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El. knyga: Fault Tolerant Attitude Estimation for Small Satellites

(Istanbul Technical University, Aeronautical Engineering Dept.),
  • Formatas: 352 pages
  • Išleidimo metai: 22-Dec-2020
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781351248822
Kitos knygos pagal šią temą:
Fault Tolerant Attitude Estimation for Small SatellitesDidesnis paveikslėlis
  • Formatas: 352 pages
  • Išleidimo metai: 22-Dec-2020
  • Leidėjas: CRC Press Inc
  • Kalba: eng
  • ISBN-13: 9781351248822
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Small satellites use commercial off-the-shelf sensors and actuators for attitude determination and control (ADC) to reduce the cost. These sensors and actuators are usually not as robust as the available, more expensive, space-proven equipment. As a result, the ADC system of small satellites is more vulnerable to any fault compared to a system for larger competitors. This book aims to present useful solutions for fault tolerance in ADC systems of small satellites. The contents of the book can be divided into two categories: fault tolerant attitude filtering algorithms for small satellites and sensor calibration methods to compensate the sensor errors. MATLAB® will be used to demonstrate simulations.











Presents fault tolerant attitude estimation algorithms for small satellites with an emphasis on algorithms practicability and applicability





Incorporates fundamental knowledge about the attitude determination methods at large





Discusses comprehensive information about attitude sensors for small satellites





Reviews calibration algorithms for small satellite magnetometers with simulated examples





Supports theory with MATLAB simulation results which can be easily understood by individuals without a comprehensive background in this field





Covers up-to-date discussions for small satellite attitude systems design

Dr. Chingiz Hajiyev is a professor at the Faculty of Aeronautics and Astronautics, Istanbul Technical University (Istanbul, Turkey).

Dr. Halil Ersin Soken is an assistant professor at the Aerospace Engineering Department, Middle East Technical University (Ankara, Turkey).
Preface xv
Author Biographies xxi
Chapter 1 Attitude Parameters
1(12)
1.1 Euler Angles
2(2)
1.1.1 Euler Angles for Vector Transformation
2(1)
1.1.2 Propagation of Euler Angles by Time
3(1)
1.2 Quaternions
4(5)
1.2.1 Vector Transformation by Quaternions
5(1)
1.2.2 Propagation of Quaternions by Time
6(2)
1.2.3 Euler Angles - Quaternions Relationship
8(1)
1.3 Gibbs Vector
9(1)
1.4 Modified Rodrigues Parameters
10(1)
1.5 Summary
11(2)
References
11(2)
Chapter 2 Mathematical Models for Small Satellite Attitude Dynamics and Kinematics
13(12)
2.1 Coordinate Frames
13(3)
2.2 Satellite Attitude Dynamics
16(1)
2.3 Disturbance Torques for a Small Satellite
16(5)
2.3.1 Gravity Gradient Torque
17(1)
2.3.2 Aerodynamic (Atmospheric) Torque
18(1)
2.3.3 Solar Radiation Torque
18(1)
2.3.4 Magnetic Torque
19(2)
2.4 Satellite Kinematics
21(1)
2.5 Summary
22(3)
References
22(3)
Chapter 3 Attitude Sensors
25(28)
3.1 Magnetometers
25(5)
3.1.1 Search-coil Magnetometer
26(1)
3.1.2 Fluxgate Magnetometer
27(1)
3.1.3 MEMS Magnetometer
28(2)
3.2 Sun Sensors
30(7)
3.2.1 Analog Sun Sensors
31(3)
3.2.2 Sun Presence Sensors
34(1)
3.2.3 Digital Sun Sensors
35(2)
3.3 Earth Horizon Sensors
37(4)
3.3.1 Scanning Earth Horizon Sensors
38(2)
3.3.2 Static Earth Horizon Sensors
40(1)
3.4 Star Trackers
41(3)
3.5 Gyroscopes
44(4)
3.5.1 Fiber Optic Gyros
45(2)
3.5.2 MEMS Gyros
47(1)
3.6 Auxiliary Attitude Sensors for Small Satellites
48(1)
3.7 Summary
49(4)
References
49(4)
Chapter 4 Attitude Sensor Measurement Models
53(14)
4.1 Magnetometer Models
53(3)
4.1.1 Magnetometer Measurement Model
53(1)
4.1.2 Models for the Earth's Magnetic Field in the Reference Frame
54(2)
4.2 Sun Sensor Models
56(3)
4.2.1 Sun Sensor Measurement Model
56(2)
4.2.2 Models for the Sun Direction Vector in the Reference Frame
58(1)
4.3 Earth Horizon Sensor Models
59(2)
4.3.1 Earth Horizon Sensor Measurement Model
59(2)
4.3.2 Models for the Earth Direction Vector in the Reference Frame
61(1)
4.4 Star Tracker Measurement Model
61(2)
4.5 Gyro Measurement Model
63(1)
4.6 Summary
64(3)
Notes
64(1)
References
64(3)
Chapter 5 Attitude Determination Using Two Vector Measurements - TRIAD Method
67(14)
5.1 TRIAD Method
67(6)
5.1.1 TRIAD Algorithm Using Magnetometer and Sun Sensor Measurements
69(1)
5.1.2 Quaternion Estimates from the Attitude Matrix
70(2)
5.1.3 Using TRIAD Algorithm for More Than Two Vector Measurements
72(1)
5.2 Analysis of the TRIAD Method Accuracy
73(4)
5.3 Increasing Accuracy of the TRIAD Method Using Redundancy Techniques
77(2)
5.4 Conclusion and Discussion
79(2)
Note
80(1)
References
80(1)
Chapter 6 Statistical Methods for Three-Axis Attitude Determination
81(12)
6.1 What is Wahba's Problem?
82(1)
6.2 Davenport's q-Method
82(2)
6.3 QUEST Method
84(3)
6.4 SVD Method
87(1)
6.5 A Brief Comparison of Statistical Methods for Small Satellite Implementations
87(1)
6.6 Attitude Determination Using GNSS Measurements
88(2)
6.7 Conclusion and Discussion
90(3)
Notes
91(1)
References
91(2)
Chapter 7 Kalman Filtering
93(24)
7.1 The Optimal Discrete LKF Derivation
94(6)
7.2 Stability of Optimal LKF
100(1)
7.3 LKF in Case of Correlated System and Measurement Noise
101(3)
7.4 Discrete Kalman Filtering when System and Measurement Noises are not Zero-mean Processes
104(1)
7.5 Divergence in the Kalman Filter and the Methods Against Divergence
105(2)
7.6 Linearized Kalman Filter
107(2)
7.7 Extended Kalman Filter
109(2)
7.8 Unscented Kalman Filter
111(2)
7.9 Other Nonlinear Filtering Algorithms
113(1)
7.10 Conclusion and Discussion
114(3)
References
114(3)
Chapter 8 Adaptive Kalman Filtering
117(22)
8.1 A Priori Uncertainty and Adaptation
119(2)
8.1.1 A Priori Uncertainty
119(1)
8.1.2 Adaptation
120(1)
8.2 Multiple Model Based Adaptive Estimation
121(3)
8.3 Adaptive Kalman Filtering with Noise Covariance Estimation
124(5)
8.3.1 Innovation Based Adaptive Estimation
124(1)
8.3.2 Innovation Based Adaptive Filtration Algorithm for Stationary Systems
125(2)
8.3.3 Innovation Based Adaptive Filtration Algorithm with Feedback
127(1)
8.3.4 Residual Based Adaptive Estimation
128(1)
8.3.5 Drawbacks of Adaptive Noise Covariance Estimation Methods
128(1)
8.4 Adaptive Kalman Filtering with Noise Covariance Scaling
129(3)
8.4.1 Innovation Based Adaptive Scaling
129(1)
8.4.1.1 R-Adaptation
129(2)
8.4.1.2 Q-Adaptation
131(1)
8.4.2 Residual Based Adaptive Scaling
132(1)
8.5 Simplified RKF Against Measurement Faults
132(4)
8.6 Conclusion
136(3)
References
137(2)
Chapter 9 Kalman Filtering for Small Satellite Attitude Estimation
139(24)
9.1 Gyro-based and Dynamics-based Attitude Filtering
140(1)
9.2 Attitude Filtering Using Euler Angles
141(1)
9.3 Attitude Filtering Using Quaternions
141(11)
9.3.1 Method of Quasi-measurement
142(1)
9.3.2 Norm-constrained Kalman Filtering
143(1)
9.3.3 Multiplicative Extended Kalman Filter
143(5)
9.3.4 Unscented Attitude Filtering
148(4)
9.4 Estimation of Additional Dynamics Parameters
152(7)
9.4.1 Disturbance Torque Estimation
153(2)
9.4.2 Residual Magnetic Moment Estimation
155(4)
9.5 Issues Related to the Attitude Filter's Computational Load
159(1)
9.6 Conclusion and Discussion
160(3)
Note
160(1)
References
160(3)
Chapter 10 Integration of Single-Frame Methods with Filtering Algorithms for Attitude Estimation
163(12)
10.1 Integration When Attitude is Represented Using Euler Angles
165(3)
10.2 Integration When Attitude is Represented Using Quaternions
168(3)
10.3 Conclusion and Discussion
171(4)
References
172(3)
Chapter 11 Active Fault Tolerant Attitude Estimation
175(24)
11.1 The Innovation and Its Statistical Properties
177(2)
11.2 Innovation Approach Based Sensor FDI
179(9)
11.2.1 Fault Detection via Mathematical Expectation Statistics of Spectral Norm of Normalized Innovation Matrix
179(3)
11.2.2 Innovation Based Sensor Fault Isolation
182(3)
11.2.3 Simulation Results of FDI Algorithms
185(3)
11.3 Kalman Filter Reconfiguration
188(6)
11.3.1 Demonstration for EKF Reconfiguration
191(3)
11.4 The Structure of the Fault Tolerant Attitude Estimation System
194(1)
11.5 Conclusion and Discussions
195(4)
Note
196(1)
References
196(3)
Chapter 12 Fault Tolerant Attitude Estimation: R-Adaptation Methods
199(22)
12.1 Robust Unscented Kalman Filter
200(3)
12.1.1 Adapting the R-matrix of UKF Using a Single Scale Factor
201(1)
12.1.2 Adapting the R-matrix of UKF Using Multiple Scale Factors
202(1)
12.2 Robust Extended Kalman Filter
203(1)
12.2.1 Adapting the R-matrix of EKF Using a Single Scale Factor
203(1)
12.2.2 Adapting the R-matrix of EKF Using Multiple Scale Factors
204(1)
12.3 Fault Detection
204(1)
12.4 Remark on Stability of the Robust Kalman Filters
205(1)
12.5 Demonstrations of REKF and RUKF for Attitude Estimation of a Small Satellite
206(11)
12.5.1 Continuous Bias in Measurements
207(3)
12.5.2 Measurement Noise Increment
210(1)
12.5.3 Zero-output Failure
211(3)
12.5.4 Discussion on the Implementation of Robust Attitude Filters on Real Small Satellite Missions
214(2)
12.5.5 Comparison of Reconfigured UKF and RUKF in the Presence of Measurement Faults
216(1)
12.6 Conclusion and Discussion
217(4)
References
218(3)
Chapter 13 Fault Tolerant Attitude Estimation: Q-Adaptation Methods
221(20)
13.1 Adaptation of a Gyro-Based Attitude Filter
222(9)
13.1.1 Intuitive Tuning of an Attitude Filter
222(2)
13.1.2 Process Noise Covariance Matrix Estimation for MEKF
224(2)
13.1.3 Process Noise Covariance Matrix Estimation for UKF
226(2)
13.1.4 Demonstration of Adaptive UKF for Augmented States
228(3)
13.2 Adaptation of a Dynamics-Based Attitude Filter
231(8)
13.2.1 Adaptive Fading UKF
232(2)
13.2.2 Demonstrations for an Adaptive Fading UKF
234(1)
13.2.2.1 Temporary Uncertainty in Dynamics
235(2)
13.2.2.2 Permanent Uncertainty in Dynamics
237(2)
13.3 Conclusion and Discussion
239(2)
Notes
239(1)
References
239(2)
Chapter 14 Integration of R- and Q-Adaptation Methods
241(24)
14.1 Integration R- and Q-Adaptation Methods by Fault Isolation
242(5)
14.1.1 Integration of R- and Q Adaptation Methods
242(2)
14.1.2 Demonstration of R- and Q-Adaptation Methods
244(3)
14.2 Simultaneous Q and R Adaptation
247(4)
14.3 Nontraditional Attitude Filtering with Q-Adaptation
251(11)
14.3.1 Adapting the Q-matrix in Nontraditional Filter
253(2)
14.3.2 Demonstrations of SVD/AUKF
255(1)
14.3.2.1 SVD/AUKF with Continuous Bias at Measurements
256(1)
14.3.2.2 SVD/AUKF with Measurement Noise Increment
257(1)
14.3.2.3 SVD/AUKF with System Change
258(4)
14.4 Conclusion and Discussion
262(3)
Note
263(1)
References
263(2)
Chapter 15 In-Orbit Calibration of Small Satellite Magnetometers: Batch Calibration Algorithms
265(12)
15.1 Requirement for Magnetometer Calibration
265(1)
15.2 Magnetometer Errors in Detail
266(3)
15.2.1 Soft Iron Error
266(1)
15.2.2 Hard Iron and Null-shift Error
267(1)
15.2.3 Time-varying Bias
268(1)
15.2.4 Scaling
268(1)
15.2.5 Nonorthogonality
268(1)
15.2.6 Misalignment
269(1)
15.3 Magnetometer Measurement Models
269(2)
15.3.1 General Model
269(2)
15.3.2 Models Considering Time-varying Errors
271(1)
15.4 Batch Magnetometer Calibration Algorithms
271(3)
15.4.1 The Cost Function
272(1)
15.4.2 The Minimization Algorithm
273(1)
15.4.3 Discussion on Batch Magnetometer Calibration
273(1)
15.5 Conclusion
274(3)
References
275(2)
Chapter 16 In-Orbit Calibration of Small Satellite Magnetometers: Recursive Calibration Algorithms
277(40)
16.1 Simultaneous Attitude Estimation and Magnetometer Calibration
278(1)
16.2 UKF for Simultaneous Attitude Estimation and Magnetometer Calibration
278(4)
16.2.1 Scale Factor Estimation
279(1)
16.2.2 Demonstration of UKF for Simultaneous Attitude Estimation and Magnetometer Calibration
280(2)
16.3 Reconfigurable UKF for Simultaneous Attitude Estimation and Magnetometer Calibration
282(7)
16.3.1 Stopping Rule for Bias Estimation
285(1)
16.3.1.1 Stopping Rule Formation
285(1)
16.3.1.2 Computation of the Covariance Matrix of the Discrepancy Between Two Successive Bias Estimates
286(1)
16.3.2 Demonstration of Reconfigured UKF for Simultaneous Attitude Estimation and Magnetometer Calibration
287(2)
16.4 Two-stage UKF for Simultaneous Attitude Estimation and Magnetometer Calibration
289(4)
16.4.1 Two-Stage Estimation Procedure
290(1)
16.4.1.1 Magnetometer Bias Estimation Stage
290(1)
16.4.1.2 Gyro Bias Estimation Stage
291(1)
16.4.1.3 Overall Look to Two-Stage Estimation Scheme
291(1)
16.4.2 Demonstration of Two-stage UKF for Simultaneous Attitude Estimation and Magnetometer Calibration
292(1)
16.4.2.1 Simulation Results for Magnetometer Bias Estimation
292(1)
16.4.2.2 Simulation Results for Gyro Bias Estimation
293(1)
16.5 Magnetometer Calibration with Known Attitude
293(9)
16.5.1 Magnetometer Bias and Scale Factor Estimation Using a Linear KF
296(3)
16.5.2 Simulation Results for Magnetometer Calibration via LKF
299(3)
16.6 TRIAD+UKF Approach for Attitude Estimation and Magnetometer Calibration
302(3)
16.7 Calibration without Attitude
305(4)
16.8 Magnetometer Bias Estimation for a Spinning Small Spacecraft
309(3)
16.9 Discussion on Recursive Magnetometer Calibration
312(1)
16.10 Conclusion
313(4)
References
314(3)
Index 317
Dr. Chingiz Hajiyev is a professor at the Faculty of Aeronautics and Astronautics, Istanbul Technical University (Istanbul, Turkey).

Dr. Halil Ersin Soken is an assistant professor at the Aerospace Engineering Department, Middle East Technical University (Ankara, Turkey).
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