Kalman Filters on Differentiable Manifolds

Understand

Kalman filter is presumably one of the most important and extensively used filtering techniques in modern control systems.

• Yet, nearly all current variants of Kalman filters are formulated in the Euclidean space $\mathbb{R}^n$, while many real-world systems (e.g., robotic systems) are really evolving on manifolds.
• In this paper, we propose a method to develop Kalman filters for such on-manifold systems.
• Utilizing $\boxplus$, $\boxminus$ operations and further defining an oplus operation on the respective manifold, we propose a canonical representation of the on-manifold system.