Applied mathematics in integrated navigation systems

Intended for those directly involved with the design, integration, and test and evaluation of navigation systems, this text/CD-ROM presents elements of basic mathematics, kinematics, equations describing navigation systems and their error models, and Kalman filtering. Detailed derivations are presen

Author Notes

Robert M. Rogers received his degrees in Aerospace Engineering from the University of Florida and is an Associate Fellow of the American Institute of Aeronautics and Astronautics. As sole proprietor of Rogers Engineering & Associates, Dr. Rogers performs research development, systems analysis, test and evaluation, and teaching for the Department of Defense and the National Aeronautics and Space Administration in integrated navigation systems

Preface	p. xiii
Part 1 Elements of Integrated Navigation Systems
Chapter 1. Introduction	p. 3
Chapter 2. Mathematical Preliminaries	p. 7
2.1 Vector/Matrix Algebra	p. 7
2.2 Vector/Matrix Calculus	p. 13
2.3 Linearization Techniques	p. 16
2.4 Direction Cosine Matrices	p. 18
2.5 Miscellaneous Mathematical Topics	p. 28
2.6 Chapter Summary	p. 30
Problems	p. 30
Chapter 3. Coordinate Systems and Transformations	p. 41
3.1 Coordinate Systems	p. 41
3.2 Coordinate Frame Transformations	p. 47
3.3 Chapter Summary	p. 54
Problems	p. 55
Chapter 4. Earth Models	p. 59
4.1 Ellipsoid Geometry	p. 59
4.2 Ellipsoid Gravity	p. 66
4.3 Chapter Summary	p. 67
Problems	p. 68
Chapter 5. Terrestrial Navigation	p. 73
5.1 Strap-Down Navigation Systems	p. 73
5.2 Local Level Navigation Frame Mechanization Equations	p. 74
5.3 Perturbation Form of Navigation System Error Equations	p. 77
5.4 Navigation System Attitude Error Equations: Psi Formulation	p. 84
5.5 Navigation System Error Equations Using Alternative Velocity Error	p. 84
5.6 Vertical Channel	p. 88
5.7 Chapter Summary	p. 90
Problems	p. 91
Chapter 6. Navigation Sensor Models	p. 101
6.1 Gyro Performance Characterizations	p. 101
6.2 Sensor Error Models	p. 105
6.3 Chapter Summary	p. 114
Problems	p. 114
Chapter 7. Navigation Aids	p. 117
7.1 Doppler Velocity Sensors	p. 117
7.2 Tactical Air Navigation Range	p. 121
7.3 Global Positioning System Range	p. 124
7.4 Forward Looking Infrared Line-of-Sight Systems	p. 132
7.5 Chapter Summary	p. 134
Problems	p. 135
Chapter 8. Kalman Filtering	p. 141
8.1 Recursive Weighted Least Squares: Constant Systems	p. 142
8.2 Recursive Weighted Least Squares: Dynamic Systems	p. 146
8.3 Discrete Linear Minimum Variance Estimator	p. 149
8.4 U--D Factored Form	p. 152
8.5 Summed Measurements	p. 158
8.6 Combined Estimate from Two Kalman Filters	p. 160
8.7 Chapter Summary	p. 163
Problems	p. 163
Part 2 Applications
Chapter 9. Strap-Down Inertial Sensor Laboratory Calibration	p. 173
9.1 Navigation Mechanization Review	p. 174
9.2 Sensor Error Model	p. 174
9.3 Solutions for Sensor Errors	p. 174
9.4 Data Collection Rotation Sequences	p. 175
9.5 Observation Equations	p. 177
9.6 Processing Sequences	p. 180
9.7 Simulated Laboratory Data Calibration	p. 180
9.8 Chapter Summary	p. 183
Chapter 10. Flight Test Evaluations	p. 189
10.1 Optical Tracking Trajectory Reconstruction	p. 190
10.2 Tactical Air Navigation/Inertial Navigation Unit Reconstruction	p. 195
10.3 Vehicle Dynamics with Radar Tracking Trajectory Reconstruction	p. 200
10.4 Chapter Summary	p. 212
Chapter 11. Inertial Navigation System Ground Alignment	p. 215
11.1 Initial Coarse Alignment and Resulting Errors	p. 215
11.2 Fine Alignment Kalman Filter	p. 218
11.3 Simulated Ground Fine Alignment	p. 220
11.4 Chapter Summary	p. 227
Chapter 12. Integration via Kalman Filtering: Global Positioning System Receiver	p. 229
12.1 Global Positioning System Receiver Kalman Filter Configurations	p. 230
12.2 Inertial Navigation System Configuration Kalman Filter	p. 230
12.3 Simulated Global Positioning System Receiver Inertial Navigation System Kalman Filter Operation	p. 237
12.4 Chapter Summary	p. 242
Chapter 13. In-Motion Alignment	p. 245
13.1 Transfer Alignment	p. 245
13.2 Alignment Without Benefit of Attitude Initialization	p. 255
13.3 Chapter Summary	p. 265
Chapter 14. Integrated Differential Global Positioning System/Dead-Reckoning Navigation	p. 267
14.1 Dead-Reckoning Navigation Equations	p. 268
14.2 Dead-Reckoning System Error Model	p. 269
14.3 Differential Global Positioning System Position Observations	p. 272
14.4 Integrated Dead-Reckoning/Differential Global Positioning System Implementation	p. 272
14.5 Test Conditions	p. 273
14.6 Test Results	p. 274
14.7 Chapter Summary	p. 277
Chapter 15. Attitude Determination and Estimation	p. 279
15.1 Terrestrial Attitude Determination	p. 279
15.2 Attitude Determination by Iteration	p. 283
15.3 Attitude Estimation	p. 284
15.4 Chapter Summary	p. 298
Chapter 16. Summary	p. 299
Appendix A. Pinson Error Model	p. 303
Appendix B. Global Positioning System Position Velocity and Acceleration Filter Error Model	p. 313
Appendix C. Coarse Alignment Error Equations	p. 315

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