# Notes on Kalman Filter (KF, EKF, ESKF, IEKF, IESKF)

arXiv: https://arxiv.org/abs/2406.06427 · HTML: https://mlsanity.com/paper/2406.06427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2024.

## 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 Kalman Filter (KF) is a powerful mathematical tool widely used for state estimation in various domains, including Simultaneous Localization and Mapping (SLAM). This paper presents an in-depth introduction to the Kalman Filter and explores its several extensions: the Extended Kalman Filter (EKF), the Error-State Kalman Filter (ESKF), the Iterated Extended Kalman Filter (IEKF), and the Iterated Error-State Kalman Filter (IESKF). Each variant is meticulously examined, with detailed derivations of their mathematical formulations and discussions on their respective advantages and limitations. By providing a comprehensive overview of these techniques, this paper aims to offer valuable insights into their applications in SLAM and enhance the understanding of state estimation methodologies in complex environments.