Article citation information:
Lalak, M.,
Krasuski, K., Wierzbicki, D. Methodology to improve the
accuracy of determining the position of UAVs equipped with single-frequency
receivers for the purposes of gathering data on aviation obstacles. Scientific Journal of Silesian
University of Technology. Series Transport. 2023, 119, 83-104. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2023.119.5.
Marta
LALAK[1], Kamil KRASUSKI[2], Damian WIERZBICKI[3]
METHODOLOGY TO
IMPROVE THE ACCURACY OF DETERMINING THE POSITION OF UAVS EQUIPPED WITH
SINGLE-FREQUENCY RECEIVERS FOR THE PURPOSES OF GATHERING DATA ON AVIATION
OBSTACLES
Summary. Low-altitude
photogrammetric studies are often applied in detection of aviation obstacles.
The low altitude of the Unmanned Aerial Vehicle (UAV) flight guarantees high
spatial resolution (X, Y) of the obtained data. At the same time, due to high
temporal resolution, UAVs have become an appropriate tool for gathering data
about such obstacles. In order to ensure the required accuracy of orientation
of the photogrammetric block, Ground Control Points (GCPs) are measured. The
recently introduced UAV positioning solutions that are based on Post-Processing
Kinematic (PPK) and Real Time Kinematic (RTK) are known to effectively reduce,
or, according to other sources, even completely eliminate the necessity to
conduct GCP measurements. However, the RTK method involves multiple limitations
that result from the need to ensure continuous communication between the
reference station and the rover receiver. The main challenge lies in achieving
accurate orientation of the block without the need to conduct time-consuming ground
measurements that are connected to signalling and measuring the GCPs. Such
solution is required if the SPP code method is applied to designation the
position of the UAV. The paper presents a research experiment aimed at
improving the accuracy of the determination of the coordinates of UAV for the
SPP method, in real time. The algorithm of the SPP method was improved with the
use of IGS products.
Keywords: IGS,
GPS, UAV, photogrammetry, aviation obstacle, accuracy analysis, SBAS
1. INTRODUCTION
In recent years, we have been
witnessing a dynamic growth in the use of low altitude photogrammetric studies
in remote sensing [13, 40], in Geographic Information Systems
(GIS) [2, 9] or aviation [10]. The potential of these miniature
aerial vehicles that has also been noticed by the aviation sector is used,
among others, in ensuring safety in the airspace [14]. The main area of focus in the fields of
photogrammetry, remote sensing and geographic information is currently the
monitoring of aviation obstacles, including the detection of such obstacles in
the vicinity of airports.
The 21st century has
become a symbol of the development of various branches of the industry. This
leads to the dramatic growth of investment areas. As a result, we are
witnessing rapidly emerging new objects (various types of structures, etc.) not
only in large agglomerations, but also in less urbanised areas and in the
neighbourhood of airports. From the point
of view of aviation safety, such objects situated near the airport may
constitute a potential threat for the operations of aerial vessels, and thus
become aviation obstacles. Their presence
requires developing flight procedures based on the height of the aviation
obstacle. Accurate and reliable data about
such obstacles, in particular about their location or dimensions, such as
height, are essential for planning safe take-off and landing paths for
aircrafts. Existing guidelines for aviation
obstacle data collection methods strictly define the accuracy of data
collection. Despite the regulation of this issue, methods are still evolving to
achieve the highest possible degree of automation [14]. The detection of small obstacles and those of
elongated shapes is becoming a major challenge [14]. If such an object is captured, it is necessary
for the scale of the image to be larger than in traditional exploratory
flights. This is possible with a lower flight altitude by using a UAV. The techniques
employed for the detection of aviation obstacles used so far were based on
Airborne Laser Scanning (ALS). However, in such cases, one cannot exclude the
possibility of omitting an obstacle [14], and the object
detection was controlled using ordinary geodetic measurements. As a result, the
process was time-consuming and strenuous, not to mention ineffective,
especially in representing large-surface areas. In order to maintain the safety of air operations, it is necessary that
the data about obstacles should be updated regularly, whenever necessary.
Unfortunately, ALS data does not guarantee high temporal resolution of
obtaining data. The latest guidelines [14] for obtaining obstacle
data recommend using data obtained from lower altitudes of flight, which may be
achieved by using UAVs.
They allow obtaining
imagery in a scale which is significantly larger than that obtained from
traditional photogrammetric flights. In addition,
the UAV altitude will allow for much higher spatial accuracy (X, Y, Z) of
aviation obstacle data.
The accuracy of
obtaining data from UAV is influenced by several
factors. Among them, one may distinguish the method and accuracy of positioning
of the Unmanned Aerial Vehicle [36] and the accuracy of
adjustment of the photogrammetric block [30, 15, 4]. Until recently, the processing of data obtained
from a photogrammetric flight required conducting a measurement of the control
points (GCP) to perform an absolute orientation of
the model. This resulted in an extended duration
of the process of measurement as well as data processing. Currently, the development of the UAV technology, among others, in photogrammetric
applications, resulted in the possibility to use numerical algorithms that
improve the positioning of the platform in real time, while the necessary
navigation analyses may be conducted in post-processing mode. As a consequence,
this may lead to the complete elimination of the need to conduct measurements
of ground control points (GCP). For more than
ten years, the main device used to detect the position of the UAV has been the GNSS (Global Navigation Satellite System)
satellite receiver with the functions of tracking, monitoring, and recording
the observations and navigation data. GNSS receivers provide the 3 main navigation
parameters of a UAV: position, velocity, and time [23]. From the point of view of photogrammetric
applications, the navigation data of the UAV enable
the determination of elements of exterior orientation, first of all linear
ones, i.e. the centres of the projection of each photograph [15]. In this case, it is necessary to know the
eccentric of the position shift of the GNSS receiver antenna and of the camera
at the moment of exposure. While the value of the eccentric is provided by the
manufacturer on the name plate of the unmanned platform, the position of the
antenna of the GNSS receiver mounted on the platform
still has to be determined. In low-cost
on-board GNSS receivers, the coordinates of the UAV
is designated in near-real time with the use of the SPP (Single Point
Positioning) method [29]. This method is based on the application of
single-frequency receivers mounted on the UAV
platform [37]. Even though this method is the most
commonly used, it is characterised by low positioning accuracy, reaching even
up to 10 m [5, 11]. Another currently used solution is an RTK system integrated with the aerial vessel, which can
allow the number of GCPs to be reduced or eliminated altogether. However,
the RTK method involves multiple limitations that result from the need to ensure
continuous communication between the base station and the mobile receiver. It should be noted that a UAV
equipped with GPS does not require the data from GNSS reference station, which
might significantly improve the efficiency of the process of collecting data on
aviation obstacles. Previous
studies [33] revealed the
possibility to obtain a high accuracy by UAVs equipped with GPS receivers.
The authors of this study took an
attempt to improve the determination of the accuracy of the positioning of UAVs for the SPP method. With this aim, IGS products were used to
improve the algorithm of the SPP method.
1.1. Related works
In recent years, many studies have
been conducted on the application of the single point
positioning method to determine the position of aerial vehicles [22]. Publications discussing the accuracy of the SPP method in positioning Unmanned Aerial Vehicles [37] and the attempts to
improve this accuracy are also becoming more common. The need to enhance the accuracy of positioning UAVs
resulted in the development of numerical algorithms that improve the
positioning of UAVs in terms of code observations for the SPP method [39] and thus, the
adjustment of the determination of the linear elements of exterior orientation.
In the study by Santerre et al. [29], the Chinese satellite
system BeiDou was used and compared to the American GPS system and the Russian
GLONASS systems. In fact, the BeiDou system consists of 14 satellites that provide complete coverage
of the whole Asia and Pacific area. Positioning with use of the SPP method was
conducted in Changsha in the Hunan Province of China, in order to demonstrate
the benefits of the use of the combined pseudo-distance solutions from these 3
satellite navigation systems, in particular in covered locations. The results demonstrated an improvement in
accuracy by 20% for the horizontal coordinates and by 50% for the vertical
coordinates. The combination of the
GPS/GLONASS/BeiDou solutions resulted in an accuracy of approx. 5 m.
Other methods of enhancing the
accuracy of the single point positioning method were presented in the study by Angrisano et al. [3]. The tests were conducted with the use of UAVs in the area of an urban agglomeration, with tall
structures such as skyscraper buildings. The navigation algorithm for positioning the UAV
was based on the weighted average model. The conducted experiments resulted in an accuracy of approx. 10 m, which was achieved in a difficult, urban area.
Furthermore, Forlani et al. [15] presented the results
of a research experiment that consisted in assessing the improvement of the
orientation accuracy of a photogrammetric block with use of various numbers of
GCP. Apart from that, the authors compared alternative positioning methods
(including the SPP method) in order to determine the position of the UAV
platform. The photogrammetric flight was
performed with the Dji Phantom 4 RTK platform on the
test military training ground in the Italian Alps. The conducted research demonstrated that
determining the coordinates of a UAV platform with
the use of the SPP code method allows obtaining a spatial accuracy of several
meters when independent ground control points are used in the whole test area.
Kai-Wei Chiang et al. [7] developed a fast and
inexpensive system for gathering spatial information in near-real time. The authors pointed out that fast collection of
information had become a new trend in remote sensing applications. During the studies, a platform for obtaining
spatial information based on UAV, without the need to
measure ground control points, was developed. The UAV-based platform shown has a Direct Georeferencing (DG) module
[6], which includes an integrated Inertial Navigation System (INS)/ Global
Positioning System (GPS).
The initially results
of the analysis of positioning accuracy in the DG
mode revealed that the accuracy of horizontal positioning was approx. 5 m at
the flight attitude of 300 m above ground. The positioning accuracy for the vertical component was lower than 10 m.
The research conducted by Himanshu Sharma et al. [34] demonstrated a
significant increase in positioning accuracy over the standard SPP solution,
after the application of the Kalman filter. H.R. Hosseinpoor et al. [20] developed an algorithm
that enables to estimate the geolocation of the target based on the video
images captured by a UAV with RTK GPS module. These results were compared to the positioning accuracy obtained with
use of the GPS solution for the SPP code method
instead of RTK. The research results revealed that
the accuracy improved by several tens of centimetres without the necessity to
perform measurements of ground control points.
In order to facilitate certain types
of applications, e.g., environmental detection or monitoring disasters, it is
essential to develop an effective system for acquiring spatial information in
near-real time. Speed and ease in gathering spatial
information has become the most important goal in land mapping technology. Meng-Lun Tsai et al. [7] presented a platform
that was developed to obtain spatial information based on UAV. Additionally, the results of the assessment of
data collection accuracy were provided. The presented platform based on UAV is
equipped with a DG module, including an integrated INS/GPS system, a digital
camera, as well as other general UAV modules in which all the necessary calibration
procedures were implemented. During the
research project, test flights were conducted in order to verify the
positioning accuracy in the direct georeferencing mode, without using ground
control points. The preliminary results of the
positioning accuracy in direct geo-referencing mode without the use of GCP demonstrated that the accuracy of horizontal
positioning was lower than 20 meters, while the vertical positioning
accuracy (z) was lower than 50 m at the flight altitude of 600 meters above
ground. The authors pointed out that the
obtained accuracy results may be useful in monitoring disasters, where it is
vital to obtain spatial information fast, in near-real time.
The
literature review revealed a recurring problem of low positioning accuracy of
unmanned aerial vehicles when the SPP code method was
used. In the conducted research, the authors of the present study took an attempt
to enhance the accuracy of positioning the UAV for
the purposes of collecting data about aviation obstacles. In order to
achieve it, the algorithm of the SPP code method was
modified by adding IGS products to determine the position of the UAV.
1.2. Research purpose
In this paper, a research question was posed: whether the
modification of the algorithm of the absolute positioning method SPP by adding IGS products will enable to enhance the
accuracy of the positioning of UAVs for the purposes of collecting data about
aviation obstacles? IGS products are understood as precise
ephemerides in the EPH format, precise clocks in the CLK format, the IONEX
ionosphere map format, the DCB instrumental error format, and the format of the
antenna phase center of the satellite/receiver ANTEX.
The paper consists of: section 2 where the research method is described;
section 3 presents the experimental materials and results; section 4 is a
description of the results obtained and section 5 provides a summary.
2. METHODS
This chapter
provides a description and presentation of the observation equation for the SPP positioning method with use of GPS navigation data and the observation equation in the
modified algorithm of the SPP positioning method with IGS products, i.e.: the precise
ephemerides EPH, precise clocks CLK, the IONEX format, DCB format, and ANTEX
format. The block diagram of the process of improving the accuracy of determining
the position of the UAV for the purposes of collecting data about obstacles is
presented in the illustration below (Fig. 1). It
presents two methods of determining the position of the UAV: with the SPP method
and with the SPP + IGS method. For these two methods, the photogrammetric block
of images was adjusted without measuring the ground
control points. Then, based on the obtained results, the
accuracy of positioning of the UAV and the adjustment of the block of images
were analysed.
In this study, two research methods were used to designation the position of the UAV. These were: the classic navigation algorithm for the code-based SPP method using the GPS navigation data and the modified algorithm of the SPP method with the added products of the IGS geodesic service. The fundamental observation equation for the SPP method using GPS navigation data takes the form presented below [18, 31]:
where:
l – code observations;
d – geometric distance between the satellite and the receiver;
(X , Y ,Z) –
unknown coordinates of the UAV;
(XGPS, YGPS,
ZGPS) – coordinates of the GPS satellites;
c – light speed;
dtr – unknown
bias of the receiver clock;
dts – correction
of the receiver clock;
Ion –
ionospheric correction;
Trop –
tropospheric delay;
Rel –
relativistic effect;
TGD – group delay
in GPS system;
Mp – multipath effect.
The positioning algorithm in
equation (1) is a classical solution of the position
in the SPP method.
The position of the UAV in the geocentric frame XYZ are determined from
equation (1) in form of parameters (X, Y, Z).
Fig. 1. The scheme of improving the accuracy of UAV position
On the other hand, the basic observation equation in the modified algorithm of the SPP method with use of the IGS products takes the following form [17, 24]:
where:
l – code observations;
d – geometric distance between
the satellite and the receiver, include the phase center offset from ANTEX format;
(X, Y, Z) –
unknown coordinates of the UAV;
(X'GPS, Y'GPS,
Z'GPS) – coordinates of GPS satellites, the coordinates
are determined with the use of Lagrange’s polynomial from the precise
ephemeris EPH obtained from the IGS geodesic services;
c – light speed;
dtr – unknown
bias of the receiver clock;
dts' – bias of the
receiver clock, determined based on the CLK format from the IGS geodesic
services;
Ion' – ionosphere
delay, which is interpolated from the GRID in the IONEX format obtained from
the IGS geodesic services;
Trop – tropospheric delay, calculated based on the determinist model of
tropospheric delay;
Rel – relativistic effect;
SDCB'P1 – hardware
delay for the SDCBP1 satellite, based on the DCB product from the
IGS geodesic services;
RDCB'P1 – hardware delay
for the SDCBP1 receiver, determined in the linear combination
Geometry-Free or based on the DCB product from the IGS geodesic services;
Mp – multipath effect.
The
algorithm in equation (2) is a modified solution of
positioning in the code-based SPP method, where IGS products were applied,
i.e.: the EPH format, CLK format, IONEX format, DCB
format, and the ANTEX format. Similarly, as with equation (1), algorithm (2) enables the designation of the
coordinates of the UAV. When comparing the observation equations (1) and (2), attention should be paid to different models
of systematic errors. Thus, if the position of the GPS satellite on the orbit is determined from equation (1),
Kepler’s model of the orbit is applied, while equation (2) uses the
Lagrange polynomial model. Apart from that, the coordinates of GPS satellites that are determined from the Lagrange
polynomial take into account the correction of the phase centre offset of the
satellite antenna based on the ANTEX format. The accuracy
of positioning from the Kepler model of the orbit is 1 m, while with the Lagrange polynomial it is 0.10 m. Additionally, the error of the satellite clock in the Kepler orbit model is
determined with use of a 2nd degree polynomial, and the accuracy of
this solution is 5 ns (approx. 0.15 m). In addition,
in equation (2), the error of the GPS satellite clock
is determined from the CLK format, and its accuracy is higher than 3 ns
(approx. 0.1 m [21]). As for the model of the ionosphere, the Klobuchar model applied in equation (1) reduces ionospheric
delay by approx. 50-60%, while the ionosphere model from the IONEX format
reduces it by approx. 80-90% respectively. As far as
hardware delay is concerned, the TGD parameter is
used in equation (1), while equation (2) is based on DCB instrumental errors [18]. The comparison of equations (1) and (2) reveals that the application of
different types of systematic errors will influence the final designation of
the coordinates of the UAV in the stochastic process, as well as the accuracy
of positioning of the UAV. The results
of the research are presented in Section 3.
3. MATERIALS AND
EXPERIMENTAL RESULTS
3.1. Study area
The research experiment was
performed near the Radom-Sadków airport (Fig. 2). The Radom-Sadków airport is located
near the city centre of Radom. The area surrounding the airport is covered by aviation obstacle data collection
zones. In the nearest vicinity of the airport, zone 2a – in the runway
strip and zone 2b that is directly connected to zone 2a and covers the take-off
sector (Fig. 2).
Fig. 2. Location of the research area
The zones of collecting data about
aviation obstacles are planes in which data about aviation obstacles are
collected. Such data are necessary in the
widely understood process of ensuring safety in airspace, from designing flight
operations procedures to developing aeronautical charts.
In the research area near the
Radom-Sadków airport, data were acquired using the VTOL WingtraOne
system. The platform was equipped with a single-frequency GPS receiver,
recording data at 10 Hz. The flight
was conducted over two test areas in June 2021. Atmospheric conditions during
the raids were good. The test block
consisted of 35 series, which constituted 850 images (Fig. 2), acquired from a
height of 250 m above the ground surface. The flight was conducted in an
east-west direction, with transverse and longitudinal coverage of 75%. The main parameters of the test block in the
conducted experiment are presented in the table below (Tab.
1).
Tab. 1
Parameters
of the test block
|
Set of coordinates |
PUWG 2000/7 |
|
Image saving format |
JPEG |
|
Number of series |
35 |
|
Sensor |
Sony RX1R II camera |
|
Lens focal length [mm] |
35 mm |
|
Average
longitudinal/ transverse coverage [%] |
75/75 |
|
Flight altitude [m] |
250 |
|
Theoretic pixel size [m] |
0.04 |
For the
purposes of conducting the study and verifying the correctness of the applied
mathematical algorithms (1) and (2), navigation calculations were performed in
the RTKLIB v. 2.4.3 software [28], and
then in the language environment Scilab v.6.1.1. [32]. The RTKLIB was used to designation the position of the UAV based on
the mathematical equations (1) and (2). For equation (1), the calculations in
RTKLIB software were configured as follows [27]:
-
source of observation data: format RINEX 2.11,
-
source of navigation data: RINEX navigation 2.11,
- observations used: code-based observations
L1-C/A from the AsteRx-m2 UAS
receiver,
- calculation interval: 1
second,
- set
of coordinates: WGS-84, geocentric
coordinates XYZ,
- positioning method: SPP,
- source of ephemeral data: GPS
navigation message,
- source of data about satellite clock error: GPS
navigation message,
- ionosphere model: Klobuchar model from the GPS navigation message,
- elevation mask: 5o,
- troposphere model: Saastamoinen
model,
- hardware delay: TGD
parameter,
- navigation system: GPS system,
- reference
time: GPS Time.
Moreover,
for equation (2), the configuration of the
computations in the RTKLIB programme was set as follows [27]:
- source of observation data: format RINEX 2.11,
- source of navigation data: RINEX navigation 2.11,
- observations used: code-based observations L1-C/A from
the AsteRx-m2 UAS receiver,
- calculation interval: 1 second,
- set of coordinates: WGS-84, geocentric coordinates
XYZ,
- positioning method: SPP,
- source of ephemeral data: EPH format and ANTEX format,
- source of data about satellite clock error: CLK format,
- ionosphere model: IONEX format,
- elevation mask: 5o,
- troposphere model: Saastamoinen model,
- hardware delay: DCB format,
- navigation system: GPS system,
- reference time: GPS Time.
The RTKLIB software was also used to
determine the reference position of the UAV flight with use of the RTK-OTF
positioning method. The
following scheme of configuration of the input parameters for the determination
of the reference position of flight was applied [27]:
- positioning type: MOVING BASE,
- source of GNSS navigation data: GPS board message,
- source of GNSS observation data from the on-board
receiver: kinematic GPS observations in the RINEX 2.12 format from the AsteRx-m2
UAS receiver,
- source of GNSS observation data from reference
station: static GPS observations in RINEX 2.12 format,
- method of determining the coordinates of the GPS
satellite: based on the parameters of Kepler’s orbit,
- elevation mask: 5°,
- ionosphere model: Klobuchar model from the GPS
navigation message,
- troposphere model: Saastamoinen model,
- model of orbit and clocks: board ephemeris,
- calculation interval of the measurement epoch: 1
second,
- set of coordinates: WGS-84,
- final format of coordinates: geocentric coordinates
XYZ,
- navigation system: GPS,
- reference time: GPS Time.
After the navigation calculations
were performed in the RTKLIB software, the authors
developed a script in the Scilab programming language to determine the accuracy
of the positioning of UAV for the SPP method using equation (1) and for the SPP
method with IGS products from equation (2).
3.2. Experimental results
The
research experiment consisted in a flight of an unmanned aerial vehicle. Then,
based on the obtained data, the accuracy of UAV positioning and the accuracy of
the adjustment of the block of images from the UAV
were analysed.
3.2.1. Analysis of UAV positioning accuracy
In the
framework of the conducted research, the UAV positioning accuracies were
determined for equations (1) and (2). Firstly,
position errors were determined, i.e., the coordinates of the UAV calculated from equations (1) and (2) were compared to
the reference position of the flight from RTK-OTF solution [38]. To achieve it,
position errors were calculated as follows:
Where:
Fig. 3. The position errors for X coordinate
Figure 3
presents the results of position errors for X coordinate for a representative
flight of the UAV in Radom. The
values of position errors along the X axis for the comparison of the
coordinates from equation (1) and the RTK-OTF technique is between -6.5 m to
+8.1 m, with the average value of -2.1 m. On the other hand, position errors
for equation (2) for the comparison of the
coordinates from equation (2) and the RTK-OTF technique ranged from -1.3 m to
+2.8 m, with the average value of -0.1 m. The comparison allows us to state that the
application of the IGS products in the SPP method
resulted in improving the accuracy of determining the position of the UAV along
the X axis by approx. 95% in comparison to the classical SPP solution for
equation (1).
Fig. 4. The position errors for Y coordinate
Figure 4
presents the results of position errors for Y coordinate based on equation (4). The values of position errors along the Y axis for the comparison of
the coordinates from equation (1) and the RTK-OTF technique range from -1.1 m
to +0.2 m, with the average value of -0.5 m. On the other hand, position errors
for equation (2) for the comparison of the coordinates from equation (2) and
the RTK-OTF technique ranged from -1.0 m to +0.3 m, with the average value of
-0.3 m. The
comparison allows us to state that the application of the IGS products in the
SPP method resulted in improving the accuracy of determining the position of
the UAV along the Y axis by 40% in comparison to the classical SPP solution for
equation (1).
Fig. 5. The position errors for Z coordinate
Figure 5
presents the results of position errors for Z coordinate based on equation (5). The values of
position errors along the Z axis for the comparison of the coordinates from
equation (1) and the RTK-OTF technique is between -6.1 m to +5.8 m, with the
average value of -1.7 m. On the other hand, position errors for equation (2)
for the comparison of the coordinates from equation (2) and the RTK-OTF
technique ranged from -1.8 m to +1.8 m, with the average value of -0.3 m. The comparison
allows us to state that the application of the IGS products in the SPP method
resulted in improving the accuracy of determining the position of the UAV along
the Z axis by over 80% in comparison to the classical SPP solution for equation
(1).
As far as
collecting data about aviation obstacles by UAVs is
concerned, a particularly important element is the designation of the resultant
accuracy of the platform in 3D space. Then it is necessary to use it as the basis for calculating the accuracy
of UAV position in 3D space, as presented below:
where:
Fig. 6. The resultant
accuracy of UAV in 3D space
Figure 6 shows the results of the determination of
parameter dS
for the position of UAV. Here, for the
comparison of the coordinates from equation (1) and
the RTK-OTF technique, the values of the dS factor range from 0.6 m to
9.9 m, with the average value of 2.8 m. On the other hand, for the comparison of the coordinates from equation
(1) and the RTK-OTF technique, the values of the dS factor are between 0.1 m to 3.2 m, with the average
value of 0.9 m. The comparison of the obtained results of the dS parameter allows us
to claim that the application of the IGS products in the SPP method enabled to
reduce the dS parameter by approx. 67% in comparison to the classic SPP
navigation solution.
3.2.2. Block adjustment accuracy
analysis
The image data obtained during the
flight were processed in the UASMaster software. The block of images obtained at a low altitude
was adjusted based on the adjustment algorithm using the independent bundle
method. Then, the exterior orientation of
the images was defined and approximate elements of exterior orientation were
introduced for each image. The linking
points were generated automatically using a digital image correlation strategy
based on the least squares method. The block was adjusted without measuring the
control points, for two variants of the UAV positioning method. The first variant was based on UAV positioning with use of the single point positioning
method, while the second one was based on UAV positioning with use of the code-based
SPP method modified to include the EPH format, CLK format, IONEX format, DCB
format, and the ANTEX format. For the purposes of accuracy analysis, the
results obtained from the block adjustment were then compared to the results of
block adjustment using GCPs. To do so,
additionally, measurements of 14 signalled ground control points were conducted
in the test area with use of the RTK method in the
GPS system. The accuracy of determination of the
coordinates of ground control points (X, Y, Z) was 0.03
m.
After the
block adjustment in the first variant of UAV
positioning, the errors were calculated for the linear and angular elements of
exterior orientation. The accuracy of
determining the coordinates of the centres of projections X0, Y0,
Z0 amounted to 3.16 m to 7.22 m. The angular elements of exterior
orientation ω, φ, κ were determined with an accuracy of
0.211° to 0.256°.
For the second variant
of UAV positioning, the accuracy of the liner elements X0, Y0,
Z0 ranged from 1.98 m to 3.22 m, while the accuracy of the angular
elements ω, φ, κ ranged from 0.172° to 0.215°. As a result of block adjustment with use of
ground control points, the following accuracy values were obtained: for linear
elements X0, Y0, Z0 from 0.13 m to 0.17 m, and
for angular elements ω, φ, κ from 0.061° to 0.078°. The results of block adjustment for specific
variants are presented in the table below (Tab. 2).
Tab. 2
Summary of blocks adjustment
|
Description |
Variant 1: without GCPs (SPP positioning) |
Variant 2: without GCPs (SPP positioning + IGS) |
With GCPs |
|
MX0 [m] |
3.16 |
2.31 |
0.14 |
|
MY0 [m] |
4.08 |
3.22 |
0.13 |
|
MZ0 [m] |
7.22 |
1.98 |
0.17 |
|
Mω [°] |
0.243 |
0.215 |
0.061 |
|
Mφ [°] |
0.211 |
0.172 |
0.068 |
|
Mκ [°] |
0.256 |
0.194 |
0.078 |
Based on
the obtained results, it was found that the application of the classical SPP method extended to include IGS products led to an
improved accuracy of the adjustment of a block of photographs. The accuracy of the determination of the linear
elements of exterior orientation increased, on average, by 58%, while the accuracy of the angular elements increased,
on average, by 18%. The proposed
modification of the absolute positioning algorithm SPP
by adding IGS products allowed us to obtain the accuracy results of block
adjustment that were very similar to those obtained when the block was adjusted
based on the measured ground control points.
4. DISCUSSION
Due to the
fact that there are two important aspects of the conducted accuracy analysis,
this section has been divided into two subsections. In the first part, the accuracy results of the proposed method of
positioning UAV are analysed. Part two discusses the
results from the adjustment of a block of images after applying the suggested
positioning method.
4.1. UAV positioning
This part
of the discussion addresses three topics: 1) the reproducibility of the proposed research method, 2) the
comparison of the obtained test results with the SPP solution with EGNOS
corrections, and 3) the comparison of the obtained results to the knowledge
state analysis.
As far as
the reproducibility of the proposed research method is concerned, the results
of the accuracy of positioning of UAV from another
test flight, from the period from 11:22:15 (40935 s) to 12:06:03 (43563 s)
according to GPS Time (GPST) were presented. This flight also took place in Radom, on the
same measurement day. Figures 7-9 present the results of the
accuracy of the UAV position determination along the XYZ axes of coordinates. Figure 7 shows that
the application of the IGS products in the SPP method resulted in improving the
accuracy of determining the coordinates of the UAV along the X axis by 96% in
comparison to the classical SPP navigation solution. Furthermore, Figure 8 shows that
the application of the IGS products in the SPP method resulted in improving the
accuracy of determining the position of the UAV along the Y axis by 31% in
comparison to the classical SPP navigation solution. Finally, Figure 9 confirms that the application of
the IGS products in the SPP method resulted in improving the accuracy of
determining the position of the UAV along the Z axis by 86% in comparison to
the classical SPP navigation solution. The obtained
experimental results demonstrated that it is justified to include IGS products in the code-based SPP method. Moreover, the comparison of the test results
presented in Fig. 3-5 and Fig. 7-9 reveals the repeatability of the calculation
process in form of the reduction in position errors when IGS products were used
in the navigation solution for the positioning of the UAV.
Fig. 7. The
position errors for X coordinate in the 2nd test flight
Fig. 8. The
position errors for Y coordinate in the 2nd test flight
Fig. 9. The
position errors for Z coordinate in the 2nd test flight
Additionally,
Figure 10 shows the results of the
The second
part of the discussion compares the obtained test results with another research
method by comparing the results from the SPP solution
with use of the IGS products to the SPP solution with EGNOS corrections [8]. The results of this
comparison are presented in Figure 11. For the
purposes of comparison, the accuracy results of
Fig. 10. The
resultant accuracy of UAV in 3D space in the 2nd test flight
Fig. 11. Comparison
of resultant accuracy
The last
element of this part of the discussion is the comparison of the obtained
results to the knowledge state analysis. The results of the research experiment presented in the work by Himanshu Sharma et al. [34] showed an improvement in the
accuracy of the positioning of an UAV with the use of the SPP method extended
by adding the Kalman filter. The obtained
results demonstrated that the accuracy of UAV
positioning improved by several tens of centimetres in comparison to the
classical SPP method. The study by Angrisano et al. [3] presented an
improvement in the accuracy of the absolute method of UAV positioning by
applying a positioning algorithm that was based on the weighted average model. As a result, although the tests were conducted
in an urban area that is difficult to measure, horizontal accuracy below 10 m
was achieved. The attempts at improving the accuracy of positioning with use of the SPP method that were discussed in previous publications
demonstrated that it is possible and realistic to obtain satisfactory results. However, the methodology of enhancing the
accuracy of determining the position of UAV proposed here, which consists in
modifying the algorithm of the SPP method by including products of the IGS
geodesic services, shows an improvement in the accuracy by as much as 95% along
the X axis, by 40% along the Y axis, and by 80% along the Z axis.
4.2. UAV block adjustment
Evaluation of the effectiveness of
the proposed method for increasing the accuracy of UAV position determination
was carried out on the basis of a research experiment of adjustment of a block
of images in two variants of the positioning method. The
application of the classical navigation solution for the code-based SPP method with use of GPS navigation data allowed us to
obtain the following accuracy values of the exterior orientation elements: from 3.16 m to 7.22 m for linear elements and
from 0.211° to 0.256° for angular elements. The determination of the UAV coordinates with use of the algorithm of
the SPP method modified by adding the products of IGS
geodesic services resulted in improving the accuracy of the adjustment of the
block of images by 58%, on average, for linear exterior orientation elements,
and by 18%, on average, for the angular elements. The reliability of the results of the conducted
accuracy analysis was compared to the accuracy of adjustment of the block of
images where ground control points were used for the internal orientation of
the model. The methodology presented in this
paper to increase the accuracy of UAV positioning allowed to achieve block
adjustment accuracy without the use of photogrammetric matrix points at a level
higher than 3.22 m. Previous publications on
the determination of the position of unmanned aerial vehicles for
single-frequency GPS receivers usually pointed to the
necessity to establish and measure a photogrammetric grid in the test area in
order to improve the accuracy of the generated photogrammetric points [25, 16, 12]. Particular
attention was paid to the influence of the number and distribution of ground
control points in the whole test area [26, 19, 35, 33, 1]. As the
research results are often quite ambiguous about this issue, the topic of the
accuracy of UAV positioning and the accuracy of the
generated photogrammetric products continues to evolve. In his studies, Shahbazi et al. [33] presented the
possibility to obtain a high level of accuracy of the adjustment of the block
obtained from a UAV equipped with a GPS receiver. Moreover, the RTK system that is also currently used is integrated with
unmanned aerial vehicle and may contribute to reducing the number of GCPs or
eliminating them completely, allows achieving an accuracy of UAV positioning on
the level of only several centimetres.
5. CONCLUSION
This paper
shows the results of the experiments and analyses concerning the determination
of the position of an UAV. The main
objective of the research was to develop a methodology to improve the accuracy
of UAV positioning based on modifying the algorithm
of the SPP method by adding products of the IGS geodesic services. The second
objective was to improve the accuracy of photogrammetric products for aviation
obstacles data collection without the need to conduct measurements of ground
control points. The tests were conducted with the
use of two methods. The first of them presented a
classic navigation solution for the code-based SPP
method with use of GPS navigation data. The second method employed the algorithm of the SPP
method that was modified to include IGS products (i.e. precision ephemeris,
precision clock, the IONEX format, the DCB format, and the ANTEX format). The conducted analyses revealed that the use of
the modification of the absolute positioning SPP
method by adding IGS products allowed to improve the accuracy of determining
the position of an UAV in order to obtain data about aviation obstacles by 95%
along the X axis, by 40% along the Y axis, and by 80% along the Z axis.
The
designation of the position of an UAV with use of the algorithm of the SPP
method modified by adding the products of IGS geodesic services resulted in
improving the accuracy of the adjustment of the block of images by 58%, on
average, for linear exterior orientation elements, and by 18%, on average, for
the angular elements. Applying the modification of the Single Point Positioning method by adding IGS products will
enable to obtain the accuracy of collecting data about aviation obstacles that
is required by the European standards [14] – for the X, Y
coordinates on the level of 5 m, and for the Z coordinate on the level up to 3
m.
Acknowledgments
We are very grateful to Creotech Instruments S.A. for
access to the UAV data.
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Received 15.12.2022; accepted in
revised form 02.03.2023
Scientific Journal of Silesian University of Technology. Series
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[1] Institute of Navigation, Polish Air Force University, Dywizjonu
303 35 Street, 08-521 Dęblin, Poland. Email: m.lalak@law.mil.pl. ORCID:
https://orcid.org/0000-0001-5485-4720
[2] Institute of Navigation, Polish Air Force University,
Dywizjonu 303 35 Street, 08-521 Dęblin, Poland. Email:
k.krasuski@law.mil.pl. ORCID: https://orcid.org/0000-0001-9821-4450
[3] Department of Imagery
Intelligence, Faculty of Civil Engineering and Geodesy, Military University of
Technology, Kaliskiego 2 Street, 00-908 Warsaw, Poland. Email:
damian.wierzbicki@wat.edu.pl. ORCID: https://orcid.org/0000-0001-6192-3894