Kalman Filtering Application to GPS, INS, and Navigation

Day 1 Review of Fundamentals         

• What is a Kalman Filter?
• Matrix Theory
• Linear Dynamic Systems
• Probability Theory
• Random Variables
• Random Vectors
• Random Processes
• Error Propagation
• Relationship Between Discrete and Continuous Noise Covariances
• Solutions—Examples

Day 2 Kalman Filtering

• Introduction—Uses and Limitations
• Nonstandard Kalman Filtering
• Discrete Linear Kalman Filter
• Continuous Kalman Filter
• Examples
• Nonlinear Kalman Filter
• Linearized and Extended Kalman Filter
• Sigma Point (Unscented Kalman Filter)
• Examples
• Kalman Filter Engineering
• Square Root Filtering, Cholesky Factors
• Computer Demo and Workshop
• Data Rejection
• Chi-squared Statistic

Day 3  Practical Considerations and Applications:  Kalman Filtering and GPS Theory

• Introduction 
• Divergence and Effective Cures 
• Nonlinearity Considerations
• Suboptimal Filtering
• Prefiltering and Data Rejection 
• Introduction to GPS 
• Segment Description of GPS 
• Codes
• GPS Signal Description
• GPS Data, Time, UTC
• Design Choices for Receivers
• Receiver Crystal Clock Modeling

Day 4 GPS and INS With Examples

• Errors in GPS
• Coordinate Transformations
• Measurement Models for GPS
• Fundamentals of Inertial Navigation
• Sensor Performance
• Error Models
• Coriolis Effect, Schular Oscillations, Coning, Sculling
• Continuous and Discrete Plant and Observation Models with Examples
• Application of Kalman Filtering to INS and GPS with Examples
• Feed Forward and Feed Back Configurations
• Tightly and Loosely Coupled
• Deep INS/GNSS Integration (Ultra Tight Configuration)
• Strapdown Navigation Equations for 23 States
• 8 Error State Estimation with 4 Pseudoranges, 4 Delta Pseudoranges with MATLAB^®
• Tightly Coupled Examples, 4 states (4, 8, 11 states on CD)
• INS Sensor Parameters
• 17 State Plant Model
• Example of Vehicular Navigation
• INS for Submarines and Ships

Day 5  GPS Theory & Applications

• Ionospheric Delay Calculations, Measurements, and Estimation (Computer Programs with MATLAB^®)
• The Multipath Problem 
• Two Dimension Nav. Solution 
• User Position & Velocity Calculations with No Errors
• Determining Satellite Positions (Computer Programs with MATLAB^®)  
• How to Select the Satellites from DOPs
• Simulations—DOPs and Covariances
• Differential GPS
• GPS Precise Positioning
• Satellite Orbit Determination
• L₁/L₂ Bias and Ionospheric Estimation
• Integrity
• GPS Evolution
• WAAS (SBAS)
• GEO Uplink Subsystem (GUS) Algorithms

INCLUDES TWO BOOKS

Kalman Filtering Theory & Practice Using MATLAB--THIRD EDITION (Grewal & Andrews, Wiley & Sons, 2008)

AND  

 Global Positioning Systems, Inertial Navigation, & Integration, Second Edition (Grewal, Weill, & Andrews, Wiley & Sons, 2007).

plus

 Course Notes, Algorithms, and Demos

Register Now for the June 2010 Course!