Cover -- Title -- Copyright -- Table of Contents -- Preface -- Chapter 1. Introduction -- I. Forces Producing Motion -- A. Gravitation -- B. Inertia -- II. Inertial Equivalence of Earth-Centered Frame -- III. Fundamental Equation of Inertial Navigation -- IV. Description of an Inertial Navigation System -- V. Inertial Measurements -- VI. Four Phases of Inertial Navigation -- VII. Role of Geodesy -- VIII. Reference Earth Model -- Part I Inertial Navigation -- Chapter 2. Notation, Coordinate Systems, and Units -- I. Notation Conventions -- II. Coordinate System Definitions -- III. Coordinate Transformation Characteristics -- IV. Commonly Used Coordinate Rotations -- V. Units -- Chapter 3. Equations of Motion in a Central Force Gravity Field -- I. Motion in Inertial Coordinates with Zero-Specific Force -- II. State-Space Form -- III. Motion in Inertial Computation Coordinates -- IV. Motion in Earth-Fixed Computation Coordinates -- V. Effect of Velocity Damping -- Chapter 4. Inertial Instrumentation -- I. Gyroscope -- II. Accelerometer -- III. Gradiometer -- IV. Gimbal Configurations -- V. Strapdown Configuration -- Chapter 5. Calibration -- I. Physical Reference Vectors -- II. Calibration Procedure -- III. Accelerometer Calibration -- IV. Gyro Calibration -- Chapter 6. Initial Alignment and Attitude Computation -- I. Initial Alignment -- II. Attitude -- Chapter 7. Geodetic Variables and Constants -- I. Method of Deriving Values for the Geodetic Variables and Constants -- II. World Geodetic System 1984 -- III. Gravity Models -- IV. Useful Incremental Terms of Geodesy -- V. Extending Gravity Surveys with Intertial Measurements -- Chapter 8. Equations of Motion with General Gravity Model -- I. State-Space Form in Earth-Centered Inertial Coordinates -- II. State-Space Form in Earth-Centered Earth-Fixed Coordinates.

III. State-Space Form in Earth-Centered Earth-Fixed Coordinates with Point-Mass Gravity Model -- IV. State-Space Form in Local Geodetic Vertical Coordinates -- V. Platform Control Laws -- VI. Integration of the Equations of Motion -- VII. Summary of Equations for Computing the Transition Matrix -- Part II Inertial Navigation with Aids -- Chapter 9. Inertial Navigation with External Measurements -- I. Basis for Using External Measurements -- II. Kalman Filter State Updates -- Chapter 10. Error Equations for the Kalman Filter -- I. Attitude Errors -- II. System Dynamic and Error Distribution Matrices in Earth-Centered Inertial Coordinates -- III. System Dynamic and Error Distribution Matrices in Earth-Centered Earth-Fixed Coordinates -- IV. System Dynamic and Error Distribution Matrices in Local Geodetic Vertical Coordinates -- Chapter 11. State Variable Error Models -- I. Inertial and External Measurement Equipment Error Shaping Functions -- II. Omission Gravity Model Error Shaping Functions -- Part III Accuracy Analysis -- Chapter 12. Accuracy Criteria and Analysis Techniques -- I. Central Limit Theorem -- II. Standard Error -- III. Gaussian Distribution Function for Navigation Position Errors -- IV. Circular Error Probable and Spherical Error Probable -- V. Accuracy Analysis Techniques -- Chapter 13. Error Equations for Calibration, Alignment, and Initialization -- I. Inertial Instrument Calibration -- II. Analytical Alignment -- III. Initialization -- IV. Kalman Filter Covariance Initialization -- Chapter 14. Evaluation of Gravity Model Error Effects -- I. Spherical Harmonic Gravity Model Errors -- II. Point-Mass Model Generation -- III. Sources of Error for Point-Mass Model -- Appendix A. Matrix Inverse Formulas -- Appendix B. Laplace Transforms -- Appendix C. Quaternions -- Appendix D. Associated Legendre Functions.

Appendix E. Associated Legendre Function Derivatives -- Appendix F. Procedure for Generating Gravity Disturbance Realizations -- Appendix G. Procedure for Generating Specific Force Profile -- Subject Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- M -- N -- O -- P -- R -- S -- T -- U -- V -- W -- Z.