Table Of Contents

List of Contributing Authors v

Foreword vii

Preface viii

Standard Notation x

PART I—BACKGROUND

1. INTRODUCTION ]

1.1 Representative Mission Profile 3

1.2 Representative Examples of A ttitude Determination and Control 10

1.3 Methods of A ttitude Determination and Control 16

1.4 Time Measurements 18

2. ATTITUDE GEOMETRY 22

2.1 The Spacecraft-Centered Celestial Sphere 22

2.2 Coordinate Systems 24

2.3 Elementary Spherical Geometry 31

3. SUMMARY OF ORBIT PROPERTIES AND TERMINOLOGY 36

3.1 Keplerian Orbits 36

3.2 Planetary and Lunar Orbits 48

3.3 Spacecraft Orbits 52

3.4 Orbit Perturbations 62

3.5 Viewing and Lighting Conditions 71

4. MODELING THE EARTH 82

4.1 Appearance of the Earth at Visual Wavelengths 83

4.2 Appearance of the Earth at Infrared Wavelengths 90

4.3 Earth Oblateness Modeling 98

4.4 Modeling the Structure of the Upper Atmosphere 106

5. MODELING THE SPACE ENVIRONMENT 113

5.1 The Earth's Magnetic Field 113

5.2 The Earth's Gravitational Field 123

5.3 Solar Radiation and the Solar Wind 129

5.4 Modeling the Position of the Spacecraft 132

5.5 Modeling the Positions of the Sun, Moon, and Planets 138

5.6 Modeling Stellar Positions and Characteristics 143

PART II—ATTITUDE HARDWARE AND DATA ACQUISITION

6. ATTITUDE HARDWARE 155

6.1 Sun Sensors 155

6.2 Horizon Sensors 166

6.3 Magnetometers 180

6.4 Star Sensors 184

6.5 Gyroscopes 196

6.6 Momentum and Reaction Wheels 201

6.7 Magnetic Coils 204

6.8 Gas Jets 206

6.9 Onboard Computers 210

7. MATHEMATICAL MODELS OF ATTITUDE HARDWARE 217

7.1 Sun Sensor Models 218

7.2 Horizon Sensor Models 230

7.3 Sun Sensor/Horizon Sensor Rotation Angle Models 237

7.4 Modeling Sensor Electronics 242

7.5 Magnetometer Models 249

7.6 Star Sensor Models 254

7.7 Star Identification Techniques 259

7.8 Gyroscope Models 266

7.9 Reaction Wheel Models 270

7.10 Modeling Gas Jet Control Systems 272

8. DATA TRANSMISSION AND PREPROCESSING 278

8.1 Data Transmission 278

8.2 Spacecraft Telemetry 293

8.3 Time Tagging 298

8.4 Telemetry Processors 304

9. DATA VALIDATION AND ADJUSTMENT 310

9.1 Validation of Discrete Telemetry Data 312

9.2 Data Validation and Smoothing 315

9.3 Scalar Checking 328

9.4 Data Selection Requiring Attitude Information 334

PART III—ATTITUDE DETERMINATION

10. GEOMETRICAL BASIS OF ATTITUDE DETERMINATION 343

10.1 Single-Axis Attitude 344

10.2 Arc-Length Measurements 346

10.3 Rotation Angle Measurements 349

10.4 Correlation Angles 353

10.5 Compound Measurements—Sun to Earth Horizon Crossing

Rotation Angle 357

10.6 Three-Axis Attitude 359

11. SINGLE-AXIS ATTITUDE DETERMINATION METHODS 362

11.1 Methods for Spinning Spacecraft 363

11.2 Solution Averaging 370

11.3 Single-Axis Attitude Determination Accuracy 373

11.4 Geometrical Limitations on Single-Axis Attitude Accuracy 389

11.5 Attitude Uncertainty Due to Systematic Errors 402

12. THREE-AXIS ATTITUDE DETERMINATION METHODS 410

12.1 Parameterization of the A ttitude 410

12.2 Three-Axis Attitude Determination 420

12.3 Covariance Analysis 429

13. STATE ESTIMATION ATTITUDE DETERMINATION METHODS 436

13.1 Deterministic Versus State Estimation Attitude Methods 436

13.2 State Vectors 438

13.3 Observation Models 443

13.4 Introduction to Estimation Theory 447

13.5 Recursive Least-Squares Estimators and Kalman Filters 459

14. EVALUATION AND USE OF STATE ESTIMATORS 471

14.1 Prelaunch Evaluation of State Estimators 471

14.2 Operational Bias Determination 473

14.3 Limitations on State Vector Observability 476

PART IV—ATTITUDE DYNAMICS AND CONTROL

15. INTRODUCTION TO ATTITUDE DYNAMICS AND CONTROL 487

15.1 Torque-Free Motion 487

15.2 Response to Torques 498

15.3 Introduction to Attitude Control 502

16. ATTITUDE DYNAMICS 510

16.1 Equations of Motion 510

16.2 Motion of a Rigid Spacecraft 523

16.3 Spacecraft Nutation 534

16.4 Flexible Spacecraft Dynamics 548

17. ATTITUDE PREDICTION 558

17.1 Attitude Propagation 558

17.2 Environmental Torques 566

17.3 Modeling Internal Torques 576

17.4 Modeling Torques Due to Orbit Maneuvers 580

18. ATTITUDE STABILIZATION 588 ISA Automatic Feedback Control 588

18.2 Momentum and Reaction Wheels 600

18.3 Autonomous Attitude Stabilization Systems 604

18.4 Nutation and Libration Damping 625

19. ATTITUDE MANEUVER CONTROL 636

19.1 Spin Axis Magnetic Coil Maneuvers 636

19.2 Spin Plane Magnetic Coil Maneuvers 642

19.3 Gas Jet Maneuvers 649

19.4 Inertial Guidance Maneuvers 655

19.5 Attitude Acquisition 661

PART V—MISSION SUPPORT

20. SOFTWARE SYSTEM DEVELOPMENT 681

20.1 Safeguards Appropriate for Mission Support Software 681

20.2 Use of Graphic Support Systems 686

20.3 Utility Subroutines 690

21. SOFTWARE SYSTEM STRUCTURE 696

21.1 General Structure for A ttitude Software Systems 696

21.2 Communications Technology Satellite Attitude Support System 700

21.3 Star Sensor A ttitude Determination System 703

21.4 A ttitude Data Simulators 709

22. DISCUSSION 714

PART VI—APPENDICES

APPENDIX A—SPHERICAL GEOMETRY 727 APPENDIX B—CONSTRUCTION OF GLOBAL GEOMETRY PLOTS 737

APPENDIX C—MATRIX AND VECTOR ALGEBRA 744

APPENDIX D—QUATERNIONS 758

APPENDIX E—COORDINATE TRANSFORMATIONS 760

APPENDIX F—THE LAPLACE TRANSFORM 767

APPENDIX G—SPHERICAL HARMONICS 775

APPENDIX H—MAGNETIC FIELD MODELS 779 APPENDIX I—SPACECRAFT ATTITUDE DETERMINATION

AN D CONTROL SYSTEMS 787

APPENDIX J —TI ME MEASUREMENT SYSTEMS 798

APPENDIX K—METRIC CONVERSION FACTORS 807

APPENDIX L —SOLAR SYSTEM CONSTANTS 814

APPENDIX M—FUNDAMENTAL PHYSICAL CONSTANTS 826

Index 830

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