Contents -- Preface -- Introduction -- 1. Vectors and Matrices -- 1.1 Introduction -- 1.2 Vector Inner Product -- 1.3 Vector Cross Products and Skew Symmetric Matrix Algebra -- 2. Coordinate Transformation between Orthonormal Frames -- 2.1 Introduction -- 2.2 Direction Cosine Matrices -- 2.3 The Direction Cosine Matrix is a Unitary Matrix -- 2.4 The Direction Cosine Matrix is a Transformation Matrix -- 2.5 DCM Fixed Axis -- 2.6 The Rotation Matrix -- 2.7 Inner and Outer Transformation Matrices -- 2.8 The Quaternion -- 3. Forms of the Transformation Matrix -- 3.1 Introduction -- 3.2 Simple Frame Rotations -- 3.3 Euler Angles -- 3.4 Rotation Vector -- 3.5 Quaternion -- 3.6 Simple Quaternions -- 3.7 Conversion between Forms -- 3.7.1 Conversion between DCM and Euler -- 3.7.2 Conversion between DCM and Quaternion -- 3.7.3 Conversion between Euler Angles and Quaternion -- 3.8 Dynamics of the Transformation Matrix -- 3.8.1 DCM Differential Equation -- 3.8.2 Quaternion Differential Equation -- 3.8.3 Rotation Vector Differential Equation -- 3.8.4 Euler Angles Differential Equation -- 4. Earth and Navigation -- 4.1 Introduction -- 4.2 Earth, Geoid and Ellipsoid -- 4.3 Radii of Curvature -- 4.4 Earth, Inertial and Navigation Frames -- 4.5 Earth Rate -- 4.6 The Craft Rate n en ω -- 4.7 Solution of the DCM n e C -- 4.8 Gravitational and Gravity Fields -- 5. The Inertial Navigation System Equations -- 5.1 Introduction -- 5.2 Body Frame of Reference -- 5.3 Inertial Sensors -- 5.3.1 The Accelerometer -- 5.3.2 The Rate Gyro -- 5.4 The Attitude Equation -- 5.5 The Navigation Equation -- 5.6 Navigation Equations Computational Flow Diagram -- 5.7 The Navigation Equation in Earth Frame -- 6. Implementation -- 6.1 Introduction -- 6.2 The Rotation Vector Differential Equation -- 6.3 The Attitude Equation -- 6.4 The Craft Velocity Equation.

6.5 The Craft Position Equation -- 6.6 The Vertical Channel -- 7. Air Data Computer -- 7.1 Introduction -- 7.2 US Standard Atmosphere 1976 -- 7.3 Pressure Altitude -- 7.4 Vertical Channel Parameter Estimation Using Inertial and Air Data -- 7.5 Density Altitude -- 7.6 Altitude (Descend/Climb) Rate -- 7.7 Air Speed -- 7.8 Indicated Air Speed (IAS) -- 8. Polar Navigation -- 8.1 Introduction -- 8.2 The Wander Azimuth Navigation -- 8.3 Prospective of the Wander Azimuth Approach -- 8.4 Polar Circle Navigation Algorithm -- 8.5 Alternative Polar Circle Navigation Frame -- 9. Alignment -- 9.1 Introduction -- 9.2 IMU Alignment -- 9.3 Alternative Algorithm for b n C -- 9.4 Estimation of the Accelerometer and Gyro Biases -- 9.5 Effects of Biases on Estimate of b n C -- 10. Attitude and Heading Reference System -- 10.1 Introduction -- 10.2 Attitude Initialization -- 10.3 Heading Initialization -- 10.4 Gyro Drift Compensation -- 10.5 G Slaving -- 10.5.1 X-Gyro Bias -- 10.5.2 Y-Gyro Bias -- 10.5.3 Z-Gyro Bias -- 10.6 Alternative Approach for Gyro Drift Compensation -- 10.7 Maneuver Detector -- 10.7.1 Rate Gyro Threshold Selection -- 11. GPS Aided Inertial System -- 11.1 Introduction -- 11.2 Navigation Frame Error Equation -- 11.2.1 Craft Rate Error n en ω δ -- 11.2.2 Earth Rate Error n ie ω δ -- 11.2.3 Position Errors -- 11.2.4 Attitude Error -- 11.2.5 Gravity Error -- 11.2.6 Velocity Error -- 11.2.7 Navigation Frame Error State Equation -- 11.2.8 Error Block Diagram -- 11.3 Earth Frame Error Equations -- 11.3.1 Attitude Error -- 11.3.2 Velocity Error -- 11.3.3 Position Error -- 11.3.4 Earth Frame Error State Equation -- 11.4 Inertial Sensors Error Models -- 11.5 The Global Positioning System -- 11.6 Mechanization of the INS/GPS Equations -- Appendix A. The Vector Dot and Cross Products -- Appendix B. Introduction to Quaternion Algebra.

Appendix C. Simulink® Models -- Appendix D. Ellipse Geometry -- Appendix E. Vector Dynamics -- Appendix F. Derivation of Air Speed Equations -- Appendix G. DCM Error Algebra -- Appendix H. Kalman Filtering -- Index.