International audienceThis work introduces a dynamic VOR receiver model for estimating the bearing error in the presence of wind turbines. The receiver processes time series generated by an electromagnetic simulation tool that takes into account the multipaths. This global model can reproduce the response of a VOR receiver on a realistic aircraft trajectory. The receiver is tested in a dynamic scenario where the multipaths change rapidly with time

Ben-Hassine, Seif

Chabory, Alexandre

Douvenot, Rémi

Morlaas, Christophe

English

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A Dynamic VOR Receiver Model for Estimating the
Bearing Error in the Presence of Wind Turbines
Seif Ben-Hassine, Alexandre Chabory, Christophe Morlaas, Rémi Douvenot
To cite this version:
Seif Ben-Hassine, Alexandre Chabory, Christophe Morlaas, Rémi Douvenot. A Dynamic VOR Re-
ceiver Model for Estimating the Bearing Error in the Presence of Wind Turbines. EuCAP 2019 13th
European Conference on Antennas and Propagation, Mar 2019, Krakow, Poland. ￿hal-02184478￿
A Dynamic VOR Receiver Model for Estimating
the Bearing Error in the Presence of Wind Turbines
Seif Ben-Hassine1, Alexandre Chabory1, Christophe Morlaas1, Re´mi Douvenot1
1: ENAC, universite´ de Toulouse, TELECOM-EMA, Toulouse, France, seif.ben-hassine@enac.fr
Abstract—This work introduces a dynamic VOR receiver
model for estimating the bearing error in the presence of
wind turbines. The receiver processes time series generated by
an electromagnetic simulation tool that takes into account the
multipaths. This global model can reproduce the response of a
VOR receiver on a realistic aircraft trajectory. The receiver is
tested in a dynamic scenario where the multipaths change rapidly
with time.
Index Terms—VOR receiver, propagation, multipath, wind
turbines
I. INTRODUCTION
The VHF Omnidirectional Range (VOR) is a ground-based
system transmitting an electromagnetic signal of frequency
between 108 and 118 MHz. This signal allows aircraft to
navigate. The VOR signal is sensitive to the presence of wind
turbines in the vicinity of the station. The wind turbines yield
multipaths which interfere with the useful signal. Therefore,
these multipaths induce an error on the azimuth assessed by
the receiver.
Several methods have been proposed to obtain the multipath
characteristics [1][2][3]. In the literature, the bearing error is
computed from the multipath characteristics by means of the
analytic expression proposed by Odunaiya [4].
The Odunaiya model is static, i.e. it computes the error
on each trajectory point as if nothing was moving. Thus,
the influence of the fast variations of the multipaths on the
VOR error cannot be accounted. Consequently, it is unable to
reproduce the response of a realistic VOR receiver in these
conditions.
In this paper, we present a dynamic model that combines a
VOR digital receiver with a time series simulator. It is capable
of reproducing the response of a VOR receiver in a realistic
way, taking into account demodulations and filtering. In Sec-
tion II, we present the electromagnetic model to compute the
direct and multipath signals [3] and the time series generator.
In Section III, a dynamic model of a VOR receiver is detailed.
In Section IV, simulation results are presented to show the
influence of the time variations on the VOR bearing error.
Section V concludes this study.
II. TIME SERIES VOR ERROR SIMULATOR
The electromagnetic model applied to compute the direct
and multipath signals is detailed in [3] and illustrated in
Figure 1. Firstly, the direct field received by the aircraft is
analytically computed using a two-ray model. Secondly, we
use the 2D parabolic equation to model the propagation above
the terrain from the VOR station to the wind turbines. Thirdly,
the wind turbines are meshed and equivalent currents are
calculated using the PO approximation. Finally, the scattered
fields are calculated at the receiver to obtain the multipaths.
The EM computation is performed all along the aircraft
trajectory.
Physical optics
Parabolic equation
2-ray model
Fig. 1: Overview of the method to compute multipath [3].
To obtain times series, a realistic aircraft trajectory is
sampled with a short enough time step so as to accurately
model the signal variations in space. Details are given in [5].
The trajectory is a series of rectilinear or circular elements
separated by way-points.
According to the Nyquist criterion, the space step must be
shorter than half a wavelength
∆x <
λ
2
. (1)
The time step is expressed in terms of the space step and
the maximum speed along the trajectory
∆tmin =
∆x
Vmax
. (2)
At each point of the trajectory, we use the method pro-
posed in [3] to compute the multipath parameters, i.e. their
amplitude an, phase θn, azimuth ϕn and Doppler ωdop. These
characteristics will be sent to a digital VOR receiver to assess
the influence of the multipath changes in time on the bearing
error.
III. VOR RECEIVER MODEL
The VOR signal is composed of a reference phase REF and
a variable phase VAR.
Fig. 2: Block diagram of the VOR receiver.
A. IQ signals
The VAR signal contains the azimuth information. The REF
signal is the reference signal to which the aircraft compares
the VAR signal to know the azimuth on which it is located
(relative to the magnetic North). For a conventional VOR,
the signal REF is modulated in phase and the signal VAR in
amplitude. For a Doppler VOR, the modulations are reversed.
The airborne VOR receiver calculates the phase shift between
the reference signal and the variable signal. Note that the same
receiver can demodulate the conventional and Doppler VOR
signals.
Our model is based on an I/Q signal generator to obtain the
data received by a VOR receiver. These signals are defined by
I(tk) =
N∑
n=0
Mn(tk) cos(ω
n
doptk + θn(tk)) + nI(tk), (3)
Q(tk) =
N∑
n=0
Mn(tk) sin(ω
n
doptk + θn(tk)) + nQ(tk). (4)
Note that the multipath n = 0 corresponds to the direct signal.
The n-th multipath signal Mn is defined by
Mn(tk) = an(tk)[1 +REF (tk) + V ARn(tk)], (5)
with
• REF (tk) = ma cos(ωsctk +mf sin(ωBF tk)) the refer-
ence signal.
• V ARn(tk) = ma cos(ωBF tk − ϕn) the variable signal
of the n-th multipath.
• nI et nQ the AWGN noises associated to the I/Q signals,
respectively.
• ωsc the subcarrier pulse (9960 Hz) in rad/s.
• ωBF the BF pulse (30 Hz) in rad/s.
• ma the modulation index (= 0.3).
• mf the modulation rate (= 16).
The sampling frequency in the propagation computation is
set typically to few hundreds of Hz using (2). In the receiver,
we need a sampling frequency of at least 20 kHz because
the VOR signal bandwidth is 10 kHz. Thus, we perform an
oversampling using a linear interpolation on the multipath
parameters.
B. Receiver components
The block diagram of our receiver is presented in Figure 2.
The envelope detector carries out an AM demodulation in
order to recover the VAR and REF signals. The complex
envelope is defined by
A(tk) =
√
I2(tk) +Q2(tk). (6)
A low-pass filter extracts the VAR signal at 30 Hz. Similarly,
the REF signal is extracted using a 9960 Hz high-pass filter.
For a conventional VOR, the signal REF is modulated in
frequency, the Figure 3 shows a block diagram of the FM
demodulator used to extract this signal.
Fig. 3: Block diagram of the FM demodulator.
In order to reduce the computation time, a decimation
operation is applied. This downsampling step consists in
keeping a number of samples as small as possible to fulfill
the Shannon criterion at 30 Hz.
The phase detector calculates the phase difference between
the AM and FM 30 Hz signals. As illustred in Figure 4, the
first step consists in creating a quadrature signal by a phase
shifter. Then, products are performed on both paths. The next
step is to sum the products and perform a low-pass filter to
recover the DC component. The azimuth information is the
phase of the filtered signal.
Fig. 4: Block diagram of the phase detector.
IV. SIMULATION RESULTS
We consider a VOR station operating at a frequency of
113.8 MHz with a power of 25 W. A wind turbine type
ENERCON E82 is placed at 1 km from the VOR station,
yielding one multipath. In order to be able to simply analyse
the results, a straight trajectory of 6 km is considered here,
although the model can deal with more complex trajectories.
Firstly, the aircraft is motionless for 5 s to ensure the end of
the receiver transient period. After that, it starts at low speed
until reaching the second waypoint at 216 km/h. We consider
a space step of λ
5
.
Fig. 5: Configuration.
In Figure 6, the azimuth of the multipath is plotted with
respect to time. The color indicates the power of the multipath
relatively to the direct path. We observe that a single multipath
exists.
The multipath is powerful during the first part of the
trajectory from 0 s to 50 s and significant at the end from
200 s to 250 s. This is because the aircraft is in the specular
reflection zone of the wind turbine.
In Figures 7a and 7b, we display the VOR errors obtained
with the Odunaiya expression and with the VOR receiver
model. During the first 2 seconds, the receiver response
changes rapidely. It is due to the filters. The receiver response
converges to the Odunaiya model during 5 s when no dynamic
effects are involved.
The aircraft moves slowly and the receiver response remains
close to the static model of Odunaya. During this phase, there
is a delay between the two models that is due to the filtering
response. When the aircraft accelerates, both models do not
give the same response from 25 s. It is due to the fast variation
of multipath. When the aircraft moves away from the VOR
and the wind turbine, the phase difference between the direct
and the multipath changes in a slower way, which explains
the slower fluctuations of the VOR error. Hence, the dynamic
model converges again to the static model despite the high
speed of the aircraft.
0 50 100 150 200 250
Time (s)
20
40
60
80
Re
la
 iv
e 
az
im
u 
h 
(°
)
Power Azimu h Profile 
 Normalized power wi h respec   o direc  signal (dB)
−80
−70
−60
−50
−40
Fig. 6: Power Azimuth Profile of the multipath along the
trajectory.
(a) Receiver response from 0 s to 250 s
(b) Receiver response from 0 s to 18 s
Fig. 7: Receiver response along the trajectory.
V. CONCLUSION
In this article, a dynamic VOR receiver model for estimating
the bearing error in the presence of wind turbines has been
studied. The computation of times series for VOR signals in
the presence of multipaths has been presented. These times
series have been sent to a digital VOR receiver to evaluate the
influence of the multipath changes in time on the VOR error.
The model has been tested in a dynamic scenario.
ACKNOWLEDGMENT
The authors would like to thank ENAC and DGAC/DTI for
funding this work.
REFERENCES
[1] I. Gonzalez, L. Lozano, J. Gomez, A. Tayebi, I. Etayo, and M. Catedra,
”Analysis of the scattering field of wind turbine using rigorous and
asymptotic techniques,” in Proceeding of the Fourth European Conference
on Antennas and Propagation (EuCAP) , April 2010, pp. 1-4.
[2] A. Calo Casanova, M. Ramon, L. de Haro y Ariet, and P. Blanco-
Gonzalez, ”Wind farming interferences effects,” in International Multi-
Conference on Systems, Signals and Devices, July 2008, pp. 1-6.
[3] L. Claudepierre, R. Douvenot, A. Chabory, and C. Morlaas, ”A determin-
istic VOR error simulation method- Application to windturbines ,” IEEE
Transactions on Aerospace and Electronic Systems, September 2016.
[4] S. Odunaiya and D. Quinet, ”Calculations and analysis of signal process-
ing by various navigation receivers architectures,” in Digital Avionics
Systems Conference, vol. 1, 2004.
[5] S. Ben-Hassine, A. Chabory, C. Morlaas, and R. Douvenot, ”VOR Times
Series for an Aircraft Trajectory in the Presence of Wind Turbines,” 22nd
International Microwave and Radar Conference MIKON, May 2018.


A Dynamic VOR Receiver Model for Estimating the Bearing Error in the Presence of Wind Turbines

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A Dynamic VOR Receiver Model for Estimating the Bearing Error in the Presence of Wind Turbines

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