COURSE OUTLINE & DAILY SCHEDULE

(L - Lecture by Instructor; D - Demonstration using Computer)

DAY 1 AM 8 - 12: GPS, INS, MULTISENSOR KALMAN

L1. GPS Satellites, Positioning, Ground Control

Navigation types. Radionavigation. Satellites.Visibility.Orbits.Coverage.Frequencies. Codes. Positioning. Segments. Ground control. PPS vs SPS. Accuracies. ProsCons.

L2. Inertial Navigation Principles, Frames, Errors

Gimballed vs strapdown. Earth shape. Coordinate frames. Accel sensing. Navigation mechanization. Error models. Schuler oscillations. Altitude instability. Augmentation. Aiding sensors. Classical error compensation. Classical vs Kalman.

L3. Least Squares, Stochastic Models, Kalman Filtering

Least squares. Extension to Kalman filter. Random variable distributions, moments. Covariance, correlation, psd. Random bias, white/correlated noise, random walk. Markov process. Kalman filter recipe. Derivation/implications. Kalman pros/cons.

L4. Simple Multisensor Kalman Integration Mechanization

Radar/Inertial simple example. Mechanization and error models. Inertial sensor error augmentation. Observable difference. Optimal mechanization. Close vs Open.

DAY 1 PM 1 - 6 : GPS SIGNALS, RECEIVERS, KALMAN FILTERS

L5. GPS Signals, Tracking Loops, Receiver Functions

C/A,P(Y) codes. Code/Carrier tracking. Position,velocity. Iterative solution.Geometry. GDOP. L1,L2 signals. Spread spectrum. Jamming. Receiver functions/processing.
Appendices: A: Efficient PDOP Algorithm, B: Satellite Position in Earth Coordinates

L6. GPS System Errors, Differential, Wide Area

Satellite clock, ephemeris, atmospheric, receiver, multipath errors.Relativistic effects. Budget. Differential concept. Corrections. Pseudosatellites. Wide area augmentation.
Appendix A: Error Elimination by Multiple Differencing of Phase Measurements

L7. GPS Least Squares, Kalman, Carrier Phase Smoothing

Pseudo range and delta range linearizations. GPS least squares and standalone Kalman. Clock/baro aiding/calibration. Carrrier phase measurements and smoothing.
Appendix A: Pseudorange, Integrated Phase Filter and Differenced Phase Smoother

L8. GPS Receiver Autonomous Integrity Monitoring

Position error. Protection Limits. Test Statistic. Missed Detection. False Alarm. Chi Square. RAIM detection,isolation. Residual. Parity. Maximum likelihood. Probabilities.

D1. Simulation Overview, Satellite and Vehicle Simulation

Multistep simulation overview. Satellite constellation and vehicle trajectory simulation and comparison to error free inertial truth values.

DAY 2 AM 8 - 12: INERTIAL SENSING PRINCIPLES/TECHNOLOGY

L9. Mechanical Accelerometers/Gyros/Platforms

Elementary accelerometer.Mass attraction. Accel Sensing equation. Sliding mass, pendulous, piezoelectric,vibrating string, torque rebalance accl. Spinning wheel gyro. Gimbal isolation. Angular momentum.Torque. Gyroscopic precession. Displacement, rate, floated, tuned rotor gyros. Stable platforms. Gimbal lock. Platform gyro control.

L10. Ring Laser & Fiber Optic Gyros

Rotating racetracks. Analogy to rotating light beams. Interference of light beams. Sagnac interferometer. Fiber optic gyro. Ring Laser Gyro. Resonant Cavity. Excitation of Cavity. Stimulated Emission. Energy transitions. Effect of rotation. Sizeand geometry, 3 vs 4 mirrors. Stability. Resolution. Lock-in/dithering. Zero lock.

L11. Micromachined Accelerometers & Gyroscopes

MEMS devices. Process technology. Thin Films. Piezoelectrics. Electroplating. Bulk vs surface. MEMS Accl and gyro principle, design, fabrication. Open vs closed loop. Errors/resolution/noise. Instrumentation requirements. Manufacturers/designs/specs.

L12. Error Calibration, Compensation, Representation

Instrument errors: bias, thermal bias, scale factor, misalignments, etc. Multi-position rotation calibration for accel and gyro. Instrument compensation. Accel and gyro residual errors. Stochastic models. IMU error budgets:MEMS,FOG,RLG etc.

DAY 2 PM 1 - 6: SIMPLE LOW COST IMPLEMENTATIONS

L13. Level Plane 2-D Grid Navigator

Simple example restrictions. Sensor selection. Mechanization and block diagrams. Gimballed/Strapdown Heading. Error sources. Error propagation and block diagrams.

L14. Spherical Plane Inertial Navigator

Rotation/corrections. Surface curvature/corrections. Centripetal/ Coriolis corrections. Rotating Frames. Coriolis Law. North-Up navigator mechanization/error models.

L15. Schuler Oscillations & Altitude Instability

Pendulous reference. Schuler pendulum. Schuler oscillations. Altitude instability.
Appendix A: Vertical Channel Classical Adaptive Feedback Compensation Design

L16. Leveling, Gyrocompassing, Testing

Physical/analytical self leveling. Coarse alignment. Gravity/Earth rate errors. Fine leveling. Gyrocompassing. Gyro Bias. Fundamental limits. Steady state conditions.

D2. MultiSensor Signal & Error Simulations

Inertial, GPS, aiding sensors specification via error budgets and their measurment simulations followed by review of statistical analysis of sensor outputs. Multiposition inertial sensor calibration simulation and analysis. AHRS simulation.

DAY 3 AM 8 - 12: INERTIAL MECHANIZATIONS/ERROR MODELS

L17. Euler Angles, Direction Cosines, Quaternions

Euler Rotations. Direction Cosine Matrices (DCM). Skew sym matrix. Quaternions. Level-to-Body transform. Euler, Direction Cosine, Quaternion Rates. Comparisons.
Appendices: A: Quaternion Operations B: Direction Cosine Orthonormalization

L18. Position, Velocity, Attitude

Vector notation. Coriolis law. Velocity rates. Earth model. Gravity. WGS 84. Radii of curvature. Craft rates. Wander azimuth. Earth-to-Nav DCM rates. Angular Position. Level-to-Body DCM/Quaternion rates. Attitude. Mechanizations. Disturbance gravity.

L19. Gimballed/Strapdown Error Formulation

Geometrical, physical, mathematical definition of angular position error and attitude error. Gimballed vs Strapdown. Psi equation. Component vs vector differences.

L20. Gimballed/Strapdown Error Propagation

Position, velocity and attitude error diff eqns. Gimballed vs strapdown gyro drift.
Appendices: A: Transfer Functions, B: Error Plots, C: Strapdown Maneuver Errors

DAY 3 PM 1 - 6: SIMPLE MULTISENSOR KALMANS

L21. Ground Align Kalman Observability Example

Error models. Duality. Observation. Control block diagram. Observabilty. Signal flow diagram. Simplifications. Alignment equations. Prestored Gains. Gimbal/Strapdown.

L22. Baro/INS Stabilization Kalman Tuning Example

Baro inertial synergism. Mechanization and error models. Vertical accel/baro errors. Dynamics matrix. Observable difference. Adaptive noise. Baro steps. Data editing.

L23. GPS/INS PosVel Kalman Partitioning Example

Single large state vs multiple smaller filters. Before/after turns. Steady state values. Acc/gyro bias/tilts. Accl/Gyro non-bias errors. Background least squares estimators.

L24. Design, Analysis, Simulations, Implementations

Closed/open loop. Linearization. Riccati equation. Mismodeling. Decoupling. White noise substitution. Prefiltering. Covariance propagation. Numerical errors. Square root factorization. Measurement decorrelation. Cholesky decomposition. Sequential processing. Simulations: Covariance analysis, Sensitivity analysis, Monte Carlo.

D3. MultiSensor Kalman Filter Simulations

GPS/INS/Multisensor Kalman filter simulations in different scenarios illustrating the effect of aiding sensor error control under different conditions of Kalman updating. For baro altimeter both classical and Kalman mechanizations are simulated.

DAY 4 AM 8 - 12: ADVANCED ERROR MODELING APPLICATIONS

L25. Strapdown INS Coning & Sculling

Coning/Sculling examples. Gyro pulses. Multirate quaternion propagation.Coning compensation. Accel pulses. Body frame transformation. Sculling compensation.
Appendices: A:General Rotation, B: Coning equation, C: Rotation vector propagation.

L26. GPS Multi-Antenna Attitude Extraction

Multiantenna attitude observation geometry. Range/Phase difference. Integer cycles. Attitude correction vector. Pseudorange initialization. Carrier phase refinement. Least squares. Motion based cycle ambiguity resolution. Single/multiple baseline motions.

L27. Aiding Sensor Observable Differences

Measurement geometry. Velocity sensor lever arm. Doppler measurement at inertial location. Observable difference. Doppler error model development. Kalman states. Radar antenna phase error model. Ship/radar/missile observable difference example.

L28. Pseudo & Delta Range Observable Differences

Geometric range and range rate perturbations. Pseudo range/delta range obsevable differences. Relationship to INS and GPS errors. Lumped errors versus filter states.

DAY 4 PM 1 6: GPS/INS/MULTISENSOR INTEGRATION

L25. MultiSensor Open/Closed Loop Extended Kalman

Close/open loop control. Linearization.Augmentation. Reduction.Linearized/Extended Kalman filters. Kalman derivation. Covariance propagation. Matrix Riccati equation.

L30. GPS/INS Kalman Implementations

Truth models, error budgets of satellite clock, ephemeris, ionosphere, troposhere, multipath; user clock, code loop and carrier loop. Filter user clock model and inertial dynamics matrix. Adaptive process noise. Loosely and tightly coupled filter states.

L31. GPS/INS Kalman Augmentation

Baroaltimeter and doppler sensor augmentation. Baro and doppler truth models and filter states. Error sources. Candidate baro/doppler aided GPS/INS Kalman filters.

L32. GPS/INS Kalman Fault Isolation

Kalman Innovations Covariance. Innovations properties and tests.Filter problems,ad hoc fixes. Innovations fault detection. Bank of filters. Multiple filter fault isolation.

D4. MultiSensor Kalman Filter Simulations

Simulations to demonstrate sensitivity to turning off selected aiding sensors at selected intervals, degraded sensor measurements, number of filter states, process noise, observation noise, scaling of tuning parameters, vehicle maneuvers.

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