, 22, 27, 12]. In its simplestform, it can be expressed mathematically as follows:

argminp∈(1,2,n)

√√√√ m∑i=1

[SSRE(i, p)− SSME(i)]2 (2)

where SSRE(i, p) represents the received signal-strengthvalue of access point i at a known reference point locationp on the radiomap, and SSME(i) is the measured signal-strength value of access point i at the current unknown lo-cation. The location p that has the minimum root-squared-differences of SS values for all available m access points be-tween reference points and the target location is consideredas the most probable estimated location.

In addition, machine-learning-based fingerprinting tech-niques have also been studied for improving the quality oflocation estimation in complex real environment, includingBayesian modeling, k-nearest-neighbor estimation, supportvector machine, neural networks and so on [2, 31, 42, 4].

3. METHODOLOGIES

3.1 Study DesignOur theoretical framework of indoor positioning and

tracking consists of three steps as shown in Figure 2.Step 1: Field sampling is a process of collecting available

indoor Wi-Fi access point set {AP1, AP2, APm} and thecorresponding received signal strength indicator (RSSI)at various locations {Loc1, Loc2, ..., Locn} with differentdistances to each access points. The output of this step is atwo-dimensional matrix {RSSI(APi, Locj)} which can berepresented as:

RSSI(AP1,Loc1) RSSI(AP1,Loc2)... RSSI(AP1,Locn)

RSSI(AP2,Loc1) RSSI(AP2,Loc2)... RSSI(AP2,Locn)

... ... ...RSSI(APm,Loc1) RSSI(APm,Loc2)... RSSI(APm,Locn)

Note that the matrix allows for ’null’ value element if

there is no signal for a given Wi-Fi access point at a certainlocation.

Step 2: The fixed location of each Wi-Fi access pointLoc(APi) can be estimated based on a sample of high qual-ity signals (i.e., RSSI value ≥ -50 decibels). The geomet-ric centroid of these clustered high quality signal locationsis stored as Loc(APi). Meanwhile, as shown in the geo-processing workflow (Figure 3), the signal surface of eachWi-Fi access point Surf(APi) can be built via spatial inter-polation (e.g., inverse distance weighted (IDW) method orKriging techniques) of collected sampling points from Step1. The AP locations and raster surfaces of these Wi-Fi ac-cess points generated from this geoprocessing step are storedon the GIS Cloud server where data can be published as

Figure 2: A geoprocessing-based framework of indoor positioning and tracking.

Figure 3: A geoprocessing workflow for generatingWi-Fi signal surface from samples. Yellow squaresrepresent spatial analysis and data conversion toolswhile green ellipse shapes represent intermediatedata layers and outputs.

standard geospatial Web services. Figure 4 shows a Wi-Fisurface with 1m*1m grids generated by the spatial interpo-lation process. Note that a grid location in this surface isassociated with an array of signal strength from a list ofavailable Wi-Fi access points.

Step 3: The developed mobile app can estimate a user’sindoor location based on a received Wi-Fi signal array[RSSI(APi)]. More detailed algorithms will be discussedin the following section. Moreover, we integrate the Fire-base4 real-time database for storing and synchronizing cross-platform app’s indoor positioning data for enabling indoormobility tracking.

3.2 Positioning AlgorithmsSeveral positioning algorithms have been developed for

4https://www.firebase.com/

Figure 4: A Wi-Fi surface with 1m*1m grids gener-ated by the spatial interpolation process.

Figure 5: The proposed heuristics-based indoor po-sitioning algorithm.

Wi-Fi positioning [42, 17, 44, 7] and can be categorized as:geometric techniques, statistical methods, fingerprinting andmachine learning algorithms. We introduce another algo-rithm based on image filtering technique and then integrateit with two widely used algorithms: Trilateration and k-nearest-neighbor in signal space (K-NNSS) [2] into our in-door positioning system relying on a Wi-Fi surface whichkeeps at least three image pixels that meets the multi-valuefiltering requirements.

As shown in Figure 5, we propose a heuristics-based in-door positioning algorithm in the online mode. It containsthree main phases. First, a mobile phone device scans thesurrounding environment and gets available Wi-Fi accesspoints with their RSSI value array: [RSSI(APs)]. Second,a multidimensional-value filtering technique is employed toextract Wi-Fi surface pixels on which the RSSI values onthe surface across all available access points are within thesignal strength ranges, which can be expressed as follows:

Loc ∈ ∃Loc(j){RSSI(APs)i − δ ≤ RSSI(Locj ,APi)

≤ RSSI(APs)i + δ, |∀i ∈ (1, 2, ..., N)}(3)

It assumes that there exist one or several pixel locations[Locj ] on the surface such that its corresponding receivedsignal strength is within a constant δ deviation away fromthe current RSSI for each available Wi-Fi access point i (seeFigure 6). Third, depending on the resulting number N ofpixels left after the image filtering step, the program deter-mines which positioning approach should be further trigged.If N = 0, the device needs to re-scan environmental Wi-FIsignals until get updated RSSI values and then repeat pre-vious processing steps; if 0 < N < 3, the algorithm willsimply return the mean coordinate of the remained surfacepixels as the estimated location; if N = 3, the geometricmethod that utilizes the aforementioned propagation modeland trilateration positioning approach (see Section 2.2 formore details about this method) is chosen, and the loca-tions of three Wi-Fi access points with largest RSSIs aretaken as the reference points for trilateration; if N>3, thek-nearest-neighbors algorithm is chosen to approximate the

Figure 6: Filtered Wi-Fi surface pixels that meetsignal strength requirements are highlighted withcyan color.

indoor location.K-nearest-neighbors is a popular method used for classifi-

cation and regression [1], in which an object is grouped tothe most class by a majority vote of its k-nearest neighbors.In the K-NNSS algorithm, it first calculates the distancesbetween the current observed vector of RSSI values and allRSSI vectors in the signal space.

distj(SSr, SSo) =

√√√√ m∑i=1

[SSr(i, j)− SSo(i)]2 (4)

where SSr(i, j) represents the RSSI of the ith Wi-Fi accesspoint at a known location j on the Wi-Fi signal surface, andSSo(i) is the measured RSSI of the same Wi-Fi access pointi at the current unknown location.

After calculating all the signal-strength distances with re-spect to all locations on the signal surface, a set of k loca-tions with smallest distances is chosen. The chosen value of kvaries in different realistic environments because of changesin available Wi-Fi access points, and a calibration processcan help to derive an appropriate value. We choose k=5in empirical studies. Then the current unknown location(lato, lono) can be approximated by averaging the coordi-nate information of each candidate location (latj , lonj) fromthose chosen k-nearest-neighbor locations in the signal spaceas follows:

(lato, lono) =1

k∗

k∑j=1

(latj , lonj) (5)

or by taking the spatial weights (distance) into considera-tion, which is the chosen algorithm in developing our indoor-positioning mobile application:

(lato, lono) =

k∑j=1

1distj(SSr,SSo)

∗ (latj , lonj)

k∑j=1

distj(SSr, SSo)

(6)

where distj(SSr, SSo) is the previously calculated dis-tance between two RSSI vectors. This algorithm is actuallyconsistent with the inverse-distance weighted interpolationin spatial analysis, which estimates the grid-cell attributevalues in a raster from a set of sample points by weightingsample-point values so that the farther a sampling point isaway from the target cell being evaluated, the less weightit contributes to the calculation of the target cell’s value.The method is inspired by Tobler’s first law of geography:“Everything is related to everything else, but near things aremore related than distant things.” [35].

4. IMPLEMENTATION AND RESULTBased on the geopeocessing framework and workflow in-

troduced above, we first developed a Wi-Fi scanning mobileapplication to scan and collect the available Wi-Fi accesspoints inside a building of Esri campus (Figure 7a). In theexperiments, we selected 18 Wi-Fi access points in a build-ing and collected at least 30 sampling RSSI values for eachWi-Fi access point (Figure 7b). Then the geoprocessing sys-tem was built for constructing the signal raster surfaces with1-meter grid spatial resolution for all available Wi-Fi accesspoints. In the online phase, the indoor position of the usercan be estimated via raster multi-value-attribute filteringon Wi-Fi signal surfaces and above introduced heuristics-based positioning algorithm. As shown in Figure 7c, whenone mobile device was put at the location Q, the red circlerepresented the estimated position based on our proposedmethod while the blue circle was the GPS location whichstill located on the outside of this building. After conduct-ing several rounds of experiments, we got about 2-meterpositioning accuracy in average in this empirical study. Theuser’ locations were also automatically sent to a real-timedatabase (i.e. Firebase) for indoor mobility tracking.

5. DISCUSSIONSIndoor positioning is a challenging problem and requires

a lot of interdisciplinary research. The biggest advantageof Wi-Fi positioning technology is that it can utilize exist-ing wireless-network infrastructures without extra hardwarecosts as Bluetooth beacons or RFID tags do need. How-ever, it also has some limitations when applying in complexindoor environments:

First, the RSSI values vary dynamically and are sensitiveto indoor environments because of signal multi-path fading,path loss, and even the direction to which human bodies arefacing. It needs a lot of work in the offline sampling processto ensure that we can get a good approximation of Wi-Fisignal strength database at difference reference locations andsurfaces with respect to the spatial structure.

Second, by comparing different positioning algorithms,fingerprinting methods based on machine learning tech-niques usually get a better position estimation than

distance-based trilateration model in real-world complexenvironments. But fingerprinting methods need databasesearching and comparison computation processes in the on-line mode, which takes long time if it involves large-size mul-tidimensional signal surfaces. When choosing the trilatera-tion method, the parameters in the propagation model forconverting signal strength to distance values need to be wellcalibrated. Otherwise sometimes no good matching resultscan be returned.

Last but not least, by applying the spatial analysis andinterpolation methods, it helps to approximate the spatialdistribution of signal strength in real-world indoor environ-ments. But it also needs to try different spatial interpolationmethods and parameter fitting processes for choosing thebest one for generating good signal surface representations.

6. CONCLUSIONS AND FUTURE WORKA practical WLAN-based positioning system has to be

adaptable to the variations of indoor environmental dynamicfactors. In this work, we propose a novel Wi-Fi indoor po-sitioning and tracking framework which employs the spatialanalysis and image processing techniques. The Wi-Fi sur-faces can be dynamically constructed and updated, and thushelp to address the challenges of signal spatial heterogeneityand environmental variations. In addition, we don’t need tocollect a very large pool of reference points for RSSI sam-pling comparing with other signal-strength database con-struction methods in the offline mode, although it is stillnecessary to get some Wi-Fi signal-strength samples fromindoor reference points. Instead, the weighted spatial in-terpolation method can help to reduce the field samplingburden. A mobile indoor positioning application has beendeveloped as a proof of concept. Based on the experimentswe conducted at Esri campus, this method can achieve about2-meter positioning accuracy. Since it falls into the generalcategory of “fingerprinting”, one can argue that the closerwe can approximate to the actual environmental signals,the more accurate we can locate the user. The proposedmethodology and theoretical framework can guide engineersto implement cost-effective indoor positioning infrastructureusing Wi-Fi in other campuses, and thus offer insights onfuture smart campus applications. The spatial analysis andgeoprocessing workflow may also bring the attention of GI-Scientists to make more efforts to conquer the indoor posi-tioning challenge.

In future work, we aim to take the signal directionalityinto consideration and try more advanced spatial interpo-lation and clustering methods to achieve better accuracyfrom meter to decimeter. In addition, a crowdsourcing Wi-Fi signal collection and sharing platform will be developed toengage more users’ contribution for advancing indoor posi-tioning technology in our campus. Last but not least, thereis a growing trend towards integrating multi-sensors thatare available in the mobiles phones, including speaker, ac-celerometer, gyrometer, barometer etc., to improve indoorpositioning accuracy and to semantically label indoor roomtypes. It is also fit into our future investigation into indoorpositioning and ambient sensing technologies.

7. REFERENCES[1] N. ALTMAN. An introduction to kernel and

nearest-neighbor nonparametric regression. TheAmerican Statistician, 46(3):175, 1992.

Figure 7: Screenshots of the indoor positioning app using Wi-Fi scanning and spatial analysis techniques. (a)Wi-Fi scanning results at a given location; (b) available Wi-Fi access points in the building (green markers);(c) online-mode indoor positioning (red dot).

[2] P. Bahl and V. N. Padmanabhan. Radar: Anin-building rf-based user location and tracking system.In INFOCOM 2000. Nineteenth Annual JointConference of the IEEE Computer andCommunications Societies. Proceedings. IEEE,volume 2, pages 775–784. Ieee, 2000.

[3] A. Bose and C. H. Foh. A practical path loss model forindoor wifi positioning enhancement. In Information,Communications & Signal Processing, 2007 6thInternational Conference on, pages 1–5. IEEE, 2007.

[4] M. Brunato and R. Battiti. Statistical learning theoryfor location fingerprinting in wireless lans. ComputerNetworks, 47(6):825–845, 2005.

[5] N. Bulusu, J. Heidemann, and D. Estrin. Gps-lesslow-cost outdoor localization for very small devices.IEEE personal communications, 7(5):28–34, 2000.

[6] A. Cayley. On a theorem in the geometry of position.Cambridge Mathematical Journal, 2:267–271, 1841.

[7] N. Chang, R. Rashidzadeh, and M. Ahmadi. Robustindoor positioning using differential wi-fi access points.IEEE Transactions on Consumer Electronics,56(3):1860–1867, 2010.

[8] M. J. De Smith, M. F. Goodchild, and P. Longley.Geospatial analysis: a comprehensive guide toprinciples, techniques and software tools. TroubadorPublishing Ltd, 2007.

[9] F. Evennou and F. Marx. Advanced integration of wifiand inertial navigation systems for indoor mobilepositioning. Eurasip journal on applied signalprocessing, 2006:164–164, 2006.

[10] R. Faragher and R. Harle. An analysis of the accuracyof bluetooth low energy for indoor positioning

applications. In Proceedings of the 27th InternationalTechnical Meeting of The Satellite Division of theInstitute of Navigation (ION GNSS+ 2014), Tampa,FL, USA, volume 812, 2014.

[11] B. Ferris, D. Fox, and N. D. Lawrence. Wifi-slamusing gaussian process latent variable models. InIJCAI, volume 7, pages 2480–2485, 2007.

[12] S. Gezici. A survey on wireless position estimation.Wireless personal communications, 44(3):263–282,2008.

[13] M. C. Gonzalez, C. A. Hidalgo, and A.-L. Barabasi.Understanding individual human mobility patterns.Nature, 453(7196):779–782, 2008.

[14] I. . W. Group et al. Wireless lan medium accesscontrol (mac) and physical layer (phy) specifications.1997.

[15] Y. Gu, A. Lo, and I. Niemegeers. A survey of indoorpositioning systems for wireless personal networks.IEEE Communications surveys & tutorials,11(1):13–32, 2009.

[16] B. Hofmann-Wellenhof, H. Lichtenegger, andJ. Collins. Global positioning system: theory andpractice. Springer Science & Business Media, 2012.

[17] K. Kaemarungsi and P. Krishnamurthy. Modeling ofindoor positioning systems based on locationfingerprinting. In INFOCOM 2004. Twenty-thirdAnnualJoint Conference of the IEEE Computer andCommunications Societies, volume 2, pages1012–1022. IEEE, 2004.

[18] C. Kang, S. Gao, X. Lin, Y. Xiao, Y. Yuan, Y. Liu,and X. Ma. Analyzing and geo-visualizing individualhuman mobility patterns using mobile call records. In

2010 18th International Conference onGeoinformatics, pages 1–7. IEEE, 2010.

[19] N. E. Klepeis, W. C. Nelson, W. R. Ott, J. P.Robinson, A. M. Tsang, P. Switzer, J. V. Behar, S. C.Hern, W. H. Engelmann, et al. The national humanactivity pattern survey (nhaps): a resource forassessing exposure to environmental pollutants.Journal of exposure analysis and environmentalepidemiology, 11(3):231–252, 2001.

[20] Y.-S. Kuo, P. Pannuto, K.-J. Hsiao, and P. Dutta.Luxapose: Indoor positioning with mobile phones andvisible light. In Proceedings of the 20th annualinternational conference on Mobile computing andnetworking, pages 447–458. ACM, 2014.

[21] B. Li, T. Gallagher, A. G. Dempster, and C. Rizos.How feasible is the use of magnetic field alone forindoor positioning? In Indoor Positioning and IndoorNavigation (IPIN), 2012 International Conference on,pages 1–9. IEEE, 2012.

[22] T.-N. Lin and P.-C. Lin. Performance comparison ofindoor positioning techniques based on locationfingerprinting in wireless networks. In 2005international conference on wireless networks,communications and mobile computing, volume 2,pages 1569–1574. IEEE, 2005.

[23] H. Liu, H. Darabi, P. Banerjee, and J. Liu. Survey ofwireless indoor positioning techniques and systems.IEEE Transactions on Systems, Man, andCybernetics, Part C (Applications and Reviews),37(6):1067–1080, 2007.

[24] J. Liu, R. Chen, L. Pei, R. Guinness, andH. Kuusniemi. A hybrid smartphone indoorpositioning solution for mobile lbs. Sensors,12(12):17208–17233, 2012.

[25] D. E. Manolakis. Efficient solution and performanceanalysis of 3-d position estimation by trilateration.IEEE Transactions on Aerospace and ElectronicSystems, 32(4):1239–1248, 1996.

[26] R. Mautz. Overview of current indoor positioningsystems. Geodezija ir kartografija, 35(1):18–22, 2009.

[27] E. Mok and G. Retscher. Location determination usingwifi fingerprinting versus wifi trilateration. Journal ofLocation Based Services, 1(2):145–159, 2007.

[28] A. Motley and J. Keenan. Personal communicationradio coverage in buildings at 900 mhz and 1700 mhz.Electronics Letters, 24(12):763–764, 1988.

[29] E. Nordstrom, C. Diot, R. Gass, and P. Gunningberg.Experiences from measuring human mobility usingbluetooth inquiring devices. In Proceedings of the 1stinternational workshop on System evaluation formobile platforms, pages 15–20. ACM, 2007.

[30] K. Pahlavan, X. Li, and J.-P. Makela. Indoorgeolocation science and technology. IEEECommunications Magazine, 40(2):112–118, 2002.

[31] T. Roos, P. Myllymaki, H. Tirri, P. Misikangas, andJ. Sievanen. A probabilistic approach to wlan userlocation estimation. International Journal of WirelessInformation Networks, 9(3):155–164, 2002.

[32] J. S. Seybold. Introduction to RF propagation. JohnWiley & Sons, 2005.

[33] H. Stange, T. Liebig, D. Hecker, G. Andrienko, andN. Andrienko. Analytical workflow of monitoring

human mobility in big event settings using bluetooth.In Proceedings of the 3rd ACM SIGSPATIALinternational workshop on indoor spatial awareness,pages 51–58. ACM, 2011.

[34] F. Thomas and L. Ros. Revisiting trilateration forrobot localization. IEEE Transactions on Robotics,21(1):93–101, 2005.

[35] W. R. Tobler. A computer movie simulating urbangrowth in the detroit region. Economic geography,46(sup1):234–240, 1970.

[36] J. Torres-Sospedra, J. Avariento, D. Rambla,R. Montoliu, S. Casteleyn, M. Benedito-Bordonau,M. Gould, and J. Huerta. Enhancing integratedindoor/outdoor mobility in a smart campus.International Journal of Geographical InformationScience, 29(11):1955–1968, 2015.

[37] Y. Wang, X. Jia, H. Lee, and G. Li. An indoorswireless positioning system based on wireless localarea network infrastructure. In 6th Int. Symp. onSatellite Navigation Technology Including MobilePositioning & Location Services, number 54, 2003.

[38] N. E. Williams, T. A. Thomas, M. Dunbar, N. Eagle,and A. Dobra. Measures of human mobility usingmobile phone records enhanced with gis data. PloSone, 10(7):e0133630, 2015.

[39] C. Wu, Z. Yang, Y. Xu, Y. Zhao, and Y. Liu. Humanmobility enhances global positioning accuracy formobile phone localization. IEEE Transactions onParallel and Distributed Systems, 26(1):131–141, 2015.

[40] Y. Xu, S.-L. Shaw, Z. Zhao, L. Yin, Z. Fang, andQ. Li. Understanding aggregate human mobilitypatterns using passive mobile phone location data: ahome-based approach. Transportation, 42(4):625–646,2015.

[41] Z. Yang and Y. Liu. Quality of trilateration:Confidence-based iterative localization. IEEETransactions on Parallel and Distributed Systems,21(5):631–640, 2010.

[42] M. A. Youssef, A. Agrawala, and A. U. Shankar. Wlanlocation determination via clustering and probabilitydistributions. In Pervasive Computing andCommunications, 2003.(PerCom 2003). Proceedings ofthe First IEEE International Conference on, pages143–150. IEEE, 2003.

[43] Y. Yue, T. Lan, A. G. Yeh, and Q. Li. Zooming intoindividuals to understand the collective: A review oftrajectory-based travel behaviour studies. TravelBehaviour and Society, 1(2):69–78, 2014.

[44] P. A. Zandbergen. Accuracy of iphone locations: Acomparison of assisted gps, wifi and cellularpositioning. Transactions in GIS, 13(s1):5–25, 2009.

[45] Y. Zheng, Q. Li, Y. Chen, X. Xie, and W.-Y. Ma.Understanding mobility based on gps data. InProceedings of the 10th international conference onUbiquitous computing, pages 312–321. ACM, 2008.