Summary of doctoral thesis on control and automation engineering attitude estimation for small earth observation satellite by fusion of gyroscope sensor and star tracker

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 OBSERV

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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

Major: Control and Automation Engineering

Code: 62 52 02 16

SUMMARY OF DOCTORAL THESIS

ON CONTROL AND AUTOMATION ENGINEERING

Hanoi – 2018

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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

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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)

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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

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- 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

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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)

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 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

4 4

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: (θrealθcmd)

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

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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:

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Nc is commaned torque

I s is satellite inertial matrix

If the scalar part q4 is separated, the remained forms a Gibbs vector:

2.1.2 Control law for attitude control

For esase of design and simulation, the control law is selected 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:

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0 2*

o T



  (rad/s)

Where Tois the Earth rotation period

In case of Sun synchronous orbit, T o 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, -ω o, 0]:

Where: x(t) is the state matrix and defined as [ω q h]

h is the angular momentum of the reaction wheelsN c lực yêu cầu

N dist 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, βis the dependant drift and η u, η vare Gaussion white noise processes

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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:

s

q q q

Where :

s

q is the output quaternion of the sensor,

qis the actual attitude,

qis the sensor noise:

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

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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

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EKF for attitude estimator is illustrated below:

Table 0.1 EKF filter for drift-compensated estimation

- Angular random walk (ARW): 0.15o/ h

- Earth pointing rate: 90∗602∗𝜋 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)

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- 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:

Table 0.2 Performance of the weighted method for attitude estimator

Figure 0.4 Pointing errors

Performances of the estimator are:

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:

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0

(0)(0)

5.2 Application of fuzzy logic for tuning the estimator

The fuzzy tuning mechanism is proposed to monitor and adjust the filter coefficients Qkand Rk:

k k

k k

- Attitude correction: qk Cor,

- Gyro drift correctios dk Cor,

- 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

- 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

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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)

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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