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Wind Estimation and Airspeed
Calibration using a UAV with
a Single-Antenna GPS Receiver
and Pitot Tube
AM CHO
JIHOON KIM
SANGHYO LEE
CHANGDON KEE, Member, IEEE
Seoul National University
This paper proposes a method that uses an aircraft with a
single-antenna GPS receiver and Pitot tube to estimate wind
speed and direction and to calibrate the airspeed. This sensor
combination alone does not determine the true attitude of the
aircraft, so the wind parameters cannot be obtained directly
from the measurements. However, if the aircraft flies at different
headings, such as in banking turns or circle maneuvers, the wind
magnitude and direction can be estimated from the geometrical
relation between the wind and the measurements. An extended
Kalman filter (EKF) is applied to estimate wind parameters.
The EKF can also estimate the scaling factor used to convert
dynamic pressure to airspeed. This is useful for the operation
of small unmanned aerial vehicles (UAVs) because of difficulty
in determining the airspeed scaling factor of a low-cost UAV.
Simulations are performed for a constant 2-D wind. To test the
effectiveness of the proposed method, flight tests of a small UAV
are conducted. Simulations and flight test results show that the
proposed method is effective.
Manuscript received February 4, 2009; revised July 6, 2009;
released for publication August 6, 2009.
IEEE Log No. T-AES/47/1/940018.
Refereeing of this contribution was handled by M. Braasch.
This research was supported in part by the Institute of Advanced
Aerospace Technology at Seoul National University.
Authors’ addresses: A. Cho, J. Kim, S. Lee, 302 dong 418-2 ho,
School of Mechanical and Aerospace Engineering, Seoul National
University, Daehak-dong, Gwanak-gu, Seoul, 151-744, Korea,
E-mail: ([email protected]); C. Kee, 301 dong 1319 ho, School of
Mechanical and Aerospace Engineering, Seoul National University,
Daehak-dong, Gwanak-gu, Seoul, 151-744, Korea.
0018-9251/11/$26.00 c° 2011 IEEE
NOMENCLATURE
(Ás,μs,'s) Conventional attitudes in stability axes
(Ás, μs, 's) Pseudo attitudes determined from a
single-antenna GPS receiver~Vw Wind velocity
(Vw,Áw) Wind speed and heading~Vg Ground velocity of an aircraft
(Vg,Ág) Ground speed and heading
~Va Velocity of the aircraft relative to air
Vpitot Airspeed measured by a Pitot tube
¢P Dynamic pressure
sf Scaling factor from dynamic pressure and
the square of the airspeed
Cnb Coordinate transformation matrix from
the body to the navigation frame
wk Process noise of Kalman filter
Qk Process noise covariance
vk Measurement noise of Kalman filter
Rk Measurement noise covariance.
I. INTRODUCTION
The mobility and economic efficiency of
unmanned aerial vehicles (UAVs) afford them a high
number of applications. Accurate wind parameters
can greatly enhance the capabilities of UAVs to
conduct various missions such as dropping objects,
target tracking, and geolocation. Sohn et al. [1]
showed that such wind information can result in more
accurate geolocation of a ground target. Additionally,
the crab-angle between ground track and heading,
obtained from estimating the wind conditions, can
help improve the control performance of a UAV in
trajectory following, landing tasks, and so on [2]. In
fact, wind estimation can itself become an important
application of the UAV.
There have been many papers published on the
meteorology of wind estimation using research
aircrafts [3]. However, there are few practical
methods of applying UAVs or light aircrafts. Some
of these infer wind conditions using the radar track
of an aircraft, which can be replaced by onboard
measurements such as a Global Positioning System
(GPS) [4—6]. Lefas developed a simple filter to
estimate wind conditions using the magnetic heading
and true airspeed measurements in addition to radar
positional measurements [4]. Hollister et al. deduced
wind conditions and true airspeed from ground radar
tracks [5, 7] or from onboard Loran measurements
[5, 7] during a turn maneuver with constant airspeed.
Delahaye suggested two extended Kalman filter (EKF)
models to estimate wind conditions [6]. One uses the
ground radar track, the true airspeed vector, and the
air turning rate. The other uses only the ground track
of an aircraft turning at a constant airspeed and at a
constant air turning rate. Rodríguez estimated wind
IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011 109
Fig. 1. Wind triangle and airspeed definition.
conditions using an optical flow sensor instead of
a magnetometer [8]. Kumon proposed an iterative
optimization method using an aerodynamic model and
sensors such as an inertial measurement unit (IMU)
and a GPS [9].
This paper proposes a new method of estimating
wind speed and direction, using a single-antenna
GPS receiver and an airspeed sensor. The proposed
method also estimates an airspeed scale factor
that makes it easy to calibrate airspeed sensors of
low-cost UAVs. This method differs from previously
used techniques [5—7] in that it does not require
the assumption that the aircraft turns at a constant
airspeed, which is otherwise essential for additional
airspeed sensors. Unlike earlier methods [4, 6, 8] the
combination of sensors in the proposed method does
not provide aircraft heading information. Therefore,
this method requires the flight of a UAV at different
headings, such as in banking turns and circular
maneuvers. Furthermore, other papers have shown
that a single-antenna GPS receiver can be used as
the sole sensor of an attitude determination system
[10, 11]. Because single-antenna GPS-based attitudes
can be improved by wind information, the proposed
method can make valuable contributions within this
system.
This paper is organized as follows. First, it details
the method for estimating wind conditions and
calibrating the airspeed sensor using a single-antenna
GPS receiver and airspeed sensor. Next, the simulated
results are presented. Third, the system configuration
chosen for the flight tests is shown. Then the real
flight test results are presented. Finally, conclusions
are drawn.
II. WIND ESTIMATION ALGORITHM
A GPS gives the aircraft velocity relative to
the ground in the East-North-Up (ENU) frame.
Wind velocity can be readily computed from the
wind triangle as shown in Fig. 1. This requires a
measurement of aircraft velocity relative to air in the
ENU frame.
~Vw = ~Vg ¡ ~Va ¼ ~Vg ¡Cnb
2641¯®
375Vpitot: (1)
In this paper, a single-antenna GPS receiver
and airspeed sensor unit is used to estimate wind
conditions. This combination does not describe the
true attitude of the aircraft, which includes the Cnbmatrix, the angle of attack (®), and the sideslip (¯).
Therefore, it is not possible to accurately measure
the aircraft velocity relative to air in the ENU frame.
Additional sensors such as an IMU and ® and ¯
sensors are needed. However, if the aircraft flies at
different headings, such as in banking turns or circular
maneuvers, the ground velocity and the airspeed
vector vary with time. These variables can then be
used to estimate wind conditions. This method thus
estimates the wind conditions and calibrates the
airspeed using the wind triangle for an aircraft flying
at different headings.
Airspeed Vpitot is calculated using the dynamic
pressure measured from a pressure sensor connected
to a Pitot tube as follows:
V2pitot =K2¢P
½, from Bernoulli’s equation (2)
where ¢P is the dynamic pressure, ½ is the air density,
and K is a correction factor. The use of Pitot tubes
assumes a perfect gas, steady temperatures, zero
air viscosity, steady flow along a streamline, etc. K
is the correction factor that compensates for these
assumptions and for installation errors [12].
In terms of the angle of attack, the sideslip angle
and Vair, Vpitot can be expressed as follows:
V2pitot = jVaj2 cos®cos¯: (3)
From (2) and (3),
V2a =V2pitot
cos®cos¯=
¢P
½cos®cos¯=(2K)´ ¢Psf: (4)
The measured dynamic pressure may have a bias, but
a simple initialization can effectively remove the bias
before takeoff. Thus, bias in the measured dynamic
pressure is ignored.
If ® and ¯ are small, sf can be used as a scaling
factor between the dynamic pressure and V2pitot. The
scaling factor is usually determined from wind
tunnel tests and must be tuned after the Pitot tube is
mounted onto the aircraft. However, while operating
low-cost UAVs, the mounting position of the Pitot
tube can differ for each flight test due to frequent
installations and removals of the setup. Consequently,
the scaling factor as well as the wind conditions must
be estimated.
Under the assumption of a constant 2-D wind, an
EKF method is suggested to simultaneously estimate
the wind conditions and scaling factor of the Pitot
tube measurement using the wind triangle. According
to Berman and Powell [13], wind shear is modeled
as a first-order Markov process with a correlation
distance of about 32 km, which is much larger than
110 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011
Fig. 2. Coordinates for wind estimation.
the flight trajectory necessary for wind estimation.
Therefore, the wind can reasonably be assumed to be
constant during the estimation process.
The parameters that must be estimated are wind
speed, wind direction, and a scaling factor that
transforms dynamic pressure in terms of the square
of the airspeed. The airspeed is shown in Fig. 2. If
the accurately tuned scaling factor is given, it can be
excluded from the list of states in the coordinated
flight. These variables can be regarded as nearly
constant during some flight times. The states are
modeled as random-walk processes.
With the state vector x= [Vw Áw sf]T, the system
dynamics are described by (5):
x(k+1) = Fx(k)+wk (5)
where
F=
2641 0 0
0 1 0
0 0 1
375 , wk »N(0,Qk):
When applied to the wind triangle, the law of cosines
gives the following relation:
V2g +V2w ¡ 2VgVw cos(Áw¡Ág) = V2a =
¢P
sf: (6)
The ground velocity Vg and the direction Ág, both of
which are outputs of the GPS receiver, are accurate
enough to be treated as known parameters in each
epoch. The measurement function h(x) is then
obtained from (6).
Let the measurement zk be the dynamic pressure
¢P. The nonlinear observation system is
zk = h(x) + vk
= sf£ [V2g +V2w ¡2VgVw cos(Áw¡Ág)] + vk (7)
wherevk »N(0,Rk):
Next, the linearized observation matrix of the
measurement equation is given by
H =
·@h
@Vw
@h
@Áw
@h
@sf
¸
=
264 2sf ¢ [Vw¡Vg cos(Áw¡Ág)]2sf ¢VgVw sin(Áw¡Ág)
V2g +V2w ¡2VgVw cos(Áw¡Ág)
375T
: (8)
TABLE I
The Extended Kalman Filter Algorithm
Initialization x= x0P= P0
Time Update xkjk¡1 = Fxk¡1jk¡1 = xk¡1jk¡1Pkjk¡1 = FkPk¡1jk¡1F
Tk+Qk = Pk¡1jk¡1 +Qk
Measurement yk = zk ¡ h(xkjk¡1)Update Sk =HkPkjk¡1H
Tk+Rk
Kk = Pkjk¡1HTkS¡1k
xkjk = xkjk¡1 +KkykPkjk = (I¡KkHk)Pkjk¡1where,
P= covariance, S= innovation covariance,
y = innovation, K=Kalman gain
In the simulations, the measurement and the process
noise covariance are tuned using real flight test
results. The initial guess at the wind vector is obtained
by estimating the aircraft velocity relative to air ~V0a asthe vector which has the same magnitude as ~Va and
the same direction as ~Vg. This is shown in Fig. 2.
~V0a ´ Va ¢~Vg
Vg=
s¢P
sf¢~Vg
Vg: (9)
Then using (9), the initial guess of the wind vector is
given by the following:
(~Vw)init ¼ ~Vg ¡ ~V0a : (10)
If wind information from other sources is
available, it could be used as an initial guess of the
filter, which will be able to decrease the convergence
time of the filter. Since the system dynamics of the
proposed method are extremely simple, the application
of the EKF to the wind estimation is straightforward.
Like the standard Kalman filter, the EKF has two
distinct phases: a time update and a measurement
update. A clearer explanation of the EKF for the wind
estimation is shown in Table I.
III. SIMULATION RESULTS
A Navion model and a linear quadratic regulator
(LQR) controller were used for the simulations [14].
This method does not assume constant airspeed.
To confirm that this method does not need constant
airspeed, the ground speed was controlled instead
of the airspeed, which simulates the same effect
as changing the airspeed, as shown in Fig. 3(c). It
was assumed that the initial estimate of the scaling
factor was approximately 10% larger than the true
value. The wind speed was set to 13 m/s, that is,
corresponding to approximately 25% of the cruise
velocity. The wind direction was set at 90±, andgusts were not considered. The measurement noise
covariance of the dynamic pressure was set to the sum
CHO ET AL.: WIND ESTIMATION AND AIRSPEED CALIBRATION USING A UAV 111
Fig. 3. Simulation results. (a) Wind speed, direction and scaling factor. (b) Residuals with 3 ¾ bounds. (c) Ground speed and airspeed.
of the variance of measurements obtained from the
airspeed sensor plus additional terms. These additional
terms serve to absorb gusts of wind and errors in the
ground velocity from the GPS receiver. During the
simulations this additional term R0 was not considered.The parameters for the EKF, used for the simulation
and the flight test are summarized in Table II.
The aircraft initially steered North, and it
performed a 30± banking turn after 10 s. Theinitial guesses of wind magnitude and direction
were obtained using (9) and (10) during the initial
straight-line flight. At the instant at which the
estimation algorithm started, the difference between
the aircraft heading and the wind direction was
approximately 90±. This was nearly the worst casewith respect to the initial value guesses. Fig. 3 shows
the simulation results with estimated wind and
residuals.
The convergence time of the filter was within one
complete turn, even for the worst initial condition, as
is shown in Fig. 3. Different magnitudes in the initial
TABLE II
Parameters of EKF for Wind Estimation
Initial covariance (P0)
24152 0 0
0 ¼2 0
0 0 0:32
35Measurement noise (R) 36+ R0 (unit: Pa2)
Process noise covariance (Q)
242£ 10¡3 0 0
0 3:5£ 10¡6 0
0 0 3£ 10¡7
35
conditions did not significantly affect convergence
rates during the simulations. The EKF cannot
converge when faced with a significant gust. However,
this problem can be solved simply by increasing the
additional measurement noise covariance of Table II
or by applying a moving average to the raw data of
the dynamic pressure, provided that the sampling rate
is fast enough compared with the rate of update of the
filter.
112 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011
Fig. 4. UAV used in flight test.
IV. SYSTEM CONFIGURATION
This section introduces the system configuration
for the flight test. The system configuration includes
the UAV and the onboard and ground systems.
The UAV used for the flight test is a fixed-wing,
twin tail-boom, pusher-type aircraft with a 48 cc
gasoline-powered propeller engine as shown in Fig. 4.
It has a wingspan of 2.5 m and a gross weight of
approximately 15 kg including the payload. The
UAV used is equipped with one single-antenna
GPS receiver and one airspeed sensor. This sensor
combination can be used as the main sensor of the
flight control system [15, 16]. This system is used for
the flight tests in this paper.
PC104 modules are used as the flight control
computer. To measure airspeed, a pressure sensor is
connected to a PC104 A/D module. The dynamic
pressure is sampled at 10 kHz. A wireless modem
and a single-frequency GPS receiver with a sampling
rate of 10 Hz are connected to a PC104 serial
communication expansion stack. To improve position
accuracy, a differential GPS (DGPS) system is
implemented on the ground. In DGPS mode in
the ENU frame and in a static state, the standard
deviation of the velocity measurement of the GPS
receiver is (0.0482 m/s, 0.0693 m/s, 0.0950 m/s).
The programming environment for both onboard
and ground computers is Microsoft Windows XP
professional. Visual C++ with Microsoft Foundation
Classes (MFC) is also used.
V. FLIGHT TEST RESULTS
To test the effectiveness of the proposed algorithm,
a flight test was performed using the UAV described
in the preceding section. The UAV was commanded
to make a 30± banking turn at an altitude of 250 m.During the banking turn if there was no wind, the
UAV would have circled around a center point.
However, the wind shifted the center of the circle.
Therefore, after two automatic banking turns, the UAV
was brought around the reference position manually
by a pilot, and then the automatic banking turns were
repeated. Fig. 6(a) shows the horizontal trajectory
taken from GPS measurements during the flight test.
Fig. 5. Wind data from AWS,approximately 15 km apart, for
1 hr.
Fig. 5 shows the wind data acquired every minute
by an automatic weather station (AWS) belonging to
the Korea Meteorological Administration located on
the ground 15 km away from the experimental area
[17]. The wind profile of the atmospheric boundary
layer (from the surface to an altitude of approximately
2000 m) is usually logarithmic in nature. The solid
line in Fig. 5(a) is the approximate wind speed at an
altitude of 250 m, determined using the wind profile
power law. This law is often used as a substitute for
the log wind profile when the surface roughness or
stability information is not available [18]. The wind
profile power-law relationship is defined as
uz = ur(z=zr)p (11)
where
uz isthe scalar mean wind speed at height z above
the ground,
ur is the scalar mean wind speed at some reference
height zr, typically 10 m, and
p is the power-law exponent.
The recommended power-law exponents can be
found in [18]. A neutral category was selected for
the overcast conditions corresponding to the weather
during the experiment. Applying the power law to the
data observed from the AWS during the flight test
showed that, approximately 15 km away, the average
wind direction was ¡70:6± and the wind speed was2.1 m/s on the ground. The wind speed at a height of
250 m, estimated from the wind profile power law,
was approximately 4.7 m/s. It should be noted that,
since this value may be erroneous, it should not be
used as a standard for comparison.
Fig. 6(b) shows the flight test results of the
estimated wind speed, direction, and the scaling
factor, using the EKF. At approximately 10 s,
the filter was initialized to show its convergence
characteristics using the initial covariance of Table II
and the initial guess from (9) and (10) without the
help of previous estimates. The initial guess of the
wind vector had the same direction as that of the
aircraft ground velocity, and its magnitude equaled
CHO ET AL.: WIND ESTIMATION AND AIRSPEED CALIBRATION USING A UAV 113
Fig. 6. Flight test results: wind estimation using EKF. (a) Horizontal trajectory (2D). (b) Wind speed, scaling factor. (c) Measurement
residual. (d) Ground speed and airspeed. (e) Ground velocity.
the difference between the ground speed Vg and the
airspeed Vpitot. The initial value of the scaling factor
was set to 0.6036, which resulted from assuming
standard air conditions, a small angle of attack, zero
sideslip, and a correction factor of 1. As shown in
Table II, the flight test used the same parameters
of the EKF as were used for the simulation. R0, themeasurement noise covariance, which is used to
absorb the ground velocity error and wind gusts, was
set to 36. During the flight test, the EKF operated at
10 Hz, which was the same as the output rate of the
GPS receiver.
114 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011
TABLE III
Wind Speed and Direction
Method Direction Speed
EKF results ¡65± 5.9 m/s
From ground speed vectors ¡62:2± 6.2 m/s
Wind data from ground AWS ¡70:6± 4.7 m/s
The UAV was controlled to keep the commanded
ground speed between 10 and 65 s, which has the
same effect as changing the airspeed. After 110 s, the
ground speed was replaced by a calibrated airspeed
by the proposed method, that is, the airspeed was kept
nearly constant, as shown in Fig. 6(d). In Fig. 6(a),
the horizontal trajectory data obtained from GPS
measurements is between approximately 110 s
and 190 s. The wind information was estimated
by curve-fitting a circle onto the ground speed
vectors, assuming the aircraft made a turn at a
constant airspeed. This was the basis of several
earlier studies [5—7]. Since the UAV maintained an
almost constant airspeed after 110 s, the center of
the fitting circle could be obtained from Fig. 6(e) by
minimizing the sum of the squared radial deviations.
The wind estimate was ¡62:2± and 6.2 m/s fromthis.
As shown in Fig. 6(b), the convergence of the
filter states was completed within one circle. In
spite of the rapid maneuver at a banking angle over
60±, which was controlled by the pilot between 65and 110 s, the filter did not diverge. During the last
turn, the means of the estimated wind speed and
direction using EKF were approximately 5.9 m/s and
65±. This result is in excellent agreement with theinformation inferred from the ground speed vectors
and is reasonable when compared with the AWS data.
The estimated results and the information from the
AWS, approximately 15 km away, are summarized in
Table III.
In Fig. 6(b), the scaling factor was estimated
as approximately 0.5337. The measured residual,
bounded by 3¾, shows that the proposed filter works
consistently over the entire region in Fig. 6(c).
VI. CONCLUSIONS
In this paper, a new approach was presented
for estimating wind speed and direction as well as
for calibrating the airspeed scaling factor using a
single-antenna GPS receiver and an airspeed sensor.
The proposed algorithm uses the geometrical relation
between ground and wind velocities and airspeed, and
does not require aircraft aerodynamics or heading
information. However, it needs flight details at
different headings, such as those found in banking
turns and circular maneuvers. Flight test results show
that the proposed method, using the EKF, works
well in real time. For the worst initial condition, the
proposed method converged within one turn. It also
showed robust results that did not diverge for rapid
maneuvers. The estimated wind speed and direction
were in excellent agreement with the results inferred
from the horizontal ground velocity, and they showed
analogous tendencies with the results measured
from an AWS on the ground although the AWS was
approximately 15 km away. The estimated scaling
factor also corrected the airspeed to a reasonable level.
Therefore, the proposed method may help reduce the
burden of the complex calibration process for the
operation of low-cost UAVs.
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116 IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS VOL. 47, NO. 1 JANUARY 2011
Am Cho is a post doctoral candidate in the School of Mechanical and AerospaceEngineering at Seoul National University, Korea. He received the B.S. degree
and Ph.D. from Seoul National University. He is a leader of the UAV team in
the GNSS Laboratory. His research interests include GPS/INS integration and
automatic flight control systems for UAVs.
Jihoon Kim received the B.S. degree and Ph.D. from Seoul National University.
He currently works at Samsung Electronics in Seoul, Korea. He has been
involved in GNSS research and has been a member of the UAV team in the
GNSS Laboratory since 2002. His research interests include estimation methods
for stability and control derivatives of UAVs and miniature vehicles.
Sanghyo Lee is a Ph.D. candidate in the School of Mechanical and AerospaceEngineering at Seoul National University, Korea. He received the B.S. and M.S.
degrees from Seoul National University. His research interests include GPS
application algorithms and automatic control of UAVs.
Changdon Kee received the B.S. and M.S. degrees from Seoul National
University and Ph.D. degree from Stanford University, Stanford, CA, in 1994.
He is a professor in the School of Mechanical and Aerospace Engineering
at Seoul National University, Korea. He has been involved in GPS research for
more than 20 years, during which time he has made numerous contributions,
most notably to the development of the wide area augmentation system (WAAS).
He served as a technical advisor for the Federal Aviation Administration (FAA)
on the WAAS in 1994. Currently he is serving as a technical advisor for Korean
Civil Aviation Safety Authority (KCASA) on CNS/ATM and Advisor for
Ministry of Government Administration and Home Affairs (MOGAHA).
Dr. Kee served as Asian representative for the ION Satellite Division
Executive Committee from 1998 to 2000 and from 2006 to the present. He is also
serving as vice president for the Korean Navigation Institute.
CHO ET AL.: WIND ESTIMATION AND AIRSPEED CALIBRATION USING A UAV 117
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