# A Quick Guide for the Iterated Extended Kalman Filter on Manifolds

arXiv: https://arxiv.org/abs/2307.09237 · HTML: https://mlsanity.com/paper/2307.09237/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [IMU-Free Body-Frame State Estimation with Sparse Scene Flow for Quadcopters](https://mlsanity.com/paper/2608.20891/) (2026)

## Abstract (arXiv)

The extended Kalman filter (EKF) is a common state estimation method for discrete nonlinear systems. It recursively executes the propagation step as time goes by and the update step when a set of measurements arrives. In the update step, the EKF linearizes the measurement function only once. In contrast, the iterated EKF (IEKF) refines the state in the update step by iteratively solving a least squares problem. The IEKF has been extended to work with state variables on manifolds which have differentiable boxplus and boxminus operators, including Lie groups. However, existing descriptions are often long, deep, and even with errors. This note provides a quick reference for the IEKF on manifolds, using freshman-level matrix calculus. Besides the bare-bone equations, we highlight the key steps in deriving them.