Enhanced descriptions from Syndetics:

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 intoduces the computational issues and discusses the physical aspects that are tied to implementing these equatrions. The book then explains alignment techniques.

Table of contents provided by Syndetics

• Preface (p. vii)
• Introduction (p. 1)
• 1 Vectors and Matrices (p. 7)
• 1.1 Introduction (p. 7)
• 1.2 Vector Inner Product (p. 9)
• 1.3 Vector Cross Products and Skew Symmetric Matrix Algebra (p. 10)
• 2 Coordinate Transformation between Orthonormal Frames (p. 17)
• 2.1 Introduction (p. 17)
• 2.2 Direction Cosine Matrices (p. 18)
• 2.3 The Direction Cosine Matrix is a Unitary Matrix (p. 20)
• 2.4 The Direction Cosine Matrix is a Transformation Matrix (p. 21)
• 2.5 DCM Fixed Axis (p. 24)
• 2.6 The Rotation Matrix (p. 26)
• 2.7 Inner and Outer Transformation Matrices (p. 29)
• 2.8 The Quaternion (p. 32)
• 3 Forms of the Transformation Matrix (p. 35)
• 3.1 Introduction (p. 35)
• 3.2 Simple Frame Rotations (p. 36)
• 3.3 Euler Angles (p. 37)
• 3.4 Rotation Vector (p. 38)
• 3.5 Quaternion (p. 39)
• 3.6 Simple Quaternions (p. 43)
• 3.7 Conversion between Forms (p. 45)
• 3.7.1 Conversion between DCM and Euler (p. 45)
• 3.7.2 Conversion between DCM and Quaternion (p. 45)
• 3.7.3 Conversion between Euler Angles and Quaternion (p. 47)
• 3.8 Dynamics of the Transformation Matrix (p. 47)
• 3.8.1 DCM Differential Equation (p. 48)
• 3.8.2 Quaternion Differential Equation (p. 50)
• 3.8.3 Rotation Vector Differential Equation (p. 52)
• 3.8.4 Euler Angles Differential Equation (p. 55)
• 4 Earth and Navigation (p. 58)
• 4.1 Introduction (p. 58)
• 4.2 Earth, Geoid and Ellipsoid (p. 59)
• 4.3 Radii of Curvature (p. 63)
• 4.4 Earth, Inertial and Navigation Frames (p. 65)
• 4.5 Earth Rate (p. 67)
• 4.6 The Craft Rate [Characters not reproducible] (p. 67)
• 4.7 Solution of the DCM [Characters not reproducible] (p. 70)
• 4.8 Gravitational and Gravity Fields (p. 70)
• 5 The Inertial Navigation System Equations (p. 75)
• 5.1 Introduction (p. 75)
• 5.2 Body Frame of Reference (p. 76)
• 5.3 Inertial Sensors (p. 77)
• 5.3.1 The Accelerometer (p. 77)
• 5.3.2 The Rate Gyro (p. 78)
• 5.4 The Attitude Equation (p. 78)
• 5.5 The Navigation Equation (p. 80)
• 5.6 Navigation Equations Computational Flow Diagram (p. 83)
• 5.7 The Navigation Equation in Earth Frame (p. 84)
• 6 Implementation (p. 86)
• 6.1 Introduction (p. 86)
• 6.2 The Rotation Vector Differential Equation (p. 87)
• 6.3 The Attitude Equation (p. 92)
• 6.4 The Craft Velocity Equation (p. 95)
• 6.5 The Craft Position Equation (p. 99)
• 6.6 The Vertical Channel (p. 101)
• 7 Air Data Computer (p. 104)
• 7.1 Introduction (p. 104)
• 7.2 US Standard Atmosphere 1976 (p. 105)
• 7.3 Pressure Altitude (p. 107)
• 7.4 Vertical Channel Parameter Estimation Using Inertial and Air Data (p. 111)
• 7.5 Density Altitude (p. 116)
• 7.6 Altitude (Descend /Climb) Rate (p. 117)
• 7.7 Air Speed (p. 117)
• 7.8 Indicated Air Speed (IAS) (p. 119)
• 8 Polar Navigation (p. 121)
• 8.1 Introduction (p. 121)
• 8.2 The Wander Azimuth Navigation (p. 123)
• 8.3 Prospective of the Wander Azimuth Approach (p. 126)
• 8.4 Polar Circle Navigation Algorithm (p. 128)
• 8.5 Alternative Polar Circle Navigation Frame (p. 132)
• 9 Alignment (p. 136)
• 9.1 Introduction (p. 136)
• 9.2 IMU Alignment (p. 137)
• 9.3 Alternative Algorithm for [Characters not reproducible] (p. 144)
• 9.4 Estimation of the Accelerometer and Gyro Biases (p. 149)
• 9.5 Effects of Biases on Estimate of [Characters not reproducible] (p. 150)
• 10 Attitude and Heading Reference System (p. 152)
• 10.1 Introduction (p. 152)
• 10.2 Attitude Initialization (p. 152)
• 10.3 Heading Initialization (p. 155)
• 10.4 Gyro Drift Compensation (p. 159)
• 10.5 G Slaving (p. 160)
• 10.5.1 X-Gyro Bias (p. 160)
• 10.5.2 Y-Gyro Bias (p. 162)
• 10.5.3 Z-Gyro Bias (p. 163)
• 10.6 Alternative Approach for Gyro Drift Compensation (p. 163)
• 10.7 Maneuver Detector (p. 165)
• 10.7.1 Rate Gyro Threshold Selection (p. 165)
• 11 GPS Aided Inertial System (p. 167)
• 11.1 Introduction (p. 167)
• 11.2 Navigation Frame Error Equation (p. 168)
• 11.2.1 Craft Rate Error [Characters not reproducible] (p. 169)
• 11.2.2 Earth Rate Error [Characters not reproducible] (p. 170)
• 11.2.3 Position Errors (p. 171)
• 11.2.4 Attitude Error (p. 173)
• 11.2.5 Gravity Error (p. 176)
• 11.2.6 Velocity Error (p. 177)
• 11.2.7 Navigation Frame Error State Equation (p. 179)
• 11.2.8 Error Block Diagram (p. 179)
• 11.3 Earth Frame Error Equations (p. 180)
• 11.3.1 Attitude Error (p. 181)
• 11.3.2 Velocity Error (p. 182)
• 11.3.3 Position Error (p. 183)
• 11.3.4 Earth Frame Error State Equation (p. 183)
• 11.4 Inertial Sensors Error Models (p. 183)
• 11.5 The Global Positioning System (p. 187)
• 11.6 Mechanization of the INS/GPS Equations (p. 191)
• Appendix A The Vector Dot and Cross Products (p. 194)
• Appendix B Introduction to Quaternion Algebra (p. 197)
• Appendix C Simulink Models (p. 202)
• Appendix D Ellipse Geometry (p. 206)
• Appendix E Vector Dynamics (p. 213)
• Appendix F Derivation of Air Speed Equations (p. 219)
• Appendix G DCM Error Algebra (p. 222)
• Appendix H Kalman Filtering (p. 226)
• Index (p. 237)