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1
USING GPS SYSTEM NEAR THE FOREST AND QUALITY
CONTROL
A. Pırtı
Yildiz Technical University, Faculty of Civil Engineering, Department of Geodetic
and Photogrammetric Engineering, Besiktas, Istanbul - Turkey.
E-Mail : atinc@yildiz.edu.tr
ABSTRACT
This paper attempts to provide some insights into the fading properties of GPS signals. When a GPS
signal reaches the antenna, it suffers from masking and blocking effects from surrounding objects. With
respect to these effects, GPS signals can be divided into clear signals, shadowed signals, and blocked
signals.
In this article we shall examine the performance and use of GPS based data acquisition systems near
forest. As a general rule, a clear view of the sky is preferred when using GPS for determining location.
This means that using GPS near forest is one of the most demanding uses of technology and one that
requires particular attention when evaluating GPS receivers that will be used in such an environment.
The signal transmitted by GPS satellites are extremely low power, and the GPS signal is about 100
times weaker than the general background radiation at that frequency. The signal passing through your
body right now from a local television or radio station is almost certainly several thousand times
stronger than a GPS signal. GPS receivers use sophisticated signal processing techniques to lock onto
and track the GPS satellites. However, the relatively low power of these signals can indeed pose
problems when the signal is further degraded by a forest canopy.
Humidity of the leaves and the forest is the critical factor for GPS performance near the forest area.
Water laden leaves of tree attenuate more signal than those that are dry. GPS signals will be present
with weak signal strengths and positions that are computed from weak signals tend to be less accurate.
This paper evaluates GPS positional accuracy, precision and performance near forest areas. As a
result of this attenuation, positions are computed from weak signals and tend to be less accurate.
2
INTRODUCTION
In many applications GPS has been used as a reliable method in high precision
surveys. However, in some work the attainable accuracy is significantly decreased.
Most of these poor results have a common error source – GPS signal diffraction.
Signal diffraction occurs whenever the direct line-of-sight between the GPS satellite
and the antenna is obstructed but the signal is not completely masked [8].
The satellite-to-land user links can be categorized in one of three forms: 1) Line of
sight, unshadowed, 2) Shadowed by trees or foliage; 3) Completely obstructed where
the link is totally blocked by hills or other major obstructions [11].
The unshadowed link is characterized by a clear line of sight to the satellite, but there
can also be a scattered and/or specular multipath component in addition to the line-of-
sight link. The multipath component can be caused by ground reflections. Partially
shadowed links have a randomly attenuated direct link in addition to the scattered
component. Signals are attenuated when passing by trees or leaves because the GPS
signals are transmitted at a microwave frequency, which is affected easily. The
attenuation generally is caused by individual trees, utility poles, clusters of trees, or
forests in the project area. A single or small tree is sufficient to allow some signal to go
through and reach the antenna. The completely obstructed link may be blocked by hills
or large man-made structures and has no useful signal component at all over a
substantial period of time. Diffuse obstacles such as bushes and trees are a common
source of GPS signal diffraction. Beside these circumstances, it is possible that GPS
signals ‘bend around’ the edges of a wall, i.e. satellite signals are visible although from
the geometric point of view they should be obstructed. Possibilities of using GPS
receivers in forest measurements have not been studied on a larger scale. Application
of GPS receivers in forest is faced by an extra obstacle-the canopy trees. Trees above
the measurement object weaken the signal coming from satellites. Passing through the
canopy of trees the signal may reach the receiver not only directly, but also reflected
from the trees. Thus, trees are the source of additional refraction and subsequently,
greater measurement errors. In addition, trees restrict signal transmission from some
satellites located low above the horizon [5].
The power of a GPS signal is a measure of its quality. GPS signals are transmitted
from the satellites with different powers, at +19.7 dBW (P-code L2), 23.8 dBW (P code
L1) and +26.8 dBW (C/A code L1). The propagation effects between the satellite and
the antenna attenuate the GPS signals which are finally received with a power near the
noise level. Usually the power is expressed as the ratio of the power level of the signal
carrier to the noise level in a 1 Hz bandwidth, termed the C/N0. The C/N0 values are
measured by-products of the GPS observations, and can be used to calculate the phase
variances. Only a few attempts are published in literature where the C/N0
measurements are used for modeling GPS phase variances. Some scientists
successfully use the signal-to-noise ratio (SNR) to model multipath effect [1], [2]. The
relationship between the C/N0 values and the elevation of a GPS satellite was used to
weight GPS observations in order to overcome satellite geometry problems. This
weighting scheme was called the SIGMA- model. One of the most important
developments to date in this field are the SIGMA models which were developed to
overcome artificially introduced periods of weak satellite geometry by proper
weighting of phase observations (SIGMA model) and to reduce signal diffraction
effects of the phase observations (SIGMA Δ model). A different approach to the
SIGMA models also uses signal quality indicators such as signal-to-noise ratio (SNR)
to reduce the errors due to multipath [3], [8], [13], [14].
3
Diffracted GPS signals are usually associated with low C/N0 values. SIGMA Δ can
be used for the treatment of signal diffraction effects using the measured C/N0 values.
It is an attempt to generate intelligent GPS processing software which automatically
models phase signal diffraction. No interaction between the user and the software is
required to prevent the decrease of accuracy. The characteristic feature of GPS signal
diffraction effects is used by the SIGMA-Δ model. The SIGMA-Δ algorithm is
implemented in the GPS software package GRAZIA. GRAZIA is a Kalman filter
based kinematic GPS software with several data modeling features for high accuracy
performance. The processing steps of GRAZIA software are first and foremost, the
transmitted GPS data is validated. Then the weights of the phase observations are
calculated using the SIGMA models. Step three is the tropospheric correction using the
Saastamoinen model together with Neill mapping function. Cycle slips are detected
and repaired by a method based on triple differenced phase observations. Finally, the
position and velocity are calculated by a Kalman filter. Depended on the specific
application the power of the filter can be adjusted [3], [8], [13], [14].
Similar to the SIGMA- model, the SIGMA-Δ model weights the phase observations
with the C/N0 but, in addition, compares the difference of the measured C/N0 and the
expected C/N0 (C/N0 template), i.e. the Δ value. The C/N0 template is defined as the
highest C/N0 value of a signal at a certain elevation of a specific antenna-receiver
combination. Δ is the difference between the measured C/N0 value and the template
value at the appropriate satellite elevation. Δ can be used as an indicator for the
diffraction noise which yields a larger variance than the σi2 (from a measured C/N0
value the appropriate σi2 can be calculated). The SIGMA-Δ model is an excellent
model to reduce signal diffraction effects [3], [8], [13], [14].
MATHEMATICAL APPROACH TO FOREST ATTENUATION
Consider first the attenuation caused by an individual tree where a GPS satellite is
viewed by a stationary user at an elevation angle E deg. The approximate geometry of
the tree and relative position of the receiver are shown in Fig. 1. These measurements
were taken at 870 MHz, but the results can be translated to L-band after being scaled
up to 1.575 GHz using the following relationship [6], [7], [11]:
Atténuation (f) ~
f
Atténuation (1.575 Ghz) dB
MHz
MHz
870
1575
Atténuation (870 MHz) dB
where the attenuation in dB is scaled by
345.1870/1575
. That is, foliage
attenuation varies approximately as the square root of frequency. It has also been
shown that the attenuation of a tree in full foliage is roughly 35% greater in dB that of
a deciduous tree without foliage. Thus, the bulk of a tree’s attenuation is clearly caused
by the wood tree limbs, branches, and trunk rather than by the leaves. Foliage
attenuation is often characterized as attenuation in dB/m of foliage penetration. These
numbers of attenuation per metre tend to vary widely depending on the type of tree and
the height of the ray relative to the top of the tree because the foliage density varies
with height. The attenuation also varies with the distance of the tree from the user.
Fresnel diffraction analyses have been used to explain the average decrease of
attenuation with increasing distance of the receiver to the tree [6], [11].
To obtain a simple purely empirical geometric interpretation of the foliage
attenuation refers to Fig. 1. Consider a ray path through a foliage slab where for each
incremental distance s along the ray path there is some random value of attenuation
in dB/m.
4
Figure 1. Simplified geometric configuration of a single callery pear tree vs. elevation
angle in measurements made by Goldhirsh and Vogel as viewed by a stationary user.
The origin of the x, y coordinates used in the text is the base of the tree trunk [11], [7].
The mean attenuation coefficient at that position depends on various parameters,
such as type of tree, density of trees, position relative to centre, and base of tree. The
total attenuation then depends on the distance w from the receiver to the edge of the
trees, the elevation angle to the satellite, and the geometric extent of the foliage. In
effect, we consider the trees to be a slab of foliage with no uniform attenuation where
the attenuation density in dB/m varies with position. The quantity H0 is the height of
the foliage slab. It is assumed that Ad(x, y) represents the mean attenuation density vs.
position, and the actual attenuation is either 0 or k0 depending on whether that position
in space has foliage or not. The probability of the incremental ray being attenuated at
that position cell is p, and all cells are independent. Thus, the mean attenuation for that
incremental cell of length s is pk0 where k0 varies with position relative to the base of
each tree. We can easily show that the total distance d through the foliage of the model
of Fig.1 does not change substantially as we vary the elevation angle from 0 to 45 deg.;
d remains at approximately 10 m. Consequently, a uniform attenuation density foliage
slab model would show little variation in total attenuation with elevation angle. The
attenuation density in dB/m obviously must vary substantially with position relative to
this base of the tree if the attenuation vs. elevation angle of the model is to match the
measurement. That variation is consistent with what we might expect from a simple
observation of the wood portion of a typical tree, which has a greater wood density
near the base of the trunk [6], [7], [11].
An empirical attenuation density profile (in dB/m) is selected that varies with
position relative to the base of the tree’s centre (the trunk), which seems to match
fairly well-measured data for the tree of Fig.1.
The mean attenuation density in dB/m of this empirical model varies as follows:
Ad (x, y) = (1 – y/14)2 (1 -
x
/ 5.5) K dB/m (1)
This attenuation density profile can be integrated along the path s through the tree at
a given elevation angle E to obtain the total attenuation AT(E) where the following
obtains:
AT(E) =
Path
dds)y,x(A
(2)
x
Tree Trunk
Satellite
s
d
2.4 m
11.6 m
H0
Height y
Elevation Angle E
Approximate
Outline of Tree
7 m
8 m
w
11 m
5
Assume a rectangular tree of 14 m height, 11 m width, and a trunk 8 m away from
the receiver, and the receiver 2.4 m above ground. The mean total attenuation AT is
then [6], [7], [11]
AT(E)
8
5.2
5.13
8
22 dx)x5.13()14/y1(dx)5.2x()14/y1(
5.5
)Esec(K
(3)
where
y =2.4+xTan E.
Thus AT(E)
K [3.78 sec E – 5.21 sec E tan E + 1.937sec E tan2E] (4)
K [3.726 – 0.0670 E] for a least mean square fit
24.6 – 0.442 E
In this frequency region (870 MHz), tree foliage attenuation varies approximately as
the square root of frequency; i.e.,
MHz870f1L /
and results are scaled to 1.575 GHz
in terms of increased dB/m attenuation. Trees with full foliage have approximately
1.35 times the attenuation in dB/m compared to attenuation for deciduous trees bare of
foliage. Goldhirsh and Vogel empirical model:
AT (E) = 25.8 – 0.47 E (5)
which is rather close to the measured points and the linear best fit result using the
geometric model of Fig.1. We can conclude that the attenuation density is clearly not
uniform with position, and that the empirical model of Fig.1, at least for this example,
gives a good match for the limited range of elevation data available (between 12 and
50 degrees) [6], [7], [11].
DESCRIPTION OF THE GPS EXPERIMENTS
The survey of this project was performed in the Alpine area of Navistal, Austria. A
geodetic network consisting of 6 stations was surveyed using static GPS surveying
methods.
Figure 2. Project area and GPS network in the project area [4].
The GPS data was acquired using six GPS receivers (Using P1, P2, P3, P4 and P6
Ashtech Z 12 Receivers, P2, P5 Ashtech G12 receivers, Ashtech choke ring (DM)
antennas. The minimum elevation cut-off angle is 5 degrees; data was collected for 24h
with a sampling rate interval of 5sec (15-16 October 2002) and 10sec (13-14 May 2002).
The purpose of this experiment was identification of signal distortion at a GPS site
close to the forest. Figure 2 shows the project area [4].
P1
P2
P6
P5
P3
P4
500 m
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DATA PROCESSING AND ANALYSIS
First, the continuous 24h of GPS data was processed by the GPS processing software
GRAZIA. In this chapter the selecting baseline (P1-P2) is very close to the forest area,
and the results of this baseline in October measurements were examined for the signal
(diffraction) attenuation effects. The purpose of this experiment was the identification
of signal diffraction effects at a GPS site close to the forest area [4].
Figure 3. Point 1 and Point 2 [2]
The trees caused severe obstruction of almost 20% sky, see Fig.4. The problem
shown by the skyplot of 17:30-22:00 is typical for the whole day: Several satellites are
shaded by trees, but are still tracked by the receiver. Subsequent investigations refer to
the L1 processing of the baseline P1-P2.
As an obstacle, the forest mainly caused shading of satellites, and signal diffraction
effects, seen in Fig. 4. From the skyplot, (Fig.4) the receiver tracked the satellite PRN
3, PRN 22, PRN 25 continuously while the satellite was shaded by the forest area.
Figure 4.Skyplot of the reference site (P1) and the rover site (P2) and C/N0 values,
17:30 – 22:00 with obstruction by trees (in October)
The “signature” of the obstructing trees is shown by the DDR time series of some
satellites in Fig.6, Fig.8 and Fig.10. Satellite PRN 3 is initially tracked at a low
elevation in the obstructed area of the sky. During this period (21:00-21:30), the
satellite PRN 3 is hidden behind the trees, and signal diffraction effects occurred, see
Fig.6. Signal diffractions are caused by obstructions of the satellite signal due to the
trees. Satellite PRN 3 is tracked between the trees by the receiver, the receiver receives
the weak signal, and then loses lock to the satellite signals which are not received
signal because of the trees. Satellite PRN 3 rises to elevations above 300 at the end of
the session, so the signal quality is increased and DDR values indicate no bias during
this period (21:30-22:00), (Fig.6). The maximum bias shown by the DDR residuals
P1
P2
Reference Point (P1)
Rover Point (P2)
7
exceeds 15 cm. Its DDR has an rms of 34 mm during this period (21:00 – 21:30), 11
mm during this period (21:30- 22:00).
Satellite PRN 22 is initially tracked at 300 elevations in the obstructed area of the
sky, see Fig.4. During this period (20:00-20:15), the DDR values of PRN 22 show
strong fluctuations. Its DDR has an rms of 68 mm. At the end of the session (20:15-
21:45), its DDR has an rms of 4 mm, see Fig.8.
Satellite PRN 25 is initially tracked at 300 elevations in the obstructed area of the
sky, seen Fig. 4. Satellite PRN 25 encounters the same situation as PRN 22. At the
beginning of the session (17:45-18:00), the satellite is hidden behind the trees; its DDR
shows fluctuations, see Fig.10. These are due to signal diffraction effects caused by
foliage and branches of the trees.
The combined effects of forest cover and terrain will degrade the performance of all
GPS receivers. The GPS signals are affected by the surrounding trees and earth and
that affects both accuracy and productivity (how much of the time the receiver is
tracking enough satellites). In certain locations, at certain times of the day, it may
become very difficult or even impossible to do GPS work. In order to productively use
GPS under the forest canopy, field operators must use careful planning and field
methods [5], [9], [11].
For the following experiment, the selecting baseline (P1-P2) is examined for the
results of this baseline in the May measurement for signal attenuation (diffraction)
effects. The reference and rover station antenna were mounted close to the forest. The
problem shown by the skyplot of 5:00-11:00 is typical for the whole day. Several
satellites are shaded by the trees, but are still tracked by the receiver, see Fig. 5.
Figure 5.Skyplot of the reference site (P1) and the rover site (P2) and C/N0 values 5:00
– 11:00 with obstruction by trees (in May)
The “signature” of the obstructing trees is shown by the DDR time series of some
satellites in Fig.7, Fig.9 and Fig.11. Satellite PRN 3, is initially tracked at high
elevation (800) and then dropped the elevation (100) during this period (9:40 – 12:30).
At the end of the session (6:45 – 8:15) the elevation of PRN 3 is increased to about
400, see Fig.5. When the satellite starts to disappear behind the trees at about 6:45 –
8:15, its DDR indicates increasing bias, see Fig.7. In addition, the receiver loses lock
on the satellite signals several times, because the signal strength drops below the
acquisition threshold because of the trees.
Satellite PRN 22 is initially tracked at a low elevation in the obstructed area of the
sky during this period (9:45-10:45). After that, the elevation of the satellite PRN 22 is
increased to about 700, see Fig.5.
Satellite PRN 25 is initially tracked at a low elevation in the obstructed area of the
sky, seen Fig. 5. At the beginning of the session (4:15-4:30), the satellite is hidden
Reference Point (P1)
Rover Point (P2)
8
behind the trees; its DDR shows fluctuations, see Fig.11. These are due to signal
diffraction effects caused by foliage and branches of the trees.
Comparing L1 DD Residuals of PRN 22, PRN 3, and PRN 25 in May with those in
October, L1 DD Residuals in October are much greater than in May (see Fig. 6, 7, 8, 9,
10, 11). This problem will be evident in weak signal strengths. In October 2002, Tirol
Area in Austria, the maximum quantity of rain in mm is 35, and percent of in the daily
raining quantity is % 108 and in May 2002, the maximum quantity of rain in mm is 23,
and percent of the daily raining quantity is % 78 [15]. In October, the trees in forest
are laden with much more water and moisture than in May. Materials that have high
water content (such as leaves from trees, surface of the forest) can also attenuate GPS
signals. In brief, the moisture on the forest and water content within the leaf is much
more than in May. These two parameters influence GPS measurements and accuracy
[5], [11].
The forest area caused a significant bias in the phase measurements of PRN3. Fig.4.
shows the position of PRN 3 as observed by the reference and rover antenna. The
reference and rover antenne were able to track the satellite signals of PRN 3 during the
sessions in May and in October. This is a typical case of signal diffraction where a
satellite signal is received although the line-of-sight is obstructed. The C/N0 values of
PRN 3 indicate this diffraction effect, see Fig.6, 7.
The diffraction effect is indicated by the changes in the C/N0 values. The C/N0
template values of PRN3 in October and in May for rover point (P2) are expected to be
around 48 dB-Hz, see Fig. 6, 7 (The selected part in the graphics is very close to the
forest area). However, the diffraction effect caused by the trees reduces the C/N0
values of this satellite to the much smaller value of about 35 dB-Hz. In addition to the
C/N0 values the double-difference residuals DDR also display the diffraction effect,
see Fig. 6, 7. The residuals display the diffraction phase errors of the signals of PRN 3.
The maximum phase error is about 150 mm which is about 1 L1 cycle. The phase error
in October is a little bigger than the phase error in May; see in Fig. 6, 7.
Figure 6.C/N0 and Elevation and DDR graphic of PRN 3 in October (P1 – P2)
9
Figure 7.C/N0 and Elevation and DDR graphic of PRN 3 in May (P1 – P2)
The C/N0 template values of PRN 22 in October and in May for rover point (P2) are
expected to be around 48 dB-Hz. However, the diffraction effect caused by the trees
reduces the C/N0 values of this satellite the much smaller value of about 35 dB-Hz. In
addition to the C/N0 values also the double-difference residuals (DDR) display the
diffraction effect, see Fig. 8, 9. The residuals display the diffraction phase error of the
signals of PRN 22. The maximum phase error in October is about 300 mm. However,
in May the maximum phase error is about 10 mm.
Figure 8.C/N0 and Elevation and DDR graphic of PRN 22 in October (P1 – P2)
10
Figure 9.C/N0 and Elevation and DDR graphic of PRN 22 in May (P1 – P2)
Satellite PRN 25, (see Fig. 4) is very close to the forest area (elevation between 300
and 400 for rover point in October). Satellite PRN 25 in October measurement, in the
elevation (about 300 – 400 for rover point (P2)), signals are attenuated to an unusable
power. In addition the receiver loses the satellite signals, (see Fig. 10) because the
signal strength drops below the acquisition threshold by means of water content within
leaves and humidity factor in the forest.
Figure 10.C/N0 and Elevation and DDR graphic of PRN 25 in October (P1 – P2)
11
Figure 11.C/N0 and Elevation and DDR graphic of PRN 25 in May (Baseline P1 – P2)
The residuals display the diffraction phase errors of the signal of PRN 25. The
maximum phase error in October is about 300 mm. However, the maximum phase
error in May is about 100 mm, see Fig.11. The signals are weakened or attenuated by
leaves and small branches. This attenuation can make it very difficult for a GPS
receiver to track the signals. At some point, the receiver will not be able to track the
signal at all and the effect will be the same as if the signal were obstructed. Even if the
signal can be tracked, some receivers will have difficulty accurately measuring the
pseudo ranges [5], [11], [14].
This situation may be explained by larger general water content within the leaf or
needle in October. The negative impact of water on GPS signal is the prime
consideration here. This problem will be evident in weak signal strengths and the
surface moisture on the forest; water laden leaves attenuate more signal than those that
are dry. In October, the leaves of the trees contain a lot of water, and the surface of the
forest has lot of moisture because of the rain. Humidity of the leaves and the forest is
the critical factor for GPS performance near the forest. High water content (such as
leaves from trees, surface of the forest) can also attenuate the GPS signal [5], [11].
When the direct line-of-sight propagation is again possible, and thus no diffracted
signals reach the antenna, the phase errors revert back to the usual range, see Fig. 10,
11. GRAZIA software (SIGMA , SIGMA module) was used for processing the
measurements in May and October for the baseline P1-P2. After processing all of the
measurements, analysing the results and then comparing the standard deviation
graphics of the coordinate differences in October with the standard deviation graphics
of the coordinate differences in May, the coordinate differences in October are much
greater than in May, see Fig. 12, 13 [3], [4], [14].
The user may not know anything about the antenna environment or does not have to
investigate which signals are diffracted; the SIGMA-Δ model does it automatically.
The SIGMA-Δ model works at the zero difference level of phase data and on an
epoch-to-epoch basis. The core of the SIGMA-Δ model is the computation of the
12
phase noise in the ΣΔ variance matrix using the measured C/N0 data and C/N0
template.
Even the effect of weak satellite geometry can be reduced by including signals from
low elevation satellites (cut-off angle 50) and using the C/N0 measurements to
correctly weight these signals. In this experiment, the effectiveness of SIGMA in
reducing signal diffraction effects on static GPS results is demonstrated. Fig. 13 shows
the power of the SIGMA-Δ model [3], [4], [8], [14].
Figure 12. Standard deviation graphics of the coordinate differences in May and
October measurements (using SIGMA model).
Figure 13. Standard deviation graphics of the coordinate differences in May and
October measurements (using SIGMA model).
Kinematics spectral noise = 0 (GRAZIA Software)
Kinematics spectral noise = 0 (GRAZIA Software)
13
CONCLUSION
The signals are affected by the canopy and this of course affects the quality of the
computed position. Forest canopy effects on the GPS signal include obstruction,
attenuation, and reflection.
The parameters (density and humidity of leaves, season in the case of deciduous
trees) affecting attenuation under foliage have been investigated. Moisture retained in
leaves will increase signal attenuation, so the dryer the forest better. Experiment I has
shown that wet foliage in October (humidity in forest) causes much more signal
attenuation.
The results presented in this paper indicate that the extent, humidity and type of
forest canopy obstruction will have a significant effect on the accuracy, precision and
performance of GPS positions. It has also been shown that quantification of forest
canopy obstruction in terms of open sky above the measurement point provides a
means of predicting GPS signal attenuation.
We have shown the effectiveness of the SIGMA-Δ model in an experiment for using
GPS near the forest (Processing by GRAZIA Software). The errors due to GPS signal
diffraction were reduced by means of SIGMA-Δ algorithm. As a result of this, the
software GRAZIA with the SIGMA-Δ model implemented shows a superior
performance in the case of signal diffraction.
When processing the GPS observations of a static session, with a small amount of
data contaminated by diffraction, SIGMA-Δ may still yield good results, because the
model is highly redundant.
Acknowledgments
The ÖAD (Austrian Exchange Service) scholarship which allowed me to spend several
months at the Institute of Engineering Geodesy and Measurements Systems of Graz
University of Technology. I would also like to thank Georg Gassner who provided me
with the GPS data which were part of the field work for the project “Continuous
Monitoring of Landslide using GPS” funded by the Austrian Academy of Science and
for supervising me in the use of the software GRAZIA. I also wish to thank other
people at the Institute for their helps during my research.
14
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