Alternate Derivation of Geometric Extended Kalman Filter by MEKF Approach

TL;DR

This paper derives the measurement update of the geometric extended Kalman filter using the MEKF approach, establishing their equivalence and resulting in a geometric multiplicative extended Kalman filter for attitude estimation.

Contribution

It provides a new derivation of the geometric EKF measurement update via the MEKF approach, demonstrating their equivalence.

Findings

Derived the measurement update of the geometric EKF using MEKF approach

Proved the equivalence between geometric EKF and geometric MEKF

Introduced the geometric multiplicative extended Kalman filter for attitude estimation

Abstract

This note is devoted to deriving the measurement update of the geometric extended Kalman filter using the multiplicative extended Kalman filtering approach, resulting in the attitude estimator referred as geometric multiplicative extended Kalman filter. The equivalence of the derived geometric multiplicative extended Kalman filter and geometric extended Kalman filter is also demonstrated in this note.