RICH-SLAM: Radar SLAM with Incremental and Continuous Hilbert Mapping

Figure 1: Overview of the RICH-SLAM framework. Radar Doppler and range measurements pass through a multi-criteria front-end filter that rejects outliers and outputs a set of filtered radar beams. The filtered beams and the odometry are fed into the Rao-Blackwellized particle filter back end, which jointly estimates the robot pose and a per-particle continuous occupancy map. The framework outputs the position and heading together with a dense continuous occupancy map and its predictive uncertainty field.

Figure 2: Radar computation flow within one RBPF iteration at time step i . The fixed Hilbert basis is shared across all particles, whereas each particle maintains its own map posterior (dashed box), updated by the Kalman filter and reused as the prior at step i{+}1 . The odometry-driven particle propagation is omitted for clarity.

Figure 4: Experimental setup of self-collected dataset. The vehicle is equipped with a radar sensor and an IMU. Experimental validation was performed in a controlled indoor environment using a motion capture system to provide ground-truth poses.

Figure 6: The area under the receiver operating characteristic curve (AUC) values versus different numbers of map features. For Hilbert-GP , this number denotes the retained Hilbert-space basis functions; for RFF , Sparse , and Nyström , it denotes the feature components used by the corresponding map representation. Hilbert-GP achieves consistently high AUC with compact map representations, while the SGD-based baselines exhibit larger variance across datasets.

Figure 7: Mapping results under different length scales and signal variances. White regions correspond to locations not included in the queried map domain, rather than free space. The length scale controls the spatial smoothness of the occupancy field: a small length scale preserves local variation but can produce fragmented structures, whereas a large length scale over-smooths the map and spreads high occupancy probability over broad regions. The signal variance controls the amplitude of the latent occupancy function and affects the contrast and confidence of the predicted occupancy map. AUC

Figure 11: Comparisons of the localization performance on six representative sequences. Circles and squares represent the starting and ending points of the trajectories, respectively.

Figure 12: Path planning results on a partial RICH-SLAM map on ColoRadar 6. The left figure shows occupancy probability and the right one shows normalized predictive uncertainty. The red curve denotes the greedy deterministic path, and the purple curve denotes the uncertainty-aware path. Circles and squares denote start and goal positions, respectively. Although the greedy path follows a shorter route through a region that appears traversable in the occupancy map, the uncertainty-aware path avoids the high-uncertainty region and selects a longer but more reliable route, indicating that RICH-SL