Applied Mathematics in Integrated Navigation Systems

by Rogers, Robert M.

• ISBN13: 9781563474453
• ISBN10: 156347445X
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-07-01
• Publisher: AIAA AM INST OF AERO & ASTRO

Summary

"Applied Mathematics in Integrated Navigation Systems combines an on-board navigation solution (position, velocity, and attitude), and independent navigation data (aids-to-navigation). The first part of the book covers the basic elements of mathematics, kinematics, equations describing navigation systems/sensors and their error models, aids-to-navigation, and Kalman filtering. Detailed derivations are presented and examples are given. The second part of the book presents case studies that apply the elements to real-world projects. This textbook is intended for upper-level undergraduates, graduate students, and working professionals in the area of design, integration, and testing/evaluation of navigation systems. Chapter exercises, appendices, and summaries supplement the text.

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 and 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	p. xi
Elements of Integrated Navigation Systems
Introduction	p. 3
Mathematical Preliminaries	p. 7
Vector/Matrix Algebra	p. 7
Vector/Matrix Calculus	p. 13
Linearization Techniques	p. 16
Direction Cosine Matrices	p. 18
Miscellaneous Mathematical Topics	p. 27
Chapter Summary	p. 29
Problems	p. 30
Coordinate Systems and Transformations	p. 41
Coordinate Systems	p. 41
Coordinate Frame Transformations	p. 47
Chapter Summary	p. 54
Problems	p. 55
Earth Models	p. 59
Ellipsoid Geometry	p. 59
Ellipsoid Gravity	p. 66
Chapter Summary	p. 67
Problems	p. 67
Terrestrial Navigation	p. 71
Strap-down Navigation Systems	p. 71
Local Level Navigation Frame Mechanization Equations	p. 72
Perturbation Form of Navigation System Error Equations	p. 75
Navigation System Attitude Error Equations: Psi Formulation	p. 82
Navigation System Error Equations Using Alternative Velocity Error	p. 82
Chapter Summary	p. 86
Problems	p. 86
Navigation Sensor Models	p. 95
Gyro Performance Characterizations	p. 95
Sensor Error Models	p. 99
Chapter Summary	p. 108
Problems	p. 108
Navigation Aids	p. 111
Doppler Velocity Sensors	p. 111
Tactical Air Navigation Range	p. 115
Global Positioning System Range	p. 118
Forward Looking Infrared Line-of-Sight Systems	p. 126
Chapter Summary	p. 128
Problems	p. 129
Kalman Filtering	p. 133
Recursive Weighted Least Squares: Constant Systems	p. 134
Recursive Weighted Least Squares: Dynamic Systems	p. 138
Discrete Linear Minimum Variance Estimator	p. 141
U-D Factored Form	p. 144
Summed Measurements	p. 150
Combined Estimate from Two Kalman Filters	p. 152
Chapter Summary	p. 155
Problems	p. 155
Applications
Strap-Down Inertial Sensor Laboratory Calibration	p. 163
Navigation Mechanization Review	p. 164
Sensor Error Model	p. 164
Solutions for Sensor Errors	p. 164
Data Collection Rotation Sequences	p. 165
Observation Equations	p. 167
Processing Sequences	p. 170
Simulated Laboratory Data Calibration	p. 170
Chapter Summary	p. 173
Flight Test Evaluations	p. 179
Optical Tracking Trajectory Reconstruction	p. 180
Tactical Air Navigation/Inertial Navigation Unit Reconstruction	p. 185
Vehicle Dynamics with Radar Tracking Trajectory Reconstruction	p. 190
Chapter Summary	p. 202
Inertial Navigation System Ground Alignment	p. 205
Initial Coarse Alignment and Resulting Errors	p. 205
Fine Alignment Kalman Filter	p. 208
Simulated Ground Fine Alignment	p. 210
Chapter Summary	p. 217
Integration via Kalman Filtering: Global Positioning System Receiver	p. 219
Global Positioning System Receiver Kalman Filter Configurations	p. 220
Inertial Navigation System Configuration Kalman Filter	p. 220
Simulated Global Positioning System Receiver Inertial Navigation System Kalman Filter Operation	p. 227
Chapter Summary	p. 232
In-Motion Alignment	p. 235
Transfer Alignment	p. 235
Alignment Without Benefit of Attitude Initialization	p. 245
Chapter Summary	p. 255
Integrated Differential Global Positioning System/Dead-Reckoning Navigation	p. 257
Dead-Reckoning Navigation Equations	p. 258
Dead-Reckoning System Error Model	p. 259
Differential Global Positioning System Position Observations	p. 262
Integrated Dead-Reckoning/Differential Global Positioning System Implementation	p. 262
Test Conditions	p. 263
Test Results	p. 264
Chapter Summary	p. 267
Summary	p. 269
Pinson Error Model	p. 273
Global Positioning System Position Velocity and Acceleration Filter Error Model	p. 283
Coarse Alignment Error Equations	p. 285
Fine Alignment Error Equations	p. 291
References	p. 293
Bibliography	p. 295
Index	p. 297
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