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Applied Mathematics in Integrated Navigation Systems : AIAA Education Series - Robert M. Rogers

Applied Mathematics in Integrated Navigation Systems

AIAA Education Series

Hardcover

Published: 1st September 2007
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The 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 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.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 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. Additional software is included in this edition for simulating random processes and derivative free filter implementations. This edition provides a more complete foundation for addressing the different aspects of integrated navigation systems.

Prefacep. xiii
Elements of Integrated Navigation Systems
Introductionp. 3
Mathematical Preliminariesp. 7
Vector/Matrix Algebrap. 1
Vector/Matrix Calculusp. 13
Linearization Techniquesp. 17
Direction Cosine Matricesp. 19
Miscellaneous Mathematical Topicsp. 30
Chapter Summaryp. 32
Problemsp. 32
Coordinate Systems and Transformationsp. 49
Coordinate Systemsp. 49
Coordinate Frame Transformationsp. 54
Chapter Summaryp. 64
Problemsp. 65
Earth Modelsp. 71
Ellipsoid Geometryp. 71
Ellipsoid Gravityp. 79
Chapter Summaryp. 87
Problemsp. 87
Terrestrial Navigationp. 101
Strap-Down Navigation Systemsp. 101
Local-Level Navigation-Frame Mechanization Equationsp. 102
Perturbation Form of Navigation System Error Equationsp. 105
Navigation System Attitude Error Equations: [Psi] Formulationp. 113
Navigation System Error Equations Using Alternative Velocity Errorp. 113
Vertical Channelp. 116
Chapter Summaryp. 119
Problemsp. 120
Navigation Sensor Modelsp. 135
Gyro Performance Characterizationsp. 135
Sensor Error Modelsp. 140
Chapter Summaryp. 149
Problemsp. 149
Navigation Aidsp. 153
Doppler Velocity Sensorsp. 154
Tactical-Air-Navigation Rangep. 157
Global-Positioning-System Rangep. 160
Forward-Looking Infrared Line-of-Sight Systemsp. 169
Chapter Summaryp. 172
Problemsp. 172
Kalman Filteringp. 181
Recursive Weighted Least Squares: Constant Systemsp. 182
Recursive Weighted Least Squares: Dynamic Systemsp. 187
Discrete Linear Minimum Variance Estimatorp. 191
U-D Factored Formp. 194
Summed Measurementsp. 201
Combined Estimate from Two (or More) Kalman Filtersp. 204
Derivative-Free Estimationp. 207
Chapter Summaryp. 221
Problemsp. 222
Applications
Strap-Down Inertial Sensor Laboratory Calibrationp. 237
Navigation Mechanization Reviewp. 238
Sensor Error Modelp. 238
Solutions for Sensor Errorsp. 239
Data-Collection Rotation Sequencesp. 239
Observation Equationsp. 241
Processing Sequencesp. 244
Simulated Laboratory Data Calibrationp. 247
Chapter Summaryp. 250
Flight-Test Evaluationsp. 251
Optical Tracking Trajectory Reconstructionp. 252
Tactical-Air-Navigation/Inertial-Navigation-Unit Reconstructionp. 256
Vehicle Dynamics with Radar Tracking Trajectory Reconstructionp. 260
Chapter Summaryp. 273
Inertial Navigation System Ground Alignmentp. 275
Initial Coarse Alignment and Resulting Errorsp. 276
Fine-Alignment Kalman Filterp. 279
Simulated Ground Fine Alignmentp. 281
Chapter Summaryp. 287
Integration via Kalman Filtering: Global-Positioning-System Receiverp. 289
Global-Positioning-System Receiver Kalman Filter Configurationsp. 290
Inertial-Navigation-System Configuration Kalman Filterp. 290
Simulated Global-Positioning-System-Receiver Inertial-Navigation-System Kalman Filter Operationp. 299
Chapter Summaryp. 304
In-Motion Alignmentp. 305
Transfer Alignmentp. 306
Alignment Without Benefit of Attitude Initializationp. 315
Chapter Summaryp. 324
Integrated Differential Global Positioning System/Dead-Reckoning Navigationp. 327
Dead-Reckoning Navigation Equationsp. 328
Dead-Reckoning System Error Modelp. 329
Differential Global-Positioning-System Position Observationsp. 332
Integrated Dead-Reckoning/Differential Global-Positioning-System Implementationp. 332
Test Conditionsp. 333
Test Resultsp. 334
Chapter Summaryp. 337
Attitude-Determination and Estimationp. 339
Terrestrial Attitude-Determinationp. 339
Attitude-Determination by Iterationp. 344
Attitude Estimationp. 347
Chapter Summaryp. 359
Summaryp. 361
Pinson Error Modelp. 365
Navigation System Error Modelp. 365
Global-Positioning-System Latitude and Longitude Position as Measurementsp. 374
Orbital Dynamicsp. 377
Orbital Position in Earth-Centered Framep. 377
Orbital Velocity in Earth-Centered Framep. 384
Coarse-Alignment Error Equationsp. 387
Position Error Equationsp. 387
Position Error Dynamicsp. 388
Attitude Error Equationsp. 390
Velocity Error Equationsp. 392
Fine-Alignment Error Equationsp. 393
Referencesp. 395
Bibliographyp. 399
Inertial Sensorsp. 399
Kalman Filteringp. 399
Navigation Systemsp. 400
Orbital Mechanicsp. 400
Indexp. 401
Supporting Materialsp. 409
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781563479274
ISBN-10: 1563479273
Series: AIAA Education Series
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 326
Published: 1st September 2007
Publisher: American Institute of Aeronautics & Astronautics
Country of Publication: US
Dimensions (cm): 23.5 x 15.88  x 2.54
Weight (kg): 0.81
Edition Number: 3
Edition Type: Revised