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

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.