Marginalizing and Conditioning Gaussians onto Linear Approximations of Smooth Manifolds with Applications in Robotics
<|reference_start|>Marginalizing and Conditioning Gaussians onto Linear Approximations of Smooth Manifolds with Applications in Robotics: We present closed-form expressions for marginalizing and conditioning Gaussians onto linear manifolds, and demonstrate how to apply these expressions to smooth nonlinear manifolds through linearization. Although marginalization and conditioning onto axis-aligned manifolds are well-established procedures, doing so onto non-axis-aligned manifolds is not as well understood. We demonstrate the utility of our expressions through three applications: 1) approximation of the projected normal distribution, where the quality of our linearized approximation increases as problem nonlinearity decreases; 2) covariance extraction in Koopman SLAM, where our covariances are shown to be consistent on a real-world dataset; and 3) covariance extraction in constrained GTSAM, where our covariances are shown to be consistent in simulation.<|reference_end|>
@article{guo2024marginalizing,
    title={Marginalizing and Conditioning Gaussians onto Linear Approximations of
  Smooth Manifolds with Applications in Robotics},
    author={Zi Cong Guo, James R. Forbes, Timothy D. Barfoot},
    journal={arXiv preprint arXiv:2409.09871},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.09871},
    primaryClass={cs.RO}
}