Abstract

For linear systems, the well-known Kalman filter has a well-characterized behaviour that is independent of the underlying system’s trajectory in the following sense: the covariance matrix of the estimate, and the Kalman gain, are identical for all trajectories. On the other hand, for non-linear systems, due to linearizations around the estimated trajectory, the extended Kalman filter (EKF) covariance matrix, gain, and more generally behaviour, do depend on the system’s trajectory, leading to possible divergence.

For non-linear systems possessing symmetries, the invariant extended Kalman filter (IEKF) is an emerging methodology aimed at modifying the conventional EKF so as to account for those symmetries. The resulting filter’s behaviour is less (and sometimes not) dependent on the system’s trajectory, leading to improved stability and robustness properties.

In this talk, we will focus on aerospace and mobile robotics applications where the configuration space is a Lie group. The IEKF design will be detailed, along with some efficient variants of it, and some (stochastic) stability properties will be discussed. The results will be demonstrated experimentally on an attitude estimation problem for a low-cost UAV , and a scan matching SLAM problem for a mobile robot equipped with a kinect sensor and odometers.