2024/09/15 by Zi Cong Guo, Guo, Zi Cong, James Richard Forbes +3
Computer Science · Engineering · #3D Shape Modeling and Analysis #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Robotics (cs.RO) #Robotics and Sensor-Based Localization
paper · pdf · doi:10.48550/arxiv.2409.09871
openalex publication_date 2024/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.