Course Synopsis
In this intensive 3-day course a pragmatic and non intimidating approach is taken in showing participants how to build both linear and extended Kalman filters by using numerous simplified but non trivial examples. Sometimes mistakes are intentionally introduced in some filter designs in order to show what happens when a Kalman filter is not working properly. Design examples are approached in several different ways in order to show that filtering solutions are not unique and also to illustrate various design tradeoffs. The course is constructed so that participants with varied learning styles will find the courses practical approach to filter design to be both useful and refreshing.

Key Topics

• Learn how to build both linear and extended Kalman filters
• How process noise can save many filter designs from failing
• Why some choices of filter states are better than others
• Advantages and disadvantages of filtering in different coordinate systems
• Why linear filters are sometimes better than extended filters for some nonlinear problems
• Use source code to explore issues beyond the scope of the course

Course Outline

• Numerical Techniques
  • Presentation of required background for working with Kalman filters
• Method of Least Squares
  • How to build a batch processing least squares filter
• Recursive Least Squares Filtering
  • How to make batch processing least squares filter recursive
• Polynomial Kalman Filters
  • How to apply Kalman filtering and Riccati equations with several examples
• Kalman Filters in a Non Polynomial World
  • How polynomial Kalman filters perform when they are mismatched to real world
• Continuous Polynomial Kalman Filter
  • Examples of how continuous filters can be used to help understand discrete filters
• Extended Kalman Filtering
  • How to apply extended filtering and Riccati equations to a practical example
  • Showing what can go wrong with several different design approaches
• Drag and Falling Object
  • Designing two different extended filters for this problem
• Cannon Launched Projectile Tracking Problem
  • Developing extended filters in the Cartesian and polar coordinate systems and comparing performance
  • Comparing extended and linear Kalman filters in terms of performance and robustness
• Tracking a Sine Wave
  • Developing three different filter formulations and comparing results
• Satellite Navigation (Simplified GPS Examples)
  • Determining receiver location based on range measurements to several satellites
• Biases
  • Various filtering techniques for estimating biases in a satellite navigation problem
• Linearized Kalman Filtering
  • Comparing performances and robustness of linearized and extended Kalman filters
• Miscellaneous Topics
  • Detecting filter divergence in the real world and a practical illustration of inertial aiding
• Multiple Model Filters For Estimating Frequency of Sinusoid
  • Using Bayes’s rule and the likelihood function to estimate frequency from a filter bank

Instructor
Paul Zarchan has more than 35 years of experience designing, analyzing, and evaluating missile guidance systems. He has worked as Principal Engineer for Raytheon Missile Systems Division, has served as Senior Research Engineer with the Israel Ministry of Defense and was a Principal Member of the Technical Staff for C.S. Draper Laboratory. Mr. Zarchan is currently a Member of the Technical Staff at MIT Lincoln Laboratory and is working on problems related to missile defense.

Course Materials
Fundamentals of Kalman Filtering: A Practical Approach Second Edition by Paul Zarchan and Howard Musoff plus access to all of the FORTRAN, MATLAB, and TrueBASIC source codes used in both the text and course (formatted for both IBM and Macintosh platforms)
Complete set of course notes

Who Should Attend
Managers, scientists, mathematicians, engineers and programmers at all levels who work with or need to learn about Kalman filtering. No background in Kalman filtering is assumed. The heuristic arguments and numerous examples will give managers an appreciation for Kalman filtering so that they can interact effectively with specialists. Engineers and programmers will find the detailed course material and many source code listings invaluable for both learning and reference.