Fundamentals of High Accuracy Inertial Navigation Averil B. Chatfield Table of Contents

Transcription

1 Navtech Part #2440 Preface Fundamentals of High Accuracy Inertial Navigation Averil B. Chatfield Table of Contents Chapter 1. Introduction I. Forces Producing Motion A. Gravitation B. Inertia II. Inertial Equivalence of Earth-Centered Fame.3 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 A. Software Implemented B. Hardware Implemented III. Coordinate Transformation Characteristics A. Orthogonal B. Nonorthogonal IV. Commonly Used Coordinate Rotations A. Earth-Centered Inertial to Earth-Centered Earth-Fixed B. Earth-Centered Inertial to Local Geodetic Vertical C. Earth-Centered Inertial to Local Geocentric Vertical D. Earth Centered Earth-Fixed to Local Geodetic Vertical E. Earth-Centered Earth-Fixed to Local Astronomic Vertical F. Star Line-of-Sight to Platform G. Star to Earth-Centered Inertial V. Units Chapter 3. Equations of Motion in a Central Force Gravity Field I. Motion in Inertial Coordinates with Zero-Specific Force A. Zero-Specific Force B. Schuler Frequency II. State-Space Form A. Laplace Transform Form B. Frequency Response

2 III. Motion in Inertial Computation Coordinates A. Transfer Functions B. Propagation of Initial State C. Frequency Response Functions,.,...41 IV. Motion in Earth-Fixed Computation Coordinates A. Significance of Terms in Equation of Motion B. Transfer Functions C. Propagation of Initial State D. Frequency Response Functions V. Effect of Velocity Damping A. Propagation of initial State B. Frequency Response Functions Chapter 4. Inertial Instrumentation I. Gyroscope A. Rotating Wheel B. Optical C. Recently Developed Instruments II. Accelerometer A. Pendulous Integrated Gyro B. Proof Mass C. Vibrating String D. Fiber Optic III. Gradiometer A. Gravity Gradient Tensor B. Output Equations C. Output Equation Processing IV. Gimbal Configurations A. Mechanical Frame B. Floating Sphere V. Strapdown Configuration Chapter 5. Calibration I. Physical Reference Vectors A. Specific Force B. Angular Rate II. Calibration Procedure A. Inertial Measurement Unit Configuration B. Platform Rotation Schedule III. Accelerometer Calibration A. Observation Equation B. Application of the Observation Equation IV. Gyro Calibration A. Observation Equation-Magnitude Form...93 B. Observation Equation-Vector Form...99

3 Chapter 6. Initial Alignment and Attitude Computation I. Initial Alignment A. Analytical Coarse Alignment B. Aligning an IMU Stable Platform to LGV Coordinates C. Aligning a Strapdown System to LGV Coordinates II. Attitude A. Platform to Earth-Centered Inertial B. Platform to Local Astronomic Vertical C. Body-to-Earth-Centered-Inertial Using Quaternions Chapter 7. Geodetic Variables and Constants I. Method of Deriving Values for the Geodetic Variables and Constants A Apparent Gravity Magnitude B. Astronomic Coordinates C Geocentric Gravitational Constant D. Semimajor Axis, Flattening, and SHCs E. Earth Rotation Rate F. Pole Location G. Geodetic Coordinates H. Geoid Height I. Height Above Mean Sea Level II. World Geodetic System A. Spherical Harmonic Coefficients B. Equipotential Surfaces Associated with SHCs C. Physical Meaning of the Low Degree and Order SHCs D. Regional Datum Transformations III. Gravity Models A. Spherical Harmonic B. Point Mass C. Two-Dimensional Food,, Series D. Two-Dimensional Table E. Other Types of Models IV. Useful Incremental Terms of Geodesy A. Defections of the Vertical B. Azimuth Differences...._ V. Extending Gravity Surveys with Internal 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 156 III. State-Space Form in Earth-Centered Earth-Fixed Coordinates with Point-Mass Gravity Model IV. State-Space Form in Local Geodetic Vertical Coordinates A. Standard Form B. Pseudo-Velocity Form V. Platform Control Laws A. Earth Centered Inertial B. Earth-Centered Earth-Fixed C. Local Geodetic Vertical-Torqued Azimuth

4 D. Local Geodetic Vertical-Free Azimuth E. Local Geodetic Vertical-Platform Carousel F. Local Geodetic Vertical-Platform Tumble VI. Integration of the Equations of Motion VII. Summary of Equations for Computing the Transition Matrix 166 A. Earth-Centered Inertial Coordinates-Stabilized Platform B. Earth-Centered Earth-Fixed Coordinates-Stabilized Platform C. Local Geodetic Vertical Coordinates-Standard Form-Stabilized Platform D. Local Gender, Vertical Coordinates-Pseudo-Velocity Form-Stabilized Platform E. Earth-Centered Inertial Coordinates-Strapdown F. Earth-Centered Earth-Fixed Coordinates-Strapdown G. Local Geodetic Vertical Coordinates-Standard Form-Strapdown H. Local Geodetic Vertical Coordinates--Pseudo-Velocity Form-Strapdown Part II Inertial Navigation with Aids Chapter 9. Inertial Navigation with External Measurements I. Basis for Using External Measurements A. Equations of Relative Motion B. Application of the Equations of Relative Motion II. Kalman Filter State Updates A. Overview of Navigation Computations Extended Kalman Filter B. Gain Evaluation and Covariance Update C. Covariance Propagation D. Summary of Navigation Equations Extended Kalman Filter E. Summary of Navigation Equations-Linearized Kalman Filter F. Examples of External Measurement Predictions G. Examples of Partial Derivative Evaluations H. Example of a Suboptimal Filter I. Aliasing Chapter 10. Error Equations for the Kalman Filter I. Attitude Errors A. Delimit B. Angular Equivalent of the Position Error C. Actual Coordinate Rotations In Terms of Errors D. Attitude Error Vector Differential Equations II. System Dynamic and Error Distribution Matrices in Earth-Centered Inertial Coordinates A. Acceleration-Earth-Centered Inertial Coordinates B. Velocity -Earth-Centered Inertial Coordinates C. State-Space Form of Error Equations-Earth-Centered Inertial Coordinates. 218 III. System Dynamic and Error Distribution Matrices in Earth-Centered Earth-Fixed Coordinates A. Acceleration-Earth-Centered Earth-Fixed Coordinates. 219 B. Velocity-Earth-Centered Earth Fixed Coordinates

5 C. State-Space Form of Error Equations-Earth-Centered Earth-Fixed Coordinates..220 IV. System Dynamic and Error Distribution Matrices in Local Geodetic Vertical Coordinates A. Semiposition Error Definition B. Semivelocity Error Definition C. Acceleration -Local Geodetic Vertical Coordinates D. Velocity-Local Geodetic Vertical Coordinates E. State-Space Form of Error Equations-Local Geodetic Vertical Coordinates Chapter 11. Stale Variable Error Models I. Inertial and External Measurement Equipment Error Shaping Functions A. Random Constant B. Random Walk C. Random Ramp D. Markov II. Omission Gravity Model Error Shaping Functions A Gravity Database Format B. Gravity Model Error Equations of Motion C. Autocorrelation Function Approximation Method D. Influence of Vehicle Velocity on the Power Spectral Density E. Autoregressive Moving Average Method Part III Accuracy Analysis Chapter 12. Accuracy Criteria and Analysis Techniques I. Central LimitTheorem II. Standard Error A. Uncorrelated Standard Errors for Circular-Error-Probable Calculation. 254 B. Uncorrelated Standard Errors for Spherical-Error-Probable Calculation.255 III Gaussian Distribution Function for Navigation Position Errors IV. Circular Error Probable and Spherical Error Probable A. CEP for Equal Standard Errors and Zen, Means B. SEP for Equal Standard Errors and Zero Means C. CEP and SEP for Unequal Standard Errors and Nonzero Means D. Verification of the CEP and SEP Formulas V. Accuracy Analysis Techniques A. Types of Error B. Error Analysis Using Sensitivity Coefficients Chapter 13. Error Equations for Calibration, Alignment, and Initialization I. IneroallnatrumentCafiboatmn A. Apparent Gravity Magnitude B. RefereneeROlafionRate C. Pole Location

6 II. Analytical Alignment A. Astronomic Coordinates B. Geodetic Coordinates C. Specific Force and Pole Position III. Initialization A. Initial Velocity B. Initial Position C. Conversion to Earth-Centered Inertial and Local Geodetic Vertical Coordinates IV. Kalman Filter Covarience, 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 A. Representation B. Reduction C. Omission Appendix A. Matrix Inverse Formulas Appendix R. Laplace Transforms Appendix C. Quaternions Appendix D. Associated Legendre Functions Appendix E. Associated Legendre Function Derivatives Appendix E Procedure for Generating Gravity Disturbance Realizations Appendix G. Procedure for Generating Specific Force Profile Index