Before revision:  Utilizing the \boxplus \backslash \boxminus operations and further defining a \oplus operation on the respective manifold, we propose a canonical representation of the robotic system, which enables us to separate the manifold structures from the system descriptions in each step of the Kalman filter, ultimately leading to a generic , symbolic and manifold-embedding Kalman filter framework .
After revision:  Utilizing the \boxplus \backslash \boxminus operations and further defining a \oplus operation on the respective manifold, we propose a canonical representation of the on-manifold system. Such a canonical form enables us to separate the manifold structures from the system descriptions in each step of the Kalman filter, ultimately leading to a generic , symbolic and manifold-embedding Kalman filter framework .