The Kalman filter—or, more precisely, the extended Kalman filter (EKF)—is a fundamental
engineering tool that is pervasively used in control and robotics and for various estimation …

Legged robots require knowledge of pose and velocity in order to maintain stability and
execute walking paths. Current solutions either rely on vision data, which is susceptible to …

Equivariance is a common and natural property of many nonlinear control systems,
especially those associated with models of mechatronic and navigation systems. Such …

We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when
the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time …

Recent advances in the utilization of Lie Groups for robotic localization have led to dramatic
increases in the accuracy of estimation and uncertainty characterization. One of the novel …

This paper presents the theory of invariant observers, ie, symmetry-preserving observers.
We consider an observer to consist of a copy of the system and a correction term, and we …

The present thesis explores the use of non-linear state errors to devise extended Kalman
filters (EKFs). First we depart from the theory of invariant observers on Lie groups and …

A new version of the extended Kalman filter (EKF) is proposed for nonlinear systems
possessing symmetries. Instead of using a linear correction term based on a linear output …

A nonlinear observer (ie a “filter”) is proposed for estimating the attitude of a flying rigid body,
using measurements from low-cost inertial and magnetic sensors. It has by design a nice …

This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system
on a matrix Lie group with invariance properties. The problem of an invariant continuous …