2023/07/18 by Jianzhu Huai, Xiang Gao, Huai, Jianzhu +1 · 1 citation
Computer Science · Engineering · #FOS: Electrical engineering #Inertial Sensor and Navigation #Matrix Theory and Algorithms #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2307.09237
openalex publication_date 2023/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.