Introduction To Modern Navigation Systems

by Esmat Bekir

Overview

The emerging technology of very inexpensive inertial sensors is available for navigation as never before. The book lays the analytical foundation for understanding and implementing the navigation equations. It starts by demystifying the central theme of the frame rotation using such algorithms as the quaternions, the rotation vector and the Euler angles. After developing navigation equations, the book introduces the computational issues and discusses the physical aspects that are tied to implementing these equations. The book then explains alignment techniques.Introduction to Modern Navigation Systems offers an efficient algorithm for polar navigation. It also shows how to enhance the performance of the inertial system when aided by the Global Positioning System. It is an appropriate textbook for senior undergraduate and graduate students in aeronautical and electrical engineering. It could also be used as a reference book for practitioners in the field.

Product Details

ISBN-13:	9789812707659
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	07/30/2007
Pages:	256
Product dimensions:	6.35(w) x 9.00(h) x 0.81(d)

Table of Contents

Preface     vii
Introduction     1
Vectors and Matrices     7
Introduction     7
Vector Inner Product     9
Vector Cross Products and Skew Symmetric Matrix Algebra     10
Coordinate Transformation between Orthonormal Frames     17
Introduction     17
Direction Cosine Matrices     18
The Direction Cosine Matrix is a Unitary Matrix     20
The Direction Cosine Matrix is a Transformation Matrix     21
DCM Fixed Axis     24
The Rotation Matrix     26
Inner and Outer Transformation Matrices     29
The Quaternion     32
Forms of the Transformation Matrix     35
Introduction     35
Simple Frame Rotations     36
Euler Angles     37
Rotation Vector     38
Quaternion     39
Simple Quaternions     43
Conversion between Forms     45
Conversion between DCM and Euler     45
Conversion between DCM and Quaternion     45
Conversion between Euler Angles and Quaternion     47
Dynamics of the Transformation Matrix     47
DCM Differential Equation     48
Quaternion Differential Equation     50
Rotation Vector Differential Equation     52
Euler Angles Differential Equation     55
Earth and Navigation     58
Introduction     58
Earth, Geoid and Ellipsoid     59
Radii of Curvature     63
Earth, Inertial and Navigation Frames     65
Earth Rate     67
The Craft Rate [Characters not reproducible]     67
Solution of the DCM [Characters not reproducible]     70
Gravitational and Gravity Fields     70
The Inertial Navigation System Equations     75
Introduction     75
Body Frame of Reference     76
Inertial Sensors     77
The Accelerometer     77
The Rate Gyro     78
The Attitude Equation     78
The Navigation Equation     80
Navigation Equations Computational Flow Diagram     83
The Navigation Equation in Earth Frame     84
Implementation     86
Introduction     86
The Rotation Vector Differential Equation     87
The Attitude Equation     92
The Craft Velocity Equation     95
The Craft Position Equation     99
The Vertical Channel     101
Air Data Computer     104
Introduction     104
US Standard Atmosphere 1976     105
Pressure Altitude     107
Vertical Channel Parameter Estimation Using Inertial and Air Data     111
Density Altitude     116
Altitude (Descend /Climb) Rate     117
Air Speed     117
Indicated Air Speed (IAS)     119
Polar Navigation     121
Introduction     121
The Wander Azimuth Navigation     123
Prospective of the Wander Azimuth Approach     126
Polar Circle Navigation Algorithm     128
Alternative Polar Circle Navigation Frame     132
Alignment     136
Introduction     136
IMU Alignment     137
Alternative Algorithm for [Characters not reproducible]     144
Estimation of the Accelerometer and Gyro Biases     149
Effects of Biases on Estimate of [Characters not reproducible]     150
Attitude and Heading Reference System     152
Introduction     152
Attitude Initialization     152
Heading Initialization     155
Gyro Drift Compensation     159
G Slaving     160
X-Gyro Bias     160
Y-Gyro Bias     162
Z-Gyro Bias     163
Alternative Approach for Gyro Drift Compensation     163
Maneuver Detector     165
Rate Gyro Threshold Selection     165
GPS Aided Inertial System     167
Introduction     167
Navigation Frame Error Equation     168
Craft Rate Error [Characters not reproducible]     169
Earth Rate Error [Characters not reproducible]     170
Position Errors     171
Attitude Error     173
Gravity Error     176
Velocity Error     177
Navigation Frame Error State Equation     179
Error Block Diagram     179
Earth Frame Error Equations     180
Attitude Error     181
Velocity Error     182
Position Error     183
Earth Frame Error State Equation     183
Inertial Sensors Error Models     183
The Global Positioning System     187
Mechanization of the INS/GPS Equations     191
The Vector Dot and Cross Products     194
Introduction to Quaternion Algebra      197
Simulink Models     202
Ellipse Geometry     206
Vector Dynamics     213
Derivation of Air Speed Equations     219
DCM Error Algebra     222
Kalman Filtering     226
Index     237