 To avoid the tedious and repetitive derivations for implementing an error-state Kalman filter for a certain system, this paperproposes a generic symbolic representation for error-state Kalman filters on manifolds. 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 .
<clarity>  To avoid the tedious and repetitive derivations for implementing an error-state Kalman filter for a certain system, this paperproposes a generic symbolic representation for error-state Kalman filters on manifolds. 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 .
 In this paper, we propose a method to develop Kalman filters for such on-manifold systems. Utilizing \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 .