Particle Filter Based Positioning with 3GPP-LTE in

Indoor Environments

Christian Gentner, Estefanfa Munoz, Mohammed Khider, Emanuel Staudinger, Stephan Sand and Armin Dammann

Gennan Aerospace Center (DLR) Institute of Communications and Navigation Oberpfaffenhofen, 82234 Wessling, Gennany

Email: {Christian.Gentner, Estefania.MunozDiaz-Ropero, Mohammed. Khider, Emanuel.Staudinger, Stephan.Sand, Annin.Dammann} @dlr.de

Abstract-Global navigation satellite systems (GNSSs) can deliver very good position estimates under optimum conditions. However, especially in urban and indoor scenarios with severe multipath propagation and blocking of satellites by buildings the accuracy loss can be very large. Often, a position with GNSS is impossible in these scenarios. On the other hand, cellular wireless communication systems such as the third generation partnership project (3GPP) long-term evolution (LTE) provide excellent coverage in urban and most indoor environments. Thus, this paper researches timing based positioning algorithms, in this case time difference of arrival (TDoA), using 3GPP-LTE measurements. Several approaches and algorithms exist to solve the navigation equation for cellular systems, for instance Bayes filtering methods such as Kalman or particle filter. This paper specifically considers and develops a particle filter for 3GPP-LTE TDoA positioning. To obtain better positioning results, a 3GPP­LTE TDoA error model is derived. This error model is afterwards included in the likelihood function of the particle filter. The last part of this paper, evaluates the positioning performances of the developed particle filter in an indoor scenario. These evaluations show clearly the possibility of using 3GPP-LTE measurements for indoor positioning.

I. INTRODUCTION

Services and applications based on accurate knowledge of the mobile terminal (MT) location play a fundamental role in current and future wireless communications systems. In addition, the United States Federal Communications Commis­sion (FCC) has stated accuracy requirements on the location determination process of enhanced 911 (E-911) emergency callers. Global navigation satellites systems (GNSSs) based positioning provides a sufficient accuracy in rural and subur­ban environments, where a sufficient number of satellites are visible in line-of-sight conditions. However, in GNSS critical environments, such as urban canyon or even indoors, view to sky is limited. In these environments, low signal power, bad satellite constellations, severe multipath and non-line-of­sight (NLoS) propagation cause erroneous and biased position estimates. Especially in these environments, cellular wireless communication systems provide good coverage and can be used for position determination of the MT. Mobile radio communications systems like GSM, UMTS or the currently deployed third generation partnership project (3GPP) long­tenn evolution (LTE) primarily target on optimizing commu­nication perfonnance figures such as bandwidth efficiency or

978-1-4673-0387-3/12/$31.00 ©2012 IEEE 301

data throughput. Availability, signal strength or even signal bandwidths, however, make them interesting for positioning.

Hence, this paper shows an indoor positioning approach with the 3GPP-LTE mobile communication standard, which is currently deployed in many countries. Moreover, it shows the benefit of using the 3GPP-LTE mobile communication system for indoor positioning. Therefore, this paper describes a novel real-time mobile radio based positioning system using time difference of arrival (TDoA) measurements. The system consists of four transmitters and one receiver, which estimates the TDoA values. The experimental setup and its system parameters are briefly discussed in Section II. Several ap­proaches and algorithms exist to solve the navigation equation for cellular systems, especially Bayes filtering methods such as Kalman or particle filtering [1]. Section ill describes briefly the particle filter (PF), which is used in this paper, and its interface to the 3GPP-LTE system. In indoor environments, the TDoA measurements are corrupted by different kind of error sources, such as multipath, NLoS and fading errors. Different error models exist, to deal with these kind of error sources, however these models do not fit to the 3GPP-LTE system, e.g., different carrier frequency, different bandwidth. Therefore, to obtain better positioning results, Section N derives an error model for 3GPP-LTE, which is used in the likelihood function of the PE Afterwards, algorithms and error model derived in this paper are evaluated in Section V. For this, a measurement campaign was carried out with DLR's positioning system. This measurement campaign considers an indoor scenario, were the transmitters are located outdoors and the MT is moving in an office building. These evaluations show clearly the possibility and the advantages of using 3GPP-LTE measurements for indoor positioning.

II. EXPERIMENTAL SYSTEM SETUP AND PARAMETERS

In this section we briefly summarize the system parame­ters and the general setup for the positioning measurements. Fig. I shows an overview of the positioning system, which is designed as a 3GPP-LTE positioning system. The sys­tem consists of four generic transmitters, realized in two FPGA boards [2]. The downlink of 3GPP-LTE is based on orthogonal frequency division multiplexing (OFDM), which allows a spectral efficient and flexible usage of the available

Fig. I. Overview of the positioning system. The system consists of four generic transmitters, realized in two FPGA boards and a receiver system. The receiver samples the received radio signals and estimates the TDoA values which are processed in a PF to get a position estimate.

frequency spectrum. The 3GPP-LTE standard specifies signal parts, dedicated to time and frequency synchronization. Both, the so-called primary synchronization signal (PSS) and the secondary synchronization signal (SSS) are OFDM symbols within the 3GPP-LTE downlink frame. For our investigations we use these synchronization signals together with scattered pilots, which are originally dedicated to channel estimation, for signal propagation delay based 2D position estimation.

The four transmitters, transmit periodically the predefined 3GPP-LTE synchronization signals at a center frequency of 2.45 GHz. The radio frequency (RF) front-end is comprised of commercial-off-the-shelf mixers, filters, amplifiers, and omni-directional antennas. At the receiver side, the system consists of a commercial off-the-shelf RF front-end for the 2.4 GHz frequency band. Variable low noise amplifiers, mixer, baseband amplifiers etc. are fully integrated into a single platform. The output is an analog complex signal which is directly fed to the baseband receiver's analog to digital converter inputs. The baseband receiver basically consists of a modem workstation with a PCI Express FPGA prototyping development board using a custom hardware design. This system enables complex baseband sampling up to 40 MHz for the received analog complex signal, which can be processed directly on the workstation with, e.g., MATLAB routines. For a more detailed description of the 3GPP-LTE positioning system, see [2], [3]. Tab. I shows the main system parameters for DLR's positioning system [2]. Note, that the subcarrier spacing here is approximately 19 kHz compared to 15 kHz as defined in 3GPP-LTE [4]. Thus, the PSSs and the SSSs occupy around 1.4 MHz instead of 1 MHz. We use the scattered pilot structure as defined in 3GPP-LTE, where each transmitter uses a different initialization for the random sequence generator. The pilots of different transmitters are therefore orthogonal in frequency, due to different subcarrier mapping, and in time. A typical 3GPP-LTE communication receiver does an initial timing synchronization and carrier frequency offset (CFO) estimation with the PSSs and SSSs. The estimation and tracking of the channel and timings can be done by using the scattered pilot structure. For positioning purposes, the timing synchronization used for communication is not suf-

302

TABLE I SYSTEM PARAMETERS OF THE POSITIONING SYSTEM

Parameter type

OFDM core symbol length

Cyclic prefix length

Sampling frequency

Subcarrier spacing f sc

Pilot subcarrier spacing of each transmitter

Pilot subcarrier spacing between transmitters

Value

1024 samples

144 samples

20 MHz

19.53 kHz

16 subcarriers

4 subcarriers

ficient, because the plateau-like correlation results from guard interval detection [5]. Thus, we developed a new algorithm for initial access and synchronization [5]. In the first step, the receiver algorithms estimate the CFO. The scattered pilots are very sensitive to CFO due to the destroyed orthogonality of subcarriers. For more information about the CFO estimation and correction, we refer to [5]. After estimating and correcting the CFO, the data is processed by the TDoA estimation algorithm consisting of two steps. First, the receiver correlates the received signal with the PSS of each transmitter and detects the maximum peak of the correlator output. Based on this rough synchronization and the knowledge of the 3GPP-LTE framing, the position of the OFDM symbol with the pilots can be roughly estimated. Thus, the second step performs a fine timing synchronization with the wideband pilot symbols. This algorithm searches first for the maximum correlation peak and afterwards tries to detect a correlation peak before the maximum peak with at threshold of 8 dB below the maximum peak, see also [6]. These time of arrival estimations are done for all transmitters. Afterwards, the TDoA between transmitter i and j, is estimated by

TDoAi,j = ( ToAi - TOAj ) , (I)

where ToAb is the arriving time of the measured first peak for the transmitter b E {i, j}. However, the 20 MHz bandwidth limits the rough synchronization and allows only a sample based estimation within 15 meters, which hinders accurate positioning in indoor environments. The error can be reduced further significantly by oversampling the received data. The estimated TDoAs are then processed by a positioning estima­tion algorithm, in this paper by a PF, as indicated in Fig. I. In the next section this PF and the TDoA interface are explained in detail.

III. PARTICLE F ILTER Despite the enormous amount of research in the area of

indoor and urban canyons pedestrian navigation, achieving the required positioning accuracy and availability is still a challenge. Among the different approaches suggested in the literature to address this challenge, multi-sensor navigation has shown promising results in improving the accuracy, availability and reliability of estimates. Heterogeneous and noisy sensors measurements, in addition to the dynamic estimation prob­lem, make sequential Bayesian filtering the appropriate sen­sor fusion technique. Moreover, non-linear and non-Gaussian pedestrian movement models in building environments and

sensor measurement models resulted in adopting a PF in this work. Sequential importance sampling algorithm forms the basis of most PF implementations and it consists of recursive propagation of the states and their associated weights as each measurement arrives. Several flavors of PFs have been developed over the last few years. They differ in their choice of the importance sampling density and the resampling step. A Sequential Importance Resampling Particle Filter (SIR-PF) is implemented in this work. In SIR-PF, the importance density is chosen to be the transitional prior and resampling is performed every time step [7]. A pseudocode of a SIR-PF iteration is shown in Algorithm I. From Algorithm I, we can see that

Algorithm 1: SIR-PF Input:

States vector at time k - 1: {4-d�1 Measurement at time k: Zk Output:

States vector at time k: {XD�l for i = 1 : Ns do

l Draw 4 '" p(xkI4-1); Calculate wk = p(zklxk);

Calculate total weight: t = SUM[{wn�ll; for i = 1 : Ns do

L Normalize: wk = c1wk;

Resample: obtaining {xL wL - } �l using Algorithm 2 in [7]

two models have to be implemented for the SIR-PF in order to be used: a state transition model calculating the transitional prior p(xkI4_1) and the measurement model calculating the likelihood p(zkI4). These two models represent the two major blocks of any sequential Bayesian filter implementation. Their careful design leads to an efficient and accurate implemented filter. The transition and measurement models incorporated in this work is discussed in the following:

• State transition model

The user position vector Xk and the user orientation vector are the selected states to be propagated and es­timated by the SIR-PF. An appropriate pedestrian move­ment model that is capable of probabilistic ally modeling pedestrian position and orientation in challenging indoor and urban canyon environments [8], [9] is used as a transition model for the SIR-PF. A SIR-PF new time instance involves first drawing a new sample from the movement model for each particle's state Xk given the previous one Xk-l. Predicted particles positions have to be converted into predicted TDoAs since the arriving measurements are TDoAs. Using the prior knowledge of the 3GPP-LTE transmitter positions, and the reference transmitters, the different predicted TDoAs can be calculated for each particle.

303

TDoA Measurement

PVT

Fig. 2. Block diagram illustrating the implemented SIR-PF. The transition model is used to propagate the particles states over time. As a TDoA measurement arrives, it will be used to build a likelihood and applying weights on the particles. The likelihood rewards particles upon their consistency with the measurement. The output of the PF is the position, velocity and time (PVT).

• Measurement model

The 3GPP-LTE TDoA measurement is used by the mea­surement model to build the likelihood function that weights each particle. Particles that are more consistent with the arriving measurements are weighted higher than others. Low weighted particles will eventually be dis­carded due to resampling. We have selected a linear and Gaussian measurement model resulting in a likelihood function of the form:

p( zk IxU = N (T DoA� ; T DoAm, O'TDOA ) , (2)

where N (x; /1, 0') represents the probability density func­tion (pdf) of a normally distributed random variable at x with mean /1 and standard deviation 0'. Here, T DoA� is the predicted TDoA for particle i, T DoAm is the measured TDoA and O'TDoA is the standard deviation reflecting the accuracy of the TDoA measurements. This standard deviation O'TDoA is modeled in Section IV. Hence, the weight wk of particle i at time k is calculated using the Gaussian function in (2).

Fig. 2 shows a block diagram illustrating the implemented SIR-PF. As shown in this figure, the transition model is used to propagate the particles states over time. As a TDoA mea­surement arrives, it will be used to build a likelihood and to apply weights on the particles. The likelihood rewards particles upon their consistency with the measurement. minimum mean square error (MMSE) position and orientation estimates are calculated and visualized on the map of the area at each time step.

IV. TDoA ERROR MODEL S

As mentioned in the Introduction and in Section III, the TDoA errors of the 3GPP-LTE system have to be analyzed and considered in the PF, to obtain better positioning results. Several models are already available in the literature, e.g. [6], however these models do not fit to the 3GPP-LTE system, e.g., different carrier frequency, different bandwidth. Therefore, this section describes a measurement analysis to obtain a better

TDoA error model for 3GPP-LTE. This paper focuses on evaluating the TDoA error for an indoor scenario, were we have usually NLoS propagation. In these scenarios, the TDoA errors might be caused by NLoS propagations, multipath effects, limited bandwidth, SNR, and/or the synchronization strategies of the 3GPP-LTE system. In this paper we focus on the TDoA errors as a result of NLoS effect defined as the difference between the first detected path and the geometrical line-of-sight (GLoS) path. As mentioned in Section II, the TDoA errors are estimated for a correlation based first peak de­tection algorithm. Here, the incoming signal is correlated with the synchronization and pilot sequences. First, the algorithm searches for the maximum correlation peak and afterwards tries to detect a correlation peak before the maximum peak with a threshold of 8 dB below the maximum peak, see also [6]. Higher resolutions can be achieved by superresolution algorithms which are not used in this paper but considered in future research.

From (I), the TDoA error CIDoAi,j of the first peak detection between transmitter i and j is defined by

(ToAi - ToAj) - TDoA��jal (ToAi - ToAj) - (ToA?LOS - TOAJLOS)

CIDoAi,j

(3) where TDoA��jal is the ideal TDoA value, ToA�LOS is the arriving time of the GLoS, cToAb is the error of the first peak detection of transmitter b E {i, j}. Thus, the TDoA error CIDoA· . is obtained by subtracting two different ToA errors cToAb '�ith b E {i, j}.

To obtain CIDoA· . , a measurement campaign was analyzed, which was perfo�ed in September 2010 at the Institute of Communications and Navigation of the German Aerospace Center in Oberpfaffenhofen, close to Munich (10). Originally, these measurements were done to study the statistical char­acteristics of the NLoS bias based on a dynamic broadband channel sounder measurement campaign in an outdoor-to­indoor scenario,. Fig. 3 shows the measurement scenario. The transmit antenna was positioned at four different locations referred in Fig. 3 as T1, T2, T3 and T4 on the rooftop of the building TE02, 12m above ground. The transmitter emitted a signal with 90 MHz bandwidth and center frequency of 2.45 GHz (S-band). The channel sounder recorded the channel impulse response (CIR). Transmitter and receiver clocks were synchronized by cable connection. The receiver antenna was located on the ground floor inside building TEO! and was mounted on a model train as described in [10], moving with a speed of about 0.05m1s along the track marked with an arrow in Fig. 3. However, these measurements are not directly valid for 3GPP-LTE and the positioning system. To adapt the pre­viously mentioned signal to a 3GPP-LTE signal, as described in Section II, we applied the following modifications:

• Bandwidth reduction

The signal bandwidth was reduced from 90 MHz to 20 MHz which is used in the 3GPP-LTE system.

• 3GPP-LTE specific parameters

3GPP-LTE positioning system specific parameters have to

304

Building TEOl Building TE02

T,

15m

20m T,

15m

OT,

15m

T,

Fig. 3. Visualization of the scenario of the measurements campaign. The transmit antenna was positioned on the rooftop of building TE02 at four different locations and the receiver was mounted on a train on the ground floor of building TEOI indicated by the red arrow.

be added to the signal. This includes the synchronization symbols as defined in Section II, as well as characteris­tics of the front-end, e.g., nonlinearities of the receiver front-end. Thus, to obtain the CIR including the 3GPP­LTE specific parameters of the front-end, 30 frames are captured and averaged coherently.

The new channel frequency response (CFR) is defined as

where Hcs(f) denotes the measured CFR of the channel sounder with a bandwidth of 90 MHz, HLP(f) represents the low-pass filter in frequency domain with a bandwidth of 20 MHz and HLTE(f) is the coherent averaged captured 3GPP-LTE signal including front-end specific parameters in the frequency domain. By this adaptation, the measurement campaign and its results could be reused without performing a new measurement campaign. The obtained signals are ana­lyzed according to the receiver specifications as described in Section II.

To evaluate the CIDoAi,j' two different TDoAs are consid­ered, TDoA1,3 between transmitter TI and T3, and TDoA2,4 between transmitter T2 and T4. Fig. 4 shows the obtained TDoA1,3 values for the whole track. The red line indicates the ideal TDoA. Fig. 4 shows also some outliers, which have an additional delay of 40m. These delays are caused by reflections between the building TEOI, where the receiving antenna is located and the building TE02, where the transmit antenna is located. Thus, the TDoA estimation algorithm detects a reflected path as first arriving path.

The TDoA errors, are calculated according to (3). To model the TDoA error, first the spatial correlation between the TDoA errors for each time step of the moving receiver is analyzed. A certain spatial correlation could be expected as reflecting objects such as walls, will remain in their positions . However, due to the interaction of different reflected waves

-40

-50

-60�----------�----------�--------� o 10 15

dislance 1m]

Fig. 4. TDoA estimations versus the traveled distance for the transmitter pair Tl and T3. The blue line indicates the measured TDoA values and the red line indicates the true ideal TDoA.

0.9

0.8

0.7 I Q) 0.6 I g .� 0.5 � u 0.4 �--------------------------------�

0.3

o�----�------�----��----�----� o 0.1 0.2 0.3 0.4 0.5

dislance 1m]

Fig. 5. The normalized spatial covariance function of €TDoAI 3 in blue and €TDoA24 in red. The decorrelation level of e-1 = 0.3679 is indicated by the magenia line.

and correlation properties, a small change in receiver position might degrade the spatial error covariance. Fig. 5 shows the normalized spatial correlation for both TDoA errors, tIDoAI 3

in blue and tIDoA24 in red. This figure shows in both cases 'a fast decaying covariance function. Considering a decorrelation level of e-1

= 0.3679, indicated by the magenta line in Fig, 5, the obtained decorrelation distances for both TDoAs is 0.012m. Thus, changing the position of the receiver produces uncorrelated TDoA errors.

The distribution of the TDoA errors is shown in Fig, 6, which shows similarity with the Gaussian distribution, but also a larger tail than a typical Gaussian distribution. One way to model a non-Gaussian pdf is using a Gaussian mixture model (GMM), A GMM of order K (GMM(K» is defined as the

305

0.1 _TDoAerror

0.09 TOeA error - Gaussian

0.08

0.07

� 0.06

� 0.05 e "- 0.04

0.03

0.02

0.01

o TDoA error 1m]

Fig. 6. Distribution of the TDoA error in blue. The red line indicates the single Gaussian model and the green line the Gaussian mixture model, GMM(2).

TABLE II STATISTICAL PARAMETERS OF THE GAUSSIAN TDoA ERROR MODEL

JL[m] (T[m] skewness kurtosis kstest -0.6530 8.8688 5.8217 0.2381

sum of weighted Gaussian distributions with K K

f(x) = LPkN (l1k,(Jk) with LPk = 1, (5) k=l k=l

where N (11k> (Jk) represents a Gaussian distribution with mean 11k and standard deviation (Jk, weighted by Pk for k = 1, ... , K, In general, a GMM can asymptotically represent an arbitrary shaped pdf. To construct a Gaussian mixture model, we used the Akaike information criterion (AIC) and Bayesian information criterion (BIC) to define the number of necessary Gaussians [11], Both criteria show, that either a single Gaussian or a Gaussian mixture of two should be used for this modeL Thus, this paper uses the single Gaussian distribution with the parameters shown in Table II and indicated in Fig. 6 by the red line, Table II lists the mean 11 and the standard deviation (J in meters for the Gaussian distribution, Additionally, the kurtosis, skewness and the kstest of the TDoA error indicate that a single Gaussian distribution fits almost perfectly, The following evaluations uses this single Gaussian distribution TDoA error modeL Thus, the standard deviation (JTDoA of the likelihood function of the PF is set to 8.8688m.

V. INDOOR MEASUREMENTS AND PERFORMANCE

ANALYSIS

This section demonstrates and evaluates the TDoA 3GPP­LTE positioning with the PF. For this, a measurement cam­paign was carried out at the Institute of Communications and Navigation of DLR explained in detail in Section V-A. The evaluations are described afterwards in Section V-B.

Receive antenna

Fig. 7. Model train used as mobile platform. The receiving antenna is mounted on an experimental platform.

A. Measurement Setup For evaluating the obtained algorithms and the hardware

setup, we perfonned a measurement campaign for an outdoor to indoor scenario. We used for these measurements the setup as described in Section II and shown in Fig. I. Fig. 8 shows an overview of the measurement site at the DLR's Institute of Communications and Navigation. The building can be characterized as standard three-storey office building of concrete with metallized window glass. In this scenario, the transmitters were located outside of the building. The transmitters T 1 and T 2, as well as T 3 and T 4 are pairwise synchronized. The distances between the transmitters T 1 and T2 are 21.2m and 23.6m between T3 and T4. Each of the transmitters was transmitting with a power of 750 m W. Hence, the measurement scenario actually relates to a femto-cell setup. Inside the building, the receiving antenna was mounted on a experimental platfonn with a model train, as shown in Fig. 7. The model train runs on a pre-measured track as indicated in Fig. 8 by the blue line through the office building with a length of 37m and a speed of 0.16m/s. To obtain the traveled distance and thus the position of the train, the train uses a rotary encoder which counts the number of motor turns and generates 500 impulses per motor turn. Therefore, it is possible to calculate the traveled distance and thus the exact position of the train. To prevent wheel slipping the model train is driven by a cogwheel.

The transmitters are continuously transmitting the reference signals as described in Section II. On the receiver side, the signals were captured and stored and the processing was done afterwards. However, in this scenario, we captured the signals

306

'3

-Track o Base stations )( Track markers

°oL--��--�' O--�'�5--�20��2�5 ==�30==��· xlml

Fig. 8. Visualization of the measured scenario. The transmit antennas T 1 -T 4 are located outside of the office building. The receiving antenna was mounted on a model train, which runs along the track indicated by the blue line through the office building.

40 ir===�==�==��--�--�----�"� -- TOOA , ,2

30 -- TOoA3,4 _ TDoA1,2 - ideal

20 - TDoA3,4 - ideal

I 10 '" .3 >-

-10

-20

_30 L---�----�--�----�--�----�--L-� o 10 15 20 25 30 35

distance 1m)

Fig, 9. TDoA estimate versus the traveled distance. The red lines indicate the TDoA estimate of the transmit antennas T 1 and T 2, whereas the blue lines indicate the TDoA estimate of the transmit antennas T 3 and T 4. In both cases the bold line indicates the true theoretical TDoA, The dashed lines correspond to the markers in Fig. 8 and represent the change of the rooms.

of the transmitter pairs independently. Thus, the train was running two times and either the transmitter pair T 1 and T 2 or T 3 and T 4 was transmitting. At the same time, we captured the time stamp and the rotary encoder value, therefore it was possible to fuse the two different measurements.

B. Indoor Navigation Performance Analysis To estimate the TDoA values, we used the algorithm as

mentioned in Section II. Fig. 9 shows the obtained TDoA values with respect to the traveled distance for both pairwise synchronized transmitters. The pair T 1 - T 2 is represented by the blue line, whereas the pair T 3 - T 4 is represented in red. In both cases, the bold lines indicate the ideal TDoA values, whereas the thin lines indicate the obtained TDoA measure-

70 60

I 50 w (/) ri 40

30

10 15 20 distance [m]

Fig. 10. RMSE versus the traveled distance for the positioning estimation with static least squares position estimation in black and with dynamic PF position estimation in blue with an unknown initial position. The dashed lines correspond to the markers in Fig. 8 and represent the change of the rooms.

ments. The TDoA estimations show, that the measured TDoA values are in general noisy and are sometimes biased, e.g., TDoAI 2 between 15 and 24 meters. Even if the measurements are noi�y, e.g., between 5m and 15m the average error is below one meter for both TDoAs. Fig. 8 shows three marks along the track. These marks and also the dashed lines in Fig. 9 represent the change of the rooms. Therefore, until 4m the train is in the initial office, from 4m to 21m in the corridor, from 21m to 33m in the comer office and from 33m until the end of the track in the last office.

Caused by the noisy TDoA measurements, we expect that a tracking filter gives better positioning performance than a static solution. Thus, we compare in the following a least squares (LS) position estimation algorithm [12] to the PF implementation as mentioned in Section III. In the further evaluations, the PF is initialized with 8000 particles and the results were averaged by 50 runs. Fig. 10 shows the root mean square error (RMSE) of the LS position estimation algorithm compared to the PF position estimate. The mean RMSE between the static positioning solution of the LS algorithm and the PF can be decreased by more than 50 %, from 13.51m to 5.35m. Both positioning approaches use the single Gaussian TDoA error model as derived in Section IV with the standard deviation of O"lDoA = 8.8688m. Fig. 10 shows that at the beginning the RMSE of the PF is up to 14m. This is due to the the high TDoA biases in both TDoA measurements as can be seen in Fig. 9. Additionally, the initial position of the user is not known, thus, the particles are spread over the whole area in the initialization. Afterwards, gradually the error decreases and reaches the lowest value when the train is in the comer office. At this point all transmitters are LoS, which can be seen also in Fig. 8. Both TDoAs are biased when the train moves in the final office, thus the positioning error increases again.

To decrease the RMSE at the beginning, we spread the

307

14 "-"'---;==::::::=:'===========J -- PFLTE

12

10

I 8 w (/) ::;; a: 6

4

-- PF LTE, knowlege: initial position -- PF LTE. knowlege: initial position, outer walls

10

I I

15 20 25 distance [m]

35

Fig. I I. RMSE versus the traveled distance for the positioning estimation with the PF. The blue line shows the RMSE of the PF with an unknown starting position, the red line shows the RMSE of the PF with the a known starting position and the green line shows the RMSE of the PF with a known starting position and building layout information. The dashed lines correspond to the markers in Fig. 8 and represent the change of the rooms.

particles at the initialization within a circle with a radius of 1m around the correct starting position. By the knowledge of the starting position, the mean RMSE can be decreased to 4.23m, as indicated by the red line in Fig. I I, which shows the RMSE versus the traveled distance. Furthermore, by the knowledge of the building layout information such as outer walls of the building, the mean RMSE decreases again to 3.38m. This is also shown in Fig. 11 by the green line. Especially the knowledge of the outer walls helps in this scenario at the end of the track, because the particles are forced to stay inside the building. For comparison reason, Fig. I I shows also the PF position estimation without the knowledge of the starting position in blue, which was also shown in Fig. 10.

Fig. 12 visualizes as an example the MMSE positioning estimation of the PF, with the knowledge of the starting position and the outer walls. The blue line in this figure represents the true path and the green line represents the estimated path of the PF.

Fig. 13 shows the cumulative distribution functions. The blue line represents the PF position estimation with unknown initial position, the red line represents the PF position estima­tion with a known starting position, the green line represents PF position estimation with additionally the knowledge of the outer walls of the building. As mentioned before, with the knowledge of an accurate initial positioning and the knowledge of the outer walls, we obtain the best positioning performance. Thus, in 90 percent of the cases, we obtain a mean positioning error smaller than 4. However, also without these knowledge, we obtain very good positioning performances for indoor navigation, which fulfil the FCC requirements.

VI. CONCL USION

This paper studies and implements a positioning approach using the new cellular wireless communication systems,

13

OT20T3 --Truelrack -- Estimated track o Base stations °oL---�----�10---- �1 5�--�2�O--==2�5====3�O==� 36

xlm)

Fig. 12. Visualization of the measured scenario. The positioning estimation with the PF represented in green versus the true path represented in blue.

0.1

10 positioning error [mJ

15 20

Fig. 13. Cumulative distribution function for LTE positioning in blue, LTE positioning with known initial position in red and LTE positioning with known initial position and building layout information in green.

3GPP-LTE. The paper shows that stable positioning is possible with PF and 3GPP-LTE. To obtain better positioning results, a 3GPP-LTE TDoA error model is derived and included in the likelihood function of the PF. The last part of this paper, evaluates the positioning performances of the developed PF in an indoor scenario. This evaluations show clearly the possibil­ity of using 3GPP-LTE measurements for indoor positioning where we obtain a mean RMSE of 5.35m. Additionally, it shows the advantages of the knowledge of an accurate initial position and the knowledge of outer walls or floor plans, where the mean RMSE is decreased by 2m.

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