Positioning Performance of LTE Signals in RicianFading Environments Exploiting Antenna Motion

Kimia Shamaei, Joshua J. Morales, and Zaher M. KassasUniversity of California, Riverside

BIOGRAPHIES

Kimia Shamaei is a Ph.D. candidate at the University of California, Riverside and a member of the AutonomousSystems Perception, Intelligence, and Navigation (ASPIN) Laboratory. She received her B.S. and M.S. in ElectricalEngineering from the University of Tehran. Her current research interests include analysis and modeling of signalsof opportunity and software-defined radio.

Joshua J. Morales is a Ph.D. candidate at the University of California, Riverside and a member of the ASPINLaboratory. He received a B.S. in Electrical Engineering with High Honors from the University of California,Riverside. His research interests include estimation, navigation, autonomous vehicles, and intelligent transportationsystems.

Zaher (Zak) M. Kassas is an assistant professor at the University of California, Riverside and director of the AS-PIN Laboratory. He received a B.E. in Electrical Engineering from the Lebanese American University, an M.S. inElectrical and Computer Engineering from The Ohio State University, and an M.S.E. in Aerospace Engineering anda Ph.D. in Electrical and Computer Engineering from The University of Texas at Austin. In 2018, he received theNational Science Foundation (NSF) Faculty Early Career Development Program (CAREER) award. His researchinterests include cyber-physical systems, estimation theory, navigation systems, autonomous vehicles, and intelligenttransportation systems.

ABSTRACT

A navigation framework based on a multi-state constraint Kalman filter (MSCKF) is proposed to reduce the effectof time-correlated pseudorange measurement noise of cellular long-term evolution (LTE) signals. The proposedMSCKF navigation framework uses a tightly-coupled inertial navigation system (INS) aided by pseudoranges tomultiple eNodeBs to estimate the position of the receiver along with the difference of the clock bias of the receiverand each of the eNodeBs. Simulation results with a Rician fading channel multipath environment are presentedshowing a reduction of 44.31% in the two-dimensional (2D) position root mean squared-error (RMSE) using theproposed approach compared to an extended Kalman filter (EKF) approach. Experimental results on a groundvehicle navigating in an urban environment are presented showing a 2D RMSE of 6.05 m over a trajectory of 1380m using the proposed approach. The results show a reduction of 48% in the 2D position RMSE and 50% in the 3Dposition RMSE using the proposed framework compared to an EKF.

I. INTRODUCTION

Traditional approaches to overcome global positioning satellite system (GNSS) limitations focused on fusing GNSSreceivers with sensors (e.g., gyroscope, accelerometer, compass, barometer, lidar, camera, etc.). Recent approachesaimed at exploiting ambient signals of opportunity (SOPs). SOPs are radio frequency (RF) signals which are notdesigned for navigation purposes, but are freely available and may be exploited for navigation and timing when GNSSsignals become unusable [1–4]. Examples of SOPs are: (1) AM/FM radio [5,6], (2) digital television (DTV) [7,8], (3)wireless local area network (WLAN or Wi-Fi) [9, 10], and (4) cellular signals [11–16]. Cellular long-term evolution(LTE) signals are particularly attractive for navigation in deep urban canyons due to their desirable characteristics:abundance, large transmission bandwidth, high received power, frequency diversity, and geometric favorability oftransmitter locations [17].

The literature on exploiting LTE signals for navigation have analyzed the achievable navigation accuracy withdifferent types of LTE reference signals [18–20]. The navigation solution obtained from LTE signals was also evaluated

Copyright c© 2018 by K. Shamaei, J. Morales,and Z. M. Kassas

Preprint of the 2018 ION GNSS ConferenceMiami, FL, September 24–28, 2018

experimentally [21, 22]. Several software-defined receivers (SDRs) have been proposed to track LTE signals, whichhave shown meter-level accuracy [12, 23, 24]. The effect of multipath on the achievable pseudorange accuracy havealso been studied for different LTE reference signals and it was shown that the pseudorange error is reduced forsignals with higher transmission bandwidth [25, 26].

Multipath is among the most significant challenges that must be addressed for RF-based navigation. Multipathintroduces error in the estimated pseudoranges, where the magnitude of the error depends on the multipath condition,signal bandwidth, and sampling rate. The high transmission bandwidth of LTE signals (up to 20 MHz) could beused to resolve multipath. However, received LTE signals experience more multipath compared to GNSS signals,particularly for ground-based receivers in urban canyons, due to the low elevation angles at which signals are received.In a low dynamic environment, the multipath effect lasts over multiple epochs and the error due to multipath istime-correlated. Besides, the pseudorange error caused by multipath may affect multiple epochs due to the receiver’sloop filter.

Several signal processing-based methods have been proposed to remove the effect of multipath in GNSS signalsincluding a multipath-estimating delay-locked loop (MEDLL) [27], a batch filter to estimate the multipath usinga known antenna motion [28], and a technique to correct multipath errors using signal-to-noise ratio [29]. Theseapproaches have either high computational cost or they require prior knowledge of the multipath condition. Anotherapproach to reduce the effect of multipath is based on beamforming. Beamforming can be performed using anantenna array, which has a bulky structure. Alternatively, one can synthesize an antenna array by moving theantenna. In synthetic aperture navigation (SAN), the antenna movement can be uniform or arbitrary. In a uniformmovement, computationally low-cost approaches (e.g., multiple signal classification (MUSIC) or estimation of signalparameters via rotational invariance techniques (ESPRIT)) can be used to estimate the direction-of-arrival (DOA)[30,31], whereas computationally expensive algorithms (e.g., space-alternating generalized expectation-maximization(SAGE)) must be used to estimate the DOA in an arbitrary movement [32]. Uniform structures require a bulkyhardware platform, and the performance of arbitrary structures depends on the accuracy of the antenna location,which depends on the accuracy of the inertial measurement unit (IMU). It has been shown that the antenna motioncan also be used to decorrelate the error induced by multipath. Antenna motion was used in [33] to improve thedetection performance and in [34] to reduce the carrier-phase error in carrier-phase differential GNSS (CDGNSS)positioning, where a first-order Gauss-Markov process was used to model the relative antenna position with respectto the reference antenna.

In a Kalman filter, the measurement noise is assumed to be time-uncorrelated. A time-correlated measurementnoise will induce an error in the navigation solution estimate. Since the dynamics of the errors due to multipathis unknown, whitening approaches cannot be used to decorrelate the measurement noise. This paper addresses thischallenge by making two contributions. First, a navigation framework based on a multi-state constraint Kalmanfilter (MSCKF) is proposed. The MSCKF was first introduced in robotics literature [35]. In this framework, an IMUis used to capture the position of the antenna over a window of measurements. Unlike a traditional extended Kalmanfilter (EKF), which uses a single measurement epoch to update the state estimate, this paper employs an MSCKF touse a sliding window of measurement epochs along with the antenna motion to decorrelate the measurement noiseand provide constraints on the position estimate. Moreover, the difference of the clock bias of the receiver and eachof the LTE base stations (also known as evolved node Bs or eNodeBs) are estimated along with the position ofthe antenna since the eNodeBs’ clock biases are unknown to the receiver. Second, the results are evaluated withsimulations and experiments. There are several factors that characterize the behavior of a wireless channel e.g.,terrain features, relative speed of the transmitter and receiver, etc. Propagation mode including line-of-sight (LOS),reflections, diffractions, and scattering is among these factors to characterize a wireless channel. Two channel modelswere introduced to capture these factors namely Rician and Rayleigh fading channels [36]. A channel with LOS canbe modeled with a Rician fading, while a channel with no LOS can be modeled with a Raleigh fading. The simulationenvironment assumes the receiver to have access to the LOS signal and the channel is modeled as a Rician fadingchannel. The pseudorange errors are simulated assuming a time-correlated Rician channel. The trade-off betweenthe integration time and the achievable positioning accuracy is analyzed in the simulations. The experimental resultsshow a reduction of 48% in the 2-dimensional (2D) position root mean squared-error (RMSE) and a reduction of50% in the 3D position RMSE using the proposed approach compared to using a traditional EKF.

The remainder of this paper is organized as follows. Section II presents the proposed navigation framework, whichspecifies the state, propagation, and update models. Section III shows simulation results comparing the proposed

method with an EKF approach. Section IV presents experimental results. Section V concludes the paper.

II. NAVIGATION FRAMEWORK

This section presents the MSCKF-based navigation framework.

A. State Propagation and Augmentation

The MSCKF state vector comprises (1) IMU states, (2) clock error states, and (3) a history of the receiver’s pastposition and the difference of clock biases between the receiver and each of the eNodeBs. The IMU measurementsare fed to an inertial navigation system (INS) as they become available, which propagates the receiver’s positionstate. The clock error states are propagated at the same rate as the IMU states according to the standard modeldescribing the time evolution of the clock bias and drift (double integrator driven by noise) [37,38], which is composedof the clock bias and drift. Once LTE pseudorange measurements become available, the current receiver’s positionand the difference of clock biases of the receiver and each of the eNodeBs are appended to the state vector and thepseudorange measurements are appended to the measurement vector. After N measurements have been obtained,the EKF undergoes a measurement update using all N measurements to impose constraints between all N appendedreceiver positions from which the pseudorange measurements were obtained.

The vehicle’s state vector xr is defined as

xr ,[

xT

IMU , xT

clk , πT

1 , πT

2 , · · ·πT

N

]T

,

where xIMU represents the IMU state vector, xclk is the clock state vector, and πi is composed of the receiver’sposition and the difference between the clock bias of the receiver and each of the eNodeBs at the i-th pseudorangemeasurement.

The IMU state vector is given by

xIMU ,

[

IGq

T , GrT

IMU , GvT

IMU , bTg , bTa

]T

,

where IGq

T is the unit quaternion representing the rotation from a global frame G, such as an Earth-centered inertial

(ECI) frame, to the IMU frame I; GrT

IMU = [xIMU, yIMU, zIMU]T

and GvT

IMU = GrT

IMU are the 3D position andvelocity of the IMU in the global frame, respectively; and bTg and bTa are the gyroscope and accelerometer biases,respectively. Standard IMU state propagation model can be used to propagate the states of the IMU [38–41].

The clock bias state vector is defined as

xclk , [x(1)clk

T

, · · · , x(U)clk

T

]T

,

where U is the total number of eNodeBs; x(u)clk = [c∆δt(u), c∆δt(u)]; ∆δt(u) = δtr−δt

(u)s with δtr and δt

(u)s representing

the clock biases of the receiver and the u-th eNodeB, respectively; ∆δt(u) = δtr− δt(u)s with δtr and δt

(u)s representing

the clock drifts of the receiver and the u-th eNodeB, respectively.

The vector πi is defined as

πi ,

[

GrT

Ai, xci

T

]T

,

where GrAi= [xAi

, yAi, zAi

]Tand xci =

[

c∆δt(1)i , · · · , c∆δt

(U)i

]T

are antenna’s position in the global frame and

the difference between the clock bias of the receiver and each of the eNodeBs, respectively, at the i-th pseudorangemeasurement.

B. Measurement Update

Once N pseudorange measurement epochs are appended the measurement vector, an EKF measurement update isperformed. After each update, the states corresponding to the antenna’s position and the difference between theclock bias of the receiver and each of the eNodeBs corresponding to Nrem epochs are removed from the state vector.The pseudorange measurements corresponding to these states are also removed from the measurement vector andthe filter returns to the state propagation stage.

III. SIMULATION RESULTS

To evaluate the proposed framework, a simulation environment was developed comprising a receiver navigating inan urban area (downtown Riverside, California) over a 6 km trajectory that includes straight segments and turns.The locations of the eNodeBs were simulated using real eNodeBs’ locations in that environment. The simulationenvironment showing the receiver’s trajectory and the eNodeBs’ positions is shown in Fig. 1. The receiver’s andeNodeBs’ clocks were simulated with a temperature-compensated crystal oscillator (TCXO) and an oven-controlledcrystal oscillator (OCXO), respectively.

250 m0 m

Fig. 1. Simulated traversed trajectory and the positions of the LTE eNodeBs. Map data: Google Earth

The IMU’s rotational velocity and linear acceleration measurements were generated at T = 0.01 s. The IMU’smeasurement noise and time evolution of the IMU’s biases are determined by the grade of the IMU. In this work,data for a consumer-grade IMU was generated.

It is assumed that the LTE pseudoranges were estimated every LTE frame duration, which is Tsub = 10 ms. ARayleigh and a Rician fading model can be used to model the propagation mode of the wireless channel. In aRayleigh fading, it is assumed that the signal does not have LOS. While in the Rician fading channel, it is assumedthat the signal has LOS. In this section, the receiver is assumed to have access to LOS. Therefore, a Rician fadingchannel was used to model the channel impulse response (CIR). Moreover, to characterize the LOS and multipathsignal power and delay profile, the CIR was simulated based on an extended vehicular A (EVA) channel model[42] and the multipath error affecting the pseudorange was simulated based on the model presented in [43, 44].The simulated CIRs were assumed to be correlated with two different correlation coefficients = {0.8, 0.98}. Forcomparison purposes, Fig. 2 shows the simulated multipath for one of the eNodeBs over 10 s. The standard deviationof the generated multipath was 1.1 m. The measurement noise was assumed to be additive white Gaussian with astandard deviation obtained based on the carrier-to-noise ratio of the received signal for each eNodeB [45].

The simulation was repeated for 20 different multipath and noise conditions. Fig. 3 shows the average of the 2D and3D position RMSE over the entire simulated trajectory for each run using the proposed method. The values of the 2Dand 3D position RMSEs were obtained for different update time (i.e., NremTsub). The results were compared with anEKF, where the state update is done whenever a pseudorange measurement is available and no state augmentationis performed. For the sake of comparison, in the EKF approach, it is assumed that the pseudorange measurement isavailable every NremTsub. The value of N was set to 100.

The following conclusions can be drawn from the simulation results.

Time [s]Amplitudeof

% = 0.98

% = 0.8

multipatherror[m

]

Fig. 2. Example of the simulated multipath error for one eNodeB over 10 s.

Update time [s]

2DpositionRMSE[m

]

3DpositionRMSE[m

]

Update time [s]

% = 0.98

% = 0.8

MSCKF

EKF

Fig. 3. 2D and 3D position RMSE over the entire simulated trajectory for different update time.

Remark 1 For both the MSCKF and EKF approaches, the 3D position RMSE is worse than the 2D RMSE, sincethe eNodeBs have approximately similar height and the geometric diversity in the vertical direction is poor.

Remark 2 The proposed MSCKF approach outperforms the EKF approach. The reduction in the RMSE for = 0.98 is higher compared to = 0.8, which means that when the measurement noise is highly time-correlated,the proposed approach can significantly reduce the position estimation error.

Remark 3 From several sets of simulations, it was concluded that a good rule of thumb for choosing Nrem is suchthat Nrem ≈ ⌊N/2⌋. Such rule of thumb reduces the RMSE while maintaining a reasonable computational complexity(update time).

Next, the 2D position RMSE was evaluated for different values of N . For this purpose, the value of N was selectedfrom the set {0, 25, 50, 100} and Nrem was set to ⌊N/2⌋. Note that when N is zero, the MSCKF approach is equivalentto an EKF since no augmentation is performed. Fig. 4 shows the results for this simulation, which was obtained byaveraging the obtained 2D position RMSE over 20 different simulated multipath and noise realizations. The resultsshow that increasing N decreases the RMSE, especially for higher time-correlation in the measurement noise (i.e., = 0.98). However, increasing N increases the update time, which increases the computational burden.

IV. EXPERIMENTAL RESULTS

To evaluate the performance of the proposed approach, an experiment was performed in an urban area (downtownRiverside, California). This section describes the experimental hardware setup and presents the experimental results.

N

2DpositionRMSE[m

]

% = 0.98

% = 0.8

Fig. 4. 2D position RMSE over the entire simulated trajectory for different values of N and for Nrem = ⌊N/2⌋

A. Experimental Hardware Setup

A ground vehicle was equipped with two consumer-grade 800/1900 MHz cellular omnidirectional Laird antennas toreceive the LTE signals at 739 MHz and 1955 MHz carrier frequencies, which were used by AT&T operator. A dual-channel National Instruments (NI) universal software radio peripheral (USRP)-2954R, driven by a GPS-disciplinedoscillator (GPSDO) was used to simultaneously down-mix and synchronously sample LTE signals with 10 Msps. Alaptop was used to store LTE samples for post-processing. A Septentrio AsteRx-i V, which is equipped with dualantenna multi-frequency GNSS receiver with real-time kinematic (RTK) and a Vectornav VN-100 micro electroma-chanical systems (MEMS) IMU, was used to estimate the position and orientation of the ground vehicle, which wasused as the ground truth. The stored LTE samples were processed by the Multichannel Adaptive TRansceiver Infor-mation eXtractor (MATRIX) SDR developed by the Autonomous Systems Perception, Intelligence, and Navigation(ASPIN) Laboratory, producing pseudoranges to LTE eNodeBs in the environment. The proposed framework wasused to estimate the receiver’s position using the derived pseudoranges. The receiver was assumed to have access toGPS signals at its initial position. Therefore, the receiver was able to estimate the initial values of the its positionand the difference of its clock bias with each of the eNodeBs, which makes the estimation problem observable [46].Fig. 5 shows the experimental hardware setup.

USRP RIOStorageIntegratedGPS-IMU

GPS antennasCellular antennas

Fig. 5. Experimental hardware setup

Over the course of the experiment, the receiver was listening to 5 eNodeBs with the characteristics shown in TableI. The receiver traversed a trajectory of 1380 m over 190 s.

TABLE I

ENodeBs’ Characteristics

eNodeB

Carrier

frequency

(MHz)

NCell

ID

Bandwidth

(MHz)

1 1955 216 20

2 739 319 10

3 739 288 10

4 739 151 10

5 739 232 10

The receiver’s orientation, position, and velocity, and their covariances were initialized using the output of theAsteRx-i V’s GNSS-INS. The gyroscope’s and accelerometer’s biases were initialized by taking the mean of 5 secondsof IMU data, when the receiver was stationary. The initial clock bias and drift uncertainties were set to 3 m2 and0.3 (m/s)2, respectively. The measurement noise variance was determined empirically.

B. Experimental Results

Fig. 6(a) shows the estimated pseudoranges and their corresponding ranges for all eNodeBs. For comparison purposes,the initial value of the pseudoranges and ranges were subtracted from the pseudorange and range values over theentire trajectory. Therefore, the presented pseudoranges and ranges in Fig. 6(a) start from zero. Fig. 6(b) shows theempirical cumulative function (CDF) of the difference between the estimated pseudoranges and their correspondingactual ranges after removing the initial clock biases. These differences are due to the unmodeled effects, such asclock drifts, multipath, and measurement noise.

eNodeB 1

eNodeB 3eNodeB 2

eNodeB 4

eNodeB 5Dashed: Pseudoranges

Solid: Ranges

(a) (b)

Fig. 6. (a) Estimated pseudoranges and their corresponding ranges for each eNodeB. The initial values were removed for comparisonpurposes. (b) Empirical CDF of the error between the pseudoranges and their corresponding ranges after removing the initial clock bias.

Fig. 7 shows the 2D and 3D position RMSE for different values of N . In these results, it is assumed that = 0.98and Nrem = ⌊N/2⌋. It can be seen that both the 2D and 3D position RMSE decreased by increasing N from 1 to50. However, the payoff due to increasing N from 50 to 100 diminishes. Fig. 7 shows that the proposed MSCKFapproach could reduce the 2D and 3D position RMSE by 5.55 m and 10.32 m, respectively, compared to the EKFapproach, where N is set to one.

Fig. 8 compares the navigation solutions obtained by the proposed MSCKF approach and the EKF approach versusthe ground truth. Table II summarizes the resulting 2D and 3D position RMSE.

N

Fig. 7. Experimental 2D and 3D RMSE for different values of N

eNodeB 4

eNodeB 2

eNodeB 5

eNodeB 1

1000 m

Trajectories:

GPSLTE MSCKF

eNodeB 3

LTE EKFLTE MSCKF

Fig. 8. Experimental results showing the ground vehicle’s ground truth trajectory (from a GNSS-IMU RTK system), the estimatedtrajectory with the proposed MSCKF and an EKF. The total traversed trajectory was 1380 m. Image: Google Earth.

TABLE II

2D and 3D position RMSE

Method 2D RMSE [m] 3D RMSE [m]

MSCKF 6.05 10.45

EKF 11.60 20.77

V. CONCLUSION

In this work, the effect of the time-correlated pseudorange error caused by multipath and the receiver’s loop filter onthe position estimation error was addressed. A navigation framework based on an MSCKF was proposed to reducethe positioning error in the presence of time-correlated error. Simulation results were presented to evaluate the

effect of the correlation on the position estimation error. The simulation results assumed a LOS channel with Ricianfading. The simulation results showed a reduction of 44.31% in the 2D position RMSE using the proposed approachcompared to the EKF. The experimental results showed a 48% reduction in the 2D position RMSE compared to theEKF approach. The total 2D position RMSE was 6.05 m for a ground vehicle navigating in an urban environmentover a 1380 m trajectory.

ACKNOWLEDGMENT

This work was supported in part by the Office of Naval Research (ONR) under Grant N00014-16-1-2305.

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