“An Introduction to the Kalman Filter” by Welch and Bishop

  • ©Gregory (Greg) Welch and Gary Bishop


Entry Number: 08


    An Introduction to the Kalman Filter

Course Organizer(s):



    Basic linear algebra. A basic mathematical background sufficient to understand explanations that involve introductory statistics and random signals.

    An intuitive explanation of the filter. The origins and formulations of the filter equations. Practical use of the filter. Approaches for non-linear systems. A brief introduction of advanced topics such as sensor, information, and data fusion; sensitivity and stability concerns; system identification (tuning); multi-modal (multiple-model) approaches; and optimal smoothing.

    The 40-year-old Kalman filter and related optimal estimators continue to appear in a wide variety of computer graphics applications, such as simulating musical instruments in virtual reality, head tracking and motion capture, extracting lip motion from video sequences of speakers, and fitting spline surfaces over collections of points. The Kalman filter is an optimal estimator for a large class of problems and a very effective and useful estimator for an even larger class. In its most basic form it is also relatively simple to use and understand. This tutorial presents an intuitive approach that enables developers to approach the extensive literature with confidence.