A model-based approach for WLAN localization in indoor parking areas

A Model-Based Approach for WLAN Localizationin Indoor Parking Areas

Paolo Addesso*, Luigi Bruno*, Roberto Garufi**, Maurizio Longo*,Rocco Restaino* and Anton Luca Robustelli**

*DIIIE, University of Salerno, Fisciano (SA), I-84084, Italy. Email:{paddesso,lbruno,longo,restaino}@unisa.it**CoRiTeL Italy, Fisciano (SA), I-84084, Italy. Email: {roberto.garufi, antonluca.robustelli}@coritel.it

Abstract—Wireless location of a User Equipment (UE) hasreceived growing attention in recent years. The first step forthe design of a wireless location system consists in choosingthe system architecture and the localization algorithm thatmatch the requirements of the working scenario. In this paperthe area of interest is represented by an indoor parking lot,in which the variable occupancy of motor vehicles alters theelectromagnetic propagation and causes large errors in vehiclelocation estimation. The proposed strategy to deal with thisproblem is the use of a server-based architecture, that ensuressecurity and scalability and accounts for the system state in termsof number and positions of already present vehicles. This conceptof state is shown to be useful to design suitable algorithms, basedon simplified electromagnetic models, to improve the localizationperformance.

I. INTRODUCTION

Wireless location of a User Equipment (UE) is intimatelyconnected to the development of context-aware applications[1], [2] that benefit of the knowledge of the user position toprocess more specific information. The location based serviceof interested here is the automatic pricing of the vehicles ina parking lot, based on the occupied position. In particularwe face the two main application requirements: the designof the system architecture and the choice of the localizationalgorithm that match the constraints of the working scenario.

The former is conditioned by the actual tendencies forthe forthcoming data transmission infrastructures. The conve-nience of using the same end terminal to obtain seamless ser-vices across heterogeneous networks drives the developmentof fourth generation or beyond third generation (4G/B3G)networks. The main feature of the B3G network infrastructure,in addition to being based on an all-IP architecture, is the totalindependence between the various access technologies (bothmobile and fixed) on one side and session control and theservice provisioning platforms on the other.

For its convenience, cost efficiency, and ease of integrationwith other networks, easily conceivable that WLAN is such ac-cess technology. IEEE802.11 networks’ topological simplicityand technological evolution have fostered the development ofsuch services and applications, as for example e-banking andautomatic payments, requiring greater attention to security.

This work is part of the SINSIMS project, partly funded by Italian MAP(Ministero delle Attivita Produttive).

3GPP (3rd Generation Partnership Project), the main orga-nization investigating B3G (Beyond-3G) research issues andproducing the relative standardization proposals, has defineda scenario for WLAN-3G interworking called “WLAN DirectIP Access”. IEEE802.11i 2004 standard (WPA2) proposes a802.1x/EAP based authentication to grant an adequate level ofsecurity.

This paper shows a possible location system based on aWLAN Access Network (AN) architecture with the addition ofa Location Server (LS). To ensure a suitable level of security,UE access to WLAN is subject to authentication through anHome Network. After the UE performs a WLAN Direct IPAccess to a 3GPP Core Network, the messages exchangebetween UE and LS is ruled by a novel Location InformationProtocol (LIP).

The adoption of a server-based philosophy is advantageousnot only to deal with architectural issues, but also to access theexisting information about the environment state to improvethe localization performance. The main idea is to use astandard technique, properly modified to take into account theenvironment state.

In the challenging scenario of the parking lot, the main dif-ficulties arise from the extreme variability of the propagationchannel due to moving obstacles and reflection surfaces: even asingle vehicle, depending on its position, can obstruct the Line-Of-Sight toward an Access Point, as well as it can introducea new path by reflecting the electromagnetic field.

Accordingly, the purpose of this paper is to model theeffect of the vehicles inside the parking lot and to propose alocalization algorithm that, after an offline construction of thepropagation model of the empty parking area, continuouslycorrects it by the current vehicle localizations. To this aimwe investigate the possibility to employ two commonly usedlocalization algorithm, the RADAR [3] and the Bayesian grid-based filtering [4].

II. SERVER-BASED LOCALIZATION ARCHITECTURE

A. WLAN architecture

All components in a WLAN connected with a wirelessmedium are named stations and can be divided in two cate-gories: access points (APs), and clients. Access points are basestations for the wireless network, that transmit and receive atfixed radio frequencies to communicate with wireless enableddevices. More than being used for the access to other network,978-1-4244-5864-6/10$26.00 c© IEEE

a WLAN AN can provide services by itself, and to do this, it’snecessary to add other nodes, known as Application Servers(AS), to the network. Among others, one task often assignedto AS’s is to improve the overall security to a level appropriatefor the requested service.

One of the main scenarios proposed by 3GPP is just aboutthe provision of services by the AN itself. This involvesAuthentication, Authorization, Accounting (AAA) procedures,for subscribers requiring connection through a WLAN AN,to be based on the same mechanisms employed for AAA in3G networks. In this case, the AN will authenticate a useron the basis of the credentials contained in his USIM/ISIM(UMTS/IMS SIM), as it typically happens within a 3G envi-ronment.

According to IEEE802.11 standard, APs periodically emit amanagement frame, known as beacon frame, which providesinformation about the parameters and capabilities of a cell.This information is known as Basic Service Set (BSS) and isvery important because UEs use it to decide which particularAP to associate with. Implicitly these beacons also carryinformation about the link quality, which can be derivedfrom the signal strength and the background noise. Amongother information, beacon frames report about the networkname and the Basic Service Set IDentifier (BSSID), i.e. theunique identifier of an access point. IEEE802.11 specifies twoscanning mode, but the amount of information that can beretrieved is essentially the same in both. The first mode isa passive scanning: UE performs it regularly to determinethe access point with the best link quality; this is possiblethanks to a sweep from channel to channel and a record ofinformation received from any beacon. In this manner the cellidentifiers and signal strengths of all visible access points canbe determined. In the second mode, known as active scanning,UE actively probes for the available BSS.

B. Localization System

There are two main metrics that can be used to locate an UE:Cell IDentifier (CID) and Radio Signal Strength (RSS). Nearlyall Wireless LAN location systems described in literaturemake use of these quantities for proximity detection or patternrecognition techniques. CID and RSS certainly do not achievethe best location performances. Using CIDs is straightforward,but this approach only provides a limited accuracy on theorder of several tens or hundreds of meters. The use of RSSmeasurements is more promising, though multipath propa-gation in indoor environments can cause the signal strengthto vary considerably. Position estimation happens generallywith information exchange between UE and network nodes,so an indoor location system consists at least in two separatehardware: a transmitter and a receiver.

Four different architectures are possible, with significantdifferences in terms of costs of infrastructure, coverage andtotal number of UEs that can be supported.

1) Remote positioning system: UE transmits signal andfixed units receive it. The use of transmissions from a mobileterminal to the network for the estimation of position is known

as network-based. The measures from all these units are thencollected by a master station, which calculates the positionof transmitter. This information can be used by the same basestation or sent to another server, equipped with enough compu-tational resources to perform complex localization algorithmswhich mobile units could not afford. In this architecture, allthe processing takes place in one station, thus limiting thenumber of UEs that can be continuously located.

2) Self-positioning system: The UE is the measuring unitthat receives the signal from several transmitters with knownlocations. This architecture is also called mobile-based andthe mobile terminal is expected to calculate its own position,relying on measured signals and the knowledge of transmitters’positions. Since the mobile-based architecture is a passive self-positioning system, in theory there is no limit to the numberof mobile stations that can be localized using this approach,because they are not required to broadcast mobile positioningand everything takes place in the terminal. This architecturecould have problems when the number of data provided tomobile terminal is very high, since the computational capacityof terminals are much lower than those of base station.

3) Remote indirect positioning system: This topology isfeasible only if a wireless data connection is available betweenthe UE and the remote side. In fact the measures are collectedby the mobile equipment and sent to the network that providesthe position estimate. In this architecture the UE plays analmost passive role and thus, as for the remote positioningsystems, the number of users that can be localized is limitedonly by the computational capability at the remote side.

4) Indirect self-positioning system: Also in this case awireless connection is required for sending the measurementsthat are collected at the remote side. Measures are used by themobile to infer its own position, so in this latter alternative thelimits are again due to terminals computation ability.

C. Architecture choice

We require a system with a high positioning accuracy, agood level of security in dealing position information basedon the use of the beacon frame that gives continuous measuresof the received signal intensity. In order to improve theperformances by using global knowledge, we must excludeself-positioning systems. Finally since in IEEE802.11 networkbeacon frames are transmitted from APs to UE, we choose theremote indirect positioning system as indicated in Fig. 1.

Fig. 2 depicts the procedures taking place before startinglocation:

1) IEEE 802.11 association process takes place when UEenters in AP radio coverage. UE starts sending As-sociation Request to the AP. After the AP receivesthe Association Request successfully, it will reply withAssociation Reply. When UE receives the AssociationReply message, it changes its status from a new stationto a registered station.

2) The second step is WLAN Direct IP Access procedure.In this case, the AN will authenticate a user on thebasis of the credentials contained in his USIM/ISIM

Fig. 1: WLAN AN Location architecture.

Fig. 2: Association and authentication procedures.

(UMTS/IMS SIM). Furthermore, authorization and ac-counting are provided by the 3G network itself, based onsubscription data. Interworking architecture for the non-roaming case can be straightforwardly derived if the 3GAAA Server is directly connected to the WLAN. 3GPPproposes that the WLAN UE and the AAA server shallsupport both the EAP AKA and EAP SIM methods.

The solution we propose is founded on a localization pro-tocol, named LIP, for the exchange of signaling data betweenUE and LS. LIP is an application layer protocol based on UDP,employing 3 types of messages:• LIP Init Message;• LIP Info Message;• LIP Update Message.The detailed description of these messages and their func-

tion will be illustrated in the next paragraph.

D. Location message exchange

Let us see how the location process takes place in our design(Fig. 3). After a successfully completed WLAN Direct IP Ac-cess procedure between UE and AAA server, the Authenticatorsends a LIP Init message to LS, containing the new user ID.LS first checks if UE is registered to parking service, then itretrieves information about the associated vehicle, such as its

Fig. 3: Localization phase.

shape and size. Finally, in order to start the vehicle tracking,LS sends to UE a LIP Info message containing an APs listthat indicates the Mac Addresses of the involved APs and thenumber of measures Nm to collect for each AP. If this numberis set to zero, no measure is collected and the tracking phaseis skipped, otherwise UE starts collecting RSS samples. Thenit sends Nm measures for each AP to LS through LIP Updatemessages and the latter elaborates received data in order toestimate UE location.

When the vehicle stops, on the basis of the chosen al-gorithm, LS can perform another algorithm (or the samealgorithm with another setup) in order to identify with a greaterdegree of precision the parking stall in which the vehicle islocated. This new phase is started by UE that informs LS thatthe vehicle engine is turned off 1 via a LIP Info message. ThenLS sends another LIP Info message to the UE, containing theAPs list and, above all, the new Nm value. Finally, when LSsupposes to have reached the desired precision in estimatingthe vehicle position, it sends a LIP Info message to UE inorder to stop the RSS measures dispatching.

III. KNOWLEDGE-BASED LOCALIZATION ALGORITHM

The second part of the problem faced in this study concernsthe design of the localization method. Our purpose is to exploitthe network-based approach in localizing a mobile user in aparking area. The latter turns out to be a very challengingenvironment, being characterized by the presence of manyobstructing and reflecting obstacles for the electromagneticpropagation. Moreover the mobility of some obstacles, likevehicles, further worsens the situation.

Accordingly, the proposed localization method consists of apreliminary offline characterization of the signals available inthe empty parking and an online phase in which the expectedsignals are updated by using proper electromagnetic modelsfor the diffraction or reflection effects.

1It is supposed that there exists a strict integration between the vehicle andthe UE.

In the following we illustrate the used electromagneticmodel, together with the details of the positioning algorithms.They have been selected among the plethora of existing meth-ods, according to their suitability for the proposed approach. Inparticular two different algorithms, basing on two completelydifferent methodology, have been chosen for comparison. Theformer was presented in [3] and represents the most citedfingerprinting method in which a memoryless estimation al-gorithm, detailed in paragraph III-B1, is employed. The latter,on the contrary, belongs to the class of Bayesian estimationalgorithms and thus takes into account the whole trajectory ofthe mobile user. Both have been properly modified to showadaptive features aimed to compensate the nonstationarity ofthe working scenario; the performances achieved are reportedin paragraph IV.

A. Electromagnetic modelIn this study the availability of a precise electromagnetic

model plays a fundamental role. As anticipated, the character-ization of the mobile propagation channel is a very hard taskthat is faced in several references (see for example [5]).

A very common approach consists in modeling the powerof the received signals as a random process whose distributiondepends on the peculiar characteristics of the working envi-ronment. In the cited reference [5] the suitability of severalstatistical models (Rayleigh, Rice, Nakagami, Lognormal)have been justified. Some of them turn out to be very fruitful inthe practice because of their analytical tractability; for examplethe lognormal model corresponds, by measuring the receivedpowers in logarithmic scale, to data described by a Gaussiandistribution. A widely employed statistical model for signalamplitudes in indoor environments is the Rician distribution[6]

p (r) =r

σ2exp

(−(r2 + V 2

)2σ2

)I0

(rV

σ2

), r ≥ 0,

in which V is the amplitude of the Line-of-Sight component,σ2 the variance of the scattered contribution and I0 (·) isthe modified Bessel function of zeroth order. An alternativeexpression is in terms of the mean square value E

[r2]=

V 2+2σ2 and of the Rice factor Kf4= V 2/2σ2 that quantifies

the ratio among the power of the two components:

p (r) =2 (1 +Kf ) r

E [r2]exp

(−Kf −

(Kf + 1) r2

E [r2]

)× I0

(2r

√Kf (Kf + 1)

E [r2]

), r ≥ 0.

Anyway, a commonly used model for the path-loss, i.e. for theattenuation of the mean radiated power at a distance d fromthe transmitter, is given by the log-distance law

P (d) = P0 − 10α log

(d

d0

), (1)

where the power P (d) (in dB), available at a distance d fromthe AP, is function of the power P0 at a reference point d0and of the decaying rate α.

Fig. 4: Spatial quantities relevant to knife-edge diffractionevaluation.

This model, whose formal derivation follows from the freepath propagation analysis, is successfully employed also forthe indoor propagation, after a proper setting of the parameters.The latter have to be experimentally determined, since theygreatly differ with the working scenario.

In this paper we propose to exploit this approach based onpropagation model (1) by including other different effects, asfor example those due to the interposition, possibly partial,of diffracting objects. In the same direction, the presence ofa new reflecting surface can give a significant contribution tothe received powers in the adjacent positions, but in a firstapproximation we neglect such effect.

Quantifying the contribution due to diffracting objects isin general a very difficult task, since the effect is extremelyvarying with the shape and the position of the obstacles. In thiswork we use a simplified setup that has turned to be very usefulin communication theory, namely the knife-edge diffractionmodel [7]. It consists in treating the obstacle as a diffractingknife edge so allowing a easy solution evaluation of the Fresnelintegral. In that case the diffraction gain G (ν) is function onlyof the Fresnel Diffraction Parameter ν. The latter is defined,in terms of the quantities illustrated in Fig. 4, as

ν = h

√2 (d1 + d2)

λd1d2,

where λ is the signal wavelength and d1, d2 are, respectively,the distances between transmitter and obstacle and betweenreceiver and obstacle and h is the effective height. The rela-tion between the knife-edge diffraction gain and the FresnelDiffraction Parameter ν can be achieved by numerical meth-ods; however a widely employed approximation, expressed indB and valid for ν > −0.7 is the following [8]

G (ν) = 6.9+20 log

(√(ν − 0.1)

2+ 1 + ν − 0.1

)dB. (2)

An important consideration concerns the presence of multi-ple obstacles between transmitter and receiver. In this casethe exact solution in very hardly affordable, but a usefulapproximation, whose accuracy decreases with the number ofinterposed obstacles, can be achieved with the Bullington’sconstruction of equivalent knife edge [7]. For example, whenall the vehicles share the same height, this method consists inconsidering, for each position, only the closest one.

B. Localization algorithmsTwo position algorithms have been chosen for the project

and are described next. The former is one of the first proposedin literature and, despite of its simplicity, is often used asa benchmark for the other methods. In fact many effectivepractical realizations of positioning devices are today basedon the RADAR method, that benefits of its wide applicability,mainly due to the intrinsic nonparametric approach. Thispermits to avoid the acquisition of information about thestatistical distributions of data. On the contrary the otherselected method relies upon a purely probabilistic approachand thus presumes that the functional form of the data modelis perfectly specified. In the latter case superior performancescan be achieved, as illustrated in the simulations.

1) Radar: The RADAR systems has been proposed in [3]as an alternative to triangulation methods, that, despite beingsuccessfully applied to the estimation of the position of amobile user in outdoor scenarios, do not achieve satisfyingperformances indoor. This, is due, as described earlier, to thepresence of obstacles and reflection surfaces that does notallow to relate in a straightforward manner, the received powerto the distance from the transmitter.

To overcome this difficulty RADAR uses a fingerprinting(or scene analysis) approach that consists in composing adatabase, hereafter Radio Map, containing the means of thesignal powers relative to a finite number of reference positions.The localization algorithm compares the powers received inthe unknown position with those contained in the Radio Mapand chooses the closest one.

In order to fully exploit the functioning of RADAR, severaldetails have to be given. In particular the construction of theRadio Map can be performed by using the empirical method,i.e. by recording the signals in each reference point in a phase,that precedes the working moment. This approach turns out tobe very time consuming as soon the number of such pointsgrows. The alternative consists in using the radio propagationmodel described in par. III-A; however this second methodalways achieve unsatisfying performances, as fully illustratedin the cited reference.

As described until now, the RADAR approach consists in apattern recognition methods to classify the unknown position.In particular the classification is achieved by simply findingthe closest point (or nearest neighbor) in the signal space,according to the Euclidean distance. An improvement, aimedto limit the necessary discretization of the possible positions,consists in using multiple nearest neighbors; given the numberk of neighbors (whose optimal value turns out to be comprisedin the interval [2, 4]), the position is achieved by averaging thek positions.

The main difficulty of the method consists in the impossi-bility to take into account the nonstationarity of the workingscenario; at each variation the Radio Map has to be com-pletely renewed and, especially in the fully working empiricalapproach, this procedure is very expensive. In a subsequentpaper [9] the authors proposed the use of several RadioMap, corresponding to different situations for the working

environment. In the localization phase the algorithm choosesthe Radio Map that best represents the environment at themoment and thus estimates the position of the mobile user. Inthe parking application this approach is very hardly applicable,being the contributions of each vehicle very significant. Thismeans that many different Radio Map should be constructed,corresponding to the different permutations of the vehicleslayout. Therefore we propose to modify the Radio Map bymeans of the electromagnetic model described in paragraphIII-A, thus leading to the following algorithm

a) the usual training phase is performed when theparking lot is empty, in order to build a Radio Map;

b) when the first vehicle stops into a parking stall, it islocalized in the standard way, by collecting Nd RSSsamples;

c) on the basis of the estimated vehicle position andby means of the diffraction model of the vehicle,the variations in the electromagnetic environmentare predicted and the Radio Map is consequentlycorrected;

d) when another vehicle stops into another parking stall,it is localized by using the modified Radio Map;

e) The steps c) and d) are performed for each vehiclethat occupies (new correction) or leaves (remove thecorrection) a parking stall.

2) Grid-based: The other approach exploited in this studyis a particular instance of the Bayesian filtering method [4]. Itis a state-space approach in which the kinematic quantities (forexample, position and velocity) compose the state {xt}t=0,1,...

that evolves according to the equation

xt = ft (xt−1,vt) , (3)

where ft is a (possibly nonstationary and nonlinear) functionof the previous state xt−1 and of the process noise sequencevt. The estimation of the position is performed by using theobservations {yt}t=0,1,... (in this case the powers of signalsreceived at the mobile device from the available APs) thatdepend, through a possibly nonstationary nonlinear functiongt, on the state and on the measurement noise nt

yt = gt (xt,nt) . (4)

A typical assumption is the Markov property of thestate and measurement process, that permits to achievea simplified expression for the transition conditionalprobability p (xt|xt−1 . . . , ,x0) and for the likelihoodp (yt|xt,yt−1, . . . ,y0).

In particular we consider a model given by the equations

xt = At (xt)xt−1 + vt,yt = ht (xt) + nt,

(5)

where At is the motion matrix (possibly depending on theposition to consider the presence of motion obstacles), ht isthe nonlinear function taking into account the WAF model re-lationship, vt and nt are zero mean processes with covariancematrix Qt and Rt, respectively..

Fig. 5: Parking area: Positions of APs and training points.

When the state space is finite, the sequence {xt}t=0,1,...

is a Markov Chain and the formalization is called HiddenMarkov Model (HMM) since only the data {yt}t=0,1,... areaccessible [10]. Then, if complete information regarding theinvolved statistical distributions are available, the path of themobile user can be estimated by direct maximization of thepdf

p (xt, . . . ,x0|yt, . . . ,y0) ,

and a very efficient approach, the Viterbi algorithm [11] canbe exploited to limit the computational burden.

For the Viterbi algorithm the proposed localization systemconsists in the following steps:

a) the statistical model corresponding to an empty park-ing lot is calculated by employing the log distance(1) path loss;

b) the first vehicle is localized by maximizing thelikelihood relative to both the tracking phase (fromthe gate to the stall) and Nd RSS samples acquiredafter the vehicle stops;

c) on the basis of the estimated position and by meansof the diffraction model of the vehicle, the variationsin the electromagnetic environment are predicted andthe statistical model is consequently corrected;

d) when another vehicle enters the parking lot, it islocalized as in b) but using the model computed inc);

e) The steps c) and d) are performed for each vehiclethat enters (new correction) or leaves (remove thecorrection) the parking lot.

IV. EXPERIMENTAL RESULTS

Firstly we validate the described electromagnetic model bystatistical analysis of signal samples collected in an under-ground car park of the University of Salerno, sized about45× 40 m and in which a 802.11 (WiFi) network with 5 APs3COM 7760 operates (see Fig. 5). Next we report the results of

Fig. 6: Path Loss measurement layout.

Fig. 7: Path Loss boxplot.

the Monte Carlo simulations for comparing the performancesof the two chosen algorithms without and with the diffractioncorrection.

A. Electromagnetic model

The adequateness of the log-distance path loss model hasbeen confirmed by the validation campaign carried out in thecited parking lot. In particular, the box-plot correspondingto the 6 positions with no obstacles between transmitter andreceiver, as depicted in Fig. 6, is shown in Fig. 7. It indicatesthat the central tendency indicator of measured data followsthe regression line achieved by Least-squares method. Thevalue of parameters of the regression line corresponding toa confidence interval of 0.95 are the following

E[P0|db] = −28.6± 0.2

α = 1.98± 0.02

In Fig. 8(b) we report the time series of the power of thesignal transmitted by AP 1 and received by vehicle VS withthe successive interposition of the two vehicles V1 and V2,positioned according to the layout shown in Fig. 8(a). Re-garding the first vehicle V1, the heights of AP hAP = 2.55m,

(a)

(b)

Fig. 8: Experimental validation of diffraction loss model: (a)position of tested vehicles; (b) time series of the receivedpower from vehicle VS after successive interposition of vehicleV1 (green) and V2 (red).

that of vehicle hv = 1.45m and the distances D1 = 22.5mand D2 = 14.5m (see Fig. 4) yield, by simple geometricalcalculations and by using the formula (2), an expected loss of1.4 dB, very close to the actual value 1.2dB. For vehicle V2the analogous values amount to hAP = 2.55m, hv = 1.45m,D1 = 28m and D2 = 9m; the consequent expected loss is2.7dB, while the measured value is 2.6dB.

The data used in the simulations have been generatedaccording to a Rice distribution. In fact a comparison of thecumulative distribution function (cdf) of the collected dataindicates that the Rician distribution achieve the best fit onthe empirical distribution (see Fig. 9).

Fig. 9: Goodness-of-Fit of three main distributions with realdata.

Fig. 10: Attenuation G (ν) due to vehicles obstruction, calcu-lated by approximating formula (2).

B. Localization algorithms

The analysis of the performances of the localization algo-rithms has been carried out by generating datasets of signalsthat simulate the real working scenario of the park underinvestigation. The arrivals and the departures have been mod-eled by a random birth and death process. The measurementsare the power levels of the signals transmitted by the APs,that are typically acquired with sampling frequency of about2 measurements per second. With reference to the power ofsignal transmitted by a single AP, the attenuation (2) due to thepresence of vehicles is graphically exemplified in Fig. 10. Wewill not explicitly take into account the typical quantizationintroduced by the acquisition devices. In order to avoid side-effects in the vehicle contribution characterization, no wallhave been considered in the working area. Therefore receivedsignals have been generated according to a Rice distributionthat adequately models Line-Of-Sight (LOS) propagation.

To single out the effect of the diffraction factor correction,both algorithms have been first tested on a simplified setup

(a)

(b)

Fig. 11: RADAR localization algorithm without and withdiffraction factor correction: RMS error VS. number of sam-ples in the test set Ne: (a) exact position of parked vehicles;(b) estimated position of parked vehicles. Number of samplesin the training set Nt = 200, Rice factor K = 2, number ofAPs NAP = 3.

wherein exact knowledge of the state (number and positionof already parked vehicles) is assumed, thus avoiding theinfluence of the occupancy estimation phase. Thereafter thetests have been extended to the complete setup, i.e. includingthe effects of the park state estimation.

As to the RADAR algorithm, we tested its most widelyemployed version, in which the Radio Map is constructed byin-situ measurements of the signal received in the referencepoints. The spatial distribution of the latter is graphicallyillustrated by Fig. 5. The training phase is simulated byemploying 200 samples for each point. Since each possibleparking position coincides with a training point, the algorithmdoes not perform any averaging of neighbors (i.e. k = 1),which would worsen, in this case, the performances. Theresults relative to Rice factors Kf = 2, 10 and 3 APS areshown in Fig. 11 as a function of Nd, the number of samplesused in the localization phase. The arrival of vehicles issimulated by means of a Bernoulli birth and death processwhose probabilities, respectively, decays and grows linearly

with the parking lot occupancy. In particular the expectedoccupancy of the parking lot is 1/2. In the top plot we show theperformances when the system knows the actual distributionof the parked vehicles. The necessity of the diffraction losscorrection is highlighted by the accuracy degradation, fromabout 1 meter to 9 meters. The effective capability of theproposed method is clarified in Fig. 11(b), where the real-istic decision-directed framework is examined. The algorithm,besides preserving the stability (one of the main problemsof such working mode), achieves a very significant precisionenhancement. This behavior is always more evident with thegrowth of Rice factor Kf ; in fact a greater value of thelatter means a more significant presence of the Line-Of-Sightpropagation path, that is mainly affected by diffraction loss.

The correlation between the modification of the receivedpower due to interposition of obstacles is illustrated in greaterdetail in Fig. 12 that reports a toy example correspondingto the presence of a row of vehicles. In Fig. 12(a) themaximum variation of the collected power due to diffractionloss is depicted. In Fig. 12(b) the RMSE for each referencepoint shows how the positions closer to the row of carsare mainly liable to performance degradation. Finally Fig.12(c) illustrates how, after correction, the RMSE error moreuniformly distributes in the whole parking area.

Analogous considerations can be made concerning theViterbi localization algorithm. It commonly achieves perfor-mances significantly better than the RADAR algorithm, sinceit exploits a larger amount of information. In fact to makethe results comparable, Nd refers again to the number ofsamples acquired in the parking stall; however, dependingon the trajectory followed by the vehicle, several previousmeasurements are collected, from the parking access until thefinal position. Fig. 13(a) shows upper bounds on the accuracyachievable, while Fig. 13(b) shows the results concerningthe more real scenario of estimated vehicles positions. TheViterbi algorithm benefits of a reduced improvement respectto RADAR. Indeed the diffraction loss correction only impactsthe mean value of the collected power, that is the only quantityused by the latter method.

Interestingly, this method is able to face this kind ofnonstationarity, better than other existing Bayesian sequentialmethods, developed for indoor localization in time-varyingenvironments. In fact previous methods are able to estimatesome of the propagation parameters and follow their variationwith time when modifications affect the whole investigatedarea [12], but fail when, as illustrated in Fig. 12(a) for ourcase, the power variations are also spatially inhomogeneous.

V. CONCLUSION

We studied the possibility to implement a network-basedsolution to the problem of automatic localization of vehicles ina parking lot equipped by a WLAN transmission infrastructure.We propose a novel protocol, named LIP, to manage thecommunication of the mobile with the location server thatestimates the position of the arriving vehicles. Furthermore wedeal with the main problem that degrades the performances of

(a)

(b)

(c)

Fig. 12: Effect of obstacle interposition on the RMSE: (a)maximum diffraction loss; (b) RMSE without correction; (c)RMSE with correction. Number of samples in the training setNt = 200, Rice factor K = 2, number of APs NAP = 4.

(a)

(b)

Fig. 13: Viterbi localization algorithm without and withdiffraction factor correction: RMS error VS. number of sam-ples in the test set Ne: (a) exact position of parked vehicles;(b) estimated position of parked vehicles. Rice factor K = 2,number of APs NAP = 3.

each positioning algorithm in such scenarios, namely the non-stationarity of the electromagnetic environment. We approachthis problem by introducing a diffraction loss model to correctthe expected received signal strenghts, according to the currentparking occupancy. Both the ideal capability of such pathloss correction and the practical consequences of replacingthe true occupancy with an estimate thereof are considered.Future studies concern the enhancement of correction lossevaluation by more accurate modeling of the training field andan experimental validation of the proposed architecture.

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