On the Existence of Linear Observed Systems on Manifolds with Connection
<|reference_start|>On the Existence of Linear Observed Systems on Manifolds with Connection: Linear observed systems on manifolds are a special class of nonlinear systems whose state spaces are smooth manifolds but possess properties similar to linear systems. Such properties can be characterized by the ability to conduct preintegration and exact linearization with Jacobians independent of the linearization point. IMU dynamics in navigation can be constructed into linear observed settings, leading to invariant filters with guaranteed behaviors such as local convergence and consistency. In this letter, we establish linear observed property for dynamics evolving on an arbitrary smooth manifold through the connection structure endowed upon this space. Our key findings are the existence of linear observed systems on manifolds poses strong constraints on the state space itself, apart from requiring the dynamics to be in some specific forms. The existence of such systems is equivalent to the flatness of the state space, forcing the manifold to admit a group structure under mild topological assumptions.<|reference_end|>
@article{liu2024on,
    title={On the Existence of Linear Observed Systems on Manifolds with Connection},
    author={Changwu Liu, Yuan Shen},
    journal={arXiv preprint arXiv:2408.15497},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.15497},
    primaryClass={eess.SY cs.SY}
}