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Session 1520

Teaching Kalman Filters To Undergraduate Students

Andrew Love Johns Hopkins University Applied Physics Laboratory

Maurice Aburdene, Rami William Zarrouk Bucknell University

Abstract

The Kalman filter algorithm is one of the most common estimation techniques used today, yet generally engineers do not encounter it until they have begun their graduate or professional careers, even though the concepts necessary to understand it are introduced to sophomore engineering students. This paper presents an approach intended to take undergraduate students from the concept of an average to Kalman filters in a half dozen small steps. Using MATLAB or MathCAD provides some advantages in teaching the Kalman algorithm since in those languages the algorithm can fit on two pages even with extensive commenting, and the syntax of these languages does not obscure the structure of the algorithm.

I. Introduction

Kalman filtering1 is a widely used technique for process control and evaluation of mechanical, electrical, chemical, and medical systems2-12, but this technique is not often taught at an undergraduate level. This is unfortunate because issues such as instrument noise, system noise, and systems models are very important to working engineers, and Kalman filters provide a convenient framework for discussing each of these issues. Furthermore, undergraduate engineering students learn all the mathematics necessary to use the Kalman filter equations (matrix differential equations and the concept of uncertainty), if not to derive them, by their sophomore or junior year, so there is no reason not to give them the opportunity to apply this knowledge. We present an approach that was used to introduce the Kalman filter concept to first semester electrical engineering juniors in a linear systems course. Rather than simply introducing the Kalman filter equations as given in the texts2-8, 10-12, however, we have found it effective to begin with the idea of an average, and add features until the general Kalman filter is developed.

II. Averaging

The lesson begins with the introduction of a problem to be solved: determining resistance of a circuit to high accuracy with a measurement device that is not accurate enough. First, we show the 15 measurements that have been taken, which show that the measurement device has errors of about 500 ohms, about 4 times too inaccurate for the (assumed) purpose at hand. At this

“Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright © 2001, American Society for Engineering Education”

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Zarrouk, R., & Love, A., & Aburdene, M. F. (2001, June), Teaching Kalman Filters To Undergraduate Students Paper presented at 2001 Annual Conference, Albuquerque, New Mexico. 10.18260/1-2--9870