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

Kalman filters (KFs) have become ubiquitous in modern-day technology with applications in medicine, robotics, and many others due to their straightforward implementation and impressive performance. Unfortunately, when KFs are extended for use with nonlinear systems, optimality is often no longer guaranteed and the asymptotic convergence guarantee is also lost. The Invariant Extended Kalman Filter (InEKF) is a recent extension of the KF for Lie Groups that provides log-linear error dynamics and restores the asymptotic convergence guarantee. This article provides an in-depth introduction and tutorial to the InEKF by covering the necessary mathematical background, providing derivations of its various components, and walking step by step through various examples of its usage.