Applied Mathematics in Integrated Navigation Systems

by Rogers, Robert M.; Schetz, Joseph A.

• ISBN13: 9781563476563
• ISBN10: 1563476568
• Edition: 2nd
• Format: Hardcover
• Copyright: 2003-10-01
• Publisher: Amer Inst of Aeronautics &

Author Biography

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

Table of Contents

Preface	xiii
Part 1: Elements of Integrated Navigation Systems
Chapter 1. Introduction	3	(4)
Chapter 2. Mathematical Preliminaries	7	(34)
2.1 Vector/Matrix Algebra	7	(6)
2.2 Vector/Matrix Calculus	13	(3)
2.3 Linearization Techniques	16	(2)
2.4 Direction Cosine Matrices	18	(10)
2.5 Miscellaneous Mathematical Topics	28	(2)
2.6 Chapter Summary	30	(1)
Problems	30	(11)
Chapter 3. Coordinate Systems and Transformations	41	(18)
3.1 Coordinate Systems	41	(6)
3.2 Coordinate Frame Transformations	47	(7)
3.3 Chapter Summary	54	(1)
Problems	55	(4)
Chapter 4. Earth Models	59	(14)
4.1 Ellipsoid Geometry	59	(7)
4.2 Ellipsoid Gravity	66	(1)
4.3 Chapter Summary	67	(1)
Problems	68	(5)
Chapter 5. Terrestrial Navigation	73	(28)
5.1 Strap-Down Navigation Systems	73	(1)
5.2 Local Level Navigation Frame Mechanization Equations	74	(3)
5.3 Perturbation Form of Navigation System Error Equations	77	(7)
5.4 Navigation System Attitude Error Equations: Psi Formulation	84	(1)
5.5 Navigation System Error Equations Using Alternative Velocity Error	84	(4)
5.6 Vertical Channel	88	(2)
5.7 Chapter Summary	90	(1)
Problems	91	(10)
Chapter 6. Navigation Sensor Models	101	(16)
6.1 Gyro Performance Characterizations	101	(4)
6.2 Sensor Error Models	105	(9)
6.3 Chapter Summary	114	(1)
Problems	114	(3)
Chapter 7. Navigation Aids	117	(24)
7.1 Doppler Velocity Sensors	117	(4)
7.2 Tactical Air Navigation Range	121	(3)
7.3 Global Positioning System Range	124	(8)
7.4 Forward Looking Infrared Line-of-Sight Systems	132	(2)
7.5 Chapter Summary	134	(1)
Problems	135	(6)
Chapter 8. Kalman Filtering	141	(32)
8.1 Recursive Weighted Least Squares: Constant Systems	142	(4)
8.2 Recursive Weighted Least Squares: Dynamic Systems	146	(3)
8.3 Discrete Linear Minimum Variance Estimator	149	(3)
8.4 U-D Factored Form	152	(6)
8.5 Summed Measurements	158	(2)
8.6 Combined Estimate from Two Kalman Filters	160	(3)
8.7 Chapter Summary	163	(1)
Problems	163	(10)
Part 2: Applications
Chapter 9. Strap-Down Inertial Sensor Laboratory Calibration	173	(16)
9.1 Navigation Mechanization Review	174	(1)
9.2 Sensor Error Model	174	(1)
9.3 Solutions for Sensor Errors	174	(1)
9.4 Data Collection Rotation Sequences	175	(2)
9.5 Observation Equations	177	(3)
9.6 Processing Sequences	180	(1)
9.7 Simulated Laboratory Data Calibration	180	(3)
9.8 Chapter Summary	183	(6)
Chapter 10. Flight Test Evaluations	189	(26)
10.1 Optical Tracking Trajectory Reconstruction	190	(5)
10.2 Tactical Air Navigation/Inertial Navigation Unit Reconstruction	195	(5)
10.3 Vehicle Dynamics with Radar Tracking Trajectory Reconstruction	200	(12)
10.4 Chapter Summary	212	(3)
Chapter 11. Inertial Navigation System Ground Alignment	215	(14)
11.1 Initial Coarse Alignment and Resulting Errors	215	(3)
11.2 Fine Alignment Kalman Filter	218	(2)
11.3 Simulated Ground Fine Alignment	220	(7)
11.4 Chapter Summary	227	(2)
Chapter 12. Integration via Kalman Filtering: Global Positioning System Receiver	229	(16)
12.1 Global Positioning System Receiver Kalman Filter Configurations	230	(1)
12.2 Inertial Navigation System Configuration Kalman Filter	230	(7)
12.3 Simulated Global Positioning System Receiver Inertial Navigation System Kalman Filter Operation	237	(5)
12.4 Chapter Summary	242	(3)
Chapter 13. In-Motion Alignment	245	(22)
13.1 Transfer Alignment	245	(10)
13.2 Alignment Without Benefit of Attitude Initialization	255	(10)
13.3 Chapter Summary	265	(2)
Chapter 14. Integrated Differential Global Positioning System/Dead-Reckoning Navigation	267	(12)
14.1 Dead-Reckoning Navigation Equations	268	(1)
14.2 Dead-Reckoning System Error Model	269	(3)
14.3 Differential Global Positioning System Position Observations	272	(1)
14.4 Integrated Dead-Reckoning/Differential Global Positioning System Implementation	272	(1)
14.5 Test Conditions	273	(1)
14.6 Test Results	274	(3)
14.7 Chapter Summary	277	(2)
Chapter 15. Attitude Determination and Estimation	279	(20)
15.1 Terrestrial Attitude Determination	279	(4)
15.2 Attitude Determination by Iteration	283	(1)
15.3 Attitude Estimation	284	(14)
15.4 Chapter Summary	298	(1)
Chapter 16. Summary	299	(4)
Appendix A. Pinson Error Model	303	(10)
Appendix B. Global Positioning System Position Velocity and Acceleration Filter Error Model	313	(2)
Appendix C. Coarse Alignment Error Equations	315	(6)
Appendix D. Fine Alignment Error Equations	321	(2)
Appendix E. References	323	(2)
Appendix F. Bibliography	325	(2)
Index	327	(4)
Series Listing	331