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Statistical Characterization and Mitigation of NLOSBias in UWB Localization Systems

Francesco Montorsi, Fabrizio Pancaldi, and Giorgio Matteo Vitetta

Abstract—In this paper the problem of the joint statis-tical characterization of the NLOS bias and of the mostrepresentative features of LOS/NLOS UWB waveformsis investigated. In addition, the performance of variousmaximum-likelihood (ML) estimators for joint localizationand NLOS bias mitigation is assessed. Our numericalresults evidence that: a) the accuracy of all the consideredestimators is appreciably affected by the LOS/NLOSconditions of the propagation environment; b) a statisticalknowledge of multiple signal features can be exploited tomitigate the NLOS bias, so reducing the overall localizationerror.

Index Terms—Ultra Wide Band (UWB), Radiolocaliza-tion, Bias mitigation.

I. INTRODUCTION

Wireless localization in harsh communicationenvironments (e.g., in a building where wirelessnodes are separated by concrete walls and otherobstacles) can be appreciably affected by direct pathattenuation and NLOS conditions. In principle, theeffects of NLOS errors can be mitigated adoptingtechniques for detecting LOS/NLOS conditions oralgorithms for estimating the errors themselves (i.e.,the bias due to obstacles). These approaches canpotentially improve the overall accuracy and are ex-pected to satisfy certain requirements; in particular,they should be robust against changes in the prop-agation environment, stable (i.e., they should neveramplify NLOS errors) and should be able to exploitall the available data (e.g., received waveforms anda priori information).

Various solutions for NLOS error mitigation inUWB environments are available in the technicalliterature [1], [2], [3], [4]. In particular, a simpledeterministic model, dubbed wall extra delay, is

F. Montorsi and G. M. Vitetta are with Department of Informa-tion Engineering, University of Modena e Reggio Emilia (e-mail:francesco.montorsi@unimore.it and giorgio.vitetta@unimore.it). F.Pancaldi is with Department of Science and Methods for Engi-neering, University of Modena and Reggio Emilia (email: fab-rizio.pancaldi@unimore.it).

proposed in [1] to estimate the bias introducedby walls. A non-parametric support vector ma-chine is employed in [2] for joint bias mitigationand channel status detection; this approach exploitsmultiple features extracted from received signalsin a non-statistical fashion. A few classificationalgorithms for LOS/NLOS detection are comparedin [3], where it is shown that the best solutionis offered by a statistical strategy based on thejoint probability density function (pdf) of the delayspread and the kurtosis extracted from the receivedsignals. Finally, in [4] statistical models for thetime of arrival (TOA), the received signal strength(RSS) and the root mean square delay spread (RDS)are developed and an iterative estimator for biasmitigation is devised.

The contribution of this paper is twofold. In fact,first of all, the problem of joint statistical modelingof multiple features extracted from a database ofwaveforms acquired in a TOA-based localizationsystem is investigated. Note that, as far as we know,in the technical literature only univariate models forbias mitigation have been proposed until now (e.g.,see [1], [4] and [5]). The use of multiple signalfeatures in UWB localization systems has beeninvestigated in [3] for channel state detection onlyand in [6], where, however, the considered features(namely, the kurtosis, the mean excess delay and thedelay spread) have been modelled as independentrandom variables. The second contribution offeredby this manuscript is represented by a performancecomparison of various maximum-likelihood (ML)estimators for TOA-based localization. In particular,unlike other papers (e.g., see [2], [3]) we illustratesome numerical results referring to the accuracyof different localization strategies, rather than tocapability of the bias removal on a single radio link.

The remaining part of this paper is organized asfollows. In Section II some information about ourUWB experimental campaign and about the featuresextracted from the acquired data are provided. In

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Section III some estimation algorithms for UWBradiolocalization are described, whereas their per-formance is compared in Section IV. Finally, someconclusions are given in Section V.

II. EXPERIMENTAL SETUP

A. Measurement arrangement

A measurement campaign was conducted by ourresearch group in the second half of 2010 in orderto assess the impact of NLOS bias errors on areal world UWB system for localization; all themeasured data were acquired by means of twoFCC-compliant PulsON220 radios commercialisedby TimeDomain and were collected in a database.Such devices are equipped with omnidirectionalantennas, are characterized by a -10 dB bandwidthand a central frequency equal to 3.2 GHz and4.7 GHz, respectively, and perform two-way TOAranging; they also allow to store digitised receivedwaveforms (a sampling frequency of 24.2 GHz and14 bits per sample are used).

It is worth mentioning that various databasesproviding a collection of sampled UWB waveformsacquired in experimental campaigns and useful forassessing the performance of localization algorithmsare already available (e.g., see [7], [8]). However,our database has been specifically generated toassess the correlation between the NLOS bias errorand various features extracted from the receivedsignals, as it will become clearer in the next Para-graph. Our measurement campaign consisted of twophases. First, the transmitter was placed in a givenroom (room A in Fig. 1) and the receiver in anadjacent room (room B in Fig. 1) separated fromroom A by a wall having thickness twall = 32 cm(NLOS condition); in addition, the transmit antennawas kept fixed, whereas the receive antenna wasplaced in NNLOS

acq = 174 distinct vertices of a densesquare grid (the distance between a couple of nearestvertices was equal to 21 cm). In the second phaseof our measurement campaign both the transmitterand the receiver were placed in room B; then, thetransmit antenna was kept fixed, whereas the receiveantenna was moved on the same dense grid as inthe first phase to acquire the UWB waveform inN LOSacq = 105 distinct vertices. The positions of the

transmit antenna in the two phases were (0.26, 2.97)m and (0.26, 3.97) m, respectively, if the coordi-nate system shown in Fig. 1 is employed. The

Ceiling height = 348 cm

330 cm

Room A

500 c

m

400 c

m

330 cm

Room B

32 cm

X

85 c

m

Y

Figure 1. Map of the enviroment of our experimental campaign.

distance between the two antennas varied between1 m and about 5 m; larger distances were nottaken into consideration since we were interested inindoor ranging only. It is important that to note thatthe choice of the measurement scenarios describedabove is motivated by the fact that UWB signalsexperienced similar propagation in both phases.

For each position of the receive antenna up to25 realizations of the received UWB signal wereacquired (each one lasting Tacq = 110 ns), in orderto filter out the effects of the measurement noiseand the TOA estimate outliers in the postprocessingphase. The analysis of the multiple waveforms re-ferring to each link evidenced the presence of fewtime-variant artifacts (mostly due to the movementsof the people behind the radios); as a matter offact, the channel in our measurement campaigncan be deemed quasi-static and is characterized byreflections mainly due to the walls, the ceiling andthe floor of the room (or rooms) hosting the radiodevices.

Finally, for each acquired waveform, a TOAestimate (evaluated by the PulsON220 devices) andthe actual transmitter-receiver distance (evaluated bymeans of a metric tape with an accuracy better than1 cm) were also stored in the database. The TOAestimates have been used to provide a common timeframe to all the acquired waveforms; this has madepossible the estimation of the mean excess delayand of other signal statistics in the signal processingphase.

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B. Statistical modeling of signal features

In each of the two measurement phases de-scribed in the previous Paragraph, the procedurefor acquiring UWB waveforms worked as follows.First, the UWB radios carried out their handshakingprocedure for achieving mutual time synchroniza-tion; then, the receiver sampled the incoming wave-forms and generated a TOA estimate for each ofthem; let rLOS

i (t) (rNLOSi (t)) and τ LOS

i , TOA(rLOSi (t))

(τ NLOSi , TOA(rNLOS

i (t))) denote the received wave-form and the corresponding TOA estimate (here thefunction TOA(·) represents the internal procedureadopted by the PulsON220 devices, based on energythresholds and a go-back technique, to estimate theTOA; see [9] for further details) acquired over thei-th link in LOS (NLOS) conditions. The model1

τi =dic0

+ bi + wi (1)

was adopted for the measured TOA (for both LOSand NLOS conditions). Here, c0 is the speed oflight, di denotes the distance between the transmitterand the receiver, bi is the NLOS bias (in seconds)affecting the TOA measurement (the values takenon by this random parameter are always positivefor NLOS links and null for LOS links2) andwi ∼ N (0, σ2

w,i) is the measurement noise; inaddition, the expression σ2

w,i = γσ2nd

βi is adopted

for the variance of the measurement noise, where γis a parameter depending on both the specific TOAestimator employed in the ranging measurementsand on various parameters of the physical layer,and β is the path-loss exponent (a known and fixedvalue is assumed for this parameter in both LOSand NLOS conditions [4]).

In the following we focus on the problem ofestimating the bias bi (affecting the TOA estimateτi (1)) from a set of Nf = 6 different “features”{xi,j , j = 0, 1, ..., 5} extracted from the receivedwaveform ri(t). In particular, like in [2], the fol-lowing features were evaluated for the set of thereceived waveforms:

1) the maximum signal amplitude xi,0 = rmax,i ,maxt |ri(t)|;

1The superscripts LOS and NLOS are not explicitly indicated in thefollowing expressions, when not strictly needed, to ease the reading.

2In this case the probability density function (pdf) of bi is fb(b) =δ(b).

2) the mean excess delay xi,1 = τm,i ,∫∞0t |ri(t)|

2

εidt (the parameter εi is defined be-

low);3) the delay spread xi,2 = τds,i ,

∫∞0

(t −τm,i)

2 |ri(t)|2εi

dt;4) the energy xi,3 = εi ,

∫∞0|ri(t)|2dt;

5) the rise time xi,4 = trise,i ,min {t : |ri(t)|/maxt |ri(t)| > 0.9} − min{t : |ri(t)|/maxt |ri(t)| > 0.1};

6) the kurtosis xi,5 = κi ,1

σ4|r|T

∫T

(|ri(t)| − µ|r|

)4dt, where µ|r| , 1

T∫T|ri(t)|dt, σ2

|r| ,1T

∫T

(|ri(t)| − µ|r|)2dt andT denotes the observation time.

In the following the set {ri(t)} of received wave-forms is modelled as a random process, so that theabove mentioned features form a set of correlatedrandom variables; in addition, all of them are sta-tistically correlated with the TOA bias. The lastconsideration is confirmed by the numerical resultsof Table I, which lists the absolute values of thecorrelation coefficients of the previously describedfeatures with the estimated TOA bias for both theLOS and the NLOS scenarios. From these results itcan be easily inferred that not all the consideredfeatures are equally useful to estimate the TOAbias. For this reason and to simplify our statisti-cal analysis, we restricted the group of consideredfeatures to the set {xi,0, xi,1, xi,2}, which collectsthe parameters exhibiting a strong correlation withthe bias in the NLOS scenario.

Note that, in principle, the bias bi is not influ-enced by the distance di, since it depends only onthe thickness of the walls (or of other obstacles)encountered by the transmitted signal during itspropagation; this is not true, however, for the abovementioned triple of signal features (see [1] forfurther details). Generally speaking, it is useful toderive a TOA bias estimator which is not influencedby the transmitter-receiver distance di. In the at-tempt of removing the dependence of the features{xi,0, xi,1, xi,2} on the link distance, we developedthe models

xi,0 = rmax,i = r0max − rmmaxdi, (2)

xi,1 = τm,i = τmm di (3)

andxi,2 = τds,i = τ 0ds + τmdsdi (4)

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Correlationwith bi

xi,0 xi,1 xi,2 xi,3 xi,4 xi,5 di

NLOS case 0.795 0.852 0.894 0.641 0.454 0.644 0.609LOS case 0.602 0.586 0.129 0.666 0.586 0.119 0.629

Table IABSOLUTE VALUES OF CORRELATION COEFFICIENTS BETWEEN bi AND xi,j , WITH j = 0, ...., Nf − 1.

on the basis of our experimental results (and, inparticular, on the basis of the estimates of thejoint pdf’s {fb,x0 , fb,x1 , fb,x2} referring to the threepossible couples (bi, xi,j) with j = 0, 1, 2); herer0max, τmm and τmds are random variables3, whereas τ 0dsand rmmax are deterministic parameters having knownvalues. Given these models, the vector of distance-independent features x , [r0max, τ

mm , τ

mds ]

T can beevaluated from its distance-dependent counterpartx = [rmax, τm, τds]

T and can be used in place of it.A complete statistical characterization of the es-

timated bias and of the 3 related signal features weconsider is provided by the joint pdf fb,rmax,τm,τds(·)or, equivalently, by the joint pdf fb,r0max,τ

mm ,τmds

(·);these functions have been estimated from the ac-quired data, but cannot be plotted because of thelarge dimensionality of their domains; for this rea-son, we analysed some pdf’s deriving from theirmarginalization. For instance, Fig. 2 shows theestimated joint pdf’s for the estimated bias bi andmeasured delay spread for the NLOS and the LOSscenarios; these results deserve the following com-ments:

1) a significant (limited) correlation betweenthese parameters is found in the NLOS (LOS)case;

2) the null region exhibited by the estimatedpdf’s is due to the fact that the TOA bias can-not take on values in the interval [0, twall/c0],where twall is the thickness of the wall ob-structing the direct path;

3) large values of the TOA bias are unlikelysince they are associated with small incidenceangles of the transmitted signal on the ob-structing wall.

Finally, it is important to point out that our exper-imental data were also processed to evaluate thecorrelation coefficient between the estimated biasbi and each of the distance-independent parameters

3In the rest of the document, the subscript i has been omitted forsimplicity when not strictly necessary.

Figure 2. Estimated joint pdf of the estimated TOA bias andthe delay spread in NLOS conditions (above) and LOS conditions(below). Note that the NLOS PDF has been scaled by a factor 3 toimprove its visualization.

6 7 8 9 10 11 12 13

0

0.5

1

1.5

2

2.5

3

rmax

0 [ADC counts * 1000]

NL

OS

B

ias

b [

ns]

NLOS PDF

LOS PDF

Figure 3. Estimated joint pdf of the estimated TOA bias andthe r0max random variable in NLOS conditions (above) and LOSconditions (below). Note that the NLOS PDF has been scaled by afactor 2 to improve its visualization.

r0max, τmm and τmds (see Table II and Fig. 3, whichrepresents the joint pdf of the estimated bias bi andthe parameter r0max); our results evidence that thelast parameters are less correlated with bi than theirdistance dependent counterparts. For this reason, wedecided to take into consideration also the distance-dependent features {xi,0, xi,1, xi,2} for localizationpurposes.

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Correlationwith bi

xi,0r0max,i

xi,1τmm,i

xi,2τmds,i

NLOS case 0.321 0.649 0.561LOS case 0.483 0.370 0.490

Table IIABSOLUTE VALUES OF CORRELATION COEFFICIENTS BETWEENTHE ESTIMATED BIAS bi AND EACH OF THE PARAMETERS r0max ,

τmm AND τmds . BOTH LOS AND NLOS CONDITIONS ARECONSIDERED.

III. LOCALIZATION ALGORITHMS

A. Introduction

In this Section we develop various algorithmsfor two-dimensional localization in a UWB networkcomposed by Na anchors with known positionszai , [xai , y

ai ]T ∈ R2, i = 0, ..., Na − 1 and by a

single node (dubbed mobile station, MS, in the fol-lowing) with unknown position θ , [x, y]T ∈ R2.Any couple of the given (Na+1) devices can operatein a LOS (NLOS) condition with probability PLOS

(1 − PLOS). The localization algorithms describedbelow try to mitigate the effects of the NLOSbias error and aim at generating an estimate θof θ minimizing the mean square error (MSE)Eθ

{||θ − θ||2

}. It is also important to point out

that localization algorithms developed for NLOSscenarios usually consist of two steps. In fact, firstthe NLOS bias is estimated for each involved linkand is used to remove the bias contribution in theacquired data; then the new data set is processedby a least-square (LS) procedure generating anestimate of θ (e.g., see [2], [3], [4], [6]). A differentapproach, involving implicit estimation of the biasfor each link, is adopted in the following; thisapproach is motivated by the fact that the estimationof the bias for the i-th link can benefit from theinformation acquired from the other (Na− 1) links;note that in [2] and [6] bias mitigation performed ina link-by-link fashion is exploited to assign a weightin a weighted least-square (WLS) step, but such anapproach is heuristic.

B. Maximum Likelihood Estimation

If the links between the MS and the Na differentanchors are assumed mutually independent, the MLestimation strategy of the unknown MS position θ,given a TOA estimate and a set of additional signal

features for each link, can be formulated as

θ = arg maxθ

lnNa−1∏i=0

fτ,x(τi,xi; θ). (5)

Here, θ = [x, y]T ∈ R2 denotes the MS trialposition, τi and xi are the TOA and Nf -dimensionalsignal vector collecting the received signal featuresacquired for the i-th link and fτ,x(·, ·; θ) is thejoint pdf of the TOA and the vector of featuresparameterized by the trial position θ. As alreadydiscussed in Paragraph II-B, various options for x(and, consequently, for fτ,x(·, ·; θ)) are possible; inthe following Paragraphs the impact of such optionson the ML strategy (5) is investigated.

1) ML estimation strategy for different sets of ob-served data: In this Paragraph two different optionsare considered for the set of features processed bythe ML strategy.

a) Option A: In this case it is assumed thatthe vector of features referring to the i-th link isxi = [rmax,i, τm,i, τds,i]

T ; this choice is motivated bythe large correlation between these random variablesand the link bias b (see Paragraph II-B). Then,the joint PDF fτ,x(τi,xi; θ) appearing in the MLstrategy (5) can be expressed as (see Eq. (1)):

fτ,x(τi,xi; θ) = (fb,x⊗ fw)

(τi −

di(θ)

c0, xi

), (6)

where (see Eq. (2), (3), (4))

xi =

[rmax,i + rmmaxdi(θ),

τm,i

di(θ),τds,i − τ 0dsdi(θ)

]T(7)

di(θ) is the distance between the i-th anchor and theMS trial position and fb,x⊗fw denotes the convolu-tion between the joint pdf fb,x(·) and the observationnoise pdf fw(w) = (2πσ2

w)−1/2 exp(−w2/(2σ2w)).

Note that the shape of the function fb,x(·) underthe hypothesis of LOS conditions (HLOS event) issubstantially different from that found in NLOSconditions (HNLOS event) [4]; in both cases this func-tion was estimated applying the procedure describedin [1] to the data collected in our measurementcampaign. This led to two distinct multidimensionalhistograms, which approximate the required pdf’sfb,x (b, xi|HLOS) and fb,x (b, xi|HNLOS) with a certainaccuracy depending on: a) the amount of acquireddata; b) the sizes ∆b, ∆rmax, ∆τm and ∆τds ofthe quantization bins adopted in the generation of

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the histograms. Note that these sizes need to beaccurately selected, since large bins imply a coarseapproximation of pdf’s, whereas excessively smallbins require a huge amount of data.

Given an estimate of the above mentioned coupleof pdf’s, the pdf fb,x(·) can be evaluated as

fb,x (b, xi) = PLOSfb,x (b, xi|HLOS) +

(1− PLOS) fb,x (b, xi|HNLOS) (8)

if the probabilities PLOS , Pr{HLOS} and PNLOS ,Pr{HNLOS} = 1− Pr{HLOS} are available, or as

fb,x (b, xi) =1

2fb,x (b, xi|HLOS) +

1

2fb,x (b, xi|HNLOS)

(9)if no a priori information about the LOS/NLOSconditions are available.

In principle, evaluating the joint PDFfτ,x(τi,xi; θ) of the ML strategy entails thecomputation of the convolution appearing in (6);this has not been done in our work, since it isnumerically complicated and a form of implicitsmoothing is already included in the generation ofthe above mentioned histograms extracted from theavailable measurements.

b) Option B: In this case the set of featuresemployed in ML estimation consists of a singleelement, namely the delay spread (which exhibitsthe largest correlation with the NLOS bias; seeTable I), so that xi = τds,i and the pdf fτ,x(τi,xi; θ)of (5) becomes (see (6))

fτ,x(τi,xi; θ) = (fb,τmds⊗fw)

(τi −

di(θ)

c0,τds,i − τ 0dsdi(θ)

)(10)

Like in the previous case, the pdf fb,τmds(·) wasestimated in the LOS and NLOS scenarios (seeFig. 2) from the data acquired in our measurementcampaign. Note that this option leads to a MLlocalization algorithm which is substantially simplerthan that proposed in the analysis of option A.

2) Parameterization of the observations: TheML strategies developed above are based on thejoint pdf’s fb,r0max,τ

mm ,τmds

(·) and fb,τmds(·), which referto a set of distance-independent parameters. Sincethe parameters r0max, τmm and τmds exhibit a lowercorrelation with b than their distance-dependentcounterparts rmax, τm, τds (see Tables I and II), theuse of the joint PDF

fτ,x(τi,xi; θ) = (fb,x⊗ fw)

(τi −

di(θ)

c0,xi

)(11)

in place of (6) has been also investigated (similarcomments apply to (10)).

3) Estimation of joint pdf’s: As already ex-plained above, the joint pdf’s involved in the pro-posed ML localization strategies can be easily es-timated from the acquired data using a simpleprocedure based on dividing the space of observeddata in a set of bins of proper size. Such a pro-cedure generates an histogram, which, unluckily,entails poor localization performance if employedas it is, because of the relatively small numberof bins (adopted to avoid empty bins). To miti-gate this problem, interpolation followed by low-pass filtering can be applied to raw experimentalhistograms. In particular, we found out that cubicspline interpolation followed by moving averagefiltering (with a window size equal to about 1/15of the size of the histogram) provides good results(an example of the resulting pdf is shown in Fig.2); the localization strategies adopting this approachare dubbed interpolated-histogram estimators in thefollowing.

An alternative to this approach is represented byfitting the histograms with analytical functions (e.g.,polynomials). On the one hand, this solution offerssome advantages with respect to the previous one,since it requires less memory (only the values of thecoefficients of the fitting equations need to be saved)and provides better accuracy (the resulting pdf’s aresmoother). On the other hand, the use of (multi-dimensional) fitting raises a number of problems. Infact, global performance figures, like the root meansquare error4 (RMSE) are certainly useful, but donot account for the fact that fitting errors where apdf takes on small values are less critical than thosein points where the same pdf takes on large values.In addition, if the dimensionality of the pdf domainis larger than two, an analytical function generatedby a fitting procedure cannot be easily represented.

In our statistical analysis, the use of polyno-mial fitting was investigated. A polynomial degreeNpol = 8 was selected, since this choice ensures thatthe resulting RMSE is smaller than εfitting = 5·10−4

in both LOS and NLOS scenarios. In the follow-ing localization algorithms employing pdf’s gener-ated by polynomial fitting will be dubbed fitted-histogram estimators.

4This parameter is evaluated as the root mean square of the differ-ence between the values of the original experimental histogram andthe corresponding values generated by a fitting analytical function.

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Assume

LOSHH 0b

Compute the posterior probabilities:

0 ,

1 ,

( , | )

( , | ) 0,1,..., 1j

b LOS

j b x j LOS j f

p f b H db

p f b x H dx j N

xx

0 ,

1 ,

( , | )

( , | ) 0,1,..., 1j

b NLOS

j b x j NLOS j f

q f b H db

q f b x H dx j N

xx

Form the

decision

variables:

fN

j

jL pD0

fN

j

jN qD0

NL DD

LOSHH

NLOSHH

Recompute the bias

estimate:

)ˆ|,(maxargˆ, HHbfb b

bx

x

No

Yes

Figure 4. Flow diagram of the proposed iterative estimator.

C. Iterative Estimation

Recently, an iterative estimator of both the chan-nel state (i.e., LOS or NLOS conditions) and theNLOS bias b has been proposed in [4]. Such anestimator relies on the availability of univariatestatistical models for the estimates of TOA, RSS andRDS; it is shown, however, that estimation accuracyis improved if the delay-spread is exploited as theonly discriminant feature.

In the following, a modified version of this itera-tive algorithm (dubbed iterative estimator), employ-ing the joint pdf’s described above and extractedfrom our experimental database, is proposed. Thisalgorithm is summarized by the flow diagram shownin Fig. 4 and operates as follows. In its first iterationit starts with a null estimate of the NLOS biasand, for each link, generates a set of posteriorprobabilities integrating the pdf’s estimated in LOSand NLOS conditions. Then, such probabilities areemployed to compute a couple of decision vari-ables on the basis of which a decision H on theLOS/NLOS conditions is taken. Finally, such adecision is exploited to compute a new bias estimatewhich is used to start the next iteration. Note thatthis algorithm operates in a link-by-link fashion andthat in the diagram of Fig. 4 the dependence on thelink index has been omitted to ease the reading.

IV. NUMERICAL RESULTS

Our experimental database has also been ex-ploited to assess the RMSE performance of the

proposed algorithms for localization and NLOSbias mitigation schemes via computer simula-tions. In our simulations the MS coordinates arealways (0; 0); then, following [2], for the i-th anchor a received waveform from either theLOS database (with probability PLOS) or from theNLOS database (with probability PNLOS) was drawnrandomly and was associated with the positionzai =

(di sin(2π i−1

Na); di cos(2π i−1

Na))

, where di is thedistance measured for the selected waveform. Notethat these waveforms already include the experimen-tal noise and thus no simulated noise was imposedon the waveforms (so that the signal-to-noise ratiois the experimental one). Finally, the parameter Na

has been set to 3 (worst case which still theoreticallyallows unambiguous localization).

The RMSE performance of the following algo-rithms has been evaluated:

1) LS - A standard LS estimator for LOS en-vironments; the estimation strategy can beexpressed as θ = arg minθ

∑Na−1i=0 (c0τi −

di(θ))2.2) VE - A LS estimator exploiting TOA mea-

surements corrected by the algorithm pro-posed by Venkatesh and Buehrer in [4]; thisalgorithm relies on a statistical modeling ofthe propagation environment based on ourexperimental database.

3) ML-4D - A ML estimator based on (9) andemploying an interpolated histogram for theevaluation of its likelihood function referringto a distance-dependent parameterization.

4) ML-2D - A ML estimator based on (10) andemploying an interpolated histogram for theevaluation of its likelihood function referringto a distance-dependent parameterization.

5) ML-2D-ID - A ML estimator based on (10)and employing an interpolated histogram forthe evaluation of its likelihood function refer-ring to a distance-independent parameteriza-tion.

6) ML-4D-F - A ML estimator based on (9) andemploying a fitted histogram for the evalua-tion of its likelihood function referring to adistance-dependent parameterization.

7) ML-4D-IT - A LS estimator based on (9)and exploiting TOA measurements correctedby the modified iterative algorithm illustratedin Section III-C.

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8) ML-2D-IT - A LS estimator based on (10)and exploiting TOA measurements correctedby the modified iterative algorithm illustratedin Section III-C.

In estimating the RMSE performance of the MLalgorithms listed above the likelihood functionswere always evaluated at the vertices of a squaregrid characterized by a step size equal to 10 mm.Some numerical results are compared in Fig. 5,which illustrates the RMSE performance versus theprobability PLOS. These results evidence that:

1) Different estimators can provide significantlydifferent accuracies for distinct values of PLOS,when this probability is not close to unity.

2) The simple LS algorithm is outperformed byall the other algorithms when PLOS ≤ 0.9; thisis due to the fact that this strategy does nottry to mitigate the NLOS bias.

3) The VE algorithm performs well at the costof a reasonable complexity, but offers limitedbias mitigation when PLOS = 0; in this case theML-2D, ML-2D-ID and ML-4D-F estimatorsperform much better.

4) The exploitation of a large set of receivedsignal features does not necessarily allow toachieve better accuracy than a subset of them(see the curves referring to ML-2D and ML-4D estimators); this is due to the fact that thecorrelation between the different couples ofextracted features is typically large, so thatthey provide strongly correlated informationabout the NLOS bias.

5) Distance-dependent parameterization providesbetter accuracy (see the curves referring to theML-2D and ML-2D-ID estimators); this canbe related to the fact that τmds is less corre-lated with the NLOS bias than its distance-dependent counterpart τds.

6) The ML-4D-F estimator performs better thanthe ML-4D estimator in NLOS conditions;this means that the use of fitted histogramsentails an improvement in localization accu-racy.

Finally, Fig. 6 shows the cumulative density func-tion (CDF) of the RMSE localization error charac-terizing the LS, VE, ML-2D and ML-2D-IT algo-rithms when PLOS = 0.2. These results evidence that:a) the RMSE localization error of the consideredalgorithms remains below 0.5 m in average the

0.4

0.3

0.2

0.1

0.0

RMSE

(m)

1.00.80.60.40.20.0

PLOS

LS VE ML - 2D ML - 2D - ID

ML - 2D - IT ML - 4D ML - 4D - F ML - 4D - IT

Figure 5. RMSE performance versus PLOS offered by variouslocalization algorithms.

1.0

0.8

0.6

0.4

0.2

0.0

CDF

1.00.80.60.40.20.0

PLOS

LS

VE

ML - 2D

ML - 2D - IT

Figure 6. CDFs of the RMSE characterizing various localizationalgorithms when PLOS = 0.2.

80% of the cases; b) the ML-2D technique is moreaccurate than the other algorithms, in terms ofRMSE, for small NLOS errors.

V. CONCLUSIONS

In this paper various UWB localization tech-niques processing multiple features extracted fromthe received signal to mitigate the problem of NLOSbias have been described and their accuracy hasbeen assessed exploiting the experimental data ac-quired in an measurement campaign. Our resultsevidence that: a) a restricted set of features has to beemployed; b) the use of distance-dependent featuresand of fitted histograms provide better performancethan that offered by distance-independent featuresand interpolated histograms.

ADVANCES IN ELECTRONICS AND TELECOMMUNICATIONS, ACCEPTED FOR PUBLICATION 9

ACKNOWLEDGEMENTS

The authors would like to thank Prof. MarcoChiani and Prof. Davide Dardari (both from theUniversity of Bologna, Italy) for lending us theUWB devices employed in our measurement cam-paign and the PhD students Alessandro Barbieriand Fabio Gianaroli for their invaluable help inour experimental work. Finally, the authors wish toacknowledge the activity of the Network of Excel-lence in Wireless COMmunications (NEWCOM++,contract n. 216715), supported by the EuropeanCommission which motivated this work.

REFERENCES

[1] D. Dardari, A. Conti, J. Lien, and M. Z. Win, “The effect ofcooperation on localization systems using UWB experimentaldata,” EURASIP J. Adv. Signal Process, vol. 2008, Jan. 2008.

[2] S. Marano, W. Gifford, H. Wymeersch, and M. Z. Win, “NLOSidentification and mitigation for localization based on UWB ex-perimental data,” IEEE J. Sel. Areas Commun., vol. 28, pp. 1026–1035, Sept. 2010.

[3] N. Decarli, D. Dardari, S. Gezici, and A. A. D’Amico,“LOS/NLOS detection for UWB signals: A comparative studyusing experimental data,” in Proc. of the 5th IEEE InternationalSymposium on Wireless Pervasive Computing (ISWPC 2010),pp. 169 –173, May 2010.

[4] S. Venkatesh and R. Buehrer, “Non-line-of-sight identificationin ultra-wideband systems based on received signal statistics,”IET Microwaves, Antennas Propagation, vol. 1, pp. 1120 –1130,Dec. 2007.

[5] N. Alsindi, C. Duan, J. Zhang, and T. Tsuboi, “NLOS channelidentification and mitigation in ultra wideband toa-based wirelesssensor networks,” in Proc. of the 6th Workshop on Positioning,Navigation and Communication (WPNC 2009), pp. 59 –66, Mar.2009.

[6] I. Guvenc, C.-C. Chong, F. Watanabe, and H. Inamura, “NLOSidentification and weighted least-squares localization for UWBsystems using multipath channel statistics,” EURASIP J. Adv.Signal Process, vol. 2008, Jan. 2008.

[7] “WPR.B database.” Available online at http://www.vicewicom.eu.

[8] J.-Y. Lee, “USC ranging test database.” Available online at http://ultra.usc.edu/uwb database/ranging test.htm.

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Francesco Montorsi received the Laurea degree (summa cum laude)and the Laurea Specialistica degree (summa cum laude) in ElectronicEngineering from the University of Modena and Reggio Emilia, Italy,in 2007 and 2009, respectively.

Since 2010 he is a Ph.D. candidate in the ICT PhD school of theUniversity of Modena and Reggio Emilia. Since January 2011 he isa visiting PhD student at the Wireless Communications and NetworkScience Laboratory of Massachusetts Institute of Technology (MIT).His current research interests include wideband communication sys-tems, indoor localization and inertial navigation systems.

Mr. Montorsi is a member of IEEE Communications Society andserved as a reviewer for the IEEE Transactions on Wireless Commu-nications, IEEE Transactions on Signal Processing and several IEEEconferences.

Fabrizio Pancaldi was born in Modena, Italy, in July 1978. Hereceived the Dr. Eng. Degree in Electronic Engineering (cum laude)and the Ph. D. degree in 2006, both from the University of Modenaand Reggio Emilia, Italy. From March 2006 he is holding the positionof Assistant Professor at the same university and he gives the coursesof Telecommunication Networks and ICT Systems. He works inthe field of digital communications, both radio and powerline. Hisparticular interests lie in the wide area of digital communications,with emphasis on channel equalization, statistical channel modelling,space-time coding, radio localization, channel estimation and clocksynchronization.

Giorgio Matteo Vitetta (S’89, M’91, SM99) was born in ReggioCalabria, Italy, in April 1966. He received the Dr. Ing. Degree inElectronic Engineering (cum Laude) in 1990 and the Ph. D. degreein 1994, both from the University of Pisa, Italy. In 1992/1993he spent a period at the University of Canterbury, Christchurch,New Zealand, doing research for digital communications on fadingchannels. From 1995 to 1998 he was a Research Fellow at theDepartment of Information Engineering of the University of Pisa.From 1998 to 2001 he has been holding the position of AssociateProfessor of Telecommunications at the University of Modena andReggio Emilia. He is now Full Professor of Telecommunications inthe same university. His main research interests lie in the broadarea of communication theory, with particular emphasis on codedmodulation, synchronization, statistical modeling of wireless channelsand channel equalization. He is serving as an Editor of both theIEEE Transactions on Communications (Editor for Channel Modelsand Equalization in the Area of Transmission Systems) and theIEEE Transactions on Wireless Communications (in the Area ofTransmission Systems).