An Introduction to the Invariant Extended Kalman Filter [Lecture Notes]

Easton Potokar, Randal Beard, Joshua G Mangelson

Abstract:

Successfully and accurately estimating the 3D position of
a vehicle is a necessary step for any form of robotic autonomy. In a linear setting, there are straightforward optimal
(in the mean-square-error sense) solutions, such as the KF,
that provide out-of-the-box methods for estimation. Unfortunately, most systems in the real world are highly nonlinear,
and while there are many formulations of the KF that empirically work well with nonlinear systems, the KF convergence
guarantees do not apply to general nonlinear systems.
For systems tracking states that meet a minimal form of
symmetry, such as 3D rotations, the InEKF provides a stateindependent linearization that provides convergence guarantees similar to the KF. This article provides an in-depth
introduction to and tutorial on the InEKF by covering the
necessary mathematical background, providing derivations
of the InEKF’s various components, and walking step by step
through various examples of its usage. Additionally, an open
source library is provided for straightforward implementation
under a variety of process and measurement models.