Kalman Filtering Consultant Associates

Application of Kalman Filtering to GPS, INS, & Navigation Short Course

Kalman Filtering Consultant Associates
PO Box 17224
Anaheim, CA 92817
ph: 714-281-4619
fax: 714-281-4619
KFCAS@aol.com

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

GPS Errors
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 & Advanced Inertial Navigation

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/L₂Bias and Ionospheric Estimation
Integrity
GPS Evolution
WAAS (SBAS)
GEO Uplink Subsystem (GUS) Algorithms

From Day 4--

The instructor is thoroughly grounded in the practical real life application of the Kalman filter... (Participant, National Research Council of Canada)

Excellent. It is a pleasure to learn the material from someone that is not just a mathematician, but a practicing, experienced veteran. The practical insights and intuition were invaluable and made the whole course. (Participant, Sensor Platforms, Inc. )

Great course, great approach to real world problem. This approach is really missing in many Kalman filter courses. …(Participant, NAVCOM Technology )

This was by far the best professional development technical training course I have ever attended. I now understand intuitively how a KF works and what are the various techniques for testing their performance……(Participant, MTSI )

Dr. Grewal presents the material with clarity and insight. (Participant )

Well done! It was definitely worth my time and will aid me in my current work. (Participant, ENSCO, Inc. )

(Most useful) Concepts and tricks to getting Kalman filters to work in the real world. How to build and tune the models, choose states, apply pre-filters or shape filters, determine unknowns, etc. ……(Participant, Pinnacle Technologies )

…Days 2 and 3 were worth the price of admission alone…Dr. Grewal did an excellent job of explaining/clarifying some issues that I was uncertain on……(Participant, McMaster University )

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