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: (cho1838@snu.ac.kr); 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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