Article citation information:
Krasuski, K.,
Wierzbicki, D., Kirschenstein, M., Żukowska, M., Gołda P. Accuracy
analysis of UAV coordinates using EGNOS and SDCM augmentation systems. Scientific Journal of Silesian
University of Technology. Series Transport. 2024, 123, 75-100. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2024.123.4.
Kamil KRASUSKI[1],
Damian WIERZBICKI[2],
Małgorzata KIRSCHENSTEIN[3],
Marta ŻUKOWSKA[4],
Paweł GOŁDA[5]
ACCURACY ANALYSIS OF UAV COORDINATES USING EGNOS AND SDCM AUGMENTATION
SYSTEMS
Summary. SBAS systems
are applied in precise positioning of UAV. The paper presents the results of
studies on the improvement of UAV positioning with the use of the EGNOS+SDCM
solutions. In particular, the article focuses on the application of the model
of totaling the SBAS positioning accuracy to improve the accuracy of
determining the coordinates of UAVs during the realisation of a test flight.
The developed algorithm takes into account the position errors determined from
the EGNOS and SDCM solutions. as well as the linear coefficients that are used
in the linear combination model. The research was based on data from GPS
observations and SBAS corrections from the AsteRx-m2 UAS receiver installed on
a Tailsitter platform. The tests were conducted in September 2020 in northern
Poland. The application of the proposed algorithm that sums up the positioning
accuracy of EGNOS and SDCM allowed for the improvement of the accuracy of
determining the position of the UAV by 82-87% in comparison to the application
of either only EGNOS or SDCM. Apart from that, another important result of the
application of the proposed algorithm was the reduction of outlier positioning
errors that reduced the accuracy of the positioning of UAV when a single SBAS
solution (EGNOS or SDCM) was used. The study also presents the effectiveness of
the proposed algorithm in terms of calculating the accuracy of EGNOS+SDCM
positioning for the weighted average model. The developed algorithm may be used
in research conducted on other SBAS supporting systems.
Keywords: SBAS,
EGNOS, SDCM, accuracy, position errors, UAV
1.
INTRODUCTION
The preparation and development of the project,
the construction as well as the final validation and certification of the UAV
(Unmanned Aerial Vehicle) for performing flights also involves the necessity to
implement mathematical algorithms to improve the UAV coordinates in real time
and to carry out the necessary navigation analyses in post-processing mode [1].
In consequence, this requires an appropriate selection of sensors and equipment
to localise the platform and the correct configuration of input data and
mathematical models to describe the equation of the position of UAV movement
[2]. In the 21st century, the navigational position of the UAV was estimated
using GNSS (Global Navigation Satellite System) data [3, 4]. Other, optional
navigation functions of the flight include the estimation of the acceleration
and the angles of UAV orientation in the aerial space [5]. The knowing of the
position of the UAV is essential from the point of view of navigation [6], as
well as of the dynamics and kinematics of the flight [7] and, finally, of the
safety process of the flight itself [8]. All the more reasons for the issues of
improving the positioning to be continuously developed as part of the UAV
technology. This is obviously a result of the development of the GNSS systems
and precise positioning methods in aerial navigation [9]. Moreover, the
UAV-related topics are being increasingly used in photogrammetric, remote
sensing and geoinformation applications [5, 10, 11, 12, 13]. As a standard, the
low-cost on-board GNSS receivers usually employ the SPP (Single Point
Positioning) method [14] to designation the coordinates of the UAV in near-real
time. However, one of the problems of this method in aviation applications in
UAVs is its low positioning accuracy, which may reach even up to 10 m [15, 16,
17]. This method is used by single-frequency receivers installed on the UAV
platform [18]. This led to various attempts to develop mathematical algorithms
that would improve the positioning of UAVs in the SPP method [19]. One of the
GNSS satellite positioning methods that allows for the improvement of code
positioning results is the SBAS (Satellite Based Augmentation System) method
[20]. Although it still uses the algorithm of the code-based SPP method, its
calculations are based on the corrections from the given SBAS support system
[21]. However, the SBAS method significantly increases the accuracy of UAV
positioning, to the level of 1÷3 m [22], which, in turn, influences the
value of the determined coordinates of the UAV and, obviously, the linear
elements of external orientation
2. RELATED WORKS
The
literature on the subject of this study provides numerous references to the
application of SBAS support systems in the navigation solution of UAV
positioning. For example, publication [23] presents a concept of the
application of the SBAS system for the territory of South Korea for the
purposes of the UAV technology. In particular, various aspects of using UAV as
part of the KASS (Korea Augmentation Satellite System) support system are
discussed. Study [24] presents a possibility to employ the SBAS support system
for the purposes of determining the position of UAV during a performed
photogrammetric flight. The authors also compare the SBAS positioning method
with the DGPS (Differential GPS) differential technique. The authors of [25]
present the possibilities to employ UAV for mapping the passability of roads.
In another publication [26], the WAAS support system was used in the process of
the determination of the coordinates of the centres of the projection with use
of aerial data obtained from the UAV. Moreover, the authors of [27] presented
the possibility to employ the WAAS support system in the UAV technology in
agriculture, for the purposes of drainage of agricultural areas. The authors
compared the terrain mapping results obtained from the SBAS/WAAS systems and
the RTK (Real Time Kinematic) solution. Publication [28] analyses the results
of the EGNOS and Galileo (European Navigation Satellite System) positioning for
the purposes of improving the flight safety of UAV. The study presents various
scenarios of configuration of Galileo+EGNOS positioning for the UAV technology.
The authors of [29] proposed a plan of developing new onboard avionics for UAV,
based on the SBAS and GBAS (Ground Based Augmentation System) systems and other
radio navigation systems for the unmanned platform. The works [30, 31] present
a concept of the application of the Australian GATBP (Geoscience Australia Test
Bed Project) support system to be used in UAV applications for agricultural and
forestry purposes. The authors of [32] proposed a concept of using UAV in
industrial and business applications. To this end, the SBAS system was used to
improve the accuracy and integrity of UAV positioning in terms of the altitude
of flight of the platform. Publication [33] shows the results of UAV
positioning accuracy for the navigation solution from the GPS (Global
Positioning System) system and also GPS+EGNOS. Furthermore, the authors of [34]
described the results of research on the implementation of the PBN (Performance
Based Navigation) concept for UAV navigation based on the SBAS solution. Other
publications [35, 36] present the application of UAV for flight inspection,
taking into consideration the environmental factors and financial costs. Those
publications also propose a SBAS positioning model that is based on the
correction data from the SBAS system. The authors of [37] presented the results
of the research on the management of UAV air traffic and the navigation of UAV
based on the BDSBAS (BeiDou SBAS) system for the territory of China. The
research work [38] is an elaboration of publication [37]. The authors of [38]
presented a model of operation, the configuration, architecture, and specific
elements of the BDSBAS support system, taking into account aviation
applications, including for the UAV technology. Publication [39] presented
numerous applications of the SBAS-Africa support system, including aviation
applications, also for the UAV technology. The authors of [40] presented the
possibility of integrating inertial data from the INS (Inertial Navigation
System) with the corrections from the MSAS (Multi-functional Satellite
Augmentation System) system for the purposes of UAV positioning during flight.
Apart from that, the authors also used the DGPS navigation data. Another
publication [41] presented the accuracy and integrity parameters of UAV
positioning based on MSAS solution. Article [42] presented the results of the
application of the GNSS system in the digital aerotriangulation process for the
determination of the Digital Terrain Model with use of aerial photos obtained
from the UAV. However, the conducted research revealed that it was impossible
to use the SBAS solution during the test flight. Finally, only the RTK and PPK
(Post-Processing Kinematic) solutions could be implemented. Paper [43]
described various scenarios of application and challenges faced by SBAS support
systems in the urban, highly developed environment. The authors discussed
various aspects of the application of SBAS systems in the UAV technology for
urban areas. Moreover, the publication [44] provided a direct reference to the
application of UAV in transport, logistics, and industry, considering the SBAS
support systems. Very interesting research results were presented in article
[45], namely the percentage of application of SBAS support systems in the UAV
area was described. It revealed that many users for not use the SBAS support
systems in the UAV technology. The authors of [46] developed a new algorithm to
designation the planes of the UAV based on the GNSS/SBAS or ILS (Instrument
Landing System) systems, but additionally with the use of a visual camera
during the landing process of the UAV. The computational algorithm takes into
account the solution of the position of the UAV for Kalman filtration. Finally,
the authors of [47, 48] presented a possibility to apply the EGNOS support
system to improve the flight safety of the UAV in various aviation operations.
The basic conclusions from
literature review focus on:
-
the positioning of
UAV based on SBAS system is important in navigation but also for the safety of
flight [28, 47, 48];
-
SBAS support
systems were also applied in the UAV technology for the purposes of
photogrammetric studies [24-27, 42];
-
various support
systems, e.g. EGNOS [28], WAAS [25], BDSBAS [38], MSAS [41], etc. were used in
research;
-
the utilization of
SBAS systems for UAV allows optimising the financial costs, has a lower
negative influence on the natural environment [35, 36], and may enhance the
development of the industry in urban and highly urbanised areas [43, 44];
-
the SBAS positioning
method is better than the code-based SPP method [22, 33].
The
analysis of the state of knowledge on the topic in question revealed that the
accurate positioning of UAV based on SBAS augmentation system is an important
issue in aviation. Moreover, it has a direct influence on the navigation aspect
of determining the coordinates of the UAV position, and, in photogrammetric
terms, on the determination of the linear elements of external orientation. It
should be noted, as subject literature reveals, that so far, only one SBAS
support system has been used for the precise positioning of UAV. However, this
may change if data from two or more SBAS support systems are elaborated. This
is an important research issue in the search for new solutions and algorithms
that would improve the accuracy of UAV positioning and thus the position of the
unmanned platform. The application of SBAS systems is crucial for satellite
positioning that employs single-frequency GNSS receivers installed on the UAV
platform. Moreover, such a solution might contribute to the improvement of the
determination of linear elements of external orientation, whose approximate
values are required at the initial stages of the digital aerotriangulation
process [3, 5].
For that
reason, the authors of the present paper have carried out an analysis of the
accuracy of UAV positioning based on EGNOS+SDCM solutions in UAV applications.
To this end, the variant of integration of EGNOS and SDCM data in the
navigation process of solution of the position of the UAV was developed and
presented here. Namely, the following were applied in the model summating the
parameters of UAV positioning accuracy. The developed algorithm involves the
use of linear coefficients, which, in this case, will be determined as the
reverse of the UAV flight velocity from the EGNOS solution and, respectively,
SDCM solution. The value of the linear coefficient was selected in such a way
that it refers both to the navigation aspect and to the flight dynamics of the
UAV. The developed computational strategy was tested on actual GNSS kinematic
data recorded by a single-frequency receiver installed on a UAV platform. The
variant of analysing the accuracy of SBAS positioning described here allows the
user to select the optimum model of the navigation solution of UAV positioning.
It should be mentioned that the developed algorithm may also consider other
linear coefficients that are adjusted to the needs of a specific user.
In
conclusion, the main research achievements of the study refer to: developing an
algorithm to integrate the EGNOS and SDCM navigation data in the process of
determining the coordinates of the UAV; determining the linear coefficients as
a function of the flight speed of the UAV for the proposed mathematical
algorithm; testing the correctness of the functioning of the proposed
mathematical algorithm on GNSS kinematic data that were recorded by an on-board
GNSS satellite receiver installed on a UAV platform; demonstrating the
appropriateness of the mathematical algorithm for the integration of the
EGNOS+SDCM data in reference to only EGNOS and also SDCM solutions;
demonstrating the appropriateness of the mathematical algorithm regarding the
weighted average model for calculating the accuracy of EGNOS+SDCM positioning.
The paper
is divided into 7 sections and a list of all bibliographic references is
provided at the end of the paper.
3. RESEARCH METHOD
For the
purposes of the analysis of the accuracy of EGNOS+SDCM positioning for UAV, a
variant of the mathematical algorithm was presented in form of the model
summating the accuracy parameters in the geodetic coordinates BLh (B is
Latitude, L is Longitude, h is ellipsoidal height), as presented below:
|
|
(1) |
where:
If a EGNOS and SDCM solution is included in equation
(1), the final result will be a mathematical expression in the model of the sum
of products of the accuracy parameter, as presented below:
|
|
(2) |
The consecutive position errors
|
|
(3) |
where:
Further transformation of equation (3) results in:
|
|
(4) |
Then, individual parameters may be grouped and the
equation may be written in the form:
|
|
(5) |
Equation (5) describes the algorithm to determine the
EGNOS+SDCM positioning for UAV, but it also presents the integration of the
EGNOS+SDCM navigation solution for the UAV. Thus, equation (5) is the basic
equation for analysing the EGNOS+SDCM positioning accuracy for the UAV in the
model summating the accuracy parameters.
The key parameters for the presented equations (1-5)
are the linear coefficients denoted by the symbols:
where:
The proposed algorithm (1-6) will be tested on actual kinematic GNSS
data that were recorded by a single-frequency satellite receiver installed on
the UAV platform. The test results are discussed in Section 5.
4. RESEARCH EXPERIMENT
Section 4 contains a presentation and detailed description of
the course of the research test. The research process was divided into three
stages as follows: a) Stage 1 consisted in the realisation of the test flight
of the UAV
with the aim of collecting GNSS navigation data by the AsteRx-m2 UAS receiver installed on the Tailsitter platform; b) Stage 2 involved the calculation of the position of the UAV
with the use of the code-based SPP method and the corrections from EGNOS and
SDCM; c) Finally, stage 3 consisted in the implementation and
realisation of the proposed mathematical algorithm (1-6).
During stage 1, a test flight was performed with the use of a
Tailsitter platform equipped with a single-frequency
AsteRx-m2 UAS receiver. The test flight took
place in September 2020 in northern
Poland, before noon. The Figure 1 presents the horizontal trajectory of the
flight. The dispersion in the geodesic coordinate B was from 54.351375o
to 54.359209o. Furthermore, the dispersion in the geodesic
coordinate L ranged from 19.661528o to 19.676888o.
Fig. 1. The horizontal trajectory of the UAV
Figure 2 presents the vertical trajectory of the flight in
relation to the time. The change in the flight altitude of the UAV was from
100.777 m to 131.723 m. The lowest ellipsoidal altitude of flight was obviously
noted during take-off of the UAV platform.
During the flight, the AsteRx-m2
UAS receiver recorded, respectively, from 4 to 9 GPS satellites, for which SDCM
corrections were calculated. Apart from that, the AsteRx-m2 UAS receiver recorded,
respectively, from 5 to 10 GPS satellites, for which EGNOS corrections were calculated. The number of GPS satellites with SDCM and EGNOS
corrections is presented in Figure 3. As one may notice, the lowest number of tracked GPS satellites with SDCM and EGNOS
corrections was visible in the initial phase of flight, during take-off. With time, the
number of follow satellites with SDCM
and EGNOS corrections continued to increase.
Fig. 2. The vertical flight of the UAV
Fig. 3. Number of GPS satellites with SDCM and
EGNOS corrections
Stage 2 of the research consisted in calculating the
coordinates of the UAV based on GPS code observations and EGNOS and SDCM
corrections. The calculations were performed with the use of the code SPP
positioning method in the RTKPOST module of the RTKLIB v.2.4.3 software [52]. For each SDCM and EGNOS solution, the coordinates
of the UAV were determined at a time interval of 1 s. Additionally,
the
reference trajectory of the UAV flight was defined with the use of the RTK-OTF
positioning technique [53]. The positioning accuracy
of SDCM
and EGNOS was determined based on equation (3).
Moreover, the usability of the GPS constellation for the
navigation solution of the position of the UAV was also determined, in form of
the PDOP (Position DOP) geometric coefficient [54]. As a result, Figure 4
presents the results of PDOP for the SDCM and EGNOS solutions. The values of
the PDOP coefficient based on SDCM solution ranged from 1.8 to 3.9, while the
values based on EGNOS solution ranged from 2.0 to 4.2. One may notice that the
worst values of the PDOP coefficient were noted in the initial phase of flight,
when the AsteRx-m2 UAS receiver recorded the fewest GPS observations
with SDCM and EGNOS corrections. With time, the values of the PDOP coefficient
decreased below 2.5, which means, in practice, that the conditions for
conducting GNSS measurements were very good.
Fig. 4. The PDOP values based on SDCM and
EGNOS solutions
Stage 3 of the research involved the final implementation and
performing the proposed mathematical algorithm (1-6) in the Scilab v.6.0.0
language environment [55]. The whole source code in which the mathematical
algorithm (1-6) was written with the commands that are necessary to perform the
graphic analysis of the obtained research results was developed in a numerical
script in the Scilab environment.
5. RESULTS
Chapter
5 presents the obtained research results, starting from the flight velocity
Figure
6 presents the values of the linear coefficients
Fig. 5. The total velocity of UAV based on SDCM and EGNOS solutions
Fig. 6. The values of linear coefficients
Figures 7, 8, and 9 show the position errors of EGNOS+SDCM solution in reference to the positioning accuracy from the
EGNOS system and the SDCM system. According to the mathematical equations
(1-6), the positioning accuracy is presented in form of position error
parameters for the ellipsoidal coordinates BLh of the position of the UAV.
Figure 7 presents the results of position errors for the B component. These
position errors for the B component based on the SDCM solution ranged from -1.9
m to +5.7 m. Analogically, the position errors based on the EGNOS solution
ranged from -1.2 m to +1.4 m. As a result of the application of the proposed
mathematical algorithm (1-6), the positioning errors took the values from -0.3
m to +0.2 m. As far as the accuracy of the B coordinate is concerned, one may
conclude that the proposed mathematical algorithm (1-6) for the EGNOS+SDCM
solution increased the accuracy by 83% in comparison to the SDCM solution and
by 86% in comparison to the EGNOS solution. Figure 8 presents the values of
position errors for the L component. These position errors for the L component
based on the SDCM solution ranged from -2.6 m to +1.6 m. Analogically, the
position errors based on the EGNOS solution ranged from -1.3 m to +1.2 m. When
the EGNOS+SDCM solution was applied, the position errors took the values
ranging from -0.2 m to +0.2 m. As far as the accuracy of the L coordinate is
concerned, one may conclude that the proposed mathematical algorithm (1-6) for
the EGNOS+SDCM solution increased the accuracy by 84% in comparison to the SDCM
solution and by 87% in comparison to the EGNOS solution. Figure 9 shows the
values of position errors for the h coordinate. These position errors for the h
component based on the SDCM solution ranged from -3.5 m to +14.3 m.
Analogically, the position errors based on the EGNOS solution ranged from -2.4
m to +5.5 m. When the EGNOS+SDCM solution was applied, the position errors took
the values ranging from -0.5 m to +0.9 m. As far as the accuracy of the h
coordinate is concerned, one may conclude that the proposed mathematical
algorithm (1-6) for the EGNOS+SDCM solution increased the accuracy by 82% in
comparison to the SDCM solution and by 86% in comparison to the EGNOS solution.
The analysis of specific position errors along the BLh axes reveals that the
application of the proposed mathematical algorithm (1-6) brought a quite
significant reduction of the position errors. This is rather vital when low
positioning accuracy results are obtained from the EGNOS or SDCM solutions,
which is noticeable in the initial phase of flight of the Tailsitter platform. This makes the development of
algorithms that would improve the accuracy of determining the horizontal
components, but especially the vertical component h even more important for the
safety of performing aviation operations with the use of UAV. The proposed EGNOS+SDCM solution summating the
positioning accuracy may prove to be a very interesting algorithm in the
process of developing SBAS data for the UAV technology.
Fig. 7. The position errors along B axis
6. DISCUSSION
The Discussion
Section of this paper has been divided into three parts. The first part refers
to the comparison of the obtained results of the EGNOS+SDCM positioning
accuracy based on the proposed algorithm (1-6) with the EGNOS+SDCM positioning
accuracy calculated from the weighted average model. The second part contains a
presentation of the results of EGNOS+SDCM positioning accuracy in the context
of the repeatability of the calculation process. Finally, the third stage of
the discussion provides a comparison of the obtained research results in the
light of the analysis of the state of knowledge concerning the analysed
research problems.
Fig. 8. The position errors along L axis
Fig. 9. The position errors along h axis
6.1. Comparison of the obtained
results with the weighted average model of positioning accuracy
The
weighted average model for the determination of the accuracy parameter in the
EGNOS+SDCM solution may be presented in the following form:
Using a single SBAS solution (EGNOS or SDCM) in
equation (7), the final result will be a mathematical expression in the
weighted average model of the accuracy parameter, as presented below:
Just like in equation (3), the position errors may be
written with the help of the UAV coordinates, which is shown below:
Further transformation of equation (9) and grouping
individual parameters results in:
Equation
(10) describes the final form of the weighted average model for the accuracy
parameter of the coordinates of the UAV position based on the EGNOS+SDCM
solution. Figures 10, 11, and 12 show the results of comparison of the
positioning accuracy based on the EGNOS+SDCM solution for the model summating
the accuracy (equations (1-6)) and the weighted average model (equations
(7-10)). The values of positioning accuracy based on the EGNOS+SDCM solution
for the summating model are presented in Figures 7, 8, and 9, and they have
already been discussed in detail. On the other hand, the values of position
errors for the BLh components of the position of the UAV in the weighted
average model are, respectively: from -1.5 m to +2.5 m for the B coordinate,
from -1.1 m to +1.4 m for the L coordinate, and from -2.7 m to +5.9 m for the h
coordinate. As far as the determination of the accuracy of the B coordinate is
concerned, one may conclude that the proposed algorithm summating the positioning
accuracy for the EGNOS+SDCM solution resulted in a reduction of position errors
by 84% in comparison to the EGNOS+SDCM solution for the weighted average model.
Moreover, for the determination of the accuracy of the L coordinate, it was
noted that the proposed algorithm summating the positioning accuracy for the
EGNOS+SDCM solution resulted in a reduction of position errors by 85% in
comparison to the EGNOS+SDCM solution for the weighted average model. Finally,
for the determination of the accuracy of the h coordinate, one may conclude
that the proposed algorithm summating the positioning accuracy for the
EGNOS+SDCM solution resulted in a reduction of position errors by 84% in
comparison to the EGNOS+SDCM solution for the weighted average model. The comparison
of the obtained results of position errors for the mathematical equations (1-6)
and (7-10) reveals a noticeable high effectiveness of the proposed model
summating the positioning accuracy. In reference to the weighted average model,
the proposed model for the EGNOS+SDCM solution can rightfully be used in
navigational calculations.
Fig. 10. The position
errors along B axis from summation model of
accuracy and the weighted average model
Fig. 11. The position errors along L axis from summation model of
accuracy and the weighted average model
Fig. 12. The position errors along h axis from summation model of
accuracy and the weighted average model
6.2. Repeatability of
computational processing of the summation model of accuracy
The second part of
the discussion describes the repeatability of the computational process for the
application of the proposed mathematical algorithm (1-6) but based on another
sample of GPS and SBAS data (EGNOS and SDCM). Namely, the calculations were
performed on GPS satellite data and EGNOS and SDCM corrections from a test
flight that took place on the same day, but in the afternoon. The test flight
took place in the village of Nowy Świat, which is in northern Poland. It
should be noted that the test flight was performed by a Tailsitter platform with an installed AsteRx-m2 UAS receiver. Figures 13 and 14 present, respectively, the
horizontal and vertical trajectory of the flight of the UAV. The changes in the geodesic latitude coordinate B ranged
from 54.348965o to 54.356494o, while the changes in the
geodesic longitude coordinate L ranged from 19.311990o to 19.331175o.
The change in the
flight altitude of the UAV was from 105.552 m to 227.487 m. Similarly to the
first test flight, the lowest ellipsoidal altitude of flight was obviously
noted during take-off of the UAV platform.
Furthermore, Figure 15 shows the number of tracked GPS satellites with
EGNOS and SDCM corrections, while Figure 16 presents the values of the PDOP
coefficients separately for the EGNOS and SDCM solutions. During the second
flight, the number of tracked GPS satellites with SDCM corrections ranged from
4 to 8. At the same time, AsteRx-m2
UAS tracked from 7 to 12 GPS satellites, for which EGNOS corrections were
calculated. Similarly, as during the first flight that, during flight 2 the
lowest number of tracked GPS satellites with SDCM and EGNOS corrections was
also noticed in the initial phase of the experiment. As the test progressed,
the number of tracked GPS satellites with SDCM and EGNOS corrections increased.
Fig. 13. The horizontal
trajectory of the UAV in the 2nd test flight
Fig. 14. The vertical
trajectory of the UAV in the 2nd test flight
The values of the geometric coefficient PDOP ranged from 1.7 to 2.7 for
the SDCM solution and, respectively, from 1.6 to 2.8 for the EGNOS solution.
Similarly, as in test flight 1, the worst results of the PDOP coefficient were
noted in the initial phase of flight, when the AsteRx-m2 UAS receiver recorded the
fewest GPS observations with SDCM and EGNOS corrections. As the recording time
elapsed, the PDOP coefficients became lower than
2.2.
Fig. 15. Number of GPS
satellites with SDCM and EGNOS corrections in
the 2nd test flight
Fig. 16. The PDOP values based on SDCM and EGNOS solutions in
the 2nd test flight
Figure 17 shows the parameters of flight of the UAV separately for the
EGNOS and SDCM solutions. Further, Figure 18 presents the values of the linear
coefficients calculated from equation (6). The flight velocity of the UAV based on the SDCM solution ranged from 3.9 m/s to
28.6 m/s. At the same time, the flight velocity based on the EGNOS solution
also ranged from 3.9 m/s to 28.6 m/s. The highest velocity values were noted in
the final phase of flight.
Fig. 17. The total velocity of UAV based on SDCM and EGNOS solutions
in the 2nd test flight
Fig. 18. The values of linear coefficients
The values of the
Figures 19, 20, and 21 present the values of EGNOS+SDCM positioning accuracy based on algorithm (1-6) in reference to
the positioning accuracy values determined separately for the EGNOS and SDCM
systems. The position errors for the B component based on the SDCM solution
ranged from -2.1 m to +7.7 m. Analogically, the position errors based on the
EGNOS solution ranged from -1.9 m to +6.9 m. After the application of the
proposed mathematical algorithm (1-6) that sums positioning accuracy, the
position errors take the values from -0.3 m to +1.4 m. As far as the accuracy
of the B coordinate is concerned, one may conclude that the proposed
mathematical algorithm (1-6) for the EGNOS+SDCM solution increased the accuracy
by 87% in comparison to the SDCM solution and by 77% in comparison to the EGNOS
solution. The position errors for the L component based on the SDCM solution ranged
from -15.8 m to +1.5 m. Analogically, the position errors based on the EGNOS
solution ranged from -15.4 m to +1.1 m. When the EGNOS+SDCM solution was
applied, the position errors took the values ranging from -3.3 m to +0.5 m. As
far as the accuracy of the h coordinate is concerned, one may conclude that the
proposed mathematical algorithm (1-6) for the EGNOS+SDCM solution increased the
accuracy by 86% in comparison to the SDCM solution and by 84% in comparison to
the EGNOS solution. The position errors for the h component based on the SDCM
solution ranged from -15.4 m to +5.1 m, while the position errors based on the
EGNOS solution ranged from -14.4 m to +6.6 m. When the EGNOS+SDCM solution was
applied, the position errors took the values ranging from -3.0 m to +1.8 m. As
far as the accuracy of the h coordinate is concerned, one may conclude that the
proposed mathematical algorithm (1-6) for the EGNOS+SDCM solution increased the
accuracy by 78% in comparison to the SDCM solution and by 82% in comparison to
the EGNOS solution. Similarly, as for flight 1, the application of the proposed
algorithm (1-6) enabled to reduce the values of position errors in flight 2 as
well, and thus to improve the EGNOS+SDCM positioning accuracy. This is
important, as the mathematical algorithm (1-6) allows for the reduction of
outliers for position errors, which is visible in Figures 19, 20, and 21 in the
initial phase of flight, when the positioning accuracy of EGNOS and SDCM is
low. Thus, it may be concluded that the repeatability of the computational
process was verified in test flight 2. The level of the obtained results of the
reduction of position errors are similar as in the test flight performed. This
means that the verification of the mathematical algorithm (1-6) proved to be
effective in UAV positioning for the EGNOS+SDCM solution.
6.3. Comparison between the
proposed research method and the analysis of scientific knowledge
The
last part of the discussion contains a comparison of the applied research
method in reference to the state of knowledge. The comparison of the accuracy results of EGNOS+SDCM positioning with the
analysis of the state of knowledge allows us to draw the following conclusions:
-
the accuracy of
UAV positioning based on EGNOS+SDCM positioning described here is higher than
the accuracy results described in papers [20, 21, 28, 33, 51],
-
the EGNOS and SDCM
support systems were used in precise positioning of aerial vehicles in aviation
navigation, which was described in studies [51],
-
the mathematical
algorithm presented here may be used in photogrammetric applications in the
digital aerotriangulation process [5, 10-13, 17].
Fig. 19. The position errors along B axis in the 2nd test flight
Fig. 20. The position errors along L axis in the 2nd test flight
Fig. 21. The position errors along h axis in the 2nd test flight
7. CONCLUSIONS
The article presents the results of research on the
improvement of EGNOS+SDCM positioning accuracy for the UAV technology. To this
end, the mathematical algorithm in the form of the summation model of SBAS
positioning accuracy was applied. The proposed algorithm is based on the
position errors determined with a single SBAS solution and the values of linear
coefficients used in the model. In the example analysed in this study, SBAS
data from the EGNOS and SDCM support systems were used, and the linear
coefficients were calculated as a function of the reverse velocity of movement
of the UAV. The research was based on GPS observation data and SBAS corrections
registered by the AsteRx-m2 UAS receiver
installed on an unmanned platform. The
necessary calculations were conducted first in the RTKLIB software, and then a
proprietary numerical script was applied in the Scilab language environment.
The application of the proposed algorithm allowed us to improve the position
accuracy of the UAV by 82-87% in comparison to the application of either only
EGNOS or SDCM. Apart from that, another important result of the application of
the proposed algorithm was the reduction of outlier positioning errors that
reduced the accuracy of the positioning of UAV when a EGNOS or SDCM was used.
The authors also tested the proposed algorithm in the second test flight that
was performed in the town of Nowy Świat, which is located in northern
Poland. As far as this flight is concerned, the EGNOS+SDCM positioning accuracy
was improved by 77% to 87% in comparison to the results of single EGNOS or SDCM
solutions. The study also presents the effectiveness of the proposed algorithm
in relation to the weighted average model. Future studies will be expanded by
applying the correction data from the GAGAN augmentation system in the accurate
positioning of UAV.
References
1.
Zeybek M., S. Taşkaya,
I. Elkhrachy, P. Tarolli. 2023. “Improving the Spatial Accuracy of UAV Platforms Using Direct
Georeferencing Methods: An Application for Steep Slopes”. Remote
Sensing 15: 2700. DOI: 10.3390/rs15102700.
2.
Orjales F., J. Losada-Pita, A.
Paz-Lopez, Á. Deibe. 2021. “Towards Precise
Positioning and Movement of UAVs for Near-Wall Tasks in GNSS-Denied
Environments”. Sensors 21: 2194. DOI: 10.3390/s21062194.
3.
Ichikawa A., Y. Abe, T. Ikeda, K.
Ohara, J. Kishikawa, S. Ashizawa, T. Oomichi, A. Okino, T. Fukuda. 2017. “UAV with manipulator
for bridge inspection – Hammering system for mounting to UAV”. 2017
IEEE/SICE International Symposium on System Integration (SII). Taipei,
Taiwan, 775-780. DOI: 10.1109/sii.2017.8279316.
4.
Kaniewski P., R. Gil, S. Konatowski. 2016.
“Algorithms of position and velocity estimation in GPS receivers”. Annual
of Navigation 23: 53-68.
DOI: 10.1515/aon-2016-0004.
5.
Naus K., P. Szymak, P. Piskur, M. Niedziela,
A. Nowak. 2021.
“Methodology for the Correction of the Spatial Orientation Angles of the
Unmanned Aerial Vehicle Using Real Time GNSS, a Shoreline Image and an
Electronic Navigational Chart”. Energies 14: 2810. DOI: 10.3390/en14102810.
6.
Taddia Y., F. Stecchi, A. Pellegrinelli.
2020.
“Coastal mapping using dji phantom 4 RTK in post-processing kinematic
mode”. Drones 4: 9. DOI:
10.3390/drones4020009.
7.
Adamski M. 2021. “Modelling of the unmanned
aerial vehicles flight control system”. Aviation 25(2): 79-85. DOI: 10.3846/aviation.2021.13391.
8.
Adamski M., J. Mieżaniec, A. Adamski. 2018.
„Application of drones in protection of state border”. Journal of KONES Powertrain and Transport 25(4): 9-15. DOI: 10.5604/01.3001.0012.4770.
9.
Grzegorzewski M. 2005. “Navigating an aircraft
by means of a position potential in three dimensional space”. Annual of Navigation
9: 1-111.
10. Burdziakowski P., C. Specht, P. Dabrowski, M. Specht, O.
Lewicka, A. Makar. 2020. “Using UAV Photogrammetry to Analyse Changes in the Coastal
Zone Based on the Sopot Tombolo (Salient) Measurement Project”. Sensors 20:
4000. DOI: 10.3390/s20144000.
11. Hlotov V., M. M. Fys, Z. Siejka, M. Yurkiv. 2022. “Accuracy
assessment of external orientation elements for digital images obtained from
UAVS using derivatives of implicitly specified functions”. Remote
Sensing Applications: Society and Environment 25: 100683. DOI:
10.1016/j.rsase.2021.100683.
12. Volodymyr
H., A. Hunina, M. Yurkiv, Z. Siejka. 2019. “Determining of correlation
relationship between roll, pitch, and yaw for UAVs. Reports on Geodesy and
Geoinformatics 107(1): 13-18. DOI: 10.2478/rgg-2019-0002.
13. Fys
M.M., H. Volodymyr, A.M. Brydun, Z. Siejka. 2022. Nonlinear method for determining
external orientation elements of digital images obtained from drone. Mathematical
Modelling and Computing 9(3): 627-636. DOI: 10.23939/mmc2022.03.627.
14. Santerre R., L. Pan, C. Cai, J. Zhu.
2014. “Single Point
Positioning Using GPS, GLONASS and BeiDou Satellites”. Positioning 5(4):
107-114. DOI: 10.4236/pos.2014.54013.
15. Ashraf S., P. Aggarwal, P.
Damacharla, H. Wang, AY. Javaid, V. Devabhaktuni. 2018. “A low-cost
solution for unmanned aerial vehicle navigation in a global positioning
system–denied environment”. International
Journal of Distributed Sensor Networks 14(6):
1-17. DOI: 10.1177/1550147718781750.
16. Daakir M., M.
Pierrot-Deseilligny, P. Bosser, F. Pichard, C. Thom, Y. Rabot, O. Martin. 2017.
“Lightweight UAV with on-board photogrammetry and single-frequency GPS
positioning for metrology applications”. ISPRS J. Photogramm. Remote
Sensing 127: 115-126. DOI: 10.1016/j.isprsjprs.2016.12.007.
17. Borgogno Mondino
E., R. Chiabrando. 2008. “Multi-temporal block adjustment for
aerial image time series: The Belvedere glacier case study”. The International
Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
XXXVII Pt B2: 89-94.
18. Taro S., Y. Takahashi, Y. Amano. 2016. “Precise
UAV Position and Attitude Estimation by Multiple GNSS Receivers for 3D
Mapping”. In: Proceedings of the 29th International Technical Meeting
of the Satellite Division of The Institute of Navigation (ION GNSS+ 2016).
Portland, Oregon. September 2016. P. 1455-1464. DOI: 10.33012/2016.14621.
19. Wang S., X. Zhan, Y. Zhai, C. Chi,
J. Shen. 2021. “Highly reliable relative navigation for multi-UAV formation
flight in urban environments”. Chin. J. Aeronaut. 34(7): 257-270. DOI: 10.1016/j.cja.2020.05.022.
20. Ciećko A. 2019. “Analysis of the EGNOS
quality parameters during high ionosphere activity”. IET
Radar Sonar Navigation 13: 1131-1139.
21. Ciećko A., M. Bakuła, G. Grunwald, J.
Ćwiklak. 2020.
“Examination of Multi-Receiver GPS/EGNOS Positioning with Kalman
Filtering and Validation Based on CORS Stations”. Sensors 20:
2732. DOI: 10.3390/s20092732.
22. Li L., C. Jia, L.
Zhao, K. Cheng, J. Liu, J. Ding. 2016. “Real-Time Single Frequency
Precise Point Positioning Using SBAS Corrections”. Sensors 16(8): 1261.
DOI: 10.3390/s16081261.
23. Jang J.K. 2019.
“ROK′s perspective on GBAS/SBAS implementation”. GBAS/SBAS
Implementation Workshop. Seoul, Korea. 3 to 5 June 2019. Available at:
https://www.icao.int/APAC/APAC-RSO/GBASSBAS%20Implementation%20Workshop/3-1_ROKs_perspective_on_GBAS_SBAS_implementation%20(K%20Jang).pdf.
24. Bendea H., P. Boccardo, S. Dequal,
F. G. Tonolo, D. Marenchino, M. Piras. 2008. “Low cost UAV for
post-disaster assessment”. The International Archives of the
Photogrammetry, Remote Sensing and Spatial Information Sciences XXXVII.
Part B8: 1373-1380.
25. Zhang C. 2008.
“An UAV-based photogrammetric mapping system for road condition
assessment”. The International Archives of the Photogrammetry, Remote
Sensing and Spatial Information Sciences XXXVII. Part B5: 627-632.
26. MacArthur E.Z., D.
MacArthur, C. Crane. 2005. “Use of cooperative unmanned air and ground
vehicles for detection and disposal of simulated mines”. In: Proc. SPIE
5999, Intelligent Systems in Design
and Manufacturing VI: 599909.
27. Freeland R., B.
Allred, N. Eash, L. Martinez, D. Wishart. 2019. “Agricultural drainage
tile surveying using an unmanned aircraft vehicle paired with Real-Time
Kinematic positioning – A case study”. Computers and Electronics
in Agriculture 165: 104946. DOI: 10.1016/j.compag.2019.104946.
28. Jiménez A., J. Andrade-Cetto,
I. Tesfai, I. Dontas, C. Capitán, E. Oliveres, H. Jia, A. Kostaridis.
2019. “Galileo
and EGNOS as an asset for UTM safety and security”, In: Proceedings
of 25th Ka and Broadband Communications Conference. Sorrento, Italy. P.
1-10.
29. Sabatini R. 2017.
“A novel avionics based GNSS integrity augmentation system for manned and
unmanned aircraft”. PhD thesis. University of Nottingham, 2017.
30. Amos M. 2017.
“Australia – New Zealand SBAS Demonstrator”, In: Proceedings
of 57th Meeting of CGSIC Meeting. Portland OR. 25 September 2017.
31. Rubinov E. 2018.
“Australia and New Zealand Satellite Based Augmentation System (SBAS)
Testbed”. In: Proceedings of the XXVI FIG Congress 2018.
May 6-11, 2018. Istanbul, Turkey.
32. Seok H.-J., B.-W.
Park. 2016. “Prediction of the Available Time for the SBAS Navigation of
a Drone in Urban Canyon with Various Flight Heights”. Journal of Cadastre & Land InformatiX 46(1): 133-148. DOI: 10.22640/LXSIRI.2016.46.1.133.
33. European GNSS Agency.
2019. European Global Navigation
Satellite Systems (EGNSS) for drones operations. ISBN 978-92-9206-045-9. P.
1-40.
34. Geister R., L. Limmer, M. Rippl, T.
Dautermann T. 2018. “Total system error performance of drones for an unmanned PBN
concept”. In: Proceedings of the 2018 Integrated
Communications, Navigation, Surveillance Conference (ICNS). P. 1-12.
35. Togola S., S.M.A.;
Kiemde, A.D. Kora. 2020. “Real Time and Post-Processing Flight Inspection
by Drone: A Survey”. In: Proceedings of the 43rd
International Conference on Telecommunications and Signal Processing (TSP).
P. 399-402. DOI: 10.1109/TSP49548.2020.9163498.
36. Togola S., S.M.A.
Kiemde, A.D. Kora. 2021. “Real Time and Post-Processing Flight Inspection
by Drone: A Review”. Advances in Science, Technology and Engineering
Systems Journal 6(3): 92-99. DOI: 10.25046/aj060310.
37. Jisi F., Z. Yanbo, Z. Wang. „BDS Application on
Unmanned Aerial Vehicle Air Traffic Management”, In: Proceedings of
the 27th International Technical Meeting of the Satellite Division of The
Institute of Navigation (ION GNSS+ 2014). Tampa, Florida. September 2014. P.
229-234.
38. Li R., S. Zheng, E. Wang, J. Chen,
S. Feng, D. Wang, L. Dai. 2020. “Advances in BeiDou Navigation Satellite System
(BDS) and satellite navigation augmentation technologies”. Satell
Navig. 1: 12. DOI: 10.1186/s43020-020-00010-2.
39. Ostolaza J., D.
Pérez, J.J. Lera, D. Hill, V. Boissinot, W. Roberts, S. Basker, E.
Avenant, G. Lamprecht, S. Sheppard, P. Milway, M. Reche. 2016.
“SBAS-Africa: A Cost Effective Southern African Solution Serving Multiple
Market Sectors”. In: Proceedings of the 29th International Technical
Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+
2016). Portland, Oregon. September 2016. P. 2754-2765. DOI: 10.33012/2016.14555.
40. Tomita H., M. Harigae, K. Kokue, Y.
Shiozawa. 2004.
“GPS-Aided Inertial Navigation Avionics (GAIA) Integrated with MSAS and
Maritime DGPS Beacon”. In: Proceedings of the 17th International
Technical Meeting of the Satellite Division of The Institute of Navigation (ION
GNSS 2004). Long Beach, CA. September 2004. P. 277-284.
41. Yoon H., H. Seok, C. Lim,
B. Park. 2020. “An Online SBAS Service to Improve Drone Navigation
Performance in High-Elevation Masked Areas”. Sensors 20: 3047.
DOI: 10.3390/s20113047.
42. Famiglietti N.A., G.
Cecere, C. Grasso, A. Memmolo, A. Vicari. 2021. “A Test on the Potential
of a Low Cost Unmanned Aerial Vehicle RTK/PPK Solution for Precision
Positioning”. Sensors 21: 3882. DOI: 10.3390/s21113882.
43. Bestmann U., S. Batzdorfer, M.
Becker, T. Scheide, P. Hecker. 2012. “SBAS in Urban Environment: Scenarios,
Applicability and Challenges”. In: Proceedings of the 25th
International Technical Meeting of the Satellite Division of The Institute of
Navigation (ION GNSS 2012). Nashville, TN. September 2012. P. 3481-3487.
44. TELESPAZIO. 2019.
“Role of drones in future Transportation and Logistics”. Washington.
September 5th 2019. Available at:
https://swfound.org/media/206834/role-of-drones.pdf.
45. Sheridan I. 2020.
“Drones and global navigation satellite systems: Current evidence from
polar scientists”. R. Soc. Open Sci. 7: 191494. DOI: 10.1098/rsos.191494.
46. Watanabe Y., A.
Manecy, A. Hiba, S. Nagai, A. Shin. 2019. “Vision-integrated navigation
system for aircraft final approach in case of GNSS/SBAS or ILS failures”.
In: Proceedings of the AIAA Scitech 2019. Jan 2019. San Diego, CA,
United States. P. 0113. DOI: 10.2514/6.2019-0113.
47.
Molina P., I. Colomina, T. Vitoria, P.F. Silva, J. Bandeiras,
Y. Stebler, J. Skaloud, W. Kornus, R. Prades, C. Aguilera. 2011.
“Integrity Aspects of Hybrid EGNOS-based Navigation on Support of
Search-And-Rescue Missions with UAVs”. In: Proceedings of the 24th
International Technical Meeting of the Satellite Division of The Institute of
Navigation (ION GNSS 2011). Portland, OR, USA. 20-23 September 2011. P. 3773-3781.
48. Moreno G., C. Sanz, M. Cueto, A.
Cezón, A. Viguria, A. Jiménez, T. Tavares, K. Callewaert, M.
Aguilera, I. Alcantarilla. 2020. “Positioning Performance Analysis for
Different UAV´S Use Cases and Testing Campaigns Using EGNSS”. In: Proceedings
of the 33rd International Technical Meeting of the Satellite Division of The
Institute of Navigation (ION GNSS+ 2020). September 2020. P. 219-235. DOI: 10.33012/2020.17572.
49. Specht C., J. Pawelski, L. Smolarek, M. Specht, P.
Dabrowski. 2019.
“Assessment of the Positioning Accuracy of DGPS and EGNOS Systems in the
Bay of Gdansk using Maritime Dynamic Measurements”. Journal of Navigation
72(3): 575-587. DOI: 10.1017/S0373463318000838.
50. Grzegorzewski M., W.
Jaruszewski, A. Fellner, S. Oszczak, A. Wasilewski, Z. Rzepecka, J. Kapcia, T.
Popławski. 1999. “Preliminary results
of DGPS/DGLONASS aircraft positioning in flight approaches and landings”.
Annual of Navigation 1: 41-53.
51. Mrozik M. 2023.
Application of the SBAS positioning method in the aircraft approach procedure. PhD
thesis. Silesian University of Technology, Gliwice. P. 1-147.
52. Takasu T.,
“RTKLIB ver. 2.4.2 Manual, RTKLIB: An Open Source Program. Package for
GNSS Positioning”. Available online:
http://www.rtklib.com/prog/manual_2.4.2.pdf.
53. Ueno
M., T. Nimura, T. Fujiwara, K. Nonaka. 1997. “Evaluation of RTK-OTF
Positioning System for Free Running Manoeuvrability Test of a Model
Ship”. In: Proceedings of the Oceans ‘97. MTS/IEEE Conference
Proceedings. Halifax, Canada. 6-9 October 1997. Vol. 2: 1120-1125.
54. Specht C., M. Mania, M. Skóra, M. Specht. 2015. “Accuracy
of the GPS positioning system in the context of increasing the number of
satellites in the constellation”. Pol.
Marit. Res. 22(2): 9-14. DOI: 10.1515/pomr-2015-0012.
55. Scilab Website.
Available at: https://www.scilab.org/.
Received 25.11.2023;
accepted in revised form 24.02.2024
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0
International License
[1]
Institute of Navigation, Polish Air Force University, Dywizjonu 303 no 35
Street, 08-521 Dęblin, Poland. Email: k.krasuski@law.mil.pl. ORCID:
https://orcid.org/0000-0001-9821-4450
[2]
Military University of Technology, Faculty of Civil Engineering and Geodesy,
Kaliskiego 2 Street, 00-908 Warszawa, Poland. Email:
damian.wierzbicki@wat.edu.pl. ORCID: https://orcid.org/0000-0001-6192-3894
[3]
Institute of Navigation, Polish Air Force University, Dywizjonu 303 no 35
Street, 08-521 Dęblin, Poland. Email: m.kirschenstein@law.mil.pl. ORCID:
https://orcid.org/0000-0002-4817-083X
[4]
Institute of Navigation, Polish Air Force University, Dywizjonu 303 nr 35
Street, 08-521 Dęblin, Poland. Email: m.zukowska@law.mil.pl. ORCID:
https://orcid.org/0000-0001-5485-4720
[5]
Faculty of Aviation, Polish Air Force University, Dywizjonu 303 nr 35 Street,
08-521 Dęblin, Poland. Email: p.golda@law.mil.pl. ORCID: :
https://orcid.org/0000-0003-4066-7814