Notes on Kalman Filter (KF, EKF, ESKF, IEKF, IESKF)
Gyubeom Im
TL;DR
This work surveys Kalman-type state estimators for time-varying systems, detailing KF, EKF, ESKF, IEKF, and IESKF. It derives predictive and corrective steps under Gaussian assumptions, explains Jacobian-based linearization, and contrasts single-shot versus iterated/corrective schemes. MAP and Gauss-Newton perspectives are connected to EKF and its variants, clarifying when iterated or error-state formulations offer practical advantages. The exposition emphasizes SLAM-relevant contexts, robustness, and computational considerations for real-time estimation in non-linear environments.
Abstract
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.