Navigation types. Radionavigation. Satellites.Visibility.Orbits.Coverage.Frequencies. Codes. Positioning. Segments. Ground control. PPS vs SPS. Accuracies. ProsCons.
Gimballed/strapdown overview. Acceleration Sensing. Earth rotation/corrections. Surface curvature/corrections. Centripetal/ Coriolis corrections. Coordinate Frames. Mechanization. Schuler oscillations. Altitude Instability. Augmentation.Aiding sensors.
Least squares:batch/recursive.Relationship to Kalman. Stochastic Representations: Kalman filter recipe. Radar/Inertial example. Optimal mechanization. Close vs Open.
Appendices: A:Least Squares, B:Probability Densities, Moments, C:Kalman Features
Mixing GPS/INS. Benefits. Pitfalls. Cascaded vs Integrated. Open vs closed loop. Integration node: solution,measurement,signal. Coupling type: loose, tight, full, deep.
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
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
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
Position error. Protection Limits. Test Statistic. Missed Detection. False Alarm. Chi Square. RAIM detection,isolation. Residual. Parity. Maximum likelihood. Probabilities.
Multistep simulation overview. Vehicle trajectory and maneuver constraints for a realistic vehicle profile truth will be simulated and compared to error free inertial.
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.
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.
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.
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.
Simple example restrictions. Sensor selection. Mechanization and block diagrams. Gimballed/Strapdown Heading. Error sources. Error propagation and block diagrams.
Rotating Frames. Coriolis Law. North-Up plane navigator. Mechanization and block diagrams. Error sources. North and up channel error propagation, block diagrams.
Gravity variations. Altitude instability. Pendulous reference. Schuler pendulum. Schuler
oscillations. Classical posvel feedback augmentations. Kalman comparison.
Appendix A: Classical Adaptive Feedback Compensation Design for Vertical Channel
Physical/analytical self leveling. Coarse alignment. Gravity/Earth rate errors. Fine leveling. Gyrocompassing. Gyro Bias. Fundamental limits. Steady state conditions.
Sensors truth models: inertial, GPS, aiding sensors specified via error budgets. Sensors simulation, followed by review of statistical analysis of sensor outputs.
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
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.
Geometrical, physical, mathematical definition of angular position error and attitude error. Gimballed vs Strapdown. Psi equation. Component vs vector differences.
Position, velocity and attitude error diff eqns. Gimballed vs strapdown gyro drift.
Appendices: A: Transfer Functions, B: Error Plots, C: Strapdown Maneuver Errors
Error models. Duality. Observation. Control block diagram. Observabilty. Signal flow diagram. Simplifications. Alignment equations. Prestored Gains. Gimbal/Strapdown.
Baro inertial synergism. Mechanization and error models. Vertical accel/baro errors. Dynamics matrix. Observable difference. Adaptive noise. Baro steps. Data editing.
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.
Truth vs filter model. Mismodeling. Decoupling. White noise substitution.Prefiltering. Simulation techniques: Covariance analysis, Sensitivity analysis, Monte Carlo. Covariance propagation. Numerical errors. Ill-conditioning. Adhoc methods. Square root algorithms. Cholesky decomposition. Decorrelate meas. Sequential processing.
Inertial sensor errored measurements simulated on previous day will be used to drive free inertial navigation system to access effects of various sensor errors on inertial system performance.
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.
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.
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.
Geometric range and range rate perturbations. Pseudo range/delta range obsevable differences. Relationship to INS and GPS errors. Lumped errors versus filter states.
Close/open loop control. Linearization.Augmentation. Reduction.Linearized/Extended Kalman filters. Kalman derivation. Covariance propagation. Matrix Riccati equation.
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.
Baroaltimeter and doppler sensor augmentation. Baro and doppler truth models and filter states. Error sources. Candidate baro/doppler aided GPS/INS Kalman filters.
Kalman Innovations Covariance. Innovations properties and tests.Filter problems,ad hoc fixes. Innovations fault detection. Bank of filters. Multiple filter fault isolation.
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.