Weighting with the pre-knowledge of GNSS signal state of reception in urban areas
Juliette Marais1, Sarab Tay1, Amaury Flancquart1, Cyril Meurie1
(1)
Univ Lille Nord de France, IFSTTAR, COSYS, LEOST
Villeneuve d’Ascq, France
Email:[email protected]
INTRODUCTION
GNSS accuracy still remains a challenge in dense urban areas where, unfortunately, most of the localization users
travel. Propagation effects and, in particular reflections of the signals, induce major inaccuracy measurements of the
pseudoranges. For most of the Intelligent Transport Systems (ITS), there is a need to face this source of inaccuracy in
order to offer new services in a low cost solution.
The work presented in this paper has been performed in the context of a French project named CAPLOC that aims to
propose accurate localization in dense urban areas in this context. The solutions explored in the projects propose to use
only available GNSS signals, and chose some of them or weight some of them in order to increase performances.
CAPLOC intends to use the knowledge of the propagation environment close to the antenna to enhance GNSS
positioning accuracy.
CAPLOC PROJECT AND OBJECTIVES
CAPLOC is a research project (including IFSTTAR and the University of Technology of Belfort-Montbéliard) that
aims to develop an innovative solution for accurate localization in urban environments. The approach followed consists
in using video based perception of the vehicle’s surrounding in order to better understand and use the propagation
conditions of the GNSS signal received. The main target is to mitigate multipath and inaccuracy, but propose the
availability as good as possible, which is not always guaranteed when exclusion processes are applied. The project
finished in January 2014.
Two steps of work have given results:
1. The first one indicates, in a real time process, the state of reception of satellite signals received thanks to the
sky detection process developed that work with an embedded mono camera system.
2. The second aims to reduce the induced pseudorange delay caused by reflections on the close obstacles thanks
to the construction of a 3D model based on a stereovision process.
In this paper, we will focus on the first action showing how the information related to the state of reception can be used
in different solvers to increase accuracy of the positioning.
Detection of satellite states of reception based on image processing
In the CAPLOC project, we have developed an image processing strategy to detect visible sky in fish-eye acquired
images. The aim of this strategy consists in determining satellites that are located in sky regions (satellites received with
a direct signal) and those located in non-sky regions (satellites with a blocked/reflected signal) [1]. For this, a camera
equipped with a fish-eye lens is placed on the top of a vehicle pointed vertically in the direction of the sky.
A new strategy of image simplification associated to a pixel classification has been proposed, and allows us to classify
the pixels with a very good classification rate of 97.2% with a processing time of 37ms that is described with more
details in [2].
When satellites are repositioned in the acquired image, their state is identified depending if there are in a sky pixel or
not. On the one hand, the NMEA frames available at the output of every GPS receiver give the position of every
satellite receivable in an open sky environment. On the other hand, the fish-eye image, time-synchronized with the GPS
receiver, can be seen as a polar target where satellite positions can be drawn, after considering the calibration step
required in order to take into account the distortion caused by the lens. Figure 1 illustrates the concept on one image.
The left one shows the satellite (with their PRN number) placed for a time t. Their color depends on their state of
reception. The right image shows the segmentation between the sky and non-sky areas. Every satellites detected in a
non-sky area is classified in a NLOS state, and drawn with a red cross, the others, in a sky area, are LOS and identified
with a green cross.
Fig. 1. Illustrations of the satellite state detection in a fisheye image on the original image and on classified regions.
The CAPLOC concept relies on previous works performed from 1998 to determine availability of GNSS satellites along
a railway line and the development of the PREDISSAT tool [3]. The tool has been in particular tested in the
LOCOPROL European project [4]. The idea has been declined with IR camera by [5] to be available in other light and
meteorological conditions, and is not closely approached by authors [6][7] that use 3D models in order to benefit from
knowledge of the built obstacles.
NLOS SATELLITES DETECTION AND EXCLUSION
If C/N0 can sometimes be used for satellite state determination, the difficulty is to define the threshold between LOS
and NLOS signals. The use of image segmentation is another way to classify the satellites received. In this paper, all the
results will be presented based on real data acquired along a run in the city of Belfort, France. The trajectory lasts 71
seconds, and is approximately 250m long.
After the classification step, the distribution of the C/N0 values is represented figure 2, with two different curves: the
blue one represents the C/N0 of the NLOS satellites and the red the LOS. Due to the complex local propagation
phenomena, it confirms that it is difficult to differentiate these stats only with the C/N0 criterion.
Number of occurences
120
100
80
60
LOS
40
NLOS
20
0
0
20
40
60
C/N0 value (dBHz)
Fig. 2. Distribution of the C/N0 of the satellites classified as LOS and NLOS with the image processing stage.
In a first stage of the project, we have tested an exclusion policy that consisted in excluding from the position
computation the satellites detected as NLOS thanks to the image processing steps previously presented.
In the next figure, the results of an extended Kalman filter applied on the real data set show the impact of this exclusion
process. As illustrated in figure 2, accuracy is only partially increased, depending on the geometry of the obstacles, thus,
geometry of the available satellites. In particular the first half of the trajectory (right side of the figure) gives better
results than the second part.
Thus, a solution based on a DOP threshold has been proposed that allow excluding NLOS satellites only in the case
where the DOP without stays correct. Results are also illustrated in figure 3 with the violet curve that offers an
interesting compromise. Quantities are summarized in table 1.
Fig. 3. Positions obtained with an exclusion policy: red curve is the reference trajectory, blue one uses all the available
satellites, green: only LOS signals, violet: the threshold method.
However, exclusion of NLOS signals creates unavailability where the number of LOS signals is lower than 4 (Fig. 4).
Along the 71 positions, 17 points cannot be computed.
10
Total
LOS only
Number of sat.
8
6
4
2
0
0
10
20
30
time (sec)
40
50
60
70
Fig. 4. Evolution of the number of satellites used when all satellites are used (blue) or only LOS (green)
EKF
Table 1. Main error characteristics with the exclusion process (and EKF)
All satellites
LOS only
Threshold sol.
Error (m)
Mean std
13.13 12.75
10.5 12.14
5.73 7.66
In order to limit unavailability and try to increase accuracy, we have tested other solutions and in particular weighting
least-squares in order to solve the positioning equation system.
STATE OF THE ART OF WEIGHTING SCHEMES
In GNSS applications, most of the solutions use a Kalman filter. The Kalman filter uses an a priori knowledge of the
previous state to compute the solution and smooth the measurements. Instead of applying a classical Kalman Filter,
least-squares estimation are also often used [8]. The interest of the least-squares is that it allows weighting the use of the
different signals received thanks to the weighting least-squares (WLS) method.
In our context, the weight is a good mean to benefit from all the received signals and reduce unavailability. For each
satellite i, at any time, the weight wi is equal to 1 .
In the literature, different weights have been proposed based on satellite elevation and/or signal to noise ratio.
Weights based on satellite elevation can be:

=
sin ( )

(1)
as in [9] where is the satellite elevation angle and a parameter of the model that depends on the receiver
and antenna and as to be determined previously.
−
or
= + × exp(
) as in [10] where is the satellite elevation angle and a, b and are constants.
Some others consider that the use of the C/N0 value takes into account the elevation as well as the propagation
/
conditions as [11]. The Sigma − ε model proposes a variance equal to
= ² × 10
where c is a constant of the
model.
IMAGE-BASED WEIGHTING LEAST-SQUARES
The Caploc project proposes an adaptation of these previous models. Indeed, we intend to use the deterministic
knowledge of the satellite state of reception with elevation and C/N0.
The determination of the satellite states of reception is performed by image processing as presented in the beginning of
the paper.
Thus, the variance of the Caploc model is:
=
×
(
. ×
( )
)
(2)
When the received signal is LOS, k is chosen equal to 1. Whereas, when it is NLOS, k changes. In this paper we have
chosen k=2 thanks to the conclusion of [12].
RESULTS
Our weighting scheme is compared here to:
 an ordinary least-squares (OLS)
 a WLS with the simplest elevation model (1), with = 1.
 a WLS with the Sigma-ε model (c=1.1.104m² according to [3]).
Our dataset is composed of pseudoranges recorder along a path in the city of Belfort (France) as already shown in figure
5. The set is composed of 71 positions. GPS pseudoranges are recorder simultaneously with fisheye images for the
deterministic determination of the satellite states. The trajectory is drawn on figure 5. Figure 6 is composed of two
zooms of the same trajectory. Reference is drawn with the red continuous curve; our proposal with the red stars; the
Sigma-ε WLS is light blue, Elevation-based WLS is pink; a classical ordinary least-squares estimation is performed and
drawn in blue in order to compare our proposal with the output of a classical low-cost receiver.
Figure 6a allows seeing easily the interest of the Caploc approach compared to the other weighting schemes.
Figure 7 presents the variations of the error all along the 71 points of the run. The error is computed by projecting the
estimated position on the reference track, obtained with a RTK measurement. The error curves illustrate clearly the gain
in the first half of the path where other elevation- or C/N0-based approaches are not convincing. The second part of our
test run is less perturbed by large multipath as can show the OLS solution used as a reference for classical solution (fig
6b).
100
50
Nord (m)
0
-50
RTK - reference
OLS
Elevation
Sigmae
-100
Caploc
-150
-200
-140
-120
-100
-80
-60
Est (m)
-40
-20
0
20
Fig. 5. Comparison of the different weighted least-squares.
60
0
40
-20
-40
Nord (m)
Nord (m)
20
0
-20
-60
-80
-40
RTK - reference
OLS
Elevation
Sigmae
-60
Caploc
-70
-60
-50
RTK - reference
OLS
Elevation
Sigmae
-100
Caploc
-120
-40
-30
Est (m)
-20
-10
0
10
-140
-130
-120
-110
-100
Est (m)
-90
-80
-70
a/
b/
Fig. 6. Comparison of the different weighted least-squares estimations (Zooms: a/first part and b/second part of the
trajectory).
35
OLS
Elevation
Sigmae
30
Caploc
Error (m)
25
20
15
10
5
0
0
10
20
30
40
Time (s)
50
60
70
80
Fig 7. Errors measured along the trajectory with the different solutions tested.
Results are summarized in table 2 in terms of mean, median, root mean square (rms) and 95th percentile. Same results
are represented as a cumulative distribution in figure 8. The Sigma-ε WLS does not provide interesting results here, and
would perhaps require to refine the parameters.
Compared to the classical OLS solution, EKF is the first accuracy increase. The elevation-based WLS offers a better
median than EKF but a worse mean value. The median value of the elevation-based WLS (4m) is reduced to 2.45m
with our Caploc WLS.
Table 2. Summary of the results
Mean
Median
RMS
95th percentile
OLS
EKF
10,58
4.32
15.07
27.19
6.5
6.12
8.45
13.53
El.
model
8.58
4.14
6.49
22.19
Sigma-ε
Caploc
12.2
5.81
17.33
31.08
3.28
2.88
4.11
8.98
1
0.9
0.8
0.7
F(x)
0.6
0.5
0.4
OLS
Elevation
Sigmaeps
0.3
0.2
Caploc
0.1
0
0
5
10
15
x=Error (m)
20
25
30
35
Fig. 8. Cumulative distributions of the errors measured with the different schemes.
CONCLUSIONS
The objective of the Caploc project was to develop new solutions for accurate localization in dense urban areas and in
particular to mitigate the effects of NLOS signals. The originality of the project is to use fisheye records and processing
in order to detect satellite states of reception and in particular, to identify satellites received without line of sight. Two
methods have been applied: exclusion of NLOS signals and weighting. Based on the weighting schemes presented in
the literature, we have proposed a weight based on elevation, C/N0 and the state of reception.
Results have been shown on a test trajectory, in the city of Belfort and show that the Caploc WLS allows a gain of 2 on
the mean and median values compared to a classical EKF solution. Moreover, 95% of the positions are below 9m of
accuracy compared to 13,5m with the EKF.
The work performed in the project has proved the interest of the image for a better accuracy. This has to be confirmed
with other test tracks in order to confirm that the results are also positive in other environmental configurations.
Some improvements are in progress to differentiate buildings and vegetation in the image for example.
The objective of the project was a concept proof. The video equipment can today be an obstacle to spread the solution
to mass market but will progress in time and the satellite state determination can today be performed in real time.
AKNOWLEDGMENTS
The authors want to thank the CISIT program as well as the SaPPART cost action for their support.
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