# Fundamentals of Kalman Filtering - A Practical Approach

#### Synopsis:

In this intensive short 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
• Why linear filters are sometimes better than extended filters for some nonlinear problems
• Use MATLAB source code to explore issues beyond the scope of the course
• Click below for full outline

#### 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. Engineers and programmers will find the detailed course material and many MATLAB source code listings invaluable for both learning and reference.

#### Course Information:

Type of Course: Instructor-Led Short Course
Course Level: Fundamentals/Intermediate
Course Length: 2, 3, or 4 days
AIAA CEU's available: Yes

Outline

I. Numerical Techniques

II. Presentation of required background for working with Kalman filters
A. Method of Least Squares

III. How to build a batch processing least squares filter
A. Recursive Least Squares Filtering

IV. How to make batch processing least squares filter recursive
A. Polynomial Kalman Filters

V. How to apply Kalman filtering and Riccati equations and relationship to recursive least squares filter
A. Kalman Filters in a Non Polynomial World

VI. How polynomial Kalman filters perform when they are mismatched to real world
A. Continuous Polynomial Kalman Filter

VII. Using transfer functions to represent and understand Kalman filters
A. Extended Kalman Filtering
VIII. How to apply extended filtering and Riccati equations to a practical example
A. Drag and Falling Object

IX. Designing two different extended filters for this problem and importance of process noise
A. Cannon Launched Projectile Tracking Problem

X. Developing extended and linear filters in the Cartesian and polar coordinate systems
A. Tracking a Sine Wave

XI. Developing three different filter formulations and comparing results
A. Satellite Navigation (Simplified GPS Examples)

XII. Extended Kalman filtering and a step by step approach to determining receiver location based on range measurements to several satellites
A. Biases

XIII. Various filtering techniques for estimating biases in a satellite navigation problem
A. Linearized Kalman Filtering

XIV. Comparing performances and robustness of linearized and extended Kalman filters
A. Miscellaneous Topics
B. Filter divergence in the real world and a practical illustration of inertial aiding

XV. Filter Banks
A. How filter banks can be used to improve estimation quality

Materials
Instructors

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 missile defense as a Member of the Technical Staff for MIT Lincoln Laboratory. He is author of Tactical and Strategic Missile Guidance, Fifth Edition and co-author of Fundamentals of Kalman Filtering: A Practical Approach Third Edition, both of which are books in the AIAA Progress in Astronautics and Aeronautics Series.