Kalman Filtering Consultant Associates

PO Box 17224

Anaheim, CA 92817

ph: 714-281-4619

fax: 714-281-4619

KFCAS

- 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

- 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

- 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

- 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

- 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

Behavior of *P*

Strapdown INS in Navigation Frame, NED

21 State Extended KF Block Diagram with Position Error Measurements

*(Affiliations given for reference and do not imply endorsement by participant's company.)*

The only KF course I had that focuses on practical use of KF rather than on theory. Thank you Prof. Grewal! *(Participant, French German Research Institute)*

(Most useful) Deep understanding of Kalman filters. The sigmaRho approach should be very useful for fixed point applications.* (Participant, Dialog Semiconductor)*

Very comprehensive and intensive. Professor is so experienced and subject matter expert. *(Participant, JHU Applied Physics Laboratory)*

(Most useful) Kalman filtering information and how to fix problems with it. How to combine KF and GPS, also how to set up a state transition matrix etc. for a GPS. Very good pace, probably the best short course I have taken. *(Participant, JHU Applied Physics Laboratory)*

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 )*

Kalman Filtering Theory & Practice Using MATLAB, **4th Edition**, by Grewal & Andrews, Wiley & Sons, **2015**

** **

Global Navigation Satellite Systems, Inertial Navigation, & Integration, (3rd Edition), by Grewal, Andrews, & Bartone, Wiley & Sons, 2013

"Having the books as a comprehensive resource to the presentation was very good." Participant

Very informative. Lots of key information with supporting books and software for later use. *(Participant, Garmin) *

Kalman Filtering Consultant Associates

PO Box 17224

Anaheim, CA 92817

ph: 714-281-4619

fax: 714-281-4619

KFCAS