=Paper=
{{Paper
|id=Vol-2626/paper17
|storemode=property
|title=GNSS Aided span-Line-of-Sight Radio Localization via Dual Polarized Arrays
|pdfUrl=https://ceur-ws.org/Vol-2626/paper17.pdf
|volume=Vol-2626
|authors=Marco Antonio Marques Marinho,Alexey Vinel,Felix Antreich,Per Gustafson
|dblpUrl=https://dblp.org/rec/conf/icl-gnss/MarinhoVAG20
}}
==GNSS Aided span-Line-of-Sight Radio Localization via Dual Polarized Arrays ==
https://ceur-ws.org/Vol-2626/paper17.pdf
GNSS Aided Non-Line-of-Sight Radio Localization via
Dual Polarized Arrays
Marco A. M. Marinhoa , Alexey Vinela , Felix Antreichb and Per Gustafsonc
a
Halmstad University, School of Information Technology, Halmstad, Sweden
b
Aeronautics Institute of Technology (ITA), Department of Telecommunications, São José dos Campos, Brazil
c
Gutec AB, Lomma, Sweden
Abstract
This work presents a radio based localization approach that is capable of accurately positioning radio
emitters even when no direct line-of-sight signal is available. A dual polarized array is employed along
with the space alternating generalized expectation maximization (SAGE) algorithm. To lighten the
computational load and improve the accuracy of the proposed method, Global Navigation Satellite
Systems (GNSS) positioning is used to initialize and limit the search area of SAGE. A set of numerical
simulations is presented, highlighting the performance of the proposed method.
Keywords
Antenna Arrays, Dual Polarization, GNSS, Localization, Signal Processing
1. Introduction
The ever growing demand for fast and low latency mobile communications have brought to the
forefront technologies such as massive multiple-input multiple-output (MIMO) and millimeter
wave (mmWave). Being the driving factors behind modern wireless communication standards
such as 5G, these technologies can be used to enable other future applications, in special
application which require precise and low latency positioning. Autonomous vehicles, vehicular
networks and platooning are an example of such applications [1].
In order to obtain a position estimate radio-based localization estimate parameters from a
received signal. Such parameters range from signal strength (RSS) to direction of arrival (DOA)
and time difference of arrival (TDOA). After these parameters are estimated a localization
estimate for the transmitter can be obtained.
Traditional radio-based localization methods rely on estimating parameters of the line-of-
sight (LOS) component of a received signal. The performance of these approaches is heavily
degraded in case strong non-line-of-sight (NLOS) components are present [2]. Alternative
approaches that take advantage of NLOS components’ information to improve the accuracy of
the positioning or obtain a localization estimation even when no LOS component is present
have also been proposed [3]. The application of dual-polarization antenna arrays has been
discussed for global navigation satellite systems (GNSS) signals in order to improve localization
performance in case of strong NLOS components [4].
ICL-GNSS 2020 WiP Proceedings, June 02–04, 2020, Tampere, Finland
email: marco.marinho@ieee.org (M.A.M. Marinho); alexey.vinel2@hh.se (A. Vinel); antreich@ieee.org (F.
Antreich); per@gutec.se (P. Gustafson)
orcid: 0000-0002-6715-6830 (M.A.M. Marinho); 0000-0003-4894-4134 (A. Vinel); 0000-0001-6596-0123 (F.
Antreich)
⃝
c 2020 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)
This work presents a geometric localization approach that leverages a dual-polarization an-
tenna array for positioning even under NLOS only conditions (blocked LOS component). The
method presented relies employs DOA, TDOA, and the reflection angle estimates of several
NLOS components to accurately position a radio transmitter. Furthermore, in order to im-
prove the accuracy and reduce the computational load of the space alternating generalized
expectation maximization (SAGE) algorithm, employed to acquire the parameter estimates, a
position provided by a GNSS receiver on the transmitter is used to initialize the algorithm.
The proposed method requires that the orientation of both transmitter and receiver antennas
are known.
2. Signal Model
This work assumes a polarized electromagnetic transmitter that is transmitting a broadband
signal and a dual-polarization antenna array receiver composed of M antenna elements, and
we consider N impinging wavefronts. The polarized wavefront of the nth path is propagating
in direction ⃗dn . Assuming a signal path that impinges onto a reflective surface with angle ϕ the
horizontal and vertical components of the polarized wave are reflected with relative amplitude
and phase given by
Eh,r
κh = (1)
Eh,i
Ev,r
κv = , (2)
Ev,i
where Eh,i and Ev,i refer to the complex amplitudes of the incident electric field and Eh,r and
Ev,r refer to the complex amplitudes of the reflected electric field. For a smooth, plane surface,
κh and κv can be written as [4]
√︂
µp 2
µr ηr cos ϕ − ηp ηr2 − ηp2 sin ϕ2
κh = √︂ (3)
µp 2
µr η r cos ϕ + ηp ηr2 − ηp2 sin ϕ2
√︂
µ
ηp cos ϕ − µpr ηr2 − ηp2 sin ϕ2
κv = √︂ (4)
µ
ηp cos ϕ + µpr ηr2 − ηp2 sin ϕ2
√︂ √︂
ϵp µp ϵr µr
where ηp and ηr are given by ϵ0 µ0 and ϵ0 µ0 , respectively. Here, ϵp , ϵr , and ϵ0 are the
permittivity of the propagation medium, reflection medium, and vacuum, respectively. µp ,
µr , and µ0 are the permeability of the propagating medium, reflection mediums, and vacuum,
respectively.
The received multi-carrier signal’s space-frequency response of the kth subcarrier received
by antenna m with polarization z at time snapshot t can be written as
L
∑︂
xm,z,k [t] = κl,z sl,k ejw(xm cos θl +ym sin θl ) · ej2πk∆f τl
l=1
(b) Example of search areas for transmitter and
(a) Depiction of NLOS localization scenario reflectors
+ nm,z,k [t], (5)
where sl,k is the complex symbol transmitted at the kth subcarrier of the lth signal, where
l = 1, 2, . . . , L, xm and ym are the coordinates of the position of the mth antenna element,
where m = 1, 2, . . . , M , w is the wavenumber, θl is the azimuth of the lth signal with respect
to the orientation of the antenna array, ∆f is the subcarrier spacing, and τl is the time of flight
of the lth signal.
3. Localization Method
To estimate the position of a transmitter, this work applies a dual polarized antenna array A
LOS path is not required, as the present of two distinct NLOS paths is sufficient for obtaining
a position estimate of a transmitter. A graphical description of the scenario considered in
this work is presented in Figure 1a. The figure presents two NLOS paths impinging over an
antenna array whose center serves as the origin for a two-dimensional coordinate system. The
parameters show in the figure are the angle of arrival θ, and angle of reflection ϕ of the two
different paths.
The parameters τl , θl , and ϕl of the lth signal are related to the position of the transmitter
tl and reflector rl according to
(︃ )︃
Π yrl
θl = − arctan (6)
2 x rl
⃓ ⃓
⃓ ytl − yrl ⃓
ϕl = ⃓
⃓ ⃓ + (Π − |θl |) (7)
xt − xr ⃓
l l
Equations (6) and (7) highlight the direct relationship that exists between the position of
the transmitter and reflectors and the incidence and reflection angles. Therefore the position
of the transmitter and reflectors can be calculated by obtaining as estimate of all received θl
and ϕl and following the geometric relationship shown in [5]
This work extends the work in [5] by employing the space alternating generalized expectation
maximization (SAGE) algorithm [6] to directly solve the multidimensional problem over the
transmitter and reflector positions. Directly searching over the position will yield a more robust
estimation, by eliminating nonlinear error relationships that arise when a position is estimated
geometrically with respected to angles of arrival and reflection.
However, directly searching over the possible positions greatly increases the computational
load required to obtain a position estimate for the transmitter. In order to mitigate this
problem, two steps are proposed.
The first step consists of using a position estimate provided by the transmitter itself. This
work considers that this estimate is obtained by a GNSS system. The estimate can than
be sent to the receiver in order to minimize the search area with respect to the transmitter
location. The average horizontal position accuracy of a GPS receiver in a smartphone in urban
environments ranges from 7 to 13 meters [7]. Whiles this accuracy may be insufficient for
safety of life applications, such as autonomous vehicles, it is sufficient to greatly reduce to
computational complexity of the proposed method.
To reduce the search area with respect to the reflector locations an initial angle of arrival
estimate can be used. This estimate can be obtained by applying SAGE itself over only one of
the polarization’s of the received signal, preferably the one with a higher signal to noise ratio
(SNR). Once the DOA estimates have been obtained it is possible to restrict the search area to
a given region around the line created by the DOA line crossing the receiving antenna array.
The area around the DOA line can be defined by defining a tolerance or sensitivity parameter
α such that the search area is contained within the lines that cross the center of the receiving
array with angles θl + α and θl − α. Figure 1b presents an example of the search areas for the
transmitter and for the possible reflectors.
4. Numerical Simulations
Figure 2 presents the results for a set of numerical simulations performed to access the perfor-
mance of the proposed method, refereed to as direct positioning, in comparison to the method
proposed in [5], refereed to as geometric positioning. For this set of simulations, a transmitter
is placed 30 meters in front of the receiver at coordinates (0, 30). Three reflectors are placed
at coordinates (−30, 20), (25, 10), and (15, 16). For this set of simulations it is assumed that
no LOS signal reaches the receiving antenna array. The antenna array is composed of M = 10
dual-polarized antenna elements, and T = 100 snapshots are used to estimate the position of
the transmitter. The permittivity and permeability of the reflectors are assumed to be known
in this case.
The results show that the method proposed in this paper outperforms the one presented
[5], especially at low SNRs. Furthermore, the accuracy of the proposed method is superior to
that of a commercial GPS receiver present in a modern smartphone, making it a more suitable
method for safety of life applications.
6 Geometric positioning
Direct positioning
5
4
RMSE (m)
3
2
1
5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0
SNR (dB)
Figure 2: Localization performance of the proposed method
5. Conclusion
This work presented a radio localization method based on a dual polarization antenna array.
The proposed approach utilizes a GNSS based position to reduce the search area of a SAGE
based search in order to directly estimate the position of the receiver. When compared to a
geometric based positioning approach the accuracy obtained by the proposed method is vastly
superior at low SNRs as it avoids errors caused by highly nonlinear relationships between
parameters such as angle of arrival and angle of reflection with the position of the transmitter.
Future research should focus on estimating the permittivity and permeability of the reflectors.
This would allow for a more flexible implementation of the proposed algorithm as it would be
able to respond to changes in the physical parameters of the material around the receiver that
might be caused by phenomena such as rain or rust.
Acknowledgments
The research leading to the results reported in this work has received funding from the Knowl-
edge Foundation in the framework of SafeSmart” Safety of Connected Intelligent Vehicles in
Smart Cities” Synergy project (2019– 2023), Swedish Foundation for Strategic Research (SSF)
in the framework of Strategic Mobility Program (2019-2020) and the ELLIIT Strategic Re-
search Network.
References
[1] H. Wymeersch, B. Peng, W. P. Tay, H. C. So, D. Yang, A survey on 5G massive MIMO
localization, Digital Signal Processing 94 (2019) 21–28. doi:10.1016/J.DSP.2019.05.005.
[2] J. A. Del Peral-Rosado, R. Raulefs, J. A. López-Salcedo, G. Seco-Granados, Survey of
Cellular Mobile Radio Localization Methods: From 1G to 5G, IEEE Communications
Surveys and Tutorials 20 (2018) 1124–1148. doi:10.1109/COMST.2017.2785181.
[3] C. K. Seow, S. Y. Tan, Non-Line-of-Sight localization in multipath environments, IEEE
Transactions on Mobile Computing 7 (2008) 647–660. doi:10.1109/TMC.2007.70780.
[4] F. Fohlmeister, A. Iliopoulos, M. Sgammini, F. Antreich, J. A. Nossek, Dual polariza-
tion beamforming algorithm for multipath mitigation in GNSS, Signal Processing (2017).
doi:10.1016/j.sigpro.2017.03.012.
[5] M. Marinho, F. Antreich, A. Vinel, F. Tufvesson, M. A. Yaqoob, Non-Line-of-Sight Based
Radio Localization With Dual-Polarization Antenna Arrays, in: WSA 2020; 24th Interna-
tional ITG Workshop on Smart Antennas, 2020.
[6] B. H. Fleury, M. Tschudin, R. Heddergott, D. Dahlhaus, K. I. Pedersen, Channel parameter
estimation in mobile radio environments using the SAGE algorithm, IEEE Journal on
Selected Areas in Communications 17 (1999) 434–450. doi:10.1109/49.753729.
[7] K. Merry, P. Bettinger, Smartphone gps accuracy study in an urban environment, PloS
one 14 (2019).