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A GPS Based Attitude Determination System for
a UAV Aided by Low Grade Angular Rate
Gyros
Michael Moore, Chris Rizos and Jinling Wang
School of Surveying and Spatial Information Systems
University of New South Wales
Sydney, NSW 2052, Australia,
email: michael.moore@student.unsw.edu.au
G. Boyd, K. Mathews, W. Williams, R. Smith
Newmont Australia, Research & Development
80 Leader Street, Forestville
Adelaide, South Australia 5035, Australia
BIOGRAPHY multi-antenna single-frequency GPS array, aided by low
grade angular rate gyros. The objective of the research is
Michael Moore received a B.Geomatics and B.Sc. in to develop an accurate, reliable attitude sensor solution at
1998, from the University of Melbourne, and then joined an affordable cost which can be implemented on UAVs
the School of Surveying & SIS, The University of New (Unmanned Airborne Vehicles) developed for
South Wales (UNSW) as a PhD student in March 1999. geophysical exploration by Newmont Australia.
His research interests include attitude determination with
a multi-antenna GPS arrays, Kalman filtering, and the UAVs used by the geophysical exploration industry will
associated time series analysis using digital signal be required to fly lower and for significantly longer
processing techniques. periods compared to UAVs used for most other
applications. Flying at a low height, approximately 30m
Chris Rizos is a Professor at the School of Surveying & above ground level, introduces many communications and
SIS, UNSW, and leader of the Satellite Navigation and control challenges, not the least being the need for rapid
Positioning (SNAP) Group, which specialises in response to unexpected platform movements. The GPS
addressing precise static and kinematic applications of attitude determination subsystem is important in enabling
GPS. He is president of Commission 4 'Positioning & an external, independent reference to constrain the control
Applications' of the International Association of Geodesy inputs to the UAV flight subsystem. Of particular
(IAG).. importance is a good understanding of the integrity of the
system.
Jinling Wang is a Lecturer in the School of Surveying &
SIS at UNSW. His research interests are in the areas of 1. INTRODUCTION
satellite positioning and navigation, location technologies
and applications, as well as spatial information systems. The term ‘unmanned airborne vehicle’ (UAV)
He is Chairman of the Working Group ‘Pseudolite encompasses a wide variety of robotic aircraft that vary in
Applications in Engineering Geodesy’, of the IAG, and size, shape, flight characteristics and level of operational
Editor-in-Chief of the Journal of Global Positioning autonomy. In recent years, the development and
Systems. implementation of UAVs has undergone an explosion in
the military arenas. Many of these UAVs have been large
ABSTRACT in size, and with a large capital cost to match (see Table
1). For example, the Global Hawk costs US$20,000,000
The Satellite Navigation and Positioning (SNAP) group at (UAV Roadmap, 2002). The military have prioritized the
The University of New South Wales has been conducting use of UAVs to undertake highly specialised missions that
research into high precision attitude determination using a
have the characteristics of being “dull, dirty and
dangerous” (UAV Roadmap, 2002).
It is generally accepted that the development of the
technology for autonomous capabilities for UAVs are at a
mature enough level for commercialization (Wong and
Bil, 1998). The most significant technological
developments have been compact, light and inexpensive
motion detection sensors essential to the flight control
systems, including carrier-phase differential GPS and
light low-cost computing power for autonomous flight
control.
There are many civilian organizations with a strong
demand for a low cost, moderately functional small
airborne platform. UAVs have plenty of potential in the
application areas of surveillance, border security, mineral
exploration, monitoring environmental and coastal natural
resources. UAVs are of benefit to these applications
through a reduction in operating costs over conventional
manned platforms, the ability to fly for long periods, to
carry out maneouvers too dangerous for manned vehicles,
and others.
Commercial UAV customer requirements can be basically
satisfied by two groups of UAVs. These are a low weight
Figure 1 Global Hawk (top) and Pioneer (bottom)
and low endurance UAV (up to 25kg payload, 100-
200km/h airspeed, 4-5 hours endurance), and a medium
weight and medium endurance UAV (~100kg payload,
50-100 km/h 24hrs endurance) (Wong and Bil, 1998). 2. UAV DEVELOPMENT AT NEWMONT
These correspond to the military tactical (low weight) and GEOPHYSICS
strategic (medium weight) UAVs.
The main goal of the UAV project at Newmont
Many UAV systems currently operating are still Geophysics is to develop a low-cost airborne platform to
considered too expensive for commercial operators. One conduct airborne magnetometer-based mineral
of these is the Pioneer exploration surveys. To meet these requirements a UAV
(http://uav.navair.navy.mil/pioneer), a tactical UAV that was designed to fly at a low altitude. (This is necessary as
would be an ideal platform for many commercial the quality of the magnetometer data is directly related to
applications, except for its hefty price tag of US$650,000. the altitude the UAV, as the strength of the magnetic field
The high cost of UAVs is largely due to having been decreases inversely proportional to the height cubed.)
developed to fulfill highly specialized military operations, Development of the UAV at Newmont has progressed
with stringent specifications. Future development of through a number of stages, beginning with the
UAVs needs to focus on providing engineering solutions development of simulation software for pilot training, as
that minimize costs, while maintaining reasonable well as determining the flight characteristics of the UAV,
performance standards. through to actual flight testing. The Tandem Wing is 4m
in length, has a wingspan of 2.8m, and is capable of
Table 1 Characteristics of the Global Hawk and carrying a maximum payload of 25kg. The aircraft has
Pioneer UAV (adapted from UAV Roadmap, 2002) been built from composite materials to reduce the metallic
Global Hawk Pioneer content, which helps reduce interference with the
Aircraft Cost US $20,000,000 US $650,000 magnetometer. Currently the UAV is undergoing a series
Weight (kg) 12,100 205 of flight trials to test the reliability of the aircraft frame,
Length (m) 13.5 4.3 and the live video control link currently being used to
Wingspan (m) 35.4 5.2 control the aircraft (Figures 2 & 3). For more details of
Payload (kg) 884 34 the construction of the Tandem Wing UAV see:
http://www.aerosciences.com.au/projects.htm.
Ceiling (m) 20000 4500
Radius (nm) 5400 100
Endurance (hr) 32 5
system is used to derive the six exterior orientation
parameters of the airborne platform (for details see, e.g.,
Schwarz et al., 1993). Typically, in such a set-up the GPS
position and velocity data is used solely to help constrain
the growth of the INS time-dependent errors, rather than
being used to calculate the attitude and position of the
aircraft itself.
An alternative method is to use a GPS antenna array,
where two or more GPS antennas are mounted onto a
rigid platform (Cohen, 1992). If the differential GPS
measurements are measured simultaneously, then the
coordinate differences between the antennas can be used
to calculate the attitude parameters. This method, using
single-frequency GPS receivers, is being proposed for the
Figure 2 The Ground Control Station with a live video navigation system of the Tandem Wing.
link to the UAV
A number of issues need to be addressed to ensure the
successful implementation of the attitude determination
system on the UAV. Of importance is a good
understanding of the system integrity and how the system
will react when signal loss-of-lock occurs, whether this be
due to a high banking angle, or severe turbulence.
4. AN OVERVIEW OF QUALITY CONTROL
ISSUES
Measurement outliers can cause an undesirable bias in the
estimated parameters (e.g. yaw, pitch and roll angles), and
also render invalid the quality of the estimated
parameters. The detection of these anomalies requires a
statistical hypothesis testing process, however the success
of this process is heavily dependent upon the reliability of
the system.
Reliability is a measure used to describe the quality of the
final solution with respect to the ability to detect outliers.
For instance, a highly reliable solution is one in which
outliers of small magnitude can be detected. Reliability is
generally dependent upon the redundancy of the system,
and the propagation of errors throughout the system.
Reliability can be split into two parts; internal reliability
refers to the ability of the system to detect and identify an
error, whereas external reliability is a measure of the
effect of an undetected error upon the estimated
parameters.
Figure 3 Tandem Wing UAV being developed by
Newmont Australia Separability gives a measure of how well a system can
identify the source of an outlier, once the outlier has been
3. DEVELOPING THE NAVIGATION SYSTEM detected. In general, a large outlier has the effect of
causing many test statistics to exceed the critical values. If
The easy availability of GPS has played an important role the data is correlated, then the test statistics may be
in the development of many navigation systems. GPS can misleading, in that the largest test statistic may not
be used not only for precise positioning, but also when actually correspond to the true source of the error.
more than one antenna/receiver pair is used to determine
the attitude of the platform. However, this has commonly Below are some of the factors that can influence the
involved the integration of GPS with INS, where an INS quality control measurements when using a multiple
antenna GPS array for attitude determination: the overall reliability of the navigation solution.
5
1. Antenna configuration/geometry
2. Types of GPS receiver/antenna 4
3. Processing techniques 3
4. Augmentation of additional navigational 2
sensors 1
5. External environment
Height
Base Antenna
0
The proposed attitude determination system, to be -1
implemented on the Tandem Wing, will use single- Baseline 2
-2 Baseline 1
frequency receivers on a platform with a limited choice of -3
geometric configurations of the antennas. So of interest,
was whether the antenna configuration restrictions would
-4
have a significant impact upon the overall reliability of -5
5 Baseline 3 5
the solution, and how the inclusion of a low-cost angular- 0
-5 -5
0
rate gyro could rectify this compromise of antenna North East
geometry. A detailed analysis of these issues can be found
7 7
in Moore et al. (2002), and only a summary of the
findings will be given here. 6 6
To test the effects of baseline length and geometry on
5 5
reliability four different scenarios were investigated. Two
4 4 Baseline 1
geometric configurations where investigated, an idealized
No
geometry, known as an orthogonal triad (a pyramid like
North
rth3 3
structure with an equilateral triangle as the base, see
Figure 4, and Comp, 1993, for details), and a planar
2 2
geometry. The effects of baseline length were investigated
by doubling the original baseline lengths of the two
1 1
Baseline 3 Baseline 2
Baseline
different geometric configurations. 0 3 0
Base Base Antenna
It was found that the internal reliability of the system is
-1
-4 -2
Antenna
0 2 4
-1
-4 -2 0 2 4
strongly dependent upon the geometry of the system. A East East
platform with a relatively poor geometry is liable to incur
an unacceptably large minimum detectable error (MDE). Figure 4 Inverted orthogonal triad, and a sub-optimal
It was also found that external aiding with angular rate planar geometry
measurements offered greater improvement of the system
reliability, than an improved antenna geometry. The 5. THE PROBLEMS OF UAV BANKING ANGLE
baseline length did not affect the internal reliability of the AND LOSS OF LOCK
system, however it did have a substantial impact on the
external reliability of the system. One of the major problems faced by UAV operations with
a multiple antenna GPS array, is the possibility of losing
In terms of separability, the inverted orthogonal triad lock during banking. It is expected that the Tandem Wing
achieved better results than the planar configuration. The UAV may on occasions bank up to 55° to follow the
simulation showed that the inverted orthogonal triad was appropriate flight profile for the geophysical survey.
able to correctly identify the source of a simulated outlier, Under such circumstances loss of lock will occur, and
whereas the planar configuration failed. However, with there may be less than four satellites in view. A
angular-rate sensors, the planar geometry separability simulation study was undertaken to confirm whether this
measure improved considerably, facilitating correct was indeed an issue for UAV flight operations in
identification of the simulated error source. Australia.
Clearly the inclusion of an angular-rate sensor will A flight profile was generated to simulate a flight of the
significantly improve the solutions reliability and Tandem Wing UAV experiencing high pitching angles
separability. This is to a level that will not only and high banking angles. The UAV flight simulated
compensate for the compromise of the geometric
takeoff to the north reaching a maximum pitch of 55°,
placement of the antennas due to the restricted space on
before leveling off, and then banking at a maximum of
the platform, but will also be of great benefit in improving
55°, to level off after completing a 90° turn. Three more
turns, with the same banking angle, were then simulated 100
so that the UAV had completed a rectangular circuit (see -15 90
Figure 5). This flight profile was repeated every hour for ) )
a total of 24 hours and conducted over the whole of g
e -20
80 %
(
D
Australia in a grid spacing separated by one degree in ( 70 e
g
latitude and longitude. e
d
-25 60 a
t
u n
) t 50 e
i -30 c
s t
r a 40 r
e
L
e P
-35 30
t 400
e 20
m -40
( 200 10
p 0
U 0 120 130 140 150
Longitude (Deg)
2500
2000
Figure 7 The Percentage of simulation runs where 3 or
1500
1000 less satellites are tracked at any moment by the UAV.
1000 600 800
200 400
North (meters) 500 -200 0 There are a number of possible options to overcome this
East (meters) problem. The first option is to ensure that the UAV only
operates during certain periods the GPS constellation is
Figure 5 Simulated flight profile for the UAV strong enough to maintain lock to more than four
satellites for the expected dynamics of the scheduled
A typical result was obtained from the first hour of the UAV flight path. However, this allows control of the
simulation (see Figure 6), the colour scale on the right aircraft for a pre-determined flight path, and does not
corresponds to the minimum number of satellites tracked account for the possibility of larger than usual dynamic
by the UAV during the simulated profile. As can be seen, effects upon the UAV. As only low-grade gyros are to be
there is region covering the whole of Tasmania, extending installed on the UAV, the amount of time the UAV
north-westward to western Victoria and South Australia, control system can coast on the gyro results only, will be
where the UAV maintains lock to less than four satellites a relatively short period. Therefore, the probability of
during flight. This was typical of the simulation results, in being able to quickly re-determine the ambiguity value
that there was more often than not, a region of similar size during flight, needs to be investigated.
at different locations throughout Australia at any
particular point in time.
10 6. SUCCESS OF AMBIGUITY RESOLUTION
-15 9
)
g
s
8 t Integer ambiguity resolution is an essential step to
e
achieving high-precision relative GPS positioning. The
a
D -20 S
( 7
e
f
6 o
process of GPS ambiguity resolution can be divided into
d -25
u
t
r two distinct parts: estimation and validation. The
5 e
i
t -30 b estimation component aims to find optimal estimates for
4 m
a
L
u
N the ambiguities.
-35 3
-40
2
To decide whether to accept the estimates, an ambiguity
1 validation process has to take place. As the probability
120 130 140 150
0 density function of the integer ambiguity is unknown,
Longitude (Deg) then some empirical testing needs to be carried out. This
usually involves a ratio test (e.g. f-test) between the two
Figure 6 Simulation results for Australia for the first best candidates. In order to have the ratio sufficiently
hour, shows the minimum number of satellites tracked peaked around one solution, the float ambiguities must be
Figure 7 show the percentage of simulations runs in of good accuracy. In other words, the successful
which three or less satellites where tracked at any time validation depends primarily on the precision of the
during the generated flight profile the color bar scale to ambiguities described by the variance-covariance (VCV)
the right corresponds to the total percentage of time. From matrix Qa .
ˆ
Figure 7 we can see that loss of lock is a serious problem
occurring about 30% of the time throughout Australia. Although, the stochastic nature of the least-squares
derived ambiguities is described by the VCV ambiguity
matrix, the Ambiguity Dilution of Precision (ADOP) is a
1.6
simpler measure that captures the main characteristics of
the ambiguity variance matrix, (Teunissen, 1997). The 1.4 4 Sats
ADOP is a measure based on the determinant of the VCV 7 Sats
matrix. 1.2
1
ADOP = Qa
ˆ
n
(cycles) ( 1)
P
1
O
where Qa is the VCV of the ambiguities, n is the order of
ˆ D 0.8
A
the ambiguity variance matrix, and | | denotes the matrix
determinant. 0.6
In a physical sense, the ADOP measures the volume of 0.4
the ambiguity search space and in general, the ADOP
0.2
values are dependent on several factors including: 0 5 10 15 20 25 30
Time in seconds
1. satellite redundancy
2. observation epochs redundancy, Figure 8 Plot of ADOP as a function of time for single-
3. redundancy in frequency (L1 and L2), frequency observations
4. observation type redundancy (phase and code The inclusion of inertial data can have a significant
measurements). impact on reducing the ADOP. Skaloud (1998) showed
that the volume of the ambiguity search space decreases
Teunissen (1997) shows that the problem of ambiguity by including the inertial measurements as long as the
estimation and validation are directly related to the accuracy of these observables is not considerably smaller
properties of the ambiguity search space and provides than the accuracy of the GPS observable. The INS data is
closed formulas for evaluating the intrinsic characteristics able to (over periods not longer than several tens of
with respect to different measurements (e.g. phase only, seconds) deliver coordinate differences that are superior
code and phase, etc.). For the single-frequency time- to the GPS observables with unknown float ambiguities.
averaged model, the determinant of the variance of Their inclusion into the estimator reduces the volume of
ambiguities in closed form, is given by (Teunissen, 1997): the ambiguity search space significantly, especially in the
m -1 3
case of poor satellite geometry. This, in turn, has a
Ê1 a ˆ Ê 1ˆ positive effect on the ambiguity validation problem, since
Qa = mÁ 21 ˜
ˆ Á kl ˜ Á1 + ˜ ( 2) the resulting float ambiguities are of better accuracy and
Ë 1 ¯ Ë e¯ the chances of finding a peaked solution will improve.
where a 1 is the variance of the phase on L1, b 1 is the
variance of the code on P1, k is the observation epochs, m The level of improvement strongly depends on the quality
of the inertial system, the accuracy of the initial velocity,
is the number of satellites, e = b1/a1
and the level of dynamics, while the dependence on
receiver-to-satellite geometry is less significant. However,
As can be seen from equation (2), the closed form of the
if the condition for successful validation cannot be
determinant is the product of a very small term
satisfied in less than 30 seconds the volume of the
(dominated by the phase variance), and a very large term
ambiguity search space becomes increasingly driven by
(dominated by the ratio of the code variance to the phase
the GPS observables only, with a small improvement
variance). Therefore the determinant is largely influenced
from having the inertial data.
by the variance of the code. So the ADOP will be fairly
large unless there is a large number of observation epoch
As the improvements are most significant over short time
redundancies, and a large number of satellites in view.
intervals, it is most likely to benefit the improvement of
Figure 8 shows the influence of observational epoch
the float solution, and the improved likelihood of
redundancy and the number of satellites in view upon
ambiguity resolution, after the aircraft has undergone a
ADOP.
high banking manoeuvre. Even if ambiguity resolution is
not achieved, the improved float solution is likely to be of
a high enough quality to help maintain control of the
UAV.
8. FLIGHT EXPERIMENT
A test flight was flown on July 9th 2003 from a rural )
m
airport east of Adelaide, Australia. The purpose of the test ( 300
flight was to collect some data to help develop the
t
navigation software for the UAV. Four antennas were h 200
placed on the top fuselage of a Piper Archer II aircraft g
i
(see Figure 9). The baseline lengths were pre-surveyed in e 100
before testing took place, the baseline length can be seen H
in Table 2 below. A set of gyros was also installed within 0
the aircraft, and the data from all four receivers and three
gyros logged simultaneously during the flight. 4500
4000
Table 2 Pre-flight Antenna Survey Results 3500
3.1
Base DN DE DH Distance 3000 2.9
3
4
North (m) 2.8 x 10
To R1 2.611 -0.755 -1.496 3.102 2.7
East (m)
To R2 3.618 1.030 0.197 3.766
To R3 0.042 -7.641 3.337 8.338 Figure 10 Plot of the flight path
The flight consisted of a short initialization time of
approximately 10 minutes before the aircraft taxied to
take off. The aircraft then flew a simple rectangular
course climbing initially to 300m, then descending down
again to land. A plot of the single point positioning results
obtained from the flight can be seen in Figure 10.
During the flight testing there was on average at least six
satellites visible. A skyplot of the satellites tracked during
the flight, and the number of satellites tracked by each
receiver is shown in Figures 11 and 12, respectively. As
can be seen from Figure 12, there were a number of
occasions when loss of lock to several satellites occurred
for receivers1, 3 and 4.
Figure 11 Sky plot of visible satellites during the flight
Channel 1 Channel 2
8 8
6 6
4 4
2 2
0 0
500 1000 1500 2000 500 1000 1500 2000
Channel 3 Channel 4
8 8
6 6
Figure 9 The type of aircraft used for the flight 4 4
experiment, A Pipier Archer II
2 2
0 0
500 1000 1500 2000 500 1000 1500 2000
Figure 12 No. of satellites tracked by each receiver
Initially the data was processed to test how quickly the
float solution improved after a loss of lock event, using a
sequential least-squares algorithm. The float solution
obtained did not converge to the level of accuracy
predicted by the analytical work shown in section 6. Here angular-rate aiding is dependent upon the precision of the
it was expected that the simulated ADOP would have gyros, the stability of the error terms and the level of
sufficiently decreased within 30s for ambiguity resolution dynamics experienced by the aircraft
to be likely. However, the field results show that the time
period to obtain an acceptable float solution was much
longer length than expected. REFERENCES
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The use of a multi-antenna GPS array for attitude
determination introduces a unique set of problems, such US DoD (2002) Unmanned Aerial Vehicles Roadmap,
as ensuring the reliability of the navigation solution used http://www.acq.osd.mil/usd/uav_roadmap.pdf
to control the UAV. Simulations have shown that aiding .
the GPS attitude determination system with low-grade
angular-rate gyros will significantly improve the
navigation solutions reliability and separability.
Both simulations and flight trials show that loss of lock
can occur regularly, and indeed this did happen in the
actual flight trials even without high banking angles.
Therefore it is important that the navigation system is able
to generate a precise navigation solution after loss of lock
events.
It is anticipated that with good quality GPS data the
incorporation of low-grade gyros may significantly
improve the float solution after a loss of lock event. The
time required to obtain a precise float solution with
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