Attitude estimation for small earth observation satellite by fusion of gyroscope sensor and star tracker

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
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