Fundamentals of Kalman Filtering:
A Practical Approach

Instructor: Paul Zarchan, MIT Lincoln Lab

Daniel Hotel, Herzlia

March 9-11, 2010

Summary:

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. Attendees will receive a complete set of course notes.
The course language is English.

About the Course Instructor:

Paul Zarchan has more than
40 years of experience designing, analyzing, and evaluating missile guidance
systems. He has worked as Principal Engineer for Raytheon Mission Systems
Division and has served as Senior Research Engineer with the Israel Ministry of
Defense and has worked as Principal Member of the Technical Staff at C.S.
Draper Laboratory. Mr. Zarchan is currently working
on problems related to theater missile defense as a Member of the Technical
Staff for MIT Lincoln Laboratory. He is an Associate Fellow of AIAA, author of
Tactical and Strategic Missile Guidance, Fourth Edition and co-author of Fundamentals
of Kalman Filtering: A Practical Approach Second
Edition, both of which are books in the AIAA Progress in Astronautics and
Aeronautics Series.

**Who
Should Attend:**

Engineers,
scientists, mathematicians, programmers and managers at all levels who work
with or need to learn about Kalman filtering. No background in Kalman
filtering is assumed. The Kalman Filter is a
versatile tool that has found numerous applications in control, navigation,
signal processing, computer vision, forecasting, and financial engineering. The
course will provide a basic understanding of the Kalman
Filter principles and applications, that should be of
interest to anyone working in the above-mentioned areas. Engineers and programmers will find the
detailed course material and many source code listings (FORTRAN, MATLAB and TrueBASIC) invaluable for both learning and reference.

**Course
Outline:**

**1.
****Numerical Techniques**. Presentation of the mathematical background required for
working with Kalman filters. Numerous examples to illustrate
all important techniques.

**2.
****Method of Least Squares**. How to build a batch processing least squares filter
using the original method developed by Gauss. Illustration of various
properties of the least squares filter.

**3.
****Recursive Least Squares Filtering**. How to make the batch processing least squares filter
recursive. Develop closed-form solutions for the variance reduction and
truncation error growth associated with different order filters.

**4.
****Polynomial Kalman
Filters**. Showing the relationship between
recursive least squares filtering and Kalman
filtering. How to apply Kalman filtering and Riccati equations to different real world problems with
several examples.

**5.
****Kalman**** Filters in a Non
Polynomial World**. How polynomial Kalman filters perform when they are mismatched to real
world. How process noise can fix broken filters.

**6.
****Continuous Polynomial Kalman
Filter**. Illustrating the relationship
between continuous and discrete Kalman filters.
Examples of how continuous filters can be used to help understand discrete
filters through such concepts as transfer function and bandwidth.

**7.
****Extended Kalman
Filtering**. How to apply extended Kalman filtering and Riccati
equations to a practical nonlinear problem in tracking. Showing what can go
wrong with several different design approaches and how to get designs to work.
Why choice of states can be important in a nonlinear filtering problem.

**1.
****Drag and Falling Object**. Designing two different extended filters for this
problem.

**2.
****Cannon Launched Projectile Tracking Problem**. Developing extended filters in the Cartesian and polar
coordinate systems and comparing performance. Showing why one must not always
pay attention to the academic literature. Comparing extended and linear Kalman filters in terms of performance and robustness.

**3.
****Tracking a Sine Wave**. Developing three different extended Kalman
filter formulations and comparing performance of each in terms of robustness.

**4.
****Satellite Navigation (Two-Dimensional GPS
Examples)**. Determining receiver location
based on range measurements to several satellites. Showing how receiver
location can be determined without any filtering at all. How satellite spacing
influences performance. Illustration of filter performance for both stationary
and moving receivers.

**5.
****Biases**.
Filtering techniques for estimating biases in a satellite navigation problem.
How adding extra satellite measurements helps alleviate bias problem.

**6.
****Linearized**** Kalman Filtering**.
Develop equations for linearized Kalman
filter and illustrate performance with examples. Comparing performances and
robustness of linearized and extended Kalman filters.

**7. ****Miscellaneous
Topics**. Detecting filter divergence in the
real world and a practical illustration of inertial aiding.

**Under the auspices of IEEE Israel, CS/CAS Chapter**