Article citation information:
Jafernik, H., Fellner, A., Mrozik, M.,
Krasuski, K. Results of aircraft positioning tests in post-processing using the
GNSS. Scientific Journal of Silesian
University of Technology.
Series Transport. 2017, 95, 67-74.
ISSN: 0209-3324.
DOI: https://doi.org/10.20858/sjsutst.2017.95.7.
RESULTS OF AIRCRAFT
POSITIONING TESTS IN
POST-PROCESSING USING THE GNSS
Summary. In this
paper, the results of an aircraft’s positioning in aviation during two flight
tests are presented. The aircraft’s position was established using GPS data
with a sample rate of 1 s in both experiments. The raw GPS data were collected
by a Topcon Hiper Pro receiver, which was installed in the pilot’s cabin of a
Cessna aircraft. The aircraft’s coordinates in the BLh geodetic frame were
determined using the single point positioning (SPP) method in gLAB software. The
mathematical algorithm for the aircraft’s coordinates are also described in the
article. The typical standard deviations for the aircraft’s coordinates were
less than 10 m in test I and less than 30 m in test II.
Keywords: aircraft trajectory monitoring; GPS, SPP method; accuracy;
ICAO.
1. INTRODUCTION
The
exploitation of GNSS satellite technology in aviation offers new technological
possibilities and development trends to the field of air transport. Purchasing
and equipping an aircraft with a GNSS satellite receiver is becoming a
common and obligatory technical standard. The GNSS satellite receiver makes it
possible to determine an aircraft’s position, improve the safety of air
transport movements, facilitate the aircraft’s operation and navigation, help
the crew during take-off and landing, ensure the aircraft’s orientation in
airspace etc. Usually the GNSS receiver helps to determine an aircraft’s
position using C/A code observations at the L1 frequency. This solution, which
is called the SPP method, uses pseudorange measuring [6], with the coordinates
of an aircraft determined by the ECEF geocentric system, as well as the clock
correction of the receiver. The SPP mathematical model may be solved with
Kalman filtering or the least squares method [4].
The aim
of this paper is to show the possibilities of the SPP method when applied to
determine an aircraft’s position while using the GNSS sensor in air navigation.
To verify the research method, numerical calculations were performed with gLAB
software using the SPP method for GPS code observations. GPS observations were
registered by a Topcon Hiper Pro receiver during two flight tests at the
military airport in Dêblin. A description of the research based on kinematic
tests and its results are presented in this scientific paper.
2. RESEARCH METHODS
The
mathematical model for the SPP method is described by the following
observational equation (1) [6]:
where:
C1 – C/A
code measurement at the L1 frequency in the GPS system
r – satellite-receiver geometric distance
(x, y, z)
– aircraft position in the ECEF
geocentric system
c – speed of light
dto – receiver clock correction
dts – satellite clock correction
Ion – ionospheric correction
Trop – tropospheric correction
Rel – relativistic correction
TGD – satellite’s instrumental error
for code observations
e – C/A code measurement noise
From
equation (1), we receive four parameters, i.e., three coordinates of the
aircraft in the ECEF geocentric system (x,
y, z) and the receiver clock correction. The parameters of the model,
such as the satellite-receiver geometric distance, satellite clock correction,
ionospheric correction, tropospheric correction, relativistic correction and
the satellite’s instrumental error, are determined with the use of navigational
data from broadcast ephemeris. The unknown parameters from equation (1) are
determined with the use of the least squares method or Kalman filtering for
each measurement epoch.
3. RESEARCH EXPERIMENT
AND ITS RESULTS
As part of the presented research,
aircraft coordinates were determined using the SPP method in gLAB software,
which is an open-source programming tool that was created by experts from the
Polytechnic University of Catalonia in Spain. This software offers every user
two calculation modules, namely, the SPP method and the precise point
positioning method. It is worth mentioning that, in its present form, gLAB only
uses data from the GPS system for numerical calculations [3].
While performing numerical
calculations in gLAB, the following initial parameters were set for SPP module
[3, 5]:
-
RINEX observation
file version 2.11
-
RINEX navigational
data: applied
-
source of
ephemeral data and GPS satellite clocks: on-board ephemeris
-
source of
ionospheric correction: Klobuchar model
-
troposphere model:
simple model
-
mapping function:
simple mapping
-
source of TGD
instrumental errors: on-board ephemeris
-
relativistic
correction: applied
-
the Sagnac effect:
applied
-
user’s initial
coordinates: based on the observation file
-
calculation
interval: 1 s
-
elevation mask: 5°
-
positioning mode:
kinematic
-
code observations
type: C/A code measurement at the L1 frequency
-
a priori value of
code measurement standard deviation: 1 m
-
measurement
scaling: applied
-
calculation
method: forward Kalman filtering
In
numerical calculations, raw GPS data registered and collected by a
dual-frequency Topcon Hiper Pro receiver were used. GPS code measurements came
from two flight tests, which were made using a Cessna plane on 16 June 2010 at
the military airport in Dêblin [2]. The Cessna plane flight trajectory for both
flight tests is presented, along with the BLh geodetic coordinates, in Fig. 1
and Fig. 2. During the kinematic tests, the Topcon Hiper Pro receiver was used to
register GPS observations in order to reconstruct a plausible aircraft position
during post-processing. The first flight test started at 11:58:38 and finished
at 12:34:57, according to GPS time. The second test started at 14:31:44 and
lasted until 15:00:04, again according to GPS time. The main aims of both
flight tests were the implementation of GNSS satellite technology for use in
air navigation and the determination of the accuracy of kinematic positioning
using a GNSS sensor. It should be mentioned that both flight tests were carried
out as part of a development project called “GNSS-based aircraft and commercial
vehicles’ traffic monitoring systems using public services”.
Fig. 1. The
horizontal trajectory of the aircraft in flight test I.
Fig. 2. The
horizontal trajectory of the aircraft in flight test II.
Fig. 3 and Fig. 4 present the
ellipsoidal height of the Cessna flights. During the first flight, the
ellipsoidal height reached between 150 and 640 m. In the second test, the
ellipsoidal height was between 120 and almost 380 m. In the second test, more
frequent changes in the ellipsoidal height during the take-off phase and during
the landing approach may be observed.
Fig. 3. The vertical
trajectory of the aircraft in flight test I.
Fig. 4. The vertical
trajectory of the aircraft in flight test II.
Fig. 5 and
Fig. 6 highlight the accuracy of the Cessna plane position in the BLh geodetic
frame. In the case of flight, I, the accuracy of geodetic latitude B was
between 0.5 and 8.1 m. Furthermore, the accuracy of geodetic longitude L was
between 0.2 and almost 4 m, while the values of standard deviation for the
ellipsoidal height were from 1 to almost 10 m. It is worth noting that, during
most of flight I, the accuracy of the aircraft coordinates was above 3 m.
Fig. 5. The accuracy
of the aircraft coordinates in flight test I.
Fig. 6. The accuracy of the aircraft
coordinates in flight test II.
In the case of flight II, the
accuracy of the Cessna aircraft coordinates was: from 1.1 to 16.1 m for
geodetic latitude B; from 0.8 to 11.1 m for geodetic longitude L; and from 2 to
29 m for ellipsoidal height h. The noteworthy fact is that, during flight II,
the spread of the accuracy results received is significantly wider than during
flight I. Moreover, the accuracy of the Cessna plane coordinates during flight
II worsened by around 300% in comparison to the results from flight I.
Table 1. The accuracy of the
aircraft’s coordinates in comparison to the official standards,
as per ICAO recommendations.
|
Flight test |
Accuracy of the aircraft’s
coordinates [m] |
Theoretical accuracy of the
aircraft’s coordinates, according to ICAO recommendations [m] |
|
Flight I |
For latitude: 0.5÷8.1 |
For latitude: 17 |
|
For longitude: 0.2÷4 |
For longitude: 17 |
|
|
For ellipsoidal height: 1÷10 |
For ellipsoidal height: 37 |
|
|
Flight II |
For latitude: 1.1÷16.1 |
For latitude: 17 |
|
For longitude: 0.8÷11.1 |
For longitude: 17 |
|
|
For ellipsoidal height: 2÷29 |
For ellipsoidal height: 37 |
Table 1 compares the accuracy of the
aircraft’s coordinates received during both flight tests with the ICAO’s
official standards. Today, in aviation, only the GPS and GLONASS navigational
systems and the SBAS support system are certified and accepted for use in air
operations. In the case of the GPS system, the ICAO has specified two standards
for aircraft positioning accuracy on the horizontal and vertical planes. On the
horizontal plane, the accuracy of an aircraft’s coordinates cannot be higher
than 17 m, whereas, on the vertical plane, it cannot be higher than 37 m [1].
The two flight tests performed at Dêblin Airport on 16 June 2010 prove that the
accuracy of the Cessna aircraft’s positioning was kept within the limits of the
ICAO standards. For flight I, the maximum accuracy of the Cessna aircraft
coordinates on the horizontal plane was 8.1 m, while, on the vertical plane, it
was around 10 m. In both cases, the achieved accuracy of the aircraft’s
coordinates stayed within the limits specified by ICAO technical standards. In
flight II, the accuracy of the Cessna aircraft coordinates on the horizontal
plane was 16.1 m, while, on the vertical plane, it was around 29 m. For test
flight II, the accuracy of the Cessna aircraft coordinates did not exceed the
ICAO technical standards.
4. CONCLUSIONS
The article describes the results of
tests on aircraft positioning during post-processing using GNSS satellite
technology. As part of the experiment, a Cessna aircraft position was recovered
during two flight tests, which were performed on 16 June 2010 at the military
airport in Dêblin. The calculations were carried out with gLAB software, while
the SPP method was used for C/A code observations at the L1 frequency in the
GPS system. GPS code observations were registered by a Topcon Hiper Pro
receiver placed in the pilot’s cabin during the tests. As a result of the
performed tests, the following conclusions can be made:
-
The accuracy of
the geodetic latitude B during flight I reached values between 0.5 and 8.1 m;
during flight II, the values were between 1.1 and 16.1 m.
-
The accuracy of
geodetic longitude L during flight I reached values between 0.2 and almost 4 m;
during flight II, the values were between 0.8 and 11.1 m.
-
The accuracy of
ellipsoidal height h during flight I reached values between 1 and almost 10 m;
during flight II, the values were between 2 and 29 m.
-
The achieved
accuracy of the aircrafts’ positioning for BLh coordinates in the gLAB software
did not exceed the technical standards specified by the ICAO recommendation in
Annex 10, Volume I, “Radio navigation aids”.
Acknowledgements
The authors of this article would
like to thank the gAGE research team from the Polytechnic University of
Catalonia for permission to use the gLAB programme library available at http://www.gage.upc.edu.
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Received 21.02.2017; accepted in revised form 03.04.2017
Scientific Journal of Silesian
University of Technology. Series Transport is licensed under a Creative
Commons Attribution 4.0 International License
[1] Faculty of Transport, The Silesian
University of Technology, Krasiñskiego 13 Street, 40-019 Katowice, Poland.
E-mail: henryk.jafernik@polsl.pl.
[2] Faculty of Transport, The Silesian
University of Technology, Krasiñskiego 13 Street, 40-019 Katowice, Poland.
E-mail: andrzej.fellner@polsl.pl.
[3] Faculty of Transport, The Silesian
University of Technology, Krasiñskiego 13 Street, 40-019 Katowice, Poland.
E-mail: magdamrozik@poczta.fm
[4] District Office in Ryki, Faculty of
Geodesy, Cartography and Cadastre, Ryki, e-mail: kk_deblin@wp.pl