Applied Mathematics in Integrated Navigation Systems

by Rogers, Robert M.

• ISBN13: 9781563479274
• ISBN10: 1563479273
• Edition: 3rd
• Format: Hardcover
• Copyright: 2007-10-31
• Publisher: Amer Inst of Aeronautics &

Summary

Integrated navigation systems are the combination of an onboard navigation solution (position, velocity, and attitude) and independent navigation data (aids to navigation) to update or correct navigation solutions. In this book, this combination is accomplished with Kalman filter algorithms. The third edition includes additional background material, exercises and software. The added material includes: development of general form for Earth's gravitational potential with simplification to an ellipsoid model; development of satellite orbital equations for position and velocity and the impact of non-spherical earth gravitation on satellite orbital parameters; and illustrations in the development of derivative free Kalman filters including the Unscented and Divided Difference filter forms. Additional exercises are included that expand and supplement the material in the text and demonstrate properties of the Kalman filter.

Author Biography

Roberts M. Rogers is an Associate Fellow of the American Institute of Aeronautics and Astronautics

Table of Contents

Preface	p. xiii
Elements of Integrated Navigation Systems
Introduction	p. 3
Mathematical Preliminaries	p. 7
Vector/Matrix Algebra	p. 1
Vector/Matrix Calculus	p. 13
Linearization Techniques	p. 17
Direction Cosine Matrices	p. 19
Miscellaneous Mathematical Topics	p. 30
Chapter Summary	p. 32
Problems	p. 32
Coordinate Systems and Transformations	p. 49
Coordinate Systems	p. 49
Coordinate Frame Transformations	p. 54
Chapter Summary	p. 64
Problems	p. 65
Earth Models	p. 71
Ellipsoid Geometry	p. 71
Ellipsoid Gravity	p. 79
Chapter Summary	p. 87
Problems	p. 87
Terrestrial Navigation	p. 101
Strap-Down Navigation Systems	p. 101
Local-Level Navigation-Frame Mechanization Equations	p. 102
Perturbation Form of Navigation System Error Equations	p. 105
Navigation System Attitude Error Equations: [Psi] Formulation	p. 113
Navigation System Error Equations Using Alternative Velocity Error	p. 113
Vertical Channel	p. 116
Chapter Summary	p. 119
Problems	p. 120
Navigation Sensor Models	p. 135
Gyro Performance Characterizations	p. 135
Sensor Error Models	p. 140
Chapter Summary	p. 149
Problems	p. 149
Navigation Aids	p. 153
Doppler Velocity Sensors	p. 154
Tactical-Air-Navigation Range	p. 157
Global-Positioning-System Range	p. 160
Forward-Looking Infrared Line-of-Sight Systems	p. 169
Chapter Summary	p. 172
Problems	p. 172
Kalman Filtering	p. 181
Recursive Weighted Least Squares: Constant Systems	p. 182
Recursive Weighted Least Squares: Dynamic Systems	p. 187
Discrete Linear Minimum Variance Estimator	p. 191
U-D Factored Form	p. 194
Summed Measurements	p. 201
Combined Estimate from Two (or More) Kalman Filters	p. 204
Derivative-Free Estimation	p. 207
Chapter Summary	p. 221
Problems	p. 222
Applications
Strap-Down Inertial Sensor Laboratory Calibration	p. 237
Navigation Mechanization Review	p. 238
Sensor Error Model	p. 238
Solutions for Sensor Errors	p. 239
Data-Collection Rotation Sequences	p. 239
Observation Equations	p. 241
Processing Sequences	p. 244
Simulated Laboratory Data Calibration	p. 247
Chapter Summary	p. 250
Flight-Test Evaluations	p. 251
Optical Tracking Trajectory Reconstruction	p. 252
Tactical-Air-Navigation/Inertial-Navigation-Unit Reconstruction	p. 256
Vehicle Dynamics with Radar Tracking Trajectory Reconstruction	p. 260
Chapter Summary	p. 273
Inertial Navigation System Ground Alignment	p. 275
Initial Coarse Alignment and Resulting Errors	p. 276
Fine-Alignment Kalman Filter	p. 279
Simulated Ground Fine Alignment	p. 281
Chapter Summary	p. 287
Integration via Kalman Filtering: Global-Positioning-System Receiver	p. 289
Global-Positioning-System Receiver Kalman Filter Configurations	p. 290
Inertial-Navigation-System Configuration Kalman Filter	p. 290
Simulated Global-Positioning-System-Receiver Inertial-Navigation-System Kalman Filter Operation	p. 299
Chapter Summary	p. 304
In-Motion Alignment	p. 305
Transfer Alignment	p. 306
Alignment Without Benefit of Attitude Initialization	p. 315
Chapter Summary	p. 324
Integrated Differential Global Positioning System/Dead-Reckoning Navigation	p. 327
Dead-Reckoning Navigation Equations	p. 328
Dead-Reckoning System Error Model	p. 329
Differential Global-Positioning-System Position Observations	p. 332
Integrated Dead-Reckoning/Differential Global-Positioning-System Implementation	p. 332
Test Conditions	p. 333
Test Results	p. 334
Chapter Summary	p. 337
Attitude-Determination and Estimation	p. 339
Terrestrial Attitude-Determination	p. 339
Attitude-Determination by Iteration	p. 344
Attitude Estimation	p. 347
Chapter Summary	p. 359
Summary	p. 361
Pinson Error Model	p. 365
Navigation System Error Model	p. 365
Global-Positioning-System Latitude and Longitude Position as Measurements	p. 374
Orbital Dynamics	p. 377
Orbital Position in Earth-Centered Frame	p. 377
Orbital Velocity in Earth-Centered Frame	p. 384
Coarse-Alignment Error Equations	p. 387
Position Error Equations	p. 387
Position Error Dynamics	p. 388
Attitude Error Equations	p. 390
Velocity Error Equations	p. 392
Fine-Alignment Error Equations	p. 393
References	p. 395
Bibliography	p. 399
Inertial Sensors	p. 399
Kalman Filtering	p. 399
Navigation Systems	p. 400
Orbital Mechanics	p. 400
Index	p. 401
Supporting Materials	p. 409
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