Kalman Filtering Application to GPS

Kalman Filtering Consultant Associates presents:

"Application of Kalman Filtering to

GPS, INS, & Navigation"

� Course Highlights � Registration Information (click for next course dates)

� Course Outline � Instructor's Bio� � Course, Prerequisites, and Applications

� Student Evaluations and Affiliations � Contact Information

Course Highlights

� Internationally recognized instructor/author Dr. M. S. Grewal --35+ years experience

� Instructor named one of �50+ Leaders to Watch� in GPS World May 2007 issue.

� Application oriented, including 2 volumes of course notes packed with info.

� Includes Second Edition of Kalman Filtering: Theory & Practice (Using MATLAB) with companion CD, 8th printing (Grewal/Andrews), Wiley & Sons, 2001.

� Includes 2007 Second Edition of Global Positioning Systems, Inertial Navigation & Integration , (Grewal, Weill, & Andrews), with companion CD, Wiley & Sons, 2007.

� Computer demos, filter tuning, algorithms in MATLAB, state of the art examples

� Small class size for optimal discussion and interaction.

� The added value to this course-- author/expert instructor AND small class size.

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The Course, Prerequisites, and Applications

This short course for engineering managers, computer scientists, and engineers addresses subtleties, problems, and limitations of estimation theory as applied to real world situations.

Course emphasis is on intuitive concepts and practical applications, rather than rigorous mathematical presentation. However, for the most benefits, students should have a basic understanding of matrix theory, state-space representation of linear systems, and probability theory.

Applications:

Inertial Navigation, Guidance and Control

DGPS (Differential Global Positioning System)

WAAS/SBAS (Wide Area Augmentation System)

INS (Inertial Navigation System)

IRU (Inertial Reference Unit)

IMU (Inertial Measuring Unit)

Missiles, satellites, aircraft, ships, air traffic control

Freeway traffic systems, automobile navigation system

Fleet management, tracking and surveying

Gyros and accelerometers, radar, odometer, compass (sensors)

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Course Outline

Day 1 Day 2 Day 3 Day 4 Day 5

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 & Continuous Noise Covariances

� Solutions�Examples

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Day 2: Kalman Filtering

� Introduction�Uses and Limitations

� Nonstandard Kalman Filtering

� Discrete Linear Kalman Filter

� Continuous Kalman Filter

� Examples

� Nonlinear Kalman Filter

� Unscented Kalman Filter

� Linearized and Extended Kalman Filter

� Examples

� Kalman Filter Engineering

� Square Root Filtering, Cholesky Factors

� Computer Demo and Workshop

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Day 3: PRACTICAL CONSIDERATIONS & APPLICATIONS

� Divergence and Effective Cures

� Nonlinearity Considerations

� Suboptimal Filtering

� Prefiltering and Data Rejection

� Chi-squared Statistic

� Fundamentals of Inertial Navigation

� Simplified Examples

� Position and Velocity Errors

� Examples, Advantages, Disadvantages of INS

� Sensor Performance

� INS and GPS��

� Coriolis Effect

� Error Models

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Day 4: GPS THEORY AND APPLICATIONS

� Segment Description of GPS

� Codes

� GPS Signal Description

� GPS Data, Time, UTC, UTI

� Design Choices for Receivers

� Receiver Crystal Clock Modelling

� Errors

� Ionospheric Delay Calculations, Measurements, and Estimation (Computer Programs with MATLAB)

� Carrier Smoothed Pseudorange

� The Multipath Problem

� Two Dimension Navigation Solutions

� User Position and Velocity Calculations with NO Errors

� Coordinate Transformations

� Determining Satellite Positions (Computer Programs with MATLAB)

� Measurement Models

� How to Select the Satellites from DOPs

� Differential GPS

� GPS Precise Positioning

� Satellite Orbit Determination

� L₁L₂ Bias & Ionospheric Estimation

� Integrity

� WAAS (SBAS)

� GEO Uplink Subsystem (GUS) Algorithms

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Day 5: GPS, INS INTEGRATION WITH APPLICATIONS

� Introduction

� Continuous and Discrete Plant and Observation Models

� 9 Error State Estimation with 4 Pseudoranges, 4 Delta Pseudoranges with MATLAB

� Simulations� DOPs and Covariances (with MATLAB)

� Application of Kalman Filtering to INS & GPS with Examples

� Feed Forward & Feed Back Configurations

� INS Aided with Doppler Radar

� Gyro & Accelerometer Error States

� Tightly and Loosely Coupled

� Lever Arm Compensation

� Example of Vehicular Navigation

� INS Error Models

� INS Sensor Parameters

� Tightly Coupled Examples, 4, 8, 11, 17 States

� INS for Submarines and Ships

� Informal Discussion

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Instructor's Bio

Mohinder S. Grewal, PhD, PE, has over 35 years experience in systems identification, guidance, navigation, and control. Dr. Grewal is well known for his innovative application of Kalman filtering techniques to real world modeling problems.

Grewal co-authored Kalman Filtering Theory & Practice Using MATLAB Second Edition, Wiley & Sons, 2001. Navtech describes the book as having "excellent treatment of practical considerations involved in implementing a Kalman filter, especially with respect to numerical stability problems." The book has been widely cited by other authors and researchers. Dr. Grewal also co-authored� Global Positioning Systems, Inertial Navigation & Integration SECOND EDITION, Wiley & Sons, 2007. Grewal has published over 50 papers in IEEE and ION refereed journals and proceedings, including the Institute of Navigation's (ION) most recent "Redbook," (Volume VI) and over 250 technical reports, and holds two patents in GUS clock steering and L₁/L₅ differential bias estimation.� He serves as a reviewer for IEEE, IEE, and other national and international publishers.�

Dr. Grewal's associations include Raytheon Systems, Boeing Company, Lockheed-Martin, University of California, Riverside, staff of the U. S. Department of the Interior, Boeing and Northrop. He is Professor of Electrical Engineering at California State University, Fullerton, Senior Member of IEEE, Fellow of the Institute for the Advancement of Engineering, and member of the Institute of Navigation.� GPS World magazine selected him as one of �50+ Leaders to Watch� in its May 2007 issue.

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Selected student evaluations and comments

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

� 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. )

� Great course, great professor�lot of practical examples. Participant, SeekTech, 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 )

� (Most useful) The error/noise modeling, insight in how you can know the filter is working properly��(Participant)

� �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 )

� This was exactly what I was looking for�Thanks for gearing it towards the practical applications�(Participant, Sierra Nevada Corporation )

� The course exceeded my expectation regarding application to real-world problems� (Most useful) GPS/INS integration, tightly and loosely coupled�Excellent course and instructor.� Dr. Grewal is amazingly knowledgeable on material and real-world examples.� �(Participant, MTSI )

� Participants from an on-site course at NASA Dryden stated the following in their evaluations: (Particularly effective� �Lots of examples with well-organized materials� Hands on experience from instructor and relaying this to class�The professor�s willingness to answer questions and his ability to answer them was great.� Also, the books and notes seem to be very complete and useful�Excellent, experienced, and friendly instructor�Materials were thorough.� Instructor is very knowledgeable of material presented��

� Participants from an on-site course at China Lake (Naval Air Weapons Station) stated the following in their evaluations:� �Thanks to Professor Grewal for a great series of lectures!�� He is certainly knowledgeable and well-prepared.�� Very informative.� Excellent book and software has been provided.� Excellent visuals also.�� (Most valuable aspects of course) �The algorithms and the potential errors and how to mitigate them...�� So much useful information.�� Excellent.�� Very good--easy to understand--took time to answer questions and explanations were helpful.�� It was clear, concise.� �Having the man who wrote the book--teach the class is great.��

� ��Course met all my expectations.� Great presentation.� Instructor was extremely knowledgeable and presented information clearly, concisely at an understandable level. (Most useful will be)� INS & GPS error modeling, KF equation implementation, GPS/INS integration techniques.� Course material was logically presented with theory to implementation using MATLAB.� I will recommend this course to other colleagues.�� (Participant, Holloman AFB)

� (Most useful will be) �help in model and noise formulations and advice on different implementations, and advice on how to use metrics (K, P, innovation)...�� (Participant, Chevron )

� (Most useful will be) �knowing how solutions got derived and the applications to real world problems.� I wish I took this course many years ago.� (General comments) �Excellent.� I definitely plan to recommend especially to practitioners of GPS.� Dr. Grewal is an excellent teacher, did not bore me, kept the class interesting.� (Participant )

� (General comments) �...It was great how the presentation is tied to the textbook.� Therefore, it allows you a reference for more detail to work through on your own.� (Most useful) The Kalman filter design with GPS aided INS examples...It was very helpful to walk through actual calculations and examples.� Plus the MATLAB illustrations give you better insight, rather than just looking at equations and numbers.� (Participant, DRS Sensors & Targeting Systems )

� (General comments) �Excellent.� I definitely plan to recommend especially to practitioners of GPS.� Dr. Grewal is an excellent teacher, did not bore me, kept the class interesting.� (Participant )

� (Most useful will be) �understanding how to use the covariance matrix and residues to monitor filter performance�� (Participant )

� (Most useful will be) �Data fusion/two sensors tight coupling, UDU^T algorithm, suggestions from the experience of Dr. Grewal. Very complete and interesting.� Good notes.�� (Participant )

� (Most useful will be) �GPS clock modeling, linearization technique, GPS history and description�� (Participant )