Research Article Design of an Attitude and Heading...
Transcript of Research Article Design of an Attitude and Heading...
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013, Article ID 498739, 8 pageshttp://dx.doi.org/10.1155/2013/498739
Research ArticleDesign of an Attitude and Heading Reference System Based onDistributed Filtering for Small UAV
Long Zhao1 and Qing Yun Wang2
1 Science and Technology on Aircraft Control Laboratory, Beihang University, Beijing 100191, China2 School Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
Correspondence should be addressed to Qing YunWang; [email protected]
Received 8 April 2013; Accepted 22 May 2013
Academic Editor: Wenwu Yu
Copyright Β© 2013 L. Zhao and Q. Y. Wang. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.
A development procedure for a low-cost attitude and heading reference system (AHRS) based on the distributed filter has beenproposed.The AHRS consists of three single-axis accelerometers, three single-axis gyroscopes, and one 3-axis digital compass.Theinitial attitude estimation is readily accomplished by using the complementary filtering. The attitude estimation for UAV flyingin the real time is realized by using the three low orders EKF. The validation results show that the estimated orientations of thedeveloped AHRS are within the acceptable region, and AHRS can give a stabilized attitude and heading information for a longtime.
1. Introduction
Recent advances in autonomous vehicle technologies havemade unmanned aerial vehicles (UAV) to become an attrac-tive solution for themodernmilitary and civilian applicationssuch as aerial surveying, pipeline and power line inspection,post-disaster assessment, remote sensing, and cruise missiles[1, 2]. A 2011 report by the Teal Group, who is specialized inaerospace market analysis, forecasts that UAV expendituresworldwide will double within the next ten years to reach $11.3billion dollars annually in 2020 [3]. By 2018, analysts expectthat over 15,000UAVs could be operating within UnitedStates Airspace [4]. Commonly, it needs to know the UAVβsorientation, velocity, and position to be operated, whethermanually or with computer assistance. When cost or weightis an issue, inertial navigation using very accurate inertialsensors has been excluded. Instead, low-cost systems usinginertial sensors based on microelectromechanical systems(MEMS) have been widely used. To ensure safe and reliableflight of UAV, an accurate attitude and heading referencesystem (AHRS) is a key component and can give informationabout the UAVβs orientation in three-dimensional spaces.MEMS-based AHRS are of low cost, light weight, andconsume little power.However, the advantages of inexpensive
MEMS sensors are coupled with the drawback of havinggreater potential error in reported roll, pitch, and yaw due toincreased sensor noise and drift. Most of the previous worksat fusing are based on inertial sensors with GPS for attitudedetermination [5, 6]. However, GPS signals are susceptibleto interference and deception. GPS is unreliable in hostilejammed environments or caused by shadowing effects sincethe possibility of the outage of GPS. More importantly, thetransmitters cannot afford long-term, stable, and reliablepositioning information because of the risk of destruction.Recently, many AHRS based on low-cost MEMS gyroscopes,accelerometers, and magnetometers have been developed[7β10]. A number of estimation filters have been proposedsince 1970s. The basic idea is to blend several different mea-surements to obtain the best approximation of the signals.Although many filtering techniques have been proposed andstudied to design observers for attitude determination [11β15], the Extended Kalman Filter (EKF) is still one of themost well-known and widely adopted filtering algorithms todesign such estimators [16, 17]. The Kalman filter providesthe best estimates based on the system dynamics and a prioriknowledge of the noise characteristics of the signals. How-ever, EKF divergence due to the linearization of the systemand large-state initialization error is a frequent stumbling
2 Mathematical Problems in Engineering
Zn
Yn
Xn
π
π
Zb
Yb
Xb
πΎ
Figure 1: π frame, π frame, and Euler angles.
block to the implementation of the filter. Major difficultieswhen implementing a centralized Kalman filter (CKF) on amicrocontroller arise from the complexity caused by the needfor inverting certainmatrices.This problem is exacerbated bythe need to implement an EKF in case the system is nonlinearand with a large number of states. In contrast to the CKF, thedistributed filter is simple, easy to implement, and it has beensuccessfully used for decades on a low-performance micro-controller [18].
The attitude and heading estimation filter proposed inthis work is based on the distributed filtering theory, initialattitude estimation is based on the complementary filteringtheory, and the real-time attitude estimationwill use the threelow orders EKF for UAV flying.
The paper is organized as follows. The design of attitudeestimation filter is presented in Section 2. Section 3 focuseson the implementation of the attitude estimation filter. Exper-imental results obtained during UAV flying are presentedin Section 4 to illustrate the performance of the proposedAHRS. Concluding remarks and future work are pointed outin Section 5.
2. Problem Statement and System Design
The Euler angles describe the body-axis orientation of UAVbody coordinate frame (π frame) in North, East, and Upnavigation coordinates frame (π frame). Here, π is the yawangle, π is the pitch angle, and πΎ is the roll angle, asillustrated in Figure 1. The initial attitude and heading ofthe UAV are needed to initialize the AHRS. When UAV isstationary, Initial attitude and heading of UAV are computedby accelerators and digital compass.The calculation formulasare described as follows:
πΎ = tanβ1 (ππ
π₯
(βπππ§
)) ,
π = tanβ1(ππ
π¦
(βπππ₯
2
+ πππ§
2
)
) ,
οΏ½οΏ½π
= tanβ1(ππ
π₯
cos πΎ + πππ§
sin πΎπππ₯
sin πΎ sin π + πππ¦
cos π β πππ§
cos πΎ sin π) ,
(1)
where, πππ₯
, πππ¦
, and πππ§
are the specific force of the accelerom-eters in body coordinate frame (π frame). ππ
π₯
, πππ¦
, and ππ
π§
are the components of the magnetic field strength in bodycoordinate frame.
However, stationary UAV is difficult owing to wind andengine vibration in actual test, the initial attitude and headingare seriously influenced by high-frequency noise when theinitial attitude and heading are computed by using (1). Whenthe condition of UAV is stationary or low dynamic, theattitude and heading of UAV are accurate and have good low-pass property. However, the error of attitude and headingcomputed from the gyroscopes output is large since it is easilyinfluenced by drift of the gyroscope.There is complementaryproperty between the attitude derived from the gyroscopeoutputs and the attitude derived from the accelerometer out-puts. The complementary filters theory provides an estimateof the true signal by employing two complementary high-pass and low-pass filters, and an unknown signal can beestimated using corrupted measurements from one or moresensors whose information naturally stands in distinct andcomplementary frequency bands [19β21]. The initial attitudeestimation filter based on complementary filter is to pass theattitude derived from the gyroscope through a high-pass filterand the attitude derived from the accelerometer through alow-pass filter and then to fuse those signals to obtain theestimated attitude; thus, compensating for the drift on thegyroscope and for the slow dynamics of the accelerometer,the block is shown in Figure 2.
The real attitude and heading are processed on an embed-ded processor in actual flying test, major difficulties whenimplementing a centralized extended Kalman filter (CEKF)on a embedded processor arise from the complexity causedby the need of the Jacobian matrix computing and the systemequation linearizing, and this problem is exacerbated by theneed to implement an EKF with a large number of states. Tosolve this problem, the attitude and heading estimation filterbased on the distributed filtering is designed and completed,three low-order parallel EFK are implemented on the ARM9 embedded processor. The block diagram of the orientationestimating filter based on the distributed filtering is shown inFigure 3.
3. Attitude and Heading Estimation Filter
3.1. Initial Alignment Filter. Complementary filters have beenwidely used to combine two independent noisy measure-ments of the same signal, where each measurement is cor-rupted by different types of spectral noise [19]. The com-plementary filters have first-order filter and second-order
Mathematical Problems in Engineering 3
Accelerometersoutput
Gyroscopesoutput
Computing attitude basedon accelerometers output
Computing attitude basedon Euler angle
Complementaryfiltering
πbx, π
by, π
bz
πa
fbx , f
by , f
bz
πΎa
οΏ½οΏ½
οΏ½οΏ½
π
οΏ½οΏ½
Figure 2: Flow diagram of complementary filtering.
Gyroscope
Accelerometer
Magnetometer
Kalmanfilter 1
Kalmanfilter 2
Errorcorrection
Errorcorrection
Errorcorrection
Kalmanfilter 3Computing
Computing
Initialalignment
filter
Initial attitudeInitial quaternion
πbz
πbx
πby
f bx
f by
f bz
π
πΎ
π
πΎ
πΎ
π
Mbx
Mbz
Mnx
MnyMb
x
Mbz
Mby
Mnx
Mny
Mbx
Mbz
Mby
Figure 3: Design of the orientation estimating filter based on the distributed filtering.
filter; the second-order complementary filter consists of asecond-order high-pass filter and a second-order low-passfilter. The second-order complementary filter of the attitudeis described as follows [22]:
πΎ =π2
0
(2π/π0
)π·
π·2 + 2ππ0
π· + π20
πΎπ
+π·2
π·2 + 2ππ0
π· + π20
πΎ,
π =π2
0
(2π/π0
)π·
π·2 + 2ππ0
π· + π20
ππ
+π·2
π·2 + 2ππ0
π· + π20
π,
(2)
where π· is the differential operator, π0
is the natural fre-quency, and π is the damping ratio.
With the estimated roll and pitch, the yaw can be derivedfrom the measured strength of the magnetic field in bodycoordinate frame by the digital compass:
οΏ½οΏ½π
= tanβ1(ππ
π₯
πππ¦
)
= tanβ1(ππ
π₯
cos πΎ + πππ§
sin πΎπππ₯
sin πΎ sin π + πππ¦
cos π β πππ§
cos πΎ sin π) ,
(3)
where πππ₯
, πππ¦
, and πππ§
are the components of the magneticfield strength in navigation coordinate frame (π frame). Therelationship between real heading π
π
and οΏ½οΏ½π
is described asfollows [23]:
ππ
=
{{
{{
{
οΏ½οΏ½π
, ππ
π¦
> 0, οΏ½οΏ½π
> 0,
οΏ½οΏ½π
+ 2π, ππ
π¦
> 0, οΏ½οΏ½π
< 0,
οΏ½οΏ½π
+ π, ππ
π¦
< 0.
(4)
3.2. Attitude and Heading Estimation Filter. According to theinitial attitude and heading, the initial strapdown attitudematrix is computed as follow [23]:
ππ
π
= [
[
π11
π12
π13
π21
π22
π23
π31
π32
π33
]
]
=[[[
[
π2
0
+π2
1
β π2
2
β π2
3
2(π1
π2
β π0
π3
) 2(π1
π3
+ π0
π2
)
2(π1
π2
+ π0
π3
) π2
0
β π2
1
+ π2
2
β π2
3
2 (π2
π3
β π0
π1
)
2(π1
π3
β π0
π2
) 2(π2
π3
+ π0
π1
) π2
0
β π2
1
β π2
2
+ π2
3
]]]
]
.
(5)
4 Mathematical Problems in Engineering
Table 1: The error between AHRS outputs and the reference values for the dynamic test on the ground.
Pitch angle error (β) Roll angle error (β) Yaw angle error (β)Mean Variance Mean Variance Mean Variance
Dynamic test β0.017 0.069 β0.056 0.089 β0.013 0.150
Attitude and heading estimation depend on the updatedquaternion; the system state equation selected the systemstateπ = [π
0
π1
π2
π3
]π is built as follows:
οΏ½οΏ½ =[[[
[
π0
π1
π2
π3
]]]
]
=1
2
[[[[[[[[
[
0 βοΏ½οΏ½π
π₯
βοΏ½οΏ½π
π¦
βοΏ½οΏ½π
π§
οΏ½οΏ½π
π₯
0 οΏ½οΏ½π
π§
βοΏ½οΏ½π
π¦
οΏ½οΏ½π
π¦
βοΏ½οΏ½π
π§
0 οΏ½οΏ½π
π₯
οΏ½οΏ½π
π§
οΏ½οΏ½π
π¦
βοΏ½οΏ½π
π₯
0
]]]]]]]]
]
[[[[[[
[
π0
π1
π2
π3
]]]]]]
]
=1
2
[[[[[[[[
[
0 βππ
π₯
βππ
π¦
βππ
π§
ππ
π₯
0 ππ
π§
βππ
π¦
ππ
π¦
βππ
π§
0 ππ
π₯
ππ
π§
ππ
π¦
βππ
π₯
0
]]]]]]]]
]
[[[[[[
[
π0
π1
π2
π3
]]]]]]
]
+1
2
[[[[[[
[
π1
π2
π3
βπ0
π3
βπ2
βπ3
βπ0
π1
π2
βπ1
βπ1
]]]]]]
]
[[[[
[
πΏπ
π₯
πΏπ
π¦
πΏπ
π§
]]]]
]
= πΉ (π‘)π (π‘) + πΊ (π‘)π (π‘) ,
(6)
where οΏ½οΏ½π = [οΏ½οΏ½π
π₯
οΏ½οΏ½π
π¦
οΏ½οΏ½π
π§
]π
= [ππ
π₯
β πΏπ
π₯
ππ
π¦
β πΏπ
π¦
ππ
π§
β πΏπ
π§
]π
,
ππ
= [ππ
π₯
ππ
π¦
ππ
π§
]π
, and πΏπ = [πΏππ₯
πΏπ
π¦
πΏπ
π§
]π
is the ideal value,real output value, and drift of gyroscopes in body coordinateframe (π frame), respectively. πΉ(π‘) is the state transitionmatrix; πΊ(π‘) is the covariance matrix of noise.
According to (1) and (5), the measurement equation isbuilt by the attitude derived from the gyroscope output andthe attitude derived from the accelerometers output. Themeasurement equation is described as follows:
π (π‘) =[[[
[
π1
(π‘)
π2
(π‘)
π3
(π‘)
]]]
]
=[[[
[
Ξπ
Ξπ
ΞπΎ
]]]
]
=[[[
[
ππ
β ππ
ππ
β ππ
πΎπ
β πΎπ
]]]
]
= π»(π‘, π) + π (π‘) ,
(7)
where π(π‘) = [πΏπ πΏπ πΏπ]π is the error of the attitude and
heading. ππ
is the yaw derived from the digital compass. ππ
and πΎπ
is respectively the pitch, and roll derived from theaccelerators; the computing equations are described in (1)ππ
, ππ
, and πΎπ
is respectively the yaw, pitch, and roll derived
Figure 4: Self-developed autopilot from DNC.
from the quaternion, the computing equation is described asfollows [23]:
ππ
= tanβ1 (2 (π1
π2
β π0
π3
)
π20
β π21
+ π22
β π23
) ,
ππ
= sinβ1 (2π2
π3
+ 2π0
π1
) ,
πΎπ
= tanβ1 (2 (π1
π3
β π0
π2
)
π20
β π21
β π22
+ π23
) .
(8)
The measurement matrix (See Appendix) is obtained bylinearizing (6) and (7):
π» = [πΞπ
ππ
πΞπ
ππ
πΞπΎ
ππ]
π
,
πΞπ
ππ= [
πΞπ
ππ0
πΞπ
ππ1
πΞπ
ππ2
πΞπ
ππ3
] ,
πΞπ
ππ= [
πΞπ
ππ0
πΞπ
ππ1
πΞπ
ππ2
πΞπ
ππ3
] ,
πΞπΎ
ππ= [
πΞπΎ
ππ0
πΞπΎ
ππ1
πΞπΎ
ππ2
πΞπΎ
ππ3
] .
(9)
The quaternion is updated by (6) and (7), the principalvalue of pitch, roll and yaw are derived from the updated ππ
π
[23], for example,
ππ
= sinβ1 (π32
) ,
πΎπ
= tanβ1 (βπ31
π33
) ,
ππ
= tanβ1 (βπ12π22
) .
(10)
Mathematical Problems in Engineering 5
Table 2: The attitude error between AHRS outputs and MIMU/GPS integrated system outputs for flight test.
Pitch angle error (β) Roll angle error (β) Yaw angle error (β)Mean Variance Mean Variance Mean Variance
Flighting test 1.84 3.73 β1.12 4.43 β β
0 50 100 150 200 250 300 350 400 450 500β0.6
β0.4
β0.2
0
0.2
0.4
0.6
0.8
Time (s)
Pitc
h an
gle (
deg)
ReferenceAHRS
(a)
0 50 100 150 200 250 300 350 400 450 500β1
β0.9β0.8β0.7β0.6β0.5β0.4β0.3β0.2β0.1
0
Time (s)
Roll
angl
e (de
g)ReferenceAHRS
(b)
365 370 375 380 385
468
10121416182022
Time (s)
Yaw
angl
e (de
g)
ReferenceAHRS
(c)
Figure 5: AHRS outputs and the reference values for the dynamic test on the ground, (a) pitch, (b) roll, and (c) yaw.
The domain of yaw, pitch, and roll is [0β
360β
],[β90β
90β
] and [β180β 180β], respectively. The domain andrange of pitch are the same; the real value of pitch is theprincipal value, for example, π = π
π
. The real value of yawand roll is computed as follows, respectively [23],
πΎ =
{{
{{
{
πΎπ
, π33
> 0,
πΎπ
+ π, π33
< 0, πΎπ
< 0,
πΎπ
β π, π33
< 0, πΎπ
> 0,
π =
{{
{{
{
ππ
, π22
< 0,
ππ
+ 2 β π, π22
> 0, ππ
> 0,
ππ
+ π, π22
> 0, ππ
< 0.
(11)
4. Experimental Test and Results Analysis
Experiments are conducted using an autopilot self-developedfromDigital NavigationCenter (DNC), BUAA (see Figure 4).This system is composed of three single-axis accelerometers,three single-axis gyroscopes, one 3-axis digital compass, onebarometer, one airspeed meter, and one Global PositioningSystem (GPS) receiver. In order to test the proposed atti-tude and heading calculation method based on distributedfiltering, the dynamic test on the ground and flying testare implemented by using the autopilot from DNC. In theprocess of dynamic testing, the autopilot is put on the ground,the pitch and roll of UAV do not change, the autopilot isturned around the π§ axis from the initial yaw to 360β, theyaw is turned to make a quarter turn, and the autopilot is
6 Mathematical Problems in Engineering
0 50 100 150 200 250 300 350 400 450 500β0.4
β0.3
β0.2
β0.1
0
0.1
0.2
0.3
Time (s)
Pitc
h an
gle e
rror
(s)
(a)
0 50 100 150 200 250 300 350 400 450 500β0.3
β0.2
β0.10
0.1
0.2
0.3
0.4
0.5
Time (s)
Roll
angl
e err
or (d
eg)
(b)
0 50 100 150 200 250 300 350 400 450 500β1.5
β1
β0.5
0
0.5
1
1.5
Time (s)
Yaw
erro
r (de
g)
(c)
Figure 6: The error between AHRS outputs and the reference values for the dynamic test on the ground, (a) pitch error, (b) roll error, and(c) yaw error.
stationary for a period of time. The outputs of the AHRS andthe reference values for the dynamic test on the ground isrepresented in Figure 5. The error between of AHRS outputsand the reference values are represented in Figure 6 andTable 1.
Seen from Figures 5 and 6, and Table 1 the attitude cal-culated output from the AHRS system this paper proposedis stable and can track the reference value. The pitch, roll,and yaw have big fluctuation because when the yaw is turnedmanually, the MIMU cannot maintain horizontality, and theprecision of pitch, roll, and yaw is 0.069β, 0.089β, and 0.15β,respectively.
In order to further test the AHRS system this article pro-posed, the flight test is carried out using a fixed-wing UAV.After the plane takes off through manual manipulation, thecondition is changed to automated driving condition dur-ing aircruise phases and the acceleration, gyroscope, andmagnetic compass data are stored in an SD card. The testverification is based on the actual data and the results areshown in Figure 7 and Table 2.
Seen from Figure 7 and Table 2, the attitude calculatedoutput from the AHRS system this paper proposed is alsostable under the dynamic condition through actual flight test.The attitude error betweenAHRS outputs and reference valueis small and the precisions of pitch and roll are 3.73β and
4.43β, respectively. So, AHRS can give a stabilized attitude andheading information in long time.
5. Conclusions
In this paper, based on the distributed filter, the low-costattitude and heading reference system has been developed.The dynamic test on the ground and actual flight test areimplemented, and the test results show that the presentedAHRS based on the distributed filter can give the stabilizedattitude and heading information for a long time and canimplement the automatic flight control of UAV.
Appendix
The attitude and heading based on quaternion were updatedas follows:
π = tanβ1 (2 (π1
π2
β π0
π3
)
π20
β π21
+ π22
β π23
) ,
π = sinβ1 (2π2
π3
+ 2π0
π1
) ,
πΎ = tanβ1 (2 (π1
π3
β π0
π2
)
π20
β π21
β π22
+ π23
) ,
Mathematical Problems in Engineering 7
0 100 200 300 400 500 600 700 800β60
β50
β40
β30
β20
β10
0
10
20
30
40
Time (s)
Pitc
h an
gle (
deg)
ReferenceAHRS
(a)
0 100 200 300 400 500 600 700 800β100
β50
0
50
Time (s)
Roll
angl
e (de
g)
ReferenceAHRS
(b)
0 100 200 300 400 500 600 700 800β25
β20
β15
β10
β5
0
5
10
15
20
Time (s)
Attit
ude e
rror
(deg
)
Pitch angle errorRoll angle error
(c)
Figure 7: Results of AHRS for fixed-wing UAV flight test, (a) pitch, (b) roll, and (c) attitude error.
ππ
ππ0
=β2π3
(π2
0
β π2
1
+ π2
2
β π2
3
) β 4π0
(π1
π2
β π0
π3
)
4(π1
π2
β π0
π3
)2
+ (π20
β π21
+ π22
β π23
)2
,
ππ
ππ1
=2π2
(π2
0
β π2
1
+ π2
2
β π2
3
) + 4π1
(π1
π2
β π0
π3
)
4(π1
π2
β π0
π3
)2
+ (π20
β π21
+ π22
β π23
)2
,
ππ
ππ2
=2π1
(π2
0
β π2
1
+ π2
2
β π2
3
) β 4π2
(π1
π2
β π0
π3
)
4(π1
π2
β π0
π3
)2
+ (π20
β π21
+ π22
β π23
)2
,
ππ
ππ3
=β2π0
(π2
0
β π2
1
+ π2
2
β π2
3
) + 4π3
(π1
π2
β π0
π3
)
4(π1
π2
β π0
π3
)2
+ (π20
β π21
+ π22
β π23
)2
,
ππ
ππ0
=2π1
β1 β (2(π0
π1
+ π2
π3
))2
,
ππ
ππ1
=2π0
β1 β (2(π0
π1
+ π2
π3
))2
,
ππ
ππ2
=2π3
β1 β (2(π0
π1
+ π2
π3
))2
,
ππ
ππ3
=2π2
β1 β (2(π0
π1
+ π2
π3
))2
,
8 Mathematical Problems in Engineering
ππΎ
ππ0
=β2π2
(π2
0
β π2
1
β π2
2
+ π2
3
) β 4π0
(π1
π3
β π0
π2
)
4(π1
π3
β π0
π2
)2
+ (π20
β π21
β π22
+ π23
)2
,
ππΎ
ππ1
=2π3
(π2
0
β π2
1
β π2
2
+ π2
3
) + 4π1
(π1
π3
β π0
π2
)
4(π1
π3
β π0
π2
)2
+ (π20
β π21
β π22
+ π23
)2
,
ππΎ
ππ2
=β2π0
(π2
0
β π2
1
β π2
2
+ π2
3
) + 4π2
(π1
π3
β π0
π2
)
4(π1
π3
β π0
π2
)2
+ (π20
β π21
β π22
+ π23
)2
,
ππΎ
ππ3
=2π1
(π2
0
β π2
1
β π2
2
+ π2
3
) β 4π3
(π1
π3
β π0
π2
)
4(π1
π3
β π0
π2
)2
+ (π20
β π21
β π22
+ π23
)2
.
(A.1)
Acknowledgments
This project is supported by the Key Program of the NationalNatural Science Foundation of China (Grant no. 61039003),the National Natural Science Foundation of China (Grantno. 41274038), the Aeronautical Science Foundation of China(Gratis no. 20100851018), and the Aerospace InnovationFoundation of China (CASC201102).
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