Breaking Time: A Fully Gaussian Framework for Distributed and Continuous-Time SLAM

Figure 1 : Querying continuous-time mean and covariance. G-solver GP-based trajectory estimate on a torus motion sequence. Shaded regions depict the posterior covariance, which naturally expands in segments with fewer observations and contracts where measurements are available. The model supports querying both trajectory mean and uncertainty at arbitrary timestamps.

Figure 3 : Locally linear approximation between each pair of measurement times, t_{i} and t_{i+1} , where a constant velocity model is applied. This figure illustrates the relationships between the local pose variable \boldsymbol{\xi}_{i}(t) , and the global trajectory state \{\mathbf{T}(t),\boldsymbol{\varpi}(t)\} .

Figure 13 : Rolling shutter reprojection. Reprojection of optimized 3D scene landmarks on KITTI 06 [ 17 ] under a 1 ms simulated readout time. Hyperion [ 19 ] results are shown in green and G-solver in blue . Nominal global shutter projections are shown in red . Our continuous-time Gaussian Process model explicitly accounts for row-wise exposure, producing sharper and more temporally consistent reprojections than the spline-based Hyperion approach.

Figure 2 : G-solver: Continuous-time inference via message passing. A factor graph view of our method: Gaussian Belief Propagation messages (arrows) propagate local information across the graph, while Gaussian Process priors model the trajectory continuously in time. The light-blue region illustrates the GP uncertainty envelope.

Figure 14 : Multi-camera optimization scalability. (Left) The average computation time and memory per camera graph decrease as the number of camera segments increases, as the optimization load is distributed across multiple independent subgraphs. (Right) Estimation accuracy remains stable (Absolute Trajectory Error and Absolute Rotation Error stay nearly constant), showing that distributing the optimization lowers computational cost without degrading accuracy.

Figure 6 : Ablation on Gaussian Process. Starting from a highly perturbed initial configuration (left), the trajectory optimized using only Gaussian Belief Propagation (middle) remains highly inaccurate, whereas (right) G-solver successfully recovers the helix shape thanks to Gaussian Process priors. Prior-based example with \sigma=1 , \eta_{ig}=1 (both \mathrm{[m]} and \mathrm{[rad]} ).

Figure 7 : Prior-based qualitative interpolation results. Posterior continuous-time trajectory estimates for G-solver and Hyperion (B and Z spline) for the sphere sequence, under significant perturbation and noise levels with \sigma=1 , \eta_{ig}=1 (both \mathrm{[m]} and \mathrm{[rad]} ).

Figure 8 : Prior-based experiments. Comparison of helix and sphere trajectories under varying noise levels with G-solver and Hyperion.

Figure 9 : Pose Graph Optimization experiments. Comparison of helix and sphere trajectories under varying noise levels with G-solver and Hyperion.