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Machine learning based GNSS signal classification and weighting scheme design in the built environment: a comparative experiment

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None-Line-of-Sight (NLOS) signals denote Global Navigation Satellite System (GNSS) signals received indirectly from satellites and could result in unacceptable positioning errors. To meet the high mission-critical transportation and logistics demand, NLOS signals received in the built environment should be detected, corrected, and excluded. This paper proposes a cost-effective NLOS impact mitigation approach using only GNSS receivers. By exploiting more signal Quality Indicators (QIs), such as the standard deviation of pseudorange, Carrier-to-Noise Ratio (C/N 0 ), elevation and azimuth angle, this paper compares machine-learning-based classification algorithms to detect and exclude NLOS signals in the pre-processing step. The probability of the presence of NLOS is predicted using regression algorithms. With a pre-defined threshold, the signals can be classified as Line-of-Sight (LOS) or NLOS. The probability of the occurrence of NLOS is also used for signal subset selection and specification of a novel weighting scheme. The novel weighting scheme consists of both C/N 0 and elevation angle and NLOS probability. Experimental results show that the best LOS/NLOS classification algorithm is the random forest. The best QI set for NLOS classification is the first three QIs mentioned above and the difference of azimuth angle. The classification accuracy obtained from this proposed algorithm can reach 93.430%, with 2.810% false positives. The proposed signal classifier and weighting scheme improved the positioning accuracy by 69.000% and 40.700% in the horizontal direction, 79.361% and 75.322% in the vertical direction, and 75.963% and 67.824% in the 3D direction.
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Lietal. Satellite Navigation (2023) 4:12
https://doi.org/10.1186/s43020-023-00101-w
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Satellite Navigation
https://satellite-navigation.springeropen.com/
Machine learning based GNSS signal
classication andweighting scheme design
inthebuilt environment: acomparative
experiment
Lintong Li1* , Mireille Elhajj2, Yuxiang Feng1 and Washington Yotto Ochieng1
Abstract
None-Line-of-Sight (NLOS) signals denote Global Navigation Satellite System (GNSS) signals received indirectly from
satellites and could result in unacceptable positioning errors. To meet the high mission-critical transportation and
logistics demand, NLOS signals received in the built environment should be detected, corrected, and excluded. This
paper proposes a cost-effective NLOS impact mitigation approach using only GNSS receivers. By exploiting more
signal Quality Indicators (QIs), such as the standard deviation of pseudorange, Carrier-to-Noise Ratio (C/N0), elevation
and azimuth angle, this paper compares machine-learning-based classification algorithms to detect and exclude
NLOS signals in the pre-processing step. The probability of the presence of NLOS is predicted using regression algo-
rithms. With a pre-defined threshold, the signals can be classified as Line-of-Sight (LOS) or NLOS. The probability of the
occurrence of NLOS is also used for signal subset selection and specification of a novel weighting scheme. The novel
weighting scheme consists of both C/N0 and elevation angle and NLOS probability. Experimental results show that
the best LOS/NLOS classification algorithm is the random forest. The best QI set for NLOS classification is the first three
QIs mentioned above and the difference of azimuth angle. The classification accuracy obtained from this proposed
algorithm can reach 93.430%, with 2.810% false positives. The proposed signal classifier and weighting scheme
improved the positioning accuracy by 69.000% and 40.700% in the horizontal direction, 79.361% and 75.322% in the
vertical direction, and 75.963% and 67.824% in the 3D direction.
Keywords GNSS, NLOS, FDE, Decision tree, Weighting scheme
Introduction
Demand for mission-critical transportation and logis-
tics services is increasing rapidly, particularly in urban
areas. ese services, by definition, require high-per-
formance levels from systems that provide Positioning,
Navigation, and Timing (PNT). Taking the example of
services needed to support autonomous vehicles, the
Society of Automotive Engineers (SAE) specifies the six
levels of automation in Fig.1 (SAE International, 2018).
ese levels range from 0 (full manual driving) to 5 (fully
autonomous driving). At present, self-driving vehicles
are transitioning from Level 3 to Level 4. Level 3 vehicles
can detect the road environment and then make deci-
sions by themselves, such as cruising at a fixed velocity
on a highway. For example, Audi A8L equipped with the
Traffic Jam Pilot (TJP) technology was unveiled in 2019
and certified in Germany as Level 3 (Saber etal., 2021).
However, drivers must be prepared to take over vehicle
*Correspondence:
Lintong Li
ll3919@ic.ac.uk
1 Department of Civil and Environmental Engineering, Imperial College
London, London, UK
2 Astra-Terra Limited, London, UK
Page 2 of 23
Lietal. Satellite Navigation (2023) 4:12
control when accidents occur or the autonomous driving
system fails.
Compared to Level 3, Level 4 vehicles can control
themselves when the aforementioned emergencies occur.
us, Levels 3 and 4 are also known as the fail-safe and
fail-operational levels, respectively. Example Level 4 vehi-
cles currently being tested are Alphabet’s Waymo, Baidu’s
Apollo, Magna’s MAX4, and NAVYA. To achieve a high
degree of positioning accuracy (decametric or better)
with high availability, multi-sensor integration, including
the Global Navigation Satellite System (GNSS), is com-
monly implemented.
GNSS comprises four global, two regional, and several
augmentation systems. Starting with GPS many years
ago, the development and operation of the additional
systems resulted in receiving many more GNSS signals
simultaneously (Li etal., 2020). For example, Fig.2 shows
that a U-blox receiver can receive more than 20 signals
from the various systems at Imperial College London.
Even with GPS and GLONASS, more than ten signals can
be received and used for PNT. However, using all multi-
constellation signals for positioning and navigation, par-
ticularly in built-up areas, increases the computational
burden and the possibility of significant and unaccepta-
ble measurement errors. Such measurements should be
detected and, where possible, excluded. Hence, the main
tasks are to detect and exclude faulty signals, enabling
the use of the best signals subset. Failure Detection and
Exclusion (FDE) should ideally be designed to be used
across the entire signal processing chain, including pre-
processing and the positioning, navigation, and timing
functions. is paper uses machine learning algorithms
together with GNSS measurement Quality Indicators
(QIs) for FDE in the pre-processing function.
From the generation of the data message, upload to
GNSS satellites to transmission, reception of GNSS sig-
nals, and processing them in receivers, these signals are
contaminated by error sources listed in Table 1 (Hof-
mann-Wellenhof, Lichtenegger & Wasle, 2007; Kaplan
& Hegarty, 2005). Among these error sources, mul-
tipath occurs when the direct signal and its reflection
are received together. Especially from a geometric per-
spective in the built environment, if the signal paths are
shaded, the signals are reflected by static and dynamic
objects and received by the receiver, resulting in large
measurement errors. e signals that can be received
Zero autonomy; the
driver performs all
driving tasks.
No
automation
012345
Driver
assistance
Partial
automation
Conditional
automation
High
automation
Full
automation
Vehicle is controlled by
the driver, but some
driving assist features
may be included in the
vehicle design.
Vehicle has combined
automated functions,
like acceleration and
steering, but the driver
must remain engaged
with the driving task and
monitor the environment
at all times.
Driver is a necessity, but
is not required to monitor
the environment.The
driver must be ready to
take control of the
vehicle at all times
with notice.
The vehicle is capable of
performing all driving
functions under certain
conditions. The driver
may have the option to
control the vehicle.
The vehicle is capable of
performing all driving
functions under all
conditions. The driver
may have the option to
control the vehicle.
Society of Automotive Engineers (SAE) automation levels
Fig. 1 Society of automotive engineers levels of vehicle autonomy (source: National Highway Traffic Safety Administration)
Satellite position view Date view
GNSS constellation
Filter satellites
Zoom in/out
15
GPS (G)
SBAS (S)
Galileo (E)
BDS (B)
GLONASS (R)
Show not tracked
Not used in navigation
Not tracked
minmax
Fix mode
3D-fix
TTFF
Longitude
-0.1741605°
Latitude
51.4981172°
Altitude
23.700 m
velocity
0.034 m/s
UTC time
15:41:22
3D acc.(0-50)
2D acc.(0-50)
PDOP (0-10)
1.080
HDOP(0-10)
0.640
Used in navigation
21/34
Not used in navigation
10/34
Not tracked
3/34
7/11
0/2
4/7
4/5
6/9
Fig. 2 GNSS signal reception in imperial college, London (Source:
U-blox U-center 2)
Page 3 of 23
Lietal. Satellite Navigation (2023) 4:12
directly are referred to as Line-of-Sight (LOS). Instead,
we collectively denote reflected and multipath signals
None-Line-of-Sight (NLOS).
As the multipath error in the L1 pseudorange and
carrier phase can reach 450 m, and a quarter of the
wavelength, which is approximately 5cm, respectively
(European Space Agency, 2013), LOS signals have rela-
tively small pseudorange errors (metre level) compared
to NLOS signals. us, the QI relative to pseudorange
error characteristics can be used to detect NLOS signals.
Like the PNT requirements for autonomous driving, the
multipath error also depends greatly on the surrounding
physical environment influencing traffic scenarios. In an
open area, almost all GNSS signals can be received directly
from satellites. However, there is a wide variety of complex
environmentally influenced traffic scenarios such as in the
urban canyon, semi-urban, suburb, viaducts, boulevards,
and tunnels (Wang, Groves & Ziebart, 2015). In the urban
canyon, GNSS signals can be blocked or reflected by high-
rise buildings, trees, and other static or dynamic obstacles.
ese obstacles could result in severe multipath errors,
resulting in unacceptable position errors, which cannot
be mitigated through differential techniques (MacGougan
etal., 2002; Ward, 1997). NLOS pseudorange measurement
errors can also be large (Hsu etal., 2017). erefore, the
NLOS signals are regarded as faulty signals in this paper.
e multipath impact can be mitigated by detecting and
excluding the NLOS signals or reducing the weight of these
signals.
Several methods have been proposed to mitigate the
effect of NLOS signals, including improved antenna
and receiver design, use of weighting models or statisti-
cal approaches, signal processing, consistency check-
ing, mapping- or image-aided matching, and LOS/NLOS
classification (Zhu et al., 2018). However, choke-ring,
controlled-reception pattern, and dual-polarization anten-
nas are expensive and impractical for dynamic use due
to size, weight and power consumption. e use of code
discriminator in the receiver is also expensive in terms of
power consumption and manufacture. Since this paper
seeks a cost-effective NLOS impact mitigation approach
employing only a civil GNSS receiver without external
aiding, mapping- and image-aided matching and consist-
ency-checking algorithms are not considered. is paper
proposes a machine learning-based regression algorithm
internal to the receiver to detect NLOS signals. e input
features of the machine learning model are a set of Qual-
ity Indicators (QIs), such as elevation angle and Carrier-
power-to-Noise-density ratio (C/N0), which indicate the
quality of the signals, and, therefore, enable the possibility
of accurate prediction NLOS signals. With an appropri-
ate threshold, all signals can not only be categorised as
either NLOS or LOS but also allow the latter to be ranked
to reflect the error level. A novel weighting scheme is pro-
posed to exploit this ranking to increase the availability of
the positioning function.
State‑of‑the‑art weighting schemes
Weighted Least Square (WLS) is commonly used for posi-
tioning with GNSS pseudorange measurements, using the
expressions:
where
z
is the difference between pseudorange measure-
ment and geometric range,
H
is the state matrix,
ε
is the
measurement noise vector, and
x
is a calculated vector
comprised of three-dimensional coordinates and receiver
clock offsets of all constellations. e weight matrix
W
is commonly specified based on the estimation of GNSS
measurement quality with the two basic QIs, elevation
angle and C/N0, as shown in Table2 (Collins, & Langley,
1999; Eueler & Goad, 1991; Hartinger & Brunner, 1999;
Parkinson etal., 1996; Shokri etal., 2020; Tay & Marais,
2013; Wen, 2020; Wieser & Brunner, 2000). e elevation
angle and C/N0 masks are also commonly used to exclude
(1)
z=Hx +ε
(2)
ˆ
=
HTWH
HTW
Table 1 Main GNSS error sources
Source Details
Satellite-based Clock bias
Ephemeris bias
Selective availability
Signal propagation Ionospheric delay
Tropospheric delay
Multipath
Receiver-based Clock bias
System noise
Table 2 Elements designed in the weight matrix
Number Function
(i)
|sin (elevation)|
(ii)
sin2(
elevation
)
(iii)
tan2(
elevation
)
(iv) 1/(0.244 × exp(C/N0/10))
(v) 1/(0.03 + 0.244 × exp(C/
N0/10))
(vi) 1/(0.13 + 0.56 × exp(C/
N0/10))
(vii) exp(C/N0/10 )×
sin2
(elevation
)
Page 4 of 23
Lietal. Satellite Navigation (2023) 4:12
possible outlying measurements during pre-processing in
the GNSS processing software.
As complexity increases in built environments such as
urban canyons, GNSS signal analysis also increases. e
C/N0 value could increase or decrease due to construc-
tive or destructive multipath interference, respectively
(Ward, 1997). erefore, not all signals with larger C/N0
values should be labelled as LOS. In addition, signals are
generally considered LOS when they have large eleva-
tion angles. However, there are scenarios when low-ele-
vation angle signals are LOS, for example, those in front
and behind a vehicle travelling in an urban canyon. Note
that high-rise buildings can block vehicle-side signals.
erefore, only using an elevation angle is insufficient
to capture signal quality. Direction-related indicators
such as azimuth angle and vehicle heading should also be
considered.
is paper considers more QIs, including those related
to direction, measurement statistics and vehicle, for
advanced signal quality measurement. After an initial
analysis of the correlation of all QIs to LOS/NLOS sig-
nals, some are used as input to selected machine learning
models. e NLOS probability output from the models
can then be used to label signals and improve the design
of the weight matrix. Adjrad and Groves (2017) propose
a weight matrix by multiplying the NLOS probability
with the seventh weighting scheme. As a result, horizon-
tal positioning accuracy is improved by 44%. Wen etal.
(2020) estimate the pseudorange error of NLOS signals
using an empirical formula constructed from both the
azimuth and elevation angles (Hsu, 2018). e NLOS sig-
nals are labelled based on an integrated GNSS and Lidar
system. e User Equivalent Range Errors (UERE) for
both LOS and NLOS signals are then calculated for the
new weight matrix design. Xu etal. (2020) predict a C/N0
threshold of LOS/NLOS signals using the Support Vec-
tor Machine (SVM) classification algorithm. If the pseu-
dorange residual is greater than this threshold, the weight
of this measurement decreases. Experiments show that
the mean positioning error is reduced from 26.40m to
3.03m in peri-urban scenarios. e standard deviation
was also reduced from 14.78m to 1.96m. In a deep urban
scenario, the mean and standard deviation of the posi-
tioning error is reduced by 53.77% and 90.53%, respec-
tively. e above studies indicate that an improved weight
matrix can be designed along with NLOS information.
Compared with the aforementioned studies in which
the NLOS probability or signal classification results are
obtained using a three-dimensional city model, Lidar
data, and sky-plot images, this paper proposes a machine
learning algorithm using only GNSS QIs.
State‑of‑the‑art machine learning‑based LOS/NLOS signal
classication algorithms
e aim of detecting NLOS signals is to reduce the mag-
nitude and standard deviation of the UERE. However,
since positioning accuracy is mainly influenced by Dilu-
tion of Precision (DOP) and UERE, these two aspects
should be simultaneously considered when selecting the
best signal subset (Montenbruck et al., 2002; Yin etal.,
2013).
When selecting a subset of signals, the main issue is
an excessive computational burden. For example, if four
signals are selected from ten signals, the number of DOP
calculations is
C4
10
=
210
. If the number of signals goes
up to twenty, the number will soar to 4845. is issue
requires resolution since many signals (twenty or higher)
GNSS signals from all constellations can be received
simultaneously. Simplified DOP calculation algorithms
have been proposed for fast signal subset selection (Meng
et al., 2015; Teng et al., 2018; Wang etal., 2018; Wei,
Wang & Li, 2012). Chen and Zhang (2010) exclude some
signals before the DOP calculation. e excluded signals
have elevation angles between thirty to sixty degrees and
azimuth angles approximately equal to those of other sig-
nals. Park and How (2001) and Wei etal. (2012) also pro-
pose an algorithm to eliminate signal redundancy. ey
assess signal redundancy by the angle between the two
signal LOS vectors. However, in the urban canyon, NLOS
signals account for a large proportion of those received.
erefore, reducing the number of DOP computations
directly through signal redundancy may remove LOS sig-
nals and retain NLOS signals. An effective way to solve
this issue is to select LOS signals using mathematical or
machine learning algorithms before DOP calculation
(Chen, Chien-Sheng, Lin & Lee, 2013; Chen, Chien-
Sheng, 2015; Mosavi & Divband, 2010; Simon & El-
Sherief, 1995; Teng & Wang, 2016; Wu etal., 2010; Zarei,
2014; Zhu, 1992). In this way, most NLOS signals, as well
as other faulty signals, can be removed before DOP cal-
culation. e state-of-the-art flow chart of the signal sub-
set selection algorithm is illustrated below (Fig.3).
Machine learning algorithms have previously been
used to detect GNSS NLOS signals. e three machine
learning algorithms used are supervised, unsupervised,
and reinforcement learning. e main difference between
these three categories is the availability of labels. e
supervised learning model is trained and tested with a
labelled dataset. Unlabelled data are appropriate for the
unsupervised learning model. For reinforcement learn-
ing, an agent interacts with the target environment by
performing actions and obtaining rewards or punish-
ments generated in real time. For NLOS probability pre-
diction, supervised learning algorithms are mainly used.
Page 5 of 23
Lietal. Satellite Navigation (2023) 4:12
e final dataset thus has signals labelled as either LOS
or NLOS.
is paper uses supervised learning algorithms with
QIs only from GNSS sensors as input to predict the
NLOS probability and classify LOS/NLOS signals. Exten-
sive studies have been conducted and yielded relatively
accurate results. Early research used only a single QI,
such as C/N0, as input (Irish etal., 2014a). As discussed
earlier, C/N0 is sensitive to the multipath effect, espe-
cially in urban canyons. Moreover, the C/N0 distributions
of LOS and NLOS signals tend to overlap for low-grade
receivers. us, more QIs have also been considered for
the signal classification task. Yozevitch etal., (2012, 2016)
proposed three classifiers using the C/N0, elevation angle,
measurement, carrier lock, satellite clock bias, and indif-
ferent features.
e three classification algorithms are the four-depth
decision tree, expectation maximisation, and a simple
C/N0 threshold determination. e classification accu-
racy achieved is higher than 70%. Using the same set of
QIs, Sun etal., (2020a, 2020b, 2021) improved the accu-
racy to 89% for static data. e Gradient Boost Regres-
sion Tree (GBRT) in Sun etal. performs better than the
decision tree, K Nearest Neighbor (KNN), and Artificial
Neuro-Fuzzy Inference System (ANFIS) algorithms.
However, the classification results obtained from static
and dynamic data in the urban canyon are very different.
For static data, the state of the GNSS signal changes grad-
ually. For dynamic data, the state may suddenly change
from visible to blocked and then visible again. Phan etal.
(2013) use the elevation and azimuth angle as QIs and
Support Vector Machine (SVM) regression as a regressor
to estimate multipath errors. e SVM multipath error
estimator performs better than the Carrier Smoothing
Filter (CSF). is result shows that the azimuth angle
can also be used to estimate signal quality. Hsu (2017)
introduced more QIs as input, including the change rate
of C/N0, and the difference between pseudorange rate
and delta pseudorange. e classification accuracy of the
SVM regressor achieved is 75.40%.
When using the dual polarisation antenna, the C/N0
values generated from both Left-Hand Circular Polar-
ized (LHCP) and Right-Hand Circular Polarized (RHCP)
antennas can also be used as QIs. Guermaha etal. (2018)
propose a GNSS LOS/NLOS classifier with dual-polar C/
N0 values and elevation angle as input, showing that 99%
of signals could be classified correctly. However, the data
points were just 100, and 66 LOS signals were included
Multi-constellation signals after
other pre-processing steps
Faulty signal detection, correction,
and exclusion
Signal subset selection
No enough signals for positioning
Satellite geometry is worse for
positioning
Enough signals
remains?
Minimal DOP calculation
DOP requirement
satisfied?
Yes
No
No
Positioning
Yes
Fig. 3 Flow chart of GNSS signal subset selection algorithm
Page 6 of 23
Lietal. Satellite Navigation (2023) 4:12
in the dataset. Data imbalance may have an impact on
experimental results. Sun etal. (2021) propose an ANIFS
algorithm with C/N0 and its difference, elevation angle,
and pseudorange residual as QIs to predict and correct
NLOS measurements. As a result, the positioning accu-
racy improved to 30%. Xu etal. (2019) also propose an
SVM classifier with the aforementioned QIs and others
from the Autocorrelation Function (ACF) with 90.39%
classification accuracy. In summary, many QIs could be
used to estimate signal quality. erefore, an analysis of
how all QIs relate to or influence LOS/NLOS signals is
required to inform the selection of QIs for input to the
machine learning algorithms.
Suzuki et al. (2020) use neural network and Convo-
lutional Neural Network (CNN) models to improve
classification accuracy further to approximately 98%.
However, the input to the CNN model is sky-plot images
from a fish-eye camera at a static point in the urban can-
yon rather than the QIs discussed previously. In addi-
tion, there was no dynamic experiment. is paper only
focuses on constructing a classifier using GNSS QIs
when the vehicle moves. e potential advantage of this
approach is that if a classification accuracy similar to the
CNN model’s results can be achieved, then there would
be no need for external aiding through additional sensors
and data.
Machine learning algorithms forregression
is paper uses several machine learning regression algo-
rithms together with specified thresholds to predict the
possibility of a GNSS signal being NLOS.
(i) Support Vector Regression (SVR): SVR is effectively
used to generate a high-dimension hyperplane to fit the
data (Drucker etal., 1996; Smola & Schölkopf, 2004). All
data in the training dataset are closest to the hyperplane.
Unlike the least squares method, the function of SVR
is to minimise the coefficients. In this paper, the Radial
Basis Function (RBF) kernel K
x,˜
x
is chosen for nonlin-
ear fitting. e SVR problem description and solution are
illustrated in Formula (4) and (5). e advantages of the
RBF kernel are simplicity of model design, powerful fit-
ting, and low space complexity.
where
x
and
˜
x
are QI vectors in input space, and
σ
is a
kernel parameter.
(3)
K
x,˜
x
=exp
||x˜
x||2
2σ2
(4)
min
ω,
b
1
2||ω||2+C
m
i=1
γ
f(xi)yi
where
ω
and
b
are two model parameters, C is a regulari-
zation coefficient,
γ
is
-insistency loss function,
gi
is the
function of Lagrange coefficients.
(ii) K-Nearest Neighbors (KNN): KNN is a non-para-
metric algorithm. e output is the average of k nearest
neighbours’ values (Guo et al., 2003; Song etal., 2017).
According to the result of ten-fold cross-validation, k is
chosen as five, and all neighbours have the same weight
(Fig.4).
(iii) Gradient Boosting Decision Tree (GBDT): GBDT
is an iterative decision tree model with an ensemble of
weak learners or trees (Ke etal., 2017; Sun, Wang, Zhang,
Hsu & Ochieng, 2020). e predicted output is the sum
of the outputs from all weak learners.
where
γt
and
ht(x)
are the weight and the predicted result
of each weak learner, respectively. e kth weak learner
predicts the residual between the true value and the sum
of the predicted values from 1st to k-1th. In this paper,
the GBDT model uses a Logarithmic loss function to
indicate the accuracy of the binary classification. By tun-
ing hyperparameters, the number of weak learners inside
the model is a hundred. e criterion is Friedman’s mean
squared error (Friedman & Hall, 2007) to reduce impu-
rity. e Friedman mean squared error is also used in the
decision tree and random forest algorithms.
(iv) Decision tree: As a typical tree-like model, the deci-
sion tree, or Classification and Regression Tree (CART),
divides the entire training dataset into smaller subsets
(Myles etal., 2004; Xu etal., 2005). e procedure for
generating a decision tree is illustrated in Fig.5. e Sum
of Square Error (SSE) is always chosen as the splitting
(5)
f(x)=
m
i=1
giK
x,˜
x
+
b
(6)
f(x)=
T
t=1
γtht(x
)
90.20%
90.00%
89.80%
89.60%
89.40%
Cross-validated accuracy
89.20%
89.00%
12345
The value of k for KNN
678910
Fig. 4 The results of ten-fold cross-validation in the KNN model
Page 7 of 23
Lietal. Satellite Navigation (2023) 4:12
metric for regression. To avoid overfitting, the maximum
depth of the tree is ten in this paper (Fig.6).
(v) Random forest: is ensemble algorithm uses a set
of weak learners (Rodriguez-Galiano etal., 2015; Segal,
2004). Unlike GBDT, the random forest algorithm is
a bagging method in which all weak learners are paral-
lel, and the predicted output is the average of the out-
puts from all learners. Moreover, increasing the number
of decision trees in the random forest algorithm does
not cause overfitting. However, the number of decision
trees is a key factor. A bootstrapping strategy is used in
the random forest algorithm to vary the input dataset
for all learners. Each tree’s maximum depth is also ten
to address the same concern as with the decision tree
algorithm.
(vi) Linear regression: is is the simplest and classi-
cal regression algorithm applied in various scenarios. In
this paper, the result of the linear regression algorithms is
used as a baseline.
(vii) Adaboost: is is a boosting algorithm like the
GBDT (Collins, Schapire & Singer, 2002; Solomatine &
Shrestha, 2004). e first weak learner is trained from
the initial training dataset. en, according to the first
learner’s performance, the training dataset’s distribu-
tion is adjusted in real time by increasing the weight of
data points with large relative errors. After that, the sec-
ond weak learner is trained. e process is repeated until
the number of learners is maximum. e advantages of
the Adaboost are: (i) less prone to overfitting, and (ii)
the regression model can be constructed with any weak
learners. Like the GBDT model, a hundred weak learners
are inside the Adaboost model.
(viii) Bootstrap aggregating (Bagging): Suppose the
total amount of the training data is n (Breiman, 1996;
Sutton, 2005). e
˜n
data points extracted are used for
training the first decision tree (
˜n<n
). en the extracted
data are put back into the whole training dataset. is
process is repeated k times. e predicted output is the
average of the outputs from all weak learners. e com-
putational complexity of the Bagging algorithm is small,
and the out-of-bag estimation can be performed with
enough remaining data (Martínez-Muñoz & Suárez,
Generate a
node
Split dataset
with the best
attribute
If all data
in the same
category?
Generate
breach nodes
Generate a leaf
node
If the number
of layer is
equal to
threshold?
End
Yes
No
NoYes
Fig. 5 The flow chart of the decision tree
Page 8 of 23
Lietal. Satellite Navigation (2023) 4:12
2010). However, different from the random forest, which
is also a bagging method, all QIs are involved in the train-
ing process. erefore, Bagging is more prone to overfit-
ting than the random forest algorithm.
(ix) Extremely randomised tree (Extra tree): is
method is similar to the random forest (Eslami et al.,
2020; Geurts et al., 2006). e difference is that the
extra tree is only one random QI used when dividing
the tree nodes. Extreme randomness greatly inhibits
overfitting. However, the differences between each weak
learner inside are also greater, which results in regres-
sion that tends to be less effective than the random forest
algorithm.
(x) Multi-Layer Perceptron (MLP): MLP is an artificial
neural network that contains one input layer, multiple
hidden layers, and one output layer (Gaudart etal., 2004;
Murtagh, 1991). is paper uses three hidden layers to
represent the nonlinear regression complexity as much
as possible. e following research will test the perfor-
mance of deep learning models with more hidden layers.
e output of the previous layer is the input of the cur-
rent layer. e activation function describes the nonlin-
ear relationship between input and output. e Rectified
Linear Unit (ReLU) achieves the best classification accu-
racy, as shown by experimental analysis.
Field test andanalysis ofresults
Data description
One publicly available open-source GNSS dataset was
captured in Berlin and Frankfurt (Reisdorf etal., 2016).
e highest German tower is also in Frankfurt am Main
(see the red circle in Fig.7 (iii)). ese data were recorded
using one low-grade U-blox EVK-M8T GNSS sensor
with ANN-MS antenna, one high-grade NovAtel SPAN
differential GNSS sensor with pinwheel antenna, and
one odometry sensor. e ground truth was generated by
fusing the NovAtel receiver with the ego-motion data in
the post-processing step. e ego-motion data were col-
lected from the CAN sensor (Novatel, 2016) (Figs.7, 8).
Furthermore, the LOS/NLOS labels provided inside
the dataset were generated by comparing the times-
pan and availability of the signals from both the NovA-
tel and the U-blox. e reliability of the dataset can be
proven through two aspects: (i) We randomly chose one
epoch from every four sub-datasets and drew skyplots
(see Fig.9). In these figures, we represent the width of
the road with a dotted line. Almost all signals from the
same category are clustered together. Although some
NLOS signals fall within the cluster boundary of LOS sig-
nals, this could be caused by the occlusion of balconies
or street lamps. (ii) is dataset has already been used
by two other papers for NLOS detection and LOS/NLOS
classification (Li etal., 2022; Reisdorf & Wanielik, 2018).
e driving environment is shown in Table3 (Reisdorf
etal., 2016). e data capture was conducted such that
the number of LOS and NLOS signals would be roughly
the same to avoid the imbalance classification issue (Gan-
ganwar, 2012; Sun, Wong & Kamel, 2009) (Fig.9).
In the dataset, the GPS time, GPS week and seconds of
the week, ground truth receiver position, heading, veloc-
ity, acceleration, and yaw rate of the vehicle were gener-
ated using the NovAtel data and the ego-motion data.
Broadcast ephemeris data were downloaded from the
International GNSS Service (IGS). e GNSS and satel-
lite identifier, raw measurement and estimated standard
deviation, carrier-phase lock time counter, and C/N0
were generated using the U-blox data. Using this infor-
mation, the QIs needed in this paper are generated.
Assessment metrics
e assessment metrics for the signal classification task
are classification accuracy and false positive probability.
True Positive (TP)
STP
is the result that the classifi-
cation model predicts the positive category correctly.
True Negative (TN)
STP
is the result that the classifica-
tion model predicts the negative category correctly. False
Positive (FP)
SFP
is the result that the classification model
predicts the positive category incorrectly. False Negative
(FN)
SFN
is the result that the classification model pre-
dicts the negative category incorrectly.
In the experiment, ’True’ means the signal is originally
labelled as LOS, and ’False’ means the signal is labelled as
(7)
P
CA =
S
TP
+S
TN
S
TP
+S
TN
+S
FP
+S
FN
(8)
P
FP =
S
FP
STP
+
STN
+
SFP
+
SFN
100.00%
97.50%
95.00%
92.50%
90.00%
10 20
The maximum depth of the decision tree
Train
Test
30 40 50
87.50%
85.00%
82.50%
Cross-validated accuracy
Fig. 6 The results of ten-fold cross-validation in the decision tree
model
Page 9 of 23
Lietal. Satellite Navigation (2023) 4:12
NLOS. erefore, classification accuracy is the probabil-
ity that the category of a measurement can be correctly
predicted using machine learning models. e probabil-
ity of false positive is also chosen as the second assess-
ment metric because the smaller the percentage of false
positives, the fewer NLOS measurements are left in the
remaining dataset. erefore, this metric is safety critical.
In addition, it shows the measure of trust in the remain-
ing dataset.
Discussion ofquality indicators
Eleven QIs are discussed in this section. e relationship
between each QI and the GNSS signal classification is
analysed with 50,000 LOS and 50,000 NLOS signals cho-
sen randomly.
(i) Carrier phase lock-time counter (milliseconds):
is is the length of time for which the phase-
locked loop has been locked. When the GNSS
receiver loses the lock of a transmitting signal, the
ambiguity of carrier-phase measurements changes
randomly. e U-blox receiver can provide this QI
directly in the UBX-RAM-RAWX message. Stud-
ies have shown that the signal amplitude would be
changed after being reflected. Consequently, the C/
N0 of the carrier and loss-lock state will be affected
(Ray & Cannon, 1999; Townsend etal., 1995). So,
if the lock time is zero, the signal is likely NLOS.
As illustrated in Fig.10, almost 95% of NLOS sig-
nals had less than 1000ms of lock time. In con-
trast, LOS signals had a longer lock time. More
than 50% of LOS signals had a lock time of more
than 10,000 ms. Since the maximum lock time
was 64,500ms, the smaller lock time would tend
to be close to zero after normalisation. To avoid
this issue, we use the carrier phase lock state to
replace the lock time. If the lock time exceeds
1000ms, the lock state is 1 (locked). Otherwise, it
is 0 (unlocked). In this way, 11.48% of NLOS signals
and 72.81% of LOS signals are locked.
(ii) Pseudorange standard deviation (metres): is
indicates the magnitude of the pseudorange esti-
mation error. is value and the following two
standard deviations are generated directly from
the U-blox receiver. e relationship between this
QI and LOS/NLOS signals is shown in Fig. 11.
Almost all LOS signal values of pseudorange stand-
ard deviation were concentrated at 10.24m. How-
ever, for NLOS signals, 15,670 values were 20.48m
(1694 for LOS signals), 4001 values were 40.96m
(129 for LOS signals), 856 values were 81.92m (41
for LOS signals), and 36 values were even as high
as 163.84 m (5 for LOS signals). e experiment
shows that this QI is the most effective for LOS/
NLOS classification.
(iii) Phase standard deviation (cycles): is indicates
the magnitude of the carrier phase estimation
error. e relationship between this QI and LOS/
NLOS signals is shown in Fig. 12. Similar to the
(i) Berlin-Potsdamer Platz (ii) Berlin-Gendarmenmarkt
(iii) Frankfurt am Main-Main
Tower
(iv) Frankfurt am Main-Westend
Tower
Fig. 7 Driving routes in berlin and frankfurt am main (Source:
(Reisdorf et al., 2016))
(i) Berlin-Potsdamer Platz (ii) Berlin-Gendarmenmarkt
(iii) Frankfurt am Main-Main
Tower
(iv) Frankfurt am Main-Westend
Tower
Fig. 8 Three-dimensional streetscapes in berlin and frankfurt am
main (Source: Google map)
Page 10 of 23
Lietal. Satellite Navigation (2023) 4:12
pseudorange standard deviation, the magnitude
of the phase standard deviation of the NLOS sig-
nals is relatively large. More than 30,000 NLOS
signals have the largest phase standard deviation.
However, for LOS signals, the amount does not
decrease monotonically as the phase standard devi-
ation increases. 9.33% of LOS signals still have the
largest phase standard deviation. us, this QI may
not be as effective as the former QIs for classifica-
tion.
(iv) Doppler standard deviation (Hertz): e Dop-
pler shift is the carrier-phase time derivative.
e U-blox receiver also estimated the Doppler
standard deviation. According to the relationship
between this QI and GNSS signal classification,
most LOS signals have a Doppler standard devia-
N
S
WE
30°
60°
330°
300°
20° 40° 60° 80°
240°
210° 150°
120°
N
S
WE
30°
60°
330°
300°
20° 40° 60° 80°
240°
210° 150°
120°
N
S
WE
30°
60°
330°
300°
20° 40° 60° 80°
240°
210° 150°
120°
N
S
WE
30°
60°
330°
300°
20° 40° 60° 80°
240°
210° 150°
120°
LOS
NLOS
LOS
NLOS
LOS
NLOS
LOS
NLOS
Fig. 9 Skyplots from every four sub-datasets
Table 3 Driving environment description
City Road length (m) Road width (m) Building height (m) NLOS
signal
ratio (%)
Berlin-Potsdamer Platz 1600 13–17 70–100 49
Berlin-Gendarmenmarkt 4950 20–23 20–60 37
Frankfurt am Main-Main Tower 2925 10–70 110–259 46
Frankfurt am Main-Westend Tower 2340 10–70 < 208 32
Page 11 of 23
Lietal. Satellite Navigation (2023) 4:12
tion of less than 3Hz, and the Doppler standard
deviation of most NLOS signals is between 4 and
9Hz (Fig.13).
(v) C/N0 (decibel Hertz): Carrier-power-to-Noise-den-
sity ratio (C/N0) indicates the signal strength of the
received GNSS signal and can be used for channel
scheduling and code and phase lock checking (Pini,
Falletti & Fantino, 2008). It is commonly used to
estimate signal quality. Yozevitch etal., (2012, 2016)
set a 37dB·Hz C/N0 threshold to classify LOS and
NLOS signals with 71% classification accuracy. e
relationship between this QI and LOS/NLOS sig-
nals is shown in Fig.14. When the C/N0 value is
small, there is a high probability that the signal is
NLOS. In contrast, the LOS signal has a large C/
N0 value. ere is an overlap when the C/N0 value
is between 20 and 50dB·Hz. is overlap width is
a key criterion for determining the GNSS receiver’s
quality (Irish etal., 2014b). A C/N0 mask is com-
monly set in the pre-processing step to exclude
possible faulty signals. However, many NLOS sig-
nals tend to remain undetected in the built envi-
ronment. Figure15 shows the relationship between
the C/N0 values and the ratio of NLOS signals.
Although the signal’s C/N0 is equal to 30dB·Hz,
more than 70% of the signals are NLOS. erefore,
the signal quality cannot be estimated by C/N0
only.
Normally, the ratio of NLOS signals decreases with
an increase in C/N0. However, a special circum-
stance is when the value of the C/N0 is greater than
50dB·Hz with an increased ratio of NLOS signals.
is is because constructive multipath interference
can also cause an increase in C/N0 (Ward, 1997).
(vi) Elevation angle (degrees): is is the angle between
the line of sight and the horizontal plane, meas-
ured in the vertical plane. Like C/N0, the elevation
angle mask is also set in the pre-processing step
to exclude possible outlying signals for two main
reasons. First, the magnitude of the atmospheric
40000
30000
20000
Number of signals
10000
200000
Carrier phase locktime (ms)
4000060000
LOS
NLOS
80000
0
Fig. 10 The relationship between carrier phase lock-time counter
and GNSS signal classification
30000
25000
20000
15000
10000
5000
02550
LOS
NLOS
75 100 125 150
Pseudorange standard deviation (m)
Number of signals
0
Fig. 11 The relationship between pseudorange standard deviation
and GNSS signal classification
30000
25000
20000
15000
10000
0 0.02
Carrier phase standard deviation (in cycles)
LOS
NLOS
0.04 0.06
Number of signals
5000
0
Fig. 12 The relationship between carrier phase standard deviation
and GNSS signal classification
20000
15000
10000
5000
10020
LOS
NLOS
30 40
Doppler standard deviation (Hz)
Number of signals
0
Fig. 13 The relationship between doppler standard deviation and
GNSS signal classification
Page 12 of 23
Lietal. Satellite Navigation (2023) 4:12
delay error is determined by the elevation angle of
the signal. us, the elevation angle is the variable
of empirical ionospheric and tropospheric cor-
rection models. Moreover, the GNSS signals with
small elevation angles can be blocked or reflected
when a vehicle moves in the urban canyon. e sig-
nals with relatively large elevation angles are most
likely LOS. However, in the urban canyon, the sig-
nals in the front and rear directions of the vehicle
are not prone to be obstructed. On the other hand,
signals received from both sides of the vehicle are
easily affected by the high-rise buildings. erefore,
angle-related QIs need to be analysed comprehen-
sively.
e relationship between the elevation angle and LOS/
NLOS signals is shown in Fig.16. 69.80% of LOS
and 19.10% of NLOS signals had more than 40
degrees elevation angles. Compared with the C/
N0, the distributions of the two signal categories
concerning the elevation angle overlapped with a
smaller area. is result means that the elevation
angle is more feature-important for signal classi-
fication than the C/N0. e relationship between
the elevation angle and the ratio of NLOS signals is
shown in Fig.17. Similar to the C/N0, in the urban
canyon, simply setting an elevation angle mask in
the pre-processing step is insufficient to exclude
most NLOS signals.
(vii) Azimuth (degrees): is is the angle between a
GNSS satellite and the North. It is measured clock-
wise around the antenna’s horizon or earth station’s
horizontal plane. A separate analysis of the azi-
muth angle shows no obvious relationship between
this QI and GNSS signal classification (shown in
Fig.18). is result is reasonable since the GNSS
satellites are scattered in all directions. However,
when a vehicle moves in the urban canyon, the sig-
nals in the front and rear directions of the vehicle
are not prone to be blocked or reflected. In addi-
tion, the signals received on both sides are heavily
affected by high-rise buildings. Figure9 also proves
3500
3000
2500
2000
1500
1000
10 20 30
LOS
NLOS
40
C/N0 (dB·Hz)
Number of signals
50
500
0
Fig. 14 The relationship between C/N0 and GNSS signal classification
100.00%
80.00%
60.00%
40.00%
20.00%
10 20 30
C/N
0
(dB·Hz)
Ratio of NLOS signals
40 50
0
Fig. 15 The relationship between C/N0 and the ratio of NLOS signals
4000
3000
2000
1000
20406080
Elevation (°)
Number of signals
LOS
NLOS
0
Fig. 16 The relationship between elevation angle and GNSS signal
classification
020
Ratio of NLOS signals
100.00%
80.00%
60.00%
40.00%
20.00%
0
40
Elevation (°)
6080
Fig. 17 The relationship between elevation angle and ratio of NLOS
signals
Page 13 of 23
Lietal. Satellite Navigation (2023) 4:12
that signals on both sides of the driving direc-
tion are more likely to be NLOS. us, the angle
between two vectors and the GNSS signal classifi-
cation must be related. e two vectors are those of
the azimuth angle and the vehicle’s heading angle.
e angle range is [0°, 90°]. We denote this angle as
a difference from the azimuth angle. e relation-
ship between this angle and GNSS signal classifica-
tion is shown in Fig.19. Compared to the NLOS
signals, the LOS signals have smaller differences in
azimuth angle.
(viii) Velocity (metres per second), acceleration (metres
per second squared), and yaw rate (degrees per sec-
ond): ese are all vehicle-based QIs. Results show
no relationship between these three QIs and GNSS
signal classification. Indeed, these QIs cannot be
used in a single traffic scenario to estimate the sig-
nal quality. However, in future studies, all traffic
scenarios should be analysed comprehensively. In
different traffic scenarios, the driving speed and
yaw rate, as well as the acceleration pattern, will
be different. For example, the speed limit in the
United Kingdom may vary by vehicle type. For cars
and motorcycles, the maximum speeds of vehicles
travelling in built-up areas and motorways are 30
and 70 miles per hour, respectively. us, these QIs
can effectively assist the system in determining the
current traffic scenario and further assessing the
signal quality.
(ix) Change rate of C/N0 (decibel Hertz): is is the
difference in the C/N0 of two adjacent time points
of the same signal. Figure20 shows that this QI is
irrelevant to signal classification.
(x) Measurement residual (metres): is is the dif-
ference between the pseudorange and computed
range from a GNSS satellite to the estimated
receiver position. In addition to GNSS signal qual-
ity, measurement residuals are also affected by the
positioning method and all measurements used at
that time. e results from the experiment show
some residual outliers causing this QI’s normal val-
ues to be closer to zero after normalisation.
Adopting basic and weighted least squares methods
with weighting schemes from (i) to (vii) in Table2,
the relationship between the measurement residual
and GNSS signal classification in the same GPS
time interval is shown in Fig. 21. ree findings
arise from this Figure. Firstly, the distributions of
LOS and NLOS signals almost completely overlap.
erefore, it is difficult to distinguish between two
categories of signals using this QI alone. Secondly,
the relationships vary with weighting schemes.
ere is, therefore, no generalised conclusion that
measurement residuals obtained by a specified
weighting scheme can best be used to accomplish
signal classification. Finally, LOS signals tend to
have greater measurement residual in the urban
canyon. For example, as shown in Fig.21 (vii), the
mean values of LOS and NLOS signals are 19.34
and 15.18m, with corresponding standard devia-
tions of 23.46 and 24.40m.
In addition, as the pseudorange residual is obtained
after positioning, while signal FDE is conducted
during pre-processing, this QI is not available for
classification at this stage. So instead, we use the
standard deviation of pseudorange to describe its
error characteristics.
(xi) Change rate of pseudorange (metres): is QI can
also be used to describe the error characteristics of
the pseudorange. However, it has the same draw-
back as the measurement residual. e outlier of
0100
LOS
NLOS
5000
4000
3000
2000
1000
0
200
Azimuth (°)
Number of signals
300
Fig. 18 Relationships between azimuth angle and GNSS signal
classification
1000
800
600
400
200
02040
Difference of Azimuth (°)
LOS
NLOS
Number of signals
6080
0
Fig. 19 Relationships between the difference in azimuth angle and
GNSS signal classification
Page 14 of 23
Lietal. Satellite Navigation (2023) 4:12
this QI can be extremely large with either LOS or
NLOS signals. e maximum absolute values for
LOS and NLOS signals from the experiment are
175,359.78 m and 508,235 m, respectively. ere
are 82.66% LOS and 86.72% NLOS signals with
less than 100m of this QI. After feature normalisa-
tion, the outliers caused most values of the QI to be
closer to zero. erefore, this QI is also not recom-
mended for classification.
In summary, eleven QIs are discussed in this section,
with the first seven shown to be important features
for distinguishing LOS and NLOS signals. ere-
fore, the seven QIs are used in this paper as inputs
to the machine learning algorithms to predict the
NLOS probability of each signal.
Results ofLOS/NLOS classication using machine learning
algorithms
After collecting and generating all QIs needed and
combining them with LOS/NLOS labels, one machine-
learning dataset from four sub-datasets in Berlin and
Frankfurt was created. 50,000 LOS and 50,000 NLOS
signals were chosen randomly to avoid the data imbal-
ance issue. e dataset is randomly divided into train-
ing, validating and testing sub-datasets. e ratios of the
training, validating and testing sub-datasets are 52.5%,
17.5% and 30%, respectively. is section focuses on the
classification results using this dataset. Ten regression
algorithms are implemented to predict the NLOS proba-
bility, and then the signals are classified as LOS or NLOS
by comparing the possibility to a pre-set threshold. is
paper sets the threshold as 50%. is threshold is sensi-
tive to the number of signals (e.g. in a multi-constellation
scenario), measurement redundancy and LOS/NLOS
trade-off.
Normally, the elevation angle and C/N0 masks are set to
exclude possible outlying signals in the GNSS processing
software. is approach can be regarded as a simple deci-
sion tree model. e relationships between the two QIs
and the ratio of NLOS signals were separately presented
in Figs.14 and 16. Table4 shows the results (classification
accuracy and false positives) for different elevation angles
and C/N0 masks. Note that the C/N0 mask of 37dB·Hz in
the last row of Table4 was proposed by Yozevitch etal.,
(2012, 2016).
It can be seen from Table4 that classification accuracy
increases with increasing magnitudes of the two masks
while false positives decrease. is result suggests that
larger masks could be effective for excluding NLOS sig-
nals. However, there are two drawbacks to this decision
tree model. One is that the classification accuracy is still
lower than the results of the previous studies. Compared
with directly setting two thresholds, the fifteen-layer
decision tree training with these two QIs achieves up to
7000
6000
5000
4000
Number of signals
3000
20246
Velocity (m/s)
LOS
NLOS
81012
2000
1000
0
4000
3000
Number of signals
2000
3210
Acceleration (m/s
2
)
LOS
NLOS
123
1000
0
20000
15000
Number of signals
10000
0.500.2500.25
Yawrate (rad/s)
LOS
NLOS
0.500.75
5000
0
20000
15000
Number of signals
10000
100
Change of C/N
0
(dB·Hz)
LOS
NLOS
1020
5000
0
Fig. 20 The relationship between velocity, acceleration, yaw rate, or change rate of C/N0 and GNSS signals
Page 15 of 23
Lietal. Satellite Navigation (2023) 4:12
3000
2500
2000
1500
1000
Number of signals
500
15010050
Measurement_residual (m)
050100
0
3000
3500
2500
2000
1500
1000
Number of signals
500
15010050
Measurement_residual (m)
050100
0
3000
3500
2500
2000
1500
1000
Number of signals
500
15010050
Measurement_residual (m)
050100
0
3000
3500
2500
2000
1500
1000
Number of signals
500
15010050
Measurement_residual (m)
050100
0
3000
2500
2000
1500
1000
Number of signals
500
15010050
Measurement_residual (m)
050100
0
2500
2000
1500
1000
Number of signals
500
15010050
Measurement_residual (m)
050100
0
3000
4000
2000
1000
Number of signals
15010050
Measurement_residual (m)
050100
0
2500
2000
1500
1000
Number of signals
500
15010050
Measurement_residual (m)
050100
0
LOS
NLOS
LOS
NLOS
LOS
NLOS
LOS
NLOS
LOS
NLOS
LOS
NLOS
LOS
NLOS
LOS
NLOS
(i)(ii)
(iii)(iv)
(v)
(vii)
(vi)
Original least square
Fig. 21 Relationships between measurement residual and GNSS signal classification in different weighting schemes
Page 16 of 23
Lietal. Satellite Navigation (2023) 4:12
85.95% classification accuracy and 8.19% false positive.
e first three layers of the ten-layer decision tree are
shown in Fig.22, where labels 0 and 1 represent LOS and
NLOS, respectively.
e second drawback is that the number of data points
labelled NLOS and excluded increased with two masks.
For four sets of masks in Table4, the number of signals
excluded is 4.78%, 11.49%, 20.46%, and 44.71%, respec-
tively. e proportions of NLOS in these excluded sig-
nals are 12.21%, 25.13%, 44.67%, and 78.39%, respectively.
When the elevation angle and C/N0 masks were set to
20° and 37dB·Hz, 9.66% of LOS signals were excluded.
e remaining number of signals needs to be higher to
be useful for positioning and integrity monitoring. For
the decision tree model, 38.36% of signals are excluded,
of which 94.14% were NLOS. is result suggests that
implementing machine learning algorithms can improve
classification accuracy and ensure that as many LOS sig-
nals as possible remain.
According to the previous research, two QI sets are
mainly used, which are (i) elevation angle and C/N0, (ii)
the elevation angle, C/N0, and measurement residual.
ese QI sets are listed in Table5. is paper used the
(vii) weighting scheme in Table2 to calculate the meas-
urement residual. e machine learning algorithms
mainly implemented in the previous research were the
SVR, KNN, GBDT, and decision tree. Moreover, the
random forest method is also implemented as a bagging
method. e random forest algorithm performs best in
any set of QIs.
Moreover, the experimental results show that even
though the measurement residual is not an effective
QI for signal classification, this additional QI improves
both classification accuracy and false positives. ere-
fore, in this paper, we replace the measurement residual
with the pseudorange standard deviation to describe the
error characteristics of the pseudorange. e third QI
set (iii) comprises the elevation angle, C/N0, and stand-
ard deviation of pseudorange. e results show that the
classification accuracy is improved further. erefore,
the pseudorange standard deviation is more suitable than
the pseudorange residual for LOS/NLOS classification
(Table6).
As discussed in thelast section, seven QIs, which are
carrier phase lock-time counter, pseudorange standard
deviation, phase standard deviation, doppler standard
deviation, C/N0, elevation angle, and difference of azi-
muth angle, are combined to form the fourth (iv) set to
classify LOS and NLOS signals. e classification results
of ten machine learning algorithms are listed in Table7.
In this case, the performance of the bagging algorithms
is better than the boosting algorithms, and the random
forest method performs best. As a result, the classifica-
tion accuracy of random forest methods improves from
92.20% to 93.02%, and the false positive performance
improves from 3.40 to 3.01%.
e feature importance of all QIs fed into the ran-
dom forest model is calculated and shown in Fig. 23.
e standard deviation of pseudorange, C/N0, elevation
angle, and difference of azimuth angle are the first four
important QIs to classify GNSS signals. e difference in
azimuth angle turns out to be more important than the
C/N0 in the urban canyon. Correspondingly, the other
three QIs are less important. e feature importance of
each of these three QIs is less than 0.05. Some studies
have already shown that using only the best features can
improve the model’s performance (Dewi & Chen, 2019;
Jaiswal & Samikannu, 2017). Discarding less important
Table 4 Classification results when setting two masks
Elevation angle
mask (degrees)C/N0 mask
(dB·Hz)Classication
accuracy (%) False
positive
(%)
10 10 67.26 32.48
15 15 70.11 27.70
20 20 75.59 20.48
20 37 76.30 8.00
15.3% samples
label=1
9.0% samples
label=1
True
TrueTrue
True
TrueTrueTrue
False
C/N
0
48 dB·Hz
24.3% samples
Elevation50.52°
21.9% samples
Elevation28.50°
46.2% samplesElevation40.76°
53.8% samples
Elevation53.63°
35.6% samples
C/N
0
39 dB·Hz
18.2% samples
C/N
0
33 dB·Hz
100% samples
False
False
False
FalseFalseFalse
16.1% samples
label=1
5.8% samples
label=0
8.9% samples
label=0
9.4% samples
label=0
11.8% samples
label=0
23.8% samples
label=0
Fig. 22 First three layers of the ten-layer decision tree with C/N0 and elevation angle
Page 17 of 23
Lietal. Satellite Navigation (2023) 4:12
features is more reliable, cost-effective, and time-effec-
tive. It is also important in navigation missions since the
Time to Alert (TTA) should be met.
e fifth QI set (v), comprising these first four impor-
tant QIs, is fed into the machine learning algorithms. e
results show that the classification accuracy of the ran-
dom forest model improves from 93.06% to 93.43%, and
false positives decrease from 3.01% to 2.81% (Table8).
e other two algorithms, GBDT and Bagging, perform
well in the classification task. One decision tree in the
random forest model is shown in Fig.24.
With 93.43% classification accuracy, most NLOS sig-
nals can be detected and excluded in the pre-process-
ing step. Figure25 illustrates the frequency plots of the
number of NLOS signals at one GPS second before and
after NLOS signal exclusion. Without signal exclusion,
many received NLOS signals affect positioning accuracy.
erefore, multiple failures should be detected in integ-
rity monitoring. However, after the NLOS signals are
detected and excluded by the random forest algorithm,
the frequency of only one NLOS signal in the signal set
at one GPS second is 15.28%. e frequency of more than
one NLOS signal is less than 2%.
However, after NLOS signal detection and exclu-
sion using the random forest algorithm with the (v) QI
set, 41.43% of signals are excluded, of which 8.86% are
LOS. For example, if seven measurements are needed for
Table 5 Description of all QI sets
QI set Description
(i) Elevation angle and C/N0
(ii) Elevation angle, C/N0, and measurement residual
(iii) Elevation angle, C/N0, and standard deviation of pseudorange
(iv) Carrier phase lock-time counter, pseudorange standard deviation, phase standard devia-
tion, doppler standard deviation, C/N0, elevation angle, and difference of azimuth angle
(v) Pseudorange standard deviation, C/N0, elevation angle, and difference of azimuth angle
Table 6 Classification results with three sets of QIS
QI set Machine learning
algorithm Classication
accuracy (%) False
positive
(%)
(i) SVR 82.30 9.87
(i) KNN 88.21 6.20
(i) GBDT 87.25 7.82
(i) Decision tree 85.95 8.19
(i) Random forest 89.62 5.32
(ii) SVR 85.79 7.82
(ii) KNN 88.63 5.99
(ii) GBDT 87.92 7.33
(ii) Decision tree 86.57 7.46
(ii) Random forest 90.81 4.55
(iii) SVR 86.01 7.10
(iii) KNN 89.10 5.30
(iii) GBDT 90.08 5.32
(iii) Decision tree 89.08 5.07
(iii) Random forest 92.20 3.40
Table 7 Classification results with (IV) QI set
QI set Machine learning
algorithm Classication
accuracy (%) False
positive
(%)
(iv) SVR 86.41 7.00
(iv) KNN 89.72 4.75
(iv) GBDT 92.49 3.71
(iv) Decision tree 91.53 3.95
(iv) Random forest 93.06 3.01
(iv) Linear regression 84.28 8.59
(iv) Adaboost 86.05 8.38
(iv) Bagging 93.03 3.82
(iv) Extra tree 88.94 5.89
(iv) MLP 88.01 4.48
0.4
0.3
0.2
Feature importance
0.1
(i) (ii) (iii) (iv)
QIs
(v) (vi) (vii)
0
Fig. 23 Feature importance of qis in random forest
Page 18 of 23
Lietal. Satellite Navigation (2023) 4:12
positioning at every GPS second, then there are no suf-
ficient signals for 11.19% of the time. One possible solu-
tion to this issue is to select the seven measurements
with the lowest NLOS probability values. As shown in
Table9, the GPS 16th, 18th, 26th, 27th, and GLONASS
4th and 5th signals are labelled as LOS. ese six signals
are insufficient for positioning. us, the seventh signal,
the GPS 21st signal with 50.36% NLOS probability, is also
selected. e NLOS impact can be mitigated with the
proposed weighting scheme.
Classification accuracy and false positives vary when
setting different thresholds of NLOS probability. Fig-
ures26 and27 show the results of the random forest and
GBDT algorithms. When the threshold is 0.5, classifica-
tion accuracy is the highest. Moreover, false positives
increase with a larger threshold. From the results, the
random forest algorithm is always better than the GBDT
in these two aspects.
In comparing the results of our proposed classifica-
tion algorithm with others proposed before in Table10,
we again demonstrate that the LOS/NLOS classification
accuracy depends on the selected algorithms and QIs.
With single QI, the upper bound of the classification
accuracy was 80%. e GBDT or naïve threshold might
be the best algorithm for single QI. As the number of fea-
tures increased, the classification accuracy also increased.
e QIs selected by other scholars were also related to
signal strength, pseudorange, and elevation angle that
can directly reflect the quality of the GNSS signal and
influence on multipath. In this paper, we innovatively
selected the difference between delta pseudorange and
pseudorange rates to represent the surrounding environ-
ment and vehicle driving information. With the help of
this feature, the classification accuracy increased by 3%.
Results ofweighting schemes
Since the random forest algorithm with the (v) QI set as
input can classify LOS and NLOS signals with 93.62%
classification accuracy and only 2.93% false positive,
most NLOS signals can be detected and excluded.
erefore, this paper’s second task is further to miti-
gate the NLOS impact with a novel weighting scheme.
In Table2, seven weighting schemes have been intro-
duced. e positioning accuracy of seven weighted
5.1% samples
label=1
6.3% samples
label=0
True
TrueTrue
True
TrueTrueTrue
False
Elevation28.62°
11.4% samples
Elevation22.38°
49.6% samples
Elevation59.59°
39.0% samples
STD
pseudo
15.07 m
10.2% samples
STD
pseudo
73.44 m
100% samples
C/N
0
32 dB·Hz
28.8% samples
C/N
0
31 dB·Hz
61.0% samples
False
False
False
FalseFalseFalse
5.3% samples
label=0
44.4% samples
label=0
23.0% samples
label=1
5.8% samples
label=1
6.6% samples
label=0
3.6% samples
label=1
Fig. 24 First three layers of a decision tree in the random forest with (v) QI set
1.0
0.8
0.6
0.4
0.2
00510
Before exclusion
After exclusion
Frequency
The number of NLOS signals
15 20
Fig. 25 Frequency plot of the number of NLOS signals at one GPS
time before or after NLOS signal exclusion
Table 8 Classification results with (V) QI set
QI set Machine learning
algorithm Classication
accuracy (%) False
positive
(%)
(v) SVR 86.63 6.92
(v) KNN 90.09 4.76
(v) GBDT 92.97 3.57
(v) Decision tree 92.00 3.80
(v) Random forest 93.43 2.81
(v) Linear regression 84.61 8.70
(v) Adaboost 86.04 8.59
(v) Bagging 93.31 3.43
(v) Extra tree 88.89 5.57
(v) MLP 87.36 6.43
Page 19 of 23
Lietal. Satellite Navigation (2023) 4:12
positioning algorithms is shown in Tables11 and 12.
Table 11 illustrates the positioning results with the
elevation and C/N0 masks set as 15. For Table12, these
masks are removed. It is worth mentioning that the sin-
gular matrix cannot be inverted without two masks. To
solve this issue, we set these two masks as 1.
e result shows that with the two-mask set, the
horizontal positioning error’s smallest mean and stand-
ard deviation are obtained with the (vii) weighting
scheme in Table2, which are 7.990 and 5.371m in the
horizontal direction, 16.067 and 18.040m in the verti-
cal direction, and 20.448 and 18.411 min the ree-
Dimensional (3D) direction. e positioning accuracy
is reduced when removing the masks. is result is
obvious because only the (vii) scheme is designed using
two QIs: the elevation angle and C/N0. As the number
of QIs increases, the quality of the GNSS signals can be
better estimated. For high-quality signals, their values
in the weight matrix are large. is paper proposes a
novel weighting scheme (viii) which is designed as
where
PNLOS
is the NLOS probability. When the signal
is most likely NLOS, its weight value is small, and vice
versa. e positioning results show that without NLOS
signal exclusion, the mean value and standard deviation
are 6.462 and 4.802m in the horizontal direction, 8.754
and 9.185 m in the vertical direction, and 12.973 and
10.504m in the 3D direction. Experiments have proved
that the mean and standard deviation of the positioning
error in the horizontal direction decreased by more than
10%. e mean and standard deviation of positioning
error decreased by more than 35% in the vertical and 3D
directions. Moreover, when removing the two masks, the
positioning accuracy is also the highest among all weight-
ing schemes. e impact of NLOS is well mitigated with
the term
(1PNLOS )
.
After NLOS signal detection and exclusion, the
remaining signals are referred to as LOS_ml. e posi-
tioning accuracy is improved further using either the
(vii) or (viii) weighting scheme (shown in Table 13).
Compared with the positioning accuracy results
using: (1) (vii) weighting scheme and no NLOS sig-
nal exclusion, (2) (viii) weighting scheme and NLOS
signal exclusion, the positioning accuracy improved
by 69.000% and 40.700% in the horizontal direction,
79.361% and 75.322% in the vertical direction, and
75.963% and 67.824% in the 3D direction.
(9)
(1
P
NLOS
)
×
exp (C/N0/10)
×
sin2(
elevation
)
Table 9 GNSS signal reception at one GPS second
GPS week GPS second (s) GNSS identier Satellite
identier NLOS
probability
(%)
1913 383,114.198 GPS 7 100
10 99.04
15 100
16 9.92
18 23.42
21 50.36
26 48.72
27 15.76
29 99.98
GLONASS 4 28.31
5 26.21
6 60.60
12 96.95
20 99.40
21 57.96
0.940
0.935
0.930
0.925
0.920
0.915
0.910
Classification accuracy (%)
0.905
0.900
0.3 0.4
GBDT
Random forest
0.50.6 0.7
Threshold value
Fig. 26 The relationship between the threshold value and
classification accuracy results of Random Forest and GBDT
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.3 0.4 0.5
Threshold value
GBDT
Random forest
False positive (%)
0.
60
.7
Fig. 27 The relationship between the threshold value and false
positive results of Random Forest and GBDT
Page 20 of 23
Lietal. Satellite Navigation (2023) 4:12
Conclusion
is paper investigates the GNSS LOS/NLOS signal
classification algorithm and weighting scheme for accu-
rate positioning. It is worth mentioning that we focus on
NLOS signal detection and exclusion, as well as impact
mitigation. Indeed, the GNSS signal could be blocked or
reflected by buildings, walls, trees and others when the
vehicle is driving in the built environment. To estimate
signal quality, a richer set of QIs, including carrier-phase
lock-time counter, the standard deviation of measure-
ments, vehicle-based QIs, angle-related QIs, C/N0, and
others, are evaluated. Regression algorithms using these
QIs as input are used to predict the NLOS probability of
GNSS signals. With a pre-defined threshold, these sig-
nals can be labelled as LOS or NLOS. Results show that
classification accuracy could reach 93.430%, with only
2.810% false positive of the data using the four most
important QIs as input. e NLOS probability can also
be used for signal subset selection and weighting scheme
design. A novel weighting scheme is proposed to mitigate
the impact of NLOS. e results show that the position-
ing accuracy improved by 69.000% and 40.700% in the
horizontal direction, 79.361% and 75.322% in the verti-
cal direction, and 75.963% and 67.824% in the 3D direc-
tion when using the random forest algorithm and novel
weighting scheme.
Since this paper used an open-source dataset, the
number of data points, QIs, and the urban environ-
ment were all fixed. As future scientific research work,
we will collect a dataset including more QIs and data
Table 10 Comparison of classification algorithm performance
Paper Classication algorithm QI Classication
accuracy (%)
Yozevitch et al. (2012) Naïve threshold C/N070–80
Hsu (2017) SVM C/N067.1
Hsu (2017) SVM Change rate of C/N039.4
Hsu (2017) SVM pseudorange residual 40.5
Hsu (2017) SVM difference between delta pseudorange and pseudorange rate 65.4
Sun et al. (2020a), (2020b) GBDT C/N074.1
Yozevitch et al. (2016) Decision tree C/N0, elevation angle, measurement, carrier lock, satellite clock bias, indifferent
features 78.9
Hsu (2017) SVM C/N0, Change rate of C/N0, pseudorange residual, difference between delta
pseudorange and pseudorange rate 75.4
Xu et al. (2019) SVM Correlator-Level and RINEX/NMEA-Level features 90.4
Sun et al. (2020a), (2020b) GBDT C/N0, pseudorange residual, elevation angle 89.0
Sun et al. (2020a), (2020b) Decision tree C/N0, pseudorange residual, elevation angle 76.0
Sun et al. (2020a), (2020b) Distance-weighted KNN C/N0, pseudorange residual, elevation angle 88.5
Sun et al. (2020a), (2020b) ANFIS C/N0, pseudorange residual, elevation angle 82.7
This paper, 2023 Random forest The standard deviation of pseudorange, C/N0, elevation angle, and difference of
azimuth angle 93.4
Table 11 Positioning accuracy with different weighting schemes and two masks
Weighting
scheme Signal Elevation
and C/N0
masks
Horizontal
mean (m) Horizontal
standard
deviation (m)
Vertical mean (m) Vertical
standard
deviation (m)
3D mean (m) 3D standard
deviation
(m)
(i) NLOS + LO S Yes 10.097 7.974 32.377 23.224 36.673 23.850
(ii) NLOS + LOS Yes 8.903 7.084 28.704 21.948 32.452 22.785
(iii) NLOS + LO S Yes 8.180 5.497 21.068 19.728 25.113 20.416
(iv) NLOS + LOS Yes 10.610 7.462 22.395 21.151 27.905 21.526
(v) NLOS + LOS Yes 11.584 8.569 33.385 24.159 38.564 24.481
(vi) NLOS + LOS Yes 11.721 8.702 34.245 24.532 39.484 24.833
(vii) NLOS + LOS Yes 7.990 5.371 16.067 18.040 20.448 18.411
(viii) NLOS + LOS Yes 6.462 4.802 8.754 9.185 12.973 10.504
Page 21 of 23
Lietal. Satellite Navigation (2023) 4:12
points from more constellations and more driving sce-
narios in the built environment. By labelling all driving
scenarios, the performance of the LOS/NLOS classifi-
cation algorithms can be compared and analysed thor-
oughly. Furthermore, the reduced number of GNSS
signals every second might cause a greater Dilution
of Precision (DOP) value, and then the poor satellite
geometry would cause lower positioning accuracy. Two
possible solutions can address this issue. (i) Collecting
data from four global constellations and some regional
constellations. (ii) Remaining more signals by adjusting
the LOS/NLOS threshold. Correcting and excluding
the NLOS signals as much as possible under the condi-
tion of the DOP and further improving the positioning
accuracy will be the focus of future work. To test the
performance of LOS/NLOS classification algorithms,
pseudorange positioning was used in this paper. For
real-time vehicle positioning, higher accuracy algo-
rithms are always chosen, such as Real-Time Kinematic
(RTK), Precise Point Positioning (PPP), and GNSS/INS
integration. Research is ongoing on these positioning
algorithms and relevant NLOS impact mitigation.
Acknowledgements
Thanks for the open-source GNSS dataset from the Chemnitz University of
Technology.
Author contributions
LL designed and conducted the experiments and wrote the paper; ME
and YF assisted in code debugging and model tuning; WYO helped with
constructive guidance and revisions. All authors have read and approved the
final manuscript.
Funding
This research received no specific grant from any funding agency in the pub-
lic, commercial, or not-for-profit sectors.
Availability of data and materials
The open-source GNSS dataset used in this study is provided by the Chemnitz
University of Technology (cite: https:// www. tu- chemn itz. de/ proje kt/ smart Loc/
gnss_ datas et. html. en).
Declarations
Competing interests
The authors declare that they have no competing interests.
Received: 26 October 2022 Accepted: 29 March 2023
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