Introduction to INS/GPS Integration
- Inertial navigation
- Integration architectures
- Example applications
Vectors, Matrices, and State Space
- Vectors and matrices
- State-space description
- Examples
Random Processes
- Random variables
- Covariance matrices
- Random process descriptions
Kalman Filter
- Filtering principles
- Least squares estimation
- Kalman filter derivation
Filter Implementation
- Filter processing example
- Off-line analysis
- Filter tuning
Navigation Coordinate Systems
- Earth model
- Navigation coordinates
- Earth relative kinematics
Inertial Navigation Mechanization
- Gravity model
- Navigation equations
- Implementation options
Inertial Sensor Technologies
- Accelerometer technologies
- Optical gyros
- MEMS technologies
- Technology survey
Strapdown Systems
- Quaternions
- Orientation vector
- Coning and sculling compensation
Navigation System Errors
- Tilt angle definitions
- Navigation error dynamics
- Simplified error characteristics
System Initialization
- INS static alignment
- Transfer alignment
- Simplified error analysis
Loosely-Coupled INS/GPS Design
- Measurement processing
- Filter design and tuning
- Navigation systems update
INS Aiding of Receiver Tracking
- Code and carrier tracking
- Track look deign trades
- Interference suppression
- Autocorrelation, power spectral density
- Deep integration
Tightly coupled INS/GPS Design
- Measurement processing
- Filter parameter selection
- Pseudo-range and delta pseudo-range measurement models
Multi-Sensor Integration
- Terrain aiding and relative GPS
- Carrier phase differential integration
- GPS interferometer/INS integration
Building Extended Kalman Filters
- Linearized and extended Kalman filters
- Radar tracking of a vertical body motion with non-linear dynamics
- Radar tracking of an accelerating body with non-linear measurements
Numerical Preliminaries and Considerations
- Keeping a covariance matrix well-conditioned, symmetric, and positive definite
- Sequential vs batch measurement processing
- Methods of measurement de-correlation
Discreet Time Strapdown Implementation
- Attitude updates and TOV of the acceleration
- Propagating the position DCM
- High rate vs low rate routines
- Effects of errors in initialization & IMU data
Aided Psi-Angle Navitator
- Description and demonstration of an aided Psi-angle wander azimuth navigator flying an aircraft type trajectory
Aided Phi-Angle Navitator
- Description and demonstration of an aided Phi-angle north-slaved navigator flying and aircraft type trajectory
- Modeling position error as latitude/longitude error
- Modeling position error as navigation frame tilt error
- Comparison of popular state dynamics matrix elements
Partials of Measurement Equations
- Techniques & tricks for taking partials, examples
- Psi-angle and Phi-angle feedback to strapdown
- Pros and cons of the 3 different Navigator types
Initialization and Process Noise
- Strapdown and covariance matrix initialization
- Process noise for gravity & random walk
- Common sensor error models: random constant, random walk & Gauss Markov
Measurement Editing and Adaptive Filters
- Online and offline residual analysis
- Advanced methods of outlier detection & rejection
- Multiple Model Adaptive Estimation
- Application to carrier phase integer ambiguity resolution
Methods of Smoothing
- Optimal prediction & Fixed Interval smoothing
- Fixed Point & Fixed Lag smoothing
- Applications to navigation testing
Square Root Filtering
- Square root covariance filtering and smoothing
- Information filter derivation
- Square root information filters
- UD factorization and filtering
Suboptimal Covariance Analysis
- Effects of mis-modeling errors
- Optimal & sub-optimal (two pass) covariance analysis
- Error budget and reduced state analysis
Unscented Kalman Filters
- Sigma points and the unscented transform
- Performance against the EKF
- Augmentation and application to navigation
- Spherical Simplex Sigma Points
- Square Root UKFs
Day 5, Afternoon
Ground Alignment and Integrated Velocity
- Gyro-Compassing, zero velocity & zero earth rate observations
- Large azimuth static alignment, advanced methods
- Small azimuth static alignment & leveling
- Ground alignment observability examples
- Integrated true velocity error, mapping into delta-range
Attitude Matching and Using Inexpensive IMUs
- Attitude matching & boresight error states
- Considerations for use of very inexpensive IMUs
- Non-holonomic motion constraints
- Magnetometer aiding
- In class measurement equation exercise
- Matrix partitioning for computational efficiency
Particle Filtering
- Bootstrap particle filter (PF)
- Multi-modal position solutions
- Particle filter example
- Applications to navigation