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Indoor Positioning Using LTE SignalsMarco Driusso∗, Chris Marshall†, Mischa Sabathy‡, Fabian Knutti‡, Heinz Mathis‡, and Fulvio Babich§

∗u-blox Italia S.p.a., Sgonico, Italy. Email: [email protected]†u-blox UK Ltd, Reigate, United Kingdom. Email: [email protected]

‡Institute for Communication Systems, University of Applied Sciences of Eastern SwitzerlandRapperswil, Switzerland. Email: {mischa.sabathy,fabian.knutti,heinz.mathis}@hsr.ch,

§Department of Engineering and Architecture, University of Trieste, Trieste, Italy. Email: [email protected]

Abstract—This paper presents an experiment using real Long-Term Evolution (LTE) signals to extend positioning from out-doors to indoors. LTE signals are of interest for positioningapplications because of their availability indoors, where GNSSsignal reception is limited. Different approaches for time ofarrival (TOA) extraction are evaluated for their positioningperformance, combined with an extended Kalman filter (EKF)for movement tracking. The paper shows that the performanceis surprisingly good, with high visibility of cellular signals evenin the difficult indoor test environment, and with a positioningerror once indoors smaller than 8m in 50% of cases.

I. INTRODUCTION

There are many different positioning systems for outdoorscenarios, notably global navigation satellite systems (GNSS).However, moving indoors GNSS reception is limited, mostlyas shadowing reduces the availability of the GNSS signals.Cellular wireless signals are an attractive alternative for indooruse, as the received signal levels are stronger than possiblewith satellite systems, and cellular deployments are designedto provide good coverage also indoors. In particular, the newLong-Term Evolution (LTE) signals have high bandwidth anda frame and synchronisation structure which could make themwell-suited for positioning purposes.

Previously in [1], [2], an outdoor positioning solution usingLTE signals was presented, and showed that LTE signalscould be used for practical positioning in a varied outdoorenvironment. Best performance could be achieved using theESPRIT super resolution algorithm (SRA) combined with aKalman filter for measurement and tracking of the time ofarrival in sometimes-difficult multipath. Overall this showedthat LTE signals could deliver position estimates with an errorsmaller than 21 m in 50% of cases (31m RMS), when outdoors[2]. However, GNSS itself can provide good performanceoutdoors - it is positioning indoors where the challenge lies, sothis paper explores the possibilities and limits of positioningwith LTE signals when moving into the indoor scenario.

There are few experimental works in the literature thatexploit LTE signals for indoor positioning. In [3], [4], differentLTE signals generated with prototyping hardware are exploitedfor assessing the feasibility of indoor positioning based on

978-1-5090-2425-4/16/$31.00 c©2016 IEEE

LTE signals time difference of arrival (TDOA) measurements,and on the usage of particle filters. An experimental evalu-ation is presented in [5], where the timing performance ofdifferent hardware platforms is compared by using emulatedLTE signals in line-of-sight (LOS) multipath-free channels.The authors of [6] propose and validate in the field a methodbased on LTE femtocells for detecting the floor in which theLTE receiver is located, for safety and emergency applications.In [7], a test-bed is proposed for performing indoor rangingmeasurements based on round trip delay estimation using LTE-like OFDM signals. However, to the best of the authors’knowledge, there are no works that present an indoor position-ing experiment that exploits real LTE signals opportunisticallymeasured from a commercial network.

After an introduction to the relevant aspects of the LTEsignal used in Section II, the indoor environment and exper-imental equipment are described in Section III. This sectionalso reviews the coverage of the GPS and the LTE signals vis-ible (or not visible) in the difficult indoor test. The algorithmsused for measuring the time of arrival and for estimating therange from the base station are set out in Section IV, optimisedfor the indoor environment. Finally in Section V the positionof the rover device is estimated, a process which is slightlycomplicated in this case by the need to estimate the clockdrift of the base station over the course of the experiment.The results of various algorithms are compared in Section VI,and the conclusions are summarized in Section VII.

II. THE LTE PHYSICAL LAYER

Generally 3GPP Long-Term Evolution (LTE) distinguishesbetween the time division duplexing (TDD) mode and thefrequency division duplexing (FDD) mode. FDD uses twodifferent frequency bands for uplink and downlink while inTDD mode the uplink and downlink channels are shared. Allthe work related to this paper considers the LTE FDD mode.

The downlink physical layer of LTE is based on the orthog-onal frequency division multiplexing (OFDM) modulation. AnOFDM symbol is a wideband signal where the information isstreamed on Nsc multiple orthogonal narrowband frequencysub-carriers, which are modulated independently and spacedby ∆f . For the sub-carriers to be orthogonal, the separation

2016 International Conference on Indoor Positioning and Indoor Navigation (IPIN), 4-7 October 2016, Alcala de Henares, Spain

p=0, NID,1

p=1, NID,1

p=0, NID,2

p=1, NID,2

〈k〉6=0

〈k〉6=0

〈k〉6=1

〈k〉6=1

〈k〉6=2

〈k〉6=2

〈k〉6=3

〈k〉6=3

〈k〉6=4

〈k〉6=4

〈k〉6=5

〈k〉6=5

l = 0 1 2 3 4 5 6

∆f

∆fCRS

a slot - 0.5ms

Fig. 1. CRS pattern within a resource block for two antenna ports p = {0, 1}and two different cell IDs NID,1 and NID,2. k is the sub-carrier index and lis the OFDM symbol number within the slot.

has to be ∆f = 1/Ts, where Ts is the OFDM symbolduration. The number of used sub-carriers Nsc depends onthe adopted channel transmission bandwidth. Six differentdownlink bandwidth configurations are available in LTE, witha channel bandwidth going from 1.4 MHz (Nsc = 72) up to20 MHz (Nsc = 1200). The content of the OFDM sub-carrierscan be easily accessed by using a Nfft ≥ Nsc point discreteFourier transform (DFT) on the received signal samples [8].

In the time domain, an LTE downlink signal is organized in10 ms long radio frames, each made up of 20 slots having aduration of 0.5 ms. Each slot contains NDL

symb OFDM symbols,each carrying its Nsc sub-carriers. According to the OFDMprinciple, a cyclic prefix (CP) is inserted in the guard intervalbefore each transmitted lth OFDM symbol within the slot.Finally, LTE addresses the spatial domain with the conceptof antenna port: the LTE base stations (BSs) can transmitwith different antenna port configurations, to be used either fortransmit diversity or spatial multiplexing. All the BSs receivedin this experiment were using a 2 antenna port configuration.

In LTE, the basic resource is called a resource element (RE),and corresponds to a specific sub-carrier within a specificOFDM symbol transmitted from a specific antenna port. Foreach antenna port, REs are grouped in resource blocks, whichare made of NRB

sc contiguous sub-carriers for the duration ofone slot (i.e., for NDL

symb subsequent OFDM symbols). Furtherinformation about the LTE physical layer can be found in [9].

A. Suitable signals for ranging

The LTE signal to be used for positioning should take intoaccount a number of factors. The signal should preferablyoccur in the downlink without user request, so that no specificaction by the network is needed, thus avoiding additionalnetwork traffic and cost. The signal should be unique for a basestation, so that the signals from different base stations operat-ing on the same frequency can be distinguished. Additionally,the bandwidth of the transmitted signal should be maximizedwithin the channel bandwidth, so as to give a channel impulse

TABLE IMEASURED LTE PHYSICAL LAYER DL PARAMETERS

parameter operator 1 operator 2 operator 3

DL bandwidth 20 MHz 15 MHz 15 MHz

Nsc 1200 900 900

DL mode FDD FDD FDD

center frequency fc 1815.1 MHz 1870 MHz 1850.1 MHz

Nfft 1536

∆f = 1/Ts 15 kHz

NRBsc 12

NDLsymb 7

response with a high resolution. The cell-specific referencesignal (CRS) was chosen in this study.

The LTE CRS is a specific signal intended for channelestimation and coherent demodulation, and is defined as a setof pilot tones peculiar to each base station and cell sector,according to the cell-ID NID. Moreover, different CRSs aretransmitted from different antenna ports. The CRS itself is apseudo-random complex-valued sequence, initiated with theNID as described in [9]. Fig. 1 shows the mapping of theCRSs of two cells onto a resource block for a two-antenna-port configuration. The complete mapping can be obtainedby vertically repeating the grid of Fig. 1 for Nsc/N

RBsc times,

until the full transmit bandwidth is filled. As one can see,the CRS of a single OFDM symbol pertaining to an antennaport p occupies one sub-carrier every six, leading to a totalof Ntot = Nsc/6 CRS pilots in that OFDM symbol, spacedby ∆fCRS = 6∆f . The excellent cross-correlation propertiesof the CRS, together with its particular mapping on the REs,allow a receiver to distinguish between multiple cells receivedon the same carrier frequency.

III. INDOOR MEASUREMENT SCENARIO

The indoor LTE data was recorded in building 2 of theHochschule fur Technik Rapperswil (HSR) in Rapperswil SG,Switzerland. The data gathering experimental track is shownin Fig.2a. It started and finished outdoors, about 3 m belowthe surrounding ground level, in a limited open-sky scenario.The measurement corridors do not have a view outside andremain below the ground level. One of the four corridors isshown in Fig. 2c. The duration of the whole experiment wasapproximately 15 min. At the end of each straight path thetrolley on which the data-acquisition system was mounted wasstopped and rotated by 90 degrees. Then it was moved downthe next straight path at around 0.8 m/s. A raw IQ data blockof 100 ms was recorded every second for post-processing.

The signals from three LTE service providers were mea-sured during the test, from a total of 5 base stations (BSs).Table I lists the measured downlink parameters for the threeoperators. The LTE configuration of the BSs were the same forall the BSs of one LTE service provider. Fig. 3 shows four ofthe received LTE BS locations, with the operators indicated bythe different markers and the BSs numbered for identification


start/stopposition

(a)

start/stopposition

(b)

(c)

Fig. 2. Indoor measurement track satellite view (a), view of the start/stopposition from the entrance (b), and view of one corridor (c).

purposes, and their corresponding cell sectors. In addition,the experimental track is indicated. An additional BS fromoperator 2 was received, which is not shown in Fig. 3, locatedfurther south across the lake at a distance of roughly 3 km.

A. Data acquisition system

The data acquisition system (DAS) was adopted from [1],and is shown schematically in Fig. 4. It consists of a set ofUniversal Software Radio Peripheral (USRP) software definedradios, each measuring an operator’s downlink LTE carrierfrequency, and of a reference track measuring system, whichis discussed in detail in Section III-B.

An indoor positioning system based on opportunisticallymeasured LTE signals has to deal with a number of factors,including heavy multipath propagation, low SNRs, BSs’ cov-erage and geometry, and BSs’ clock offsets. In order to beable to handle and analyse the effects of BS clock offsets and

705

231

84

86

1

183

2

52

531

72 73

74

3

237 238

239

1

X-coordinate CH1903 (Grid 1km)

Y-coordinate

CH1903(G

rid1km)

Test route

Operator 1

Operator 2

Operator 3

Fig. 3. Indoor measurement track and received LTE BSs. The index insideeach marker is used to identify the different BSs. For each BS, the receivedcells are also represented, with an approximate orientation.

PatchAntenna

Built-in LNA

Wide Band AntennaMagnetic Mount- Gain: 3dBi peak

u-blox EVK-6NGPS/GNSS Evaluation Kit

LIDAR LiteLaser distance sensor

SRS FS725Rubidium Frequency Standard

USRP N210 - fC = 1815.1MHzDaughterboard: WBX 50-2200MHz RX/TX

USRP N210 - fC = 1870MHzDaughterboard: WBX 50-2200MHz RX/TX

USRP N210 - fC = 1850.1MHzDaughterboard: WBX 50-2200MHz RX/TX

PC- Data Recording Software

1PPS

timestampsposition fixes

laser position fixes

1PPS

10MHz Ref

Ethernet1Gbps

Fig. 4. Data aquisition system for indoor experiment.

of multipath, every USRP is time synchronized to a GPS-locked Rubidium frequency standard, keeping the receiverlocal clock constantly and precisely aligned to UTC. Thecollected IQ samples are time-stamped with the correspondingUTC epochs, in order to assist in the interpretation of thesignal measurements.


building wall

DAS

DAS

pR1

pR2

DAS experimental track

d[t,pR1 ]

d[t,p

R2]

Fig. 5. Laser-based distance-to-reference point measurement during experi-ment, top view.

B. Reference track

Compared to [1], the reference track could not be measuredby means of the GPS, because of absent indoor reception.Since building plans were available, a so-called laser-baseddistance-to-reference points (LRP) measurement system wasused as a solution to generate the reference track. A networktime protocol (NTP) UTC time synchronized personal com-puter measured the distance to a particular active referencepoint using the Lidar lite laser distance module. The Lidar litemodule provides measurement distances of up to 40 m with anaccuracy of ±0.025 m. Fig. 5 shows the working principle ofthe LRP method. The distance d[t,pR

n] to a reference point inposition pR

n was determined thanks to the laser distance mod-ule throughout the whole measurement tour, with different ref-erence points depending on the location along the experimenttrack. For further processing the reference track is convertedinto the same coordinate system as used by the algorithms. Asin [1], [2], the algorithms in this paper are also in the east-north-up (ENU) plane [10], with its reference position set tothe first measurement outdoors. In this experiment the ENUreference position was set manually since no accurate GPSfix was possible at the starting location. The d[t,pR

n] distanceto reference point measurements were transformed into ENUcoordinates pLRP(t), where pLRP =

[xLRP yLRP zLRP

]ᵀ,

each corresponding to a UTC time t. These coordinates wereused as the ground truth in the experiment, for evaluating thepositioning performance.

C. GPS coverage

As one can see in Fig. 6, the GPS space vehicles (SV) re-ception disappears during the indoor period of the experiment.However, the experiment showed that the visibility of basestations was not significantly affected by being indoors, andup to five LTE BSs could still be received. All these receivedLTE signals were measured and exploited for estimating time-based ranges and evaluating the receiver position.

IV. TIME OF ARRIVAL ESTIMATION

The time of arrival (TOA) of the downlink LTE signals wasestimated by exploiting the CRS, described in Section II-A.

8:32 8:34 8:36 8:38 8:40 8:42 8:44

0

2

4

6

8

UTC time

Number

ofSVs/BSs

SVs usable

LTE BSs visible

Fig. 6. Number of usable SV detected during the measurement period,compared to the number of LTE BSs visible.

The approach for the TOA estimation is taken from previousworks documented in [2], [11]. However, improvements wereneeded for dealing with low SNRs and strong multipathconditions typical of indoor environments. These changes werecrucial for achieving a good performance in the consideredscenario, and are described in the following sections.

In a short observation window, the multipath channel en-countered by a signal propagating from a BS to a mobilereceiver may be modeled with a channel impulse response(CIR) given by h(τ) =

∑L−1l=0 hlδ(τ − τl), and a channel

frequency response (CFR) equal to H(f)=∑L−1l=0 hle

−j2πfτl ,where δ(·) denotes the Dirac delta function, hl ∈ C is thecomplex channel gain associated to the lth path, and τl is thecorresponding delay, with τ0 < · · · < τL−1 [8]. Using anestimate τ0 of the direct path (DP) TOA τ0, the pseudorangeρ = c0 · τ0 can be evaluated, which can be later corrected to adistance estimate d, where c0 is the speed of light. The CFRcan be easily estimated by exploiting the pilot tones of theLTE CRS, also thanks to the underlying OFDM modulation. Inparticular, let Hp

s,l ∈ CNtot be the least squares CFR estimationobtained as described in [12] from antenna port p, OFDMsymbol l within the slot s, in a particular measurement blockacquired at UTC time t from a certain visible cell. These CFRestimates are used in this work for the DP TOA estimation.

A. CFR estimates time-frequency combining

Because of the low speeds v involved in the considered mea-surement scenario, the channel can be considered correlatedboth in amplitude and phase for long periods. In particular,from the analysis of [13], it can be assumed that a fadingchannel has amplitude and phase with correlation coefficientgreater than 0.9 in the interval ∆t if ∆tfCv/c ≤ 0.025,where fC is the carrier frequency and v is the relativespeed between transmitter and receiver. A carrier frequency offC = 1850 MHz and a speed of v = 0.8 m/s (the average speedof the DAS during the moving segments of the measurementtour) determine a correlation interval of ∆t ≤ 5 ms, whichcorresponds to a duration of 10 LTE slots. This high channelcorrelation within 10 subsequent LTE slots was exploited intwo ways.


0 500 1000 1500

10−3

10−2

10−1

100

offset [m]

norm

.amplitude

w {τ0l }6l=0, L

0=7

γth {τ1l }6l=0, L

1=7

τT

Fig. 7. Example of TOA estimation from BS 1 operator 3 cell 237 at UTCtime t = 08:42:53. The time axis values are expressed as distance offsets inrespect to the coarse timing.

Firstly, thanks to the fact that the CRSs of the two OFDMsymbols within a slot occupy different sub-carriers (Fig. 1), thetwo estimates Hp

s,0 and Hps,4 were merged in the frequency

domain, as described in detail in [2]. This time-frequencycombination permitted to obtain the length 2Ntot CFR estimateHps , which is characterized by a reduced frequency separation

between the samples (3∆f instead of 6∆f ). The benefits ofthis merging procedure are an increased number of samplesfor each CFR estimate Hp

s and a smaller frequency separationbetween adjacent samples. Depending on the TOA estimationalgorithm adopted, this may correspond to increased resolutionand increased maximum TOA computable.

Secondly, the high channel correlation determined by pedes-trian speeds was also exploited by coherently accumulating themerged CFR estimates of up to NS = 10 subsequent slots. Theresulting CFR estimate is given by:

Hp =1

NS

NS−1∑s=0

Hps . (1)

This leads to an improved SNR thanks to the averaging ofnoise, which helps a lot in producing quality TOA estimates.

B. Threshold-to-noise ratio algorithm

The CFR estimate Hp ∈ C2Ntot can be used to evaluatethe discrete power delay profile (PDP) wp = |IDFT{Hp}|2corresponding to antenna port p. The resolution of this PDPis given by TPDP = 1

2Ntot3∆f , and the time interval spanned is[− 1

6∆f ,1

6∆f

]=[−11.11µs, 11.11µs

]. The approach used in

the work presented for estimating the TOA out of wp, buildsupon the assumption that the estimated CIR is made out ofthe sum of a signal component and of a complex Gaussiannoise component. As a consequence, the samples of the PDPw = 1

2 (w0 + w1) resulting from the accumulation of the twoantenna ports’ PDPs can be considered as random variableshaving a χ2 distribution. The threshold based estimator of [14]

H0

MDLESPRIT

H1

MDL ESPRIT

uncertaintyevaluation

measurementselection

Kalman filter

z−1

z−1

P(t0) ζ(t0)

L0 L1

τ00 , ..., τ0L0−1

τ10 , ..., τ1L1−1

y(t)

ζ(t)

P(t)

P(t− 1)

ζ(t− 1)

R(t)

Fig. 8. Flow graph of the EKAT algorithm.

was tested, which exploits this fact for evaluating a closedformula for the probability Ped to detect a false early TOA[14]. It is shown in [14] that Ped is only a function of thethreshold-to-noise ratio (TNR), TNR = γth/σ

2n, where σ2

n isthe noise variance. Hence, a TNR achieving a target earlydetection probability of, say, Ped = 10−3 can be evaluated,and used to set a threshold γth based on the estimated noisevariance σ2

n. The TOA τT is then evaluated as the first PDPsample above the set threshold, where the suffix (·)T identifiesthe TNR based estimator. An example of TNR TOA estimationis shown in Fig. 7, together with the threshold γth used in theestimation and the corresponding PDP.

C. EKAT algorithm

Besides the TOA estimation algorithm considered in SectionIV-B, an estimator which is more robust against multipathand permits more insights on the feasibility of an indoorpositioning LTE system has been considered, at the cost ofan increased complexity. More particularly, the “ESPRIT andKalman filter for time of Arrival Tracking” (EKAT) rangingalgorithm is employed, which is thoroughly described in [2],[11], and briefly presented in the following. The algorithmflow graph is shown in Figure 8. EKAT uses as an input theCFR estimates Hp from the two antenna ports p = 0 andp = 1. These are used to estimate the number of receivedmultipath components Lp using the minimum descriptionlength (MDL) criterion, and the multipath TOA τp0 , ..., τ

p

Lp−1using the ESPRIT SRA, similarly to the approach of [15]. Anexample of ESPRIT TOA estimation is shown in Fig. 7, wherethe multipath estimated from the two antenna ports p = 0 andp = 1 is plotted against the corresponding combined PDPw. After the TOA estimation, for each antenna port p, theDP is selected among the multipath TOA estimates, and themeasurement uncertainty is computed according to a boundbased approach described in [2], [11], [16]. Finally, the DPTOA estimations from the two antenna ports, collected in thevector y(t) ∈ R2, and their uncertainties, collected in the


covariance matrix R(t) ∈ R2×2, are fed into a conventionalKalman filter, which performs a tracking in the pseudorangedomain, according to the state-space model of [2], [17], [18].The tracked TOA τE at time t, where the suffix (·)E identifiesthe EKAT estimator, and its variance are given by the firstcomponent of the estimated state vector ζ(t) and the upper leftelement of the estimated covariance matrix P(t), respectively.

D. Combining measurements from cells of the same BS

An estimate τx, x ∈ {T,E}, of the DP TOA is computedfor each cell received in a particular measurement. It happensfrequently however that signals are received from a numberof sector cells served by the same BS transmitter. The mea-surements performed show that the cells controlled by thesame BS share the same clock. Hence, the TOA estimatesof cells pertaining to the same BS can be combined, in orderto produce a single pseudorange measurement per BS.

For the TNR based algorithm, a simple strategy wasadopted, to choose the earliest between the TOA estimationsgathered in the same measurement from cells controlled by thesame BS. Meanwhile, for the EKAT algorithm, the trackedTOA with the lowest estimated variance was chosen, asperformed in [2].

V. DETERMINATION OF THE ROVER POSITION

A. Base station timing

Tests confirmed that all BSs have their unique clock, and somay differ relative to each other. To use the pseudoranges ofmultiple BSs and LTE service providers, these clock offsetsmust be taken into account. The estimated pseudorange isρ = τx · c0, where τx, x ∈ {T,E}, is the DP TOA estimatecomputed according to the methods of Section IV. The valueof the pseudorange ρ depends on three factors, namely the truerange d, the time offset to UTC at start time t0 called bias Dand the drift of the BS clock d, which models the change ofbias and is assumed linear in time. Hence, for each of theN(t) received BSs at UTC time t, the pseudorange is:

ρn(t)=dn(t) + c0[Dn + (t−t0)dn], n=1, . . . , N(t). (2)

The correction of the pseudoranges is performed similarlyto [1], [2], by fitting the estimated pseudoranges ρ againsta true range d. In particular, the offset and drift (Dn, dn)characterizing the nth BS are obtained as:

arg min(D,d)

{∑t∈Tn

∣∣ρn(t)−c0[D+(t−t0)d]−dn(t)∣∣2} , (3)

where Tn is the set of UTC epochs corresponding to allthe measurements from BS n. Since no GPS reception isguaranteed indoors, the true range d is obtained differentlywith respect to [1], [2]. In this paper, the LRP positionspLRP(t) are used, as:

dn(t) = ‖pBSn − pLRP(t)‖, (4)

where pBSn is the nth BS location in the ENU coordinate

column vector pBSn =

[xBSn yBS

n zBSn

]ᵀ. The BS locations

8:32 8:34 8:36 8:38 8:40 8:42 8:44

120

140

160

180

200 c0d = 0.0491m/sc0D = 36874m

UTC time

ranges

[m]

ρ(t)− c0D

d(t0) + (t− t0)c0d

d(t) (EKAT)

LRP range

(a)

8:32 8:34 8:36 8:38 8:40 8:42 8:44

100

120

140

160

UTC timeranges

[m]

GPS range EKAT

LRP range TNR

(b)

Fig. 9. Example of pseudorange correction (a) and corresponding rangeestimations (b) from BS 1 operator 1. In (a), the EKAT pseudoranges areshown.

were retrieved from the information provided by the SwissFederal Office of Communications (OFCOM) in [19]. Finally,the range estimation from the nth received BS at UTC time t isevaluated as dn(t) = ρn(t)−c0[Dn+(t−t0)dn]. Fig. 9a showsan example of a pseudorange correction for BS 1 operator 1,and Fig. 9b shows the corresponding ranges resulting fromthe correction of the EKAT and the TNR pseudoranges. Thequantization resulting from the usage of a discrete PDP in theTNR case is evident.

In a real application, the clock properties for the various re-ceived BSs can be gathered by a network of local measurementunits (LMUs) and made available to the positioning engine.

B. Positioning Solution

As in [1], a classical extended Kalman filter (EKF) is usedto determine the receiver position, by exploiting the modeldescribed in the following. Compared to [1], the accelerationwas taken into account in addition to the position and velocity.This leads to the state vector ξ =

[pᵀ pᵀ pᵀ

]ᵀwhere

p = [x y]ᵀ, x (east) and y (north) are the estimated receivercoordinates, p the estimated receiver velocity vector and p thecorresponding acceleration. Under these conditions the linearstate transition model is a uniformly accelerated motion:

ξ(t) =

1 0 ∆t 0 ∆t2/2 0

0 1 0 ∆t 0 ∆t2/20 0 1 0 ∆t 00 0 0 1 0 ∆t0 0 0 0 1 00 0 0 0 0 1

· ξ(t− 1), (5)


TABLE IIRANGING ERRORS STATISTICS

Op. BS ε T [m] ε0.5T [m] ε0.95T [m] ε E [m] ε0.5E [m] ε0.95E [m]

11 7.72 4.39 15.35 4.80 3.19 9.212 14.17 9.14 21.70 9.45 7.98 17.42

21 9.94 5.91 19.48 7.94 5.02 14.622 21.50 9.35 50.67 18.98 8.63 46.01

3 1 20.98 9.96 44.98 13.00 8.83 22.16

where ∆t is the elapsed time since the last measurement.The model for the measurement equation is given by z(t) =[z1(t), . . . , zN(t)]

ᵀ, where N(t) is the number of received BSsat time t, and each component zn(t) is the measured rangebetween the receiver and the nth BS, which is:

zn(t) =∥∥pBS

n − p(t)∥∥ , n = 1, . . . , N(t), (6)

with the vector pBSn ∈ R2 representing the known 2D location

of the nth received BS.For this experiment, the receiver clock bias is not included

in the positioning model, as the local receiver time is alignedwith UTC, as explained in Section III-A, and has zero drift. Inthe application being considered an estimate of the local clockbias can be obtained outdoors thanks to a GNSS position fix,prior to moving indoors. The local clock is then assumed andtaken in this experiment to be known and with zero drift.

The EKF was built on the model of (5)-(6), which wasused to obtain a state estimation ξ(t) and hence a positionestimation p(t). The predict and update phases used for theimplementation of the EKF are described in [20]. The processnoise and the measurement noise matrices of the EKF wereassumed static and tuned manually. The same values were usedfor both TOA measurement methods.

VI. RESULTS

The performance of the various exploited TOA estimatorswere evaluated by defining a ranging error for each receivedBS as Ed = |d− d|, where d is the LRP true range, as definedin Section V-A. A representative set of performance figureswere evaluated and shown in Tab. II, namely the root meansquare error (RMS), calculated as ε = (E[E2

d ])1/2, the 50%circular error probability (CEP) and the 95% radius (R95),calculated as the value εp that satisfies the P (Ed < εp) = p,p = {0.5, 0.95}, respectively. As one can see, the rangingaccuracy for the set of BSs varies from 7.72 m to 21.50 mRMS for the TNR estimator, and from 4.80 m to 18.98 m RMSfor the EKAT estimator.

Fig. 10 shows the positioning results for the different TOAestimation methods. The marker colour indicates the numberof received BSs. For benchmarking and performance tests,the positioning errors were calculated by exploiting the LRPground truth pLPR, as Ep = ‖p − pLPR‖. Fig. 11 shows thecorresponding positioning error cumulative density functionP (Ep < ε) for the two TOA estimation methods employed.Performance figures similar to those of the ranging results

704.440 704.460 704.480 704.500

231.200

231.220

231.240

231.260 CEP=8.97m

R95=18.50mRMS=11.50m

X-coord. CH1903 (Grid 1km)

Y-coord.CH1903(G

rid1km)

LRP groundtruth

N(t)≤3

N(t)=4

N(t)≥5

(a)

704.440 704.460 704.480 704.500

231.200

231.220

231.240

231.260 CEP=7.69m

R95=17.13mRMS=9.61m

X-coord. CH1903 (Grid 1km)

Y-coord.CH1903(G

rid1km)

LRP groundtruth

N(t)≤3

N(t)=4

N(t)≥5

(b)

Fig. 10. Indoor positioning results achieved with the ranges evaluated throughthe TNR (a) and the EKAT (b) algorithms. The black solid line represents thelaser ground truth.

were evaluated for the positioning error Ep , namely the RMS,the 50% CEP, and the R95.

As one can see from Fig. 10, both TOA estimation methodsobtain an RMS below 12 m. This is an impressive performanceresult, bearing in mind the fact that the LTE signals usedhave 15 MHz and 20 MHz bandwidth and are transmitted fromoutside the building, while usually TOA based indoor rangingsystems use ultra-wideband signals (with a bandwidth of upto hundreds of MHz) transmitted from indoor anchor points.

Looking in more detail, the region where both the TOAestimation methods give poor positioning fixes is the first partof the route, located outdoors, which is highlighted with an


0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

ε [m]

P(|E p

|<ε)

EKAT

TNR

CEP

R95

RMS

Fig. 11. Indoor positioning error statistics achieved with the ranges evaluatedthrough the TNR and the EKAT algorithms.

orange ellipse in the plots of Fig. 10a and Fig. 10b. This partof the route is in front of the entrance of the HSR building,below the ground level, and surrounded by massive concretefacilities, as Fig. 2b depicts. Hence, it is likely that in thisposition, some of the LOS paths coming from the received BSsare completely obstructed, leading to biased range estimationsand consequently to erroneous position fixes.

The TNR method achieves an RMS of 11.5 m, a 50%CEP of 8.67 m, and a R95 of 18.5 m, which is a creditableperformance since the ranges are obtained with a simplethreshold crossing algorithm in mainly NLOS conditions. Theworst errors are obtained in the south eastern corner of thebuilding, as highlighted by the green ellipse of Fig. 10a, andare probably due to the low SNRs and low number of BSsvisible in this locality.

The EKAT method achieves slightly better figures, with anRMS of 9.61 m, a 50% CEP of 7.69 m, an R95 of 17.13 m,and an overall smoother behaviour, probably due to the track-ing performed both in the pseudorange and in the positionsdomains. The EKAT position fixes result in a maximum errorof approximately 20 m, and an estimated receiver trajectorywhich is clearly visible and always inside the building.

VII. CONCLUSION

In the difficult indoor test environment (where there wereno GNSS signals) it was found that LTE signals from a totalof 3 to 5 base stations could be received, from three serviceproviders - sufficient to be able to perform a position fix by tri-lateration. A combination of LTE CRS symbol measurementswas used to improve the estimates of the pseudoranges fromthe receiver to each base station; across the width of the LTEfrequency channel (15-20MHz), over an extended time period(10 LTE slots, corresponding to the typical slow movementwhen indoors), and for the multiple (2-3) sector signals ofthe same base station. The EKAT algorithm using SRAs wasfound to be quite accurate, robust and smooth indoors, whilethe TNR algorithm using a threshold does not perform aswell in the most difficult environments, but is simpler. Usingthe combination techniques and either TOA estimators theexperiments showed a 2D horizontal positioning performance

of around 8m 50% CEP once moving through the test building,using just these LTE signals.

Future work should consider improved dynamic models fortracking the movement of the device, and should tackle someof the typical problems of realistic applications, such as theextension of the positioning trilateration algorithms to includealso the estimation of the local clock time and drift.

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