Applied mathematics in integrated navigation systems

✍ Scribed by Robert M. Rogers, Joseph A. Schetz

• Publisher: AIAA (American Institute of Aeronautics & Ast
• Year: 2003
• Tongue: English
• Leaves: 351
• Series: Aiaa Education Series
• Edition: 2nd
• Category: Library

✦ Synopsis

he subject of integrated navigation systems covered in this book is designed for those directly involved with the design, integration, and test and evaluation of navigation systems. It is assumed that the reader has a background in mathematics, including calculus. Integrated navigation systems is 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.

This presentation is segmented into two parts. In the first part, elements of basic mathematics, kinematics, equations describing navigation systems/sensors and their error models, aids to navigation, and Kalman filtering are developed. Detailed derivations are presented and examples are given to aid in the understanding of these elements of integrated navigation systems. Problems are included to expand the application of the materials presented.

The second edition includes software, additional background material and exercises, and additional applications. Selected Chapter, Section, and Exercise related software is provided in a companion CD-ROM to enhance the learning experience of the reader. The included software has been developed using MATLAB/Simulink(TM) version 6.5 by The MathWorks, Inc. Additional material includes: integrating navigation aides for a navigation system’s vertical axis; exercises that broaden the scope of problems encountered in integrated navigation systems; and the general problem of attitude determination and estimation whether for terrestrial or space applications. This edition provides a more complete foundation for addressing the different aspects of integrated navigation systems.

✦ Table of Contents

Content......Page 10
Preface......Page 14
Part 1.Elements of Integrated Navigation Systems......Page 18
1.Introduction......Page 20
2.1 VectorIMatrix Algebra......Page 24
2.2 VectorIMatrix Calculus......Page 30
2.3 Linearization Techniques......Page 33
2.4 Direction Cosine Matrices......Page 35
2.5 Miscellaneous Mathematical Topics......Page 45
Problems......Page 47
3.1 Coordinate Systems......Page 58
3.2 Coordinate Frame Transformations......Page 64
3.3 Chapter Summary......Page 71
Problems......Page 72
4.1 Ellipsoid Geometry......Page 76
4.2 Ellipsoid Gravity......Page 83
4.3 Chapter Summary......Page 84
Problems......Page 85
5.1 Strap-Down Navigation Systems......Page 90
5.2 Local Level Navigation Frame Mechanization Equations......Page 91
5.3 Perturbation Form of Navigation System Error Equations......Page 94
5.5 Navigation System Error Equations Using Alternative......Page 101
5.6 Vertical Channel......Page 105
5.7 Chapter Summary......Page 107
Problems......Page 108
6.1 Gyro Performance Characterizations......Page 118
6.2 Sensor Error Models......Page 122
Problems......Page 131
7.1 Doppler Velocity Sensors......Page 134
7.2 Tactical Air Navigation Range......Page 138
7.3 Global Positioning System Range......Page 141
7.4 Forward Looking Infrared Line-of-Sight Systems......Page 149
7.5 Chapter Summary......Page 151
Problems......Page 152
8.Kalman Filtering......Page 158
8.1 Recursive Weighted Least Squares: Constant Systems......Page 159
8.2 Recursive Weighted Least Squares: Dynamic Systems......Page 163
8.3 Discrete Linear Minimum Variance Estimator......Page 166
8.4 U-D Factored Form......Page 169
8.5 Summed Measurements......Page 175
8.6 Combined Estimate from Two Kalman Filters......Page 177
Problems......Page 180
2.Applications......Page 188
9.Strap-Down Inertial Sensor......Page 190
9.3 Solutions for Sensor Errors......Page 191
9.4 Data Collection Rotation Sequences......Page 192
9.5 Observation Equations......Page 194
9.7 Simulated Laboratory Data Calibration......Page 197
9.8 Chapter Summary......Page 200
10.Flight Test Evaluations......Page 206
10.1 Optical Tracking Trajectory Reconstruction......Page 207
10.2 Tactical Air Navigationllnertial Navigation......Page 212
10.3 Vehicle Dynamics with Radar Tracking......Page 217
10.4 Chapter Summary......Page 229
11.1 Initial Coarse Alignment and Resulting Errors......Page 232
11.2 Fine Alignment Kalman Filter......Page 235
11.3 Simulated Ground Fine Alignment......Page 237
11.4 Chapter Summary......Page 244
12.Integration via Kalman Filtering: Global......Page 246
12.2 lnertial Navigation System Configuration Kalman Filter......Page 247
12.3 Simulated Global Positioning System Receiver Inertial......Page 254
12.4 Chapter Summary......Page 259
13.1 Transfer Alignment......Page 262
13.2 Alignment Without Benefit of Attitude Initialization12......Page 272
13.3 Chapter Summary......Page 282
14.Integrated Differential Global Positioning......Page 284
14.1 Dead-Reckoning Navigation Equations......Page 285
14.2 Dead-Reckoning System Error Model......Page 286
14.4 Integrated Dead-ReckoningIDifferential Global Positioning......Page 289
14.5 Test Conditions......Page 290
14.6 Test Results......Page 291
14.7 Chapter Summary......Page 294
15.1 Terrestrial Attitude Determination......Page 296
15.2 Attitude Determination by Iteration......Page 300
15.3 Attitude Estimation......Page 301
15.4 Chapter Summary......Page 315
16.Summary......Page 316
Appendix A . Pinson Error Model......Page 320
Appendix B . Global Positioning System Position Velocity and......Page 330
AppendixD.Fine Alignment Error Equations......Page 338
Appendix E......Page 340
Appendix F......Page 342
Index......Page 344
TEXTS PUBLISHED IN THE AIAA EDUCATION SERIES......Page 348