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

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.

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.

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

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

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.

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

Pendulous reference. Schuler pendulum. Schuler oscillations. Altitude
instability.

Appendix A: Vertical Channel Classical Adaptive Feedback Compensation
Design

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

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.

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.

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.

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.

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.