Abstract

The Kalman filter, or more precisely the extended Kalman filter (EKF), is a fundamental engineering tool that is pervasively used in control, robotics, and for various estimation tasks in autonomous systems. The recent field of Invariant extended Kalman filtering, aims at using the geometric structure of the state space and the dynamics to improve the EKF , notably in terms of mathematical guarantees. The methodology essentially applies in the field of localization, navigation, and simultaneous localization and mapping (SLAM) where it is proved to resolve the well-known inconsistencies of the conventional EKF . Albeit recent, its remarkable robustness properties have already prompted a true industrial implementation in the aerospace field.

This talk aims to provide an intuitive introduction to the methodology of invariant Kalman filtering, to underline what the important differences with the conventional EKF are, and to give the main reasons why it resolves the EKF consistency issues for SLAM . This should be of interest to students or researchers intrigued by the application of mathematical theories to practical applications, or interested in finding simple to implement and robust filters for localization, navigation, and SLAM , notably for autonomous vehicle guidance.