The term “satellite attitude” refers to the orientaiton of a satellite
in a fixed coordiate system and its angular rates around the
corresponding axis. A satellite operation on-board shall meet the
requirements in its orientation such as antenna pointing to ground
station, solar panel orientation and earth pointing for imaging.
In order to be able to estimate and control the attitude of the
satellite with programmed tasks, the attitude determination and control
subsystem (ADCS) must be provided with accurate and reliable data
from a various types of sensors such as: sun sensor, star tracker,
angular rate sensor, magnetic field sensor. It should be noted that each
type of sensor has many different features such as sampling rate,
accuracy, reliability and dependency on current position of the
satellite. Therefore: Multi-sensor data fusion is the process of
combining measurements from different sensors to produce better
results than using individual ones.

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1
MINISTRY OF EDUCATION
AND TRAINING
VIETNAM ACADEMY OF
SCIENCE AND TECHNOLOGY
GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY
-----------------------------
NGO DUY TAN
ATTITUDE ESTIMATION FOR SMALL EARTH
OBSERVATION SATELLITE BY FUSION OF
GYROSCOPE SENSOR AND STAR TRACKER
Major: Control and Automation Engineering
Code: 62 52 02 16
SUMMARY OF DOCTORAL THESIS
ON CONTROL AND AUTOMATION ENGINEERING
Hanoi – 2018
2
The thesis was completed at Graduate University of Science and
Technology, Vietnam Academy of Science and Technology.
Supervisor 1: Assoc.Prof.Dr. Thai Quang Vinh
Supervisor 2: Dr. Bui Trong Tuyen
Reviewer 1:
Reviewer 2:
Reviewer 3: .
The thesis is defended to the thesis committee for the Doctoral Degree,
at Graduate University of Science and Technology –
Vietnam Academy of Science and Technology,
on.....Date...Month...Year 2018.
Hardcopy of the thesis can be found at:
- Library of Graduate University of Science and Technology
- National Library of Vietnam
3
LIST OF AUTHOR’S WORKS
1. Dự đoán tư thế vệ tinh quan sát Trái đất bằng phương pháp hợp
nhất dữ liệu đa cảm biến, Kỷ yếu Hội thảo khoa học “Nghiên cứu
phát triển và ứng dụng công nghệ vũ trụ - 2011”, Viện Công nghệ
vũ trụ, 2011.
2. Hợp nhất dữ liệu cảm biến tốc độ quay và cảm biến sao để dự đoán
tư thế vệ tinh nhỏ, Kỷ yếu Hội thảo quốc gia lần thứ XV: Một số
vấn đề chọn lọc của Công nghệ thông tin và truyền thông- Hà Nội,
03-04/12/2012
3. Xác định tư thế bằng bộ kết hợp cảm biến sao và con quay hồi
chuyển trên vệ tinh VNREDSat-1, Kỷ yếu Hội thảo Công nghệ vũ
trụ và Ứng dụng – Hà Nội, 19/12/2014
4. Hiệu chỉnh quỹ đạo cho vệ tinh nhỏ quan sát Trái đất trên quỹ đạo
đồng bộ Mặt trời, Kỷ yếu Hội thảo Công nghệ vũ trụ và Ứng dụng
– Hà Nội, 19/12/2014.
5. Small satellite attitude determination by gyroscope and star
tracker fusion, International Conference on Information and
Convergence Technology for Smart Society - Ho Chi Minh, 1/2016
6. A New Approach for Small Satellite Gyroscope and Star Tracker
Fusion, Indian Journal of Science and Technology, Volume 9,
Issue 17, 5/2016 (tạp chí thuộc danh mục SCOPUS).
7. Xác định quỹ đạo vệ tinh viễn thám phù hợp với điều kiện Việt Nam,
Tạp chí Khoa học đo đạc và bản đồ, số 34-12/2017.
8. Proposed design of a fault-tolerance attitude estimator for small
earth observation satellite, International Journal of Mechanical
Engineering & Technology (IJMET), Volume 9, Issue 1, 1/2018
(tạp chí thuộc danh mục SCOPUS).
9. Study on the needs and proposal for high and very high resolution
satellite remote sensing systems in Viet Nam, International Journal
of Civil Engineering & Technology (IJCIET), Volume 9, Issue 1,
1/2018 (tạp chí thuộc danh mục SCOPUS).
4
FOREWORD
Data from satellite attitude sensors (orientation sensors, angular
rate sensors) needs to be merged together to produce a reliable output
provided to the controller. This is the key task. of the satellite attitude
estimator.
Some challenges and contraints are:
- Contraint in power supply.
- Processing capability: on-board tasks are mainly implemented on
FPGA (Field Gate programmable array) or SoC (System on Chip).
- Impacts by space environment and radiation: these are typical
charateristcs which determine the design and on-board part
selections.
- Ground-satellite communication period: limited duration for
contact between satellite and ground control stations.
- Real-time.
- Complexity in transformation of coordinate systems.
Algorithms for attitude estimation are normally hardware
implemented. So this is the key consideration to select compact and
reliable solutions.
Solutions for attitude estimation shall meet the following
requirements:
- Stability.
- Reliabilty.
- Responsibility against unexpected on-board circumstances such
as faulty sensors.
5
- Optimality in performance and on-board resources (power supply,
memory and processing capability).
Therefore, study and proposal of adaptive estimation algorithms
are major fields of research in satellite technology. The
implementation of the algorithms shall consider the stability and
compactness in order to keep optimal with on-board limited resources.
So adaptive mechanism shall be simple but optimal in computation.
And fuzzy logic is of suitable for adaptive approaches.
Based on the above analysys, the author chose the topic of the
thesis “Attitude estimation for small Earth observation satellite by
fusion of gyroscope sensor and star tracker”.
OBJECTIVE OF THE THESIS
The thesis focus on: study and proposal of an attitude methods by
fusion of measurements from gyroscope sensor and star tracker for
small Earth observation satellite which can meet the on-board
contraints and space environments.
6
CHAPTER I - INTRODUCTION
1.1. Satellite attitude
The term “satellite attitude” refers to the orientaiton of a satellite
in a fixed coordiate system and its angular rates around the
corresponding axis. A satellite operation on-board shall meet the
requirements in its orientation such as antenna pointing to ground
station, solar panel orientation and earth pointing for imaging.
In order to be able to estimate and control the attitude of the
satellite with programmed tasks, the attitude determination and control
subsystem (ADCS) must be provided with accurate and reliable data
from a various types of sensors such as: sun sensor, star tracker,
angular rate sensor, magnetic field sensor. It should be noted that each
type of sensor has many different features such as sampling rate,
accuracy, reliability and dependency on current position of the
satellite. Therefore: Multi-sensor data fusion is the process of
combining measurements from different sensors to produce better
results than using individual ones.
1.2. Coordianate systems in investigation of satellite motion
In order to analyze satellite motion, coordinate system shall be
specified. The coordinate systems include inertial i , orbital o and
satellite body b coordinates. In the scope of this dissertation, it is
assumed that the satellite is a circular earth rotating rigid body.
1.3. Attitude representation
Attitude representations are:
Direct Cosine Matrix (DCM)
7
Roll, Pitch, Yaw (RPY)
Euler angles and rotation
Quaternion
Modified Rodrigues Parameters (MRP)
Pivot parameters (latest proposal for satellite attitude
representation).
Attitude error
Attitude error in quaternion pres q is given by:
4
d
44
d d
T
d d
q
qq
vv 1 v
q q q
v
Of which
1d
2d d
d
3d 4d
4d
q
q
q q
q
v
q
is the desired attitude
and
1
2
3 4
4
q
q
q q
q
v
q
is real attitude.
Thanks to its advantages, quaternion is still the most popular
attitude representation for small satellite.
1.4. Key criteria for attitude determination and control
subsystem
Key criteria for ADCS are:
- Attitude accuracy parameters include attitude estimation and
attitude control accuracies:
o Pointing accuracy: difference in real and desired attitude in each
axis: ( )
real cmd
θ θ
8
o Estimation accuracy: difference in estimated and real attitude:
( )
flt cmd
θ θ
o Rate error: difference between real and desired angular rates:
arg
( )
real t et
ω ω .
- Attitude stability.
- Responsiveness: transient and convergence time
- Fault-tolerance capability.
Attitude control error places a significant impacts on the
imaging accuracy on the ground and image quality as well. So the
acuracies shall be key critera for Earth obervation missions.
1.5. Attitude estimation algorithms and on-board contraints
The attitude estimation uses measurements from gyroscope and
star tracker. Therefore, in order to design an effective and practical
estimator which is adaptive and fault-tolerant, each sensor
characteristics and its impacts should be carefully studied. The
following cases shall be considered:
- Angular rate sensor: impacts of drift and faulty sensor.
- Star tracker: impacts of noise and data unavailability (due to
big bright objects).
One the the key feature/contraint of the estimator is optimal design for
hardware implementation which is of limited processing capacity.
It is pointed out by some researches that Kalman filters especially
Extended kalman Filter (EKF) is showing significant advantages over
traditional approaches such as TRIAD or QUEST in term of hardware
implementation. Adaptive methods are applicable in the conditions of
the fluctuational satellite's parameters or faulty sensors. However, due
9
to the specific in-orbit requirements of reliability, accuracy, and and
constraint of limited computing resources, adaptive methods have not
yet been widely applied.
In control systems, fuzzy logic is popular for adtive mechanisim.
It is chosen thanks to the following features:
- Fllexibility and comprehensibility.
- Easy interface.
- Ease of computation.
- Ease of verification.
Summary: Performances of the attiude estimator or ADCS is
dependant on the following factors:
- Atittude representatioin method.
- On-board contraints.
- Estimation algorithms.
CHAPTER II - SATELLITE MODEL AND SENSORS IN THE
ATTITUDE ESTIMATION PROBLEMS
2.1 Satellite model attitude control with reaction wheel
2.1.1 Satellite model with reaction wheel as actuator
Satellite model is described as below:
Where
hw is wheel mometums
Ne is external torque
10
Nc is commaned torque
Is is satellite inertial matrix
If the scalar part q4 is separated, the remained forms a Gibbs
vector:
The state vector is given:
Commanded torque: u=Nc, then state equation of the satellite is:
2.1.2 Control law for attitude control
For esase of design and simulation, the control law is selected as:
e
p e d
u K q - K ω
Where: u is the commanded torque which is generated by reaction
wheels.
, :
p d
K K control gains
, :
ee
q ω errors in orientation and angular rate and defined as:
Where: qs, qr is the current and required attitueds respectively.
ωe and ωr is the current and required angular rates.
In the mode of Earth pointing, the ADCS is to control and
maintain the body angular rate in pitch axis as given below:
11
0
2*
o
T
(rad/s)
Where
o
T is the Earth rotation period.
In case of Sun synchronous orbit, To is around 90 minutes.
In imaging mode, the satellite attitude is following a programmed
manner (the required attitude can be calculated on-board or uploaded
from ground control station).
The satellite model is linearized around earth pointing angular
rate: [0, -ωo, 0]:
u c d dist
x(t) = Ax(t) + B N (t) + B N
Where: x(t) is the state matrix and defined as [ω q h]
h is the angular momentum of the reaction wheelsNc lực yêu cầu
Ndist is external disturbance forces
A, B are state matrices.
2.2 Attitude sensors
2.2.1 Gyroscope
A gyroscope is descibed as below :
v
u
ω = ω+β+ η
β = η
Where: ω is the measured angular rate, β is the time-
dependant drift and
uη , vη are Gaussion white noise processes.
12
2.2.2 Star tracker
Star tracker is an optical device functioning to determine satellite
attitude by precise imaging of stars. The captured image is then
compared to the star map in order to calculate the current attitude.
A star tracker is modelled as:
sq q q
Where :
sq is the output quaternion of the sensor,
q is the actual attitude,
q is the sensor noise:
2
4 4
( ) 0
( ) ( ) ( )
s
T
s s s x
E t
E t t t
q
q q σ I
Summary: Typical satellite model for ADCS analysis and
simulation utilizes reaction wheels as actuators to control its attitude,
and gyroscope and star tracker are used for attitude sensors. This
selection is enough to guarantee the practicality and trend in design of
small Earth observation satellites.
CHAPTER III - ATTITUDE ESTIMATION BY MULTI
SENSOR FUSION
Atitude demermination is considered as optimal estimation
solution based on multiple sources of sensors. The estimation
algorithm must evaluate the reliability of each sensor which is the
sensor confidence factor.
13
Some popular estimations methods are:
Weighted function
Extended Kalman Filter (EKF)
Quaternion Estimation (QUEST)
Pivot based method.
Adaptive method.
Adaptive methods are particularly effective in cases of imprecise
system parameters. However, the implementation of adaptive methods
on-board satellites shows several disadvantages such as more memory
utilization, computational burden and higher power consumption.
These are also constraints which must be balanced to ensure the real-
time operation of the satellite.
Summary: In this chapter, the attitude estimation model for small
Earth observation satellite has been described. And the estimator by
Kalam filter has been shown as well. The model is the background for
applying adaptive mechanism to improve the fault-tolerance of the
estimator and the ADCS in general.
CHAPTER IV - PROPOSAL OF A ESTIMATION
METHOD WITH GYROSCOPE DRIFT-COMPENSATION
4.1 Design of a drift-compensated estimator
The state vector is chosen as:
Where: q=[q1 q2 q3 q4] is real attitude. β= [βx βy βz] is the drift
vector of the gyroscope.
14
EKF for attitude estimator is illustrated below:
Table 0.1. EKF filter for drift-compensated estimation
4.2 Simulation results
Simulation data:
- Satelite inertial matrix:
13.5 0 0
0 12.8 0
0 0 18.8
J kg.m2
- Star tracker noises: [96” 16” 16”] (X,Y and Z axis) (3σ)
- Drift constant: 6o/h.
- Angular random walk (ARW): 0.15o/ h .
- Earth pointing rate:
2∗𝜋
90∗60
𝑟𝑎𝑑/𝑠 (Satellite obital period: T=90
minutes)
- Required angular rate: [-0.0036 -0.0074 0.0032] rad/s
- Imaging period: To+200 to To+300 (second).
15
- External torque: τ=[0 0 0];
- Initial condition: x=[1 0 0 0 0 0 0];
- Control law: PID
- Desired atttitude: roll manouver by an angle of 30o.
4.2.1 Simulation result by weighted method
Figure 0.1. Estimated attitude (Roll,
Pitch, Yaw).
Figure 0.2. Pointing errors
Performance of the estimator:
Axis/factor Roll (rad) Pitch (rad) Yaw (rad)
Mean 0.0003805 0.0007924 0.0005978
Std deviation 0.0002736 0.0004816 0.0003729
Table 0.2 Performance of the weighted method for attitude estimator.
16
4.2.2 Simulation results of EKF attitude estimator by gyro drift
compensation
Figure 0.3. Estimated attitude (Roll, Pitch,
Yaw)
Figure 0.4. Pointing errors.
Performances of the estimator are:
Axis/Parameter Roll (rad) Pitch (rad) Yaw (rad)
Mean -4.81 e-05 1.48 e-06 -1.66 e-05
Std. deviation 0.0001515 0.0001493 0.0001348
Table 0.3 Pointing errors evaluation of the estimator.
Summary: The results show that kalman filter is fully capable of
reliable attitude estimator.
CHAPTER V - PROPOSAL OF A FAULT-TOLERANCE
ATTITUDE ESTIMATOR FOR SMALL EARTH
OBSERVATION SATELLITE
5.1 Design of a Kalman filter for multi-sensor data fusion for
attitude estimation
A Gyro-stellar estimator (GSE) operation is described by the
following steps:
17
Initialization
0
0
(0)
(0)
q q
β β
Attitude prediction by kinematic
equation.
,k Gyroω : gyro measurement f
1 ,
1
1 1
ˆ
ˆ ˆ
ˆ ˆ ( )
k k Gyro k
k k
k k k
ω ω β
β β
q q q ω
Innovation calculation
,k SSTq : SST measurement.
1 , 1
ˆ2k k SST kz q q
Corrections:
- Attitude correction coefficient
,k Corq
- Gyro drift correction: ,k Cord
,
, 1
,
1, 1 ,
1, ,
ˆ ˆ
ˆ ˆ
k Cor
k Cor GSE k
k Cor
k Cor k k Cor
k Cor k k Cor
q
X K z
d
q q q
β β d
5.2 Application of fuzzy logic for tuning the estimator
The fuzzy tuning mechanism is proposed to monitor and
adjust the filter coefficients
kQ and kR :
2( 1)
_ 0
2( 1)
_ 0
k
k new
k
k new
Q Q
R R
(0.1)
Where 1 is the tuning factor, if 1the estimator is a
pure EKF,
0 0,Q R are constant matrices.
Fuzzy based algorithm is developed with two inputs of meand
and deviation values of the innovation. Tunning factor is the
outcome.
Init
0
0
0 0
0 0
(0)
(0)
( )
( )
k
k
q q
β β
P P
R R
18
Attitude prediction by
kinemtics equation.
,k Gyroω : gyro measurement
1 ,
1
1 1
ˆ
ˆ ˆ
ˆ ˆ ( )
k k Gyro k
k k
k k k
ω ω β
β β
q q q ω
Innovation calculation
,k SSTq : SST measurement.
FLO: fuzzy logic observer
1 , 1
1 1
( 2( 1))
ˆ2
(var( ),mean( ))
k k SST k
k k
k
k
FLO
k +1 k,GSE
k o
k +1,GSE k +1 k +1 k
z q q
z z
P = (I - K )P
R = R
K = P / (P + R )
Corrections:
- Attitude correction: ,k Corq
- Gyro drift correctios ,k Cord
,
, 1, 1
,
1, 1 ,
1, ,
ˆ ˆ
ˆ ˆ
k Cor
k Cor k GSE k
k Cor
k Cor k k Cor
k Cor k k Cor
q
X K z
d
q q q
β β d
5.3 Proposal of a fault-tolerance mechanism for attitude
estimator on small Earth observation satellite
A fault-tolerance mechanism for small earth observation satellite
is proposed as follows:
- If the gyrorcope is working normally: gyro measurements are used
to estimate the attitude
- If the gyroscope is degraded: reference angular rates are used
instead of gyro measurements. If the star tracker measurements
are also interrupted for longer than the designed thresholds (due
to charged particle, big bright objects), the gyro measurement
shall be used.
- If the gyroscope is faulty: reference angular rates are used instead
of gyro measurements. If the star tracker measurements are also
19
interrupted for longer than the designed thresholds, the dynamics
euqation is integrated for attitude estimation.
5.4 Simulation
5.4.1 Simulation in the normal mode
Satellite parameters:
- Inertial matrix:
13.5 0 0
0 12.8 0
0 0 18.8
J kg.m2
- Star tracker noise: [96’ 16‘ 16’] (3σ)
- Gyro drift: 6o/h.
- Angular random walk (ARW): 0.15o/ h
- Earth pointing angular rate: 2*pi/(90*60) rad/s (To=90
minutes)
- Desired angular rate during imaging phase: [-0.0036 -0.0074
0.0032] rad/s
- Imaging period: To+200 to To+300 (second).
- External torque: τ=[0 0 0];
- Initial condition: x=[1 0 0 0 0 0 0];
Simulation result for Kalman filter:
Figure 0.1. Estimated attitude by EKF
in case of noisy sensor
Figure 0.2. Fuzzy-adapted EKF filter
20
5.4.2 Simulation for imaging period
Scenarios is assumed as:
- Attitude for start imaging: [-10; 25; 20] o
- Imaging angular rate [-0.0035 -0.0073 0.0034] rad/s;
- Imaging periode: 100-200 (second)
Simulation results:
1. Normal operation:
Figure 0.3. Attitude during imaging
phase
Figure 0.4. Angular rate during
imaging
2. Noisy sensors
Figure 0.5. Estimated attitude Figure 0.6. Attitude error
21
3. Fault-tolerance estimation
Figure 0.7. Estimated attitude Figure 0.8. Estimated angular rate
Summary: EKF is effective in case of well-known system
parameters and noise processes. Nevertheless, various paramters are
imprecise, so the filter may not be working as expected in this case.
This statement is convinced when multiple sensors are used. In order
to overcome this limiatation, fuzzy logic is applied to observe and
evaluate the confidence of the output then reasonable adaptation
mechanism is introduced to establish a fault-tolerance estimator.
22
CONCLUSIONS
1. On estimation methods: Kalman filter is showing effectiveness in
case of normal operation in terms of accuracy, computation and
compactness, which makes the filter easy for hardware
implementation.
2. Adaptive mechanism by fuzzy logic is effective in the following
cases: degraded sensor due to noisy measuments (star tracker) or
accumulated noise (gyrosco