In safety-critical robotics applications, guaranteed and practical uncertainty quantification (UQ) in perception is vital. Many existing works either offer no formal containment guarantee, rely on restrictive modeling assumptions, or focus only on pose estimation rather than a complete SLAM pipeline. This paper presents provably guaranteed UQ algorithms for 3D-3D landmark-based SLAM. The algorithms consist of three basic UQ modules: forward UQ for mapping, backward UQ for pose tracking, and pose compound. Each module produces a certified uncertainty set; when the input uncertainty bounds are deterministic, the output sets inherit deterministic guarantees, i.e., they provably contain the true poses and landmarks. Specifically, we use polytopes to represent uncertainty sets, enabling tractable computations and a unified treatment of pose uncertainty. To enhance algorithms' practical usability, we incorporate conformal prediction to calibrate measurement uncertainty from data with prescribed probability. Simulations and experiments demonstrate that the proposed algorithms provide both strong theoretical guarantees and practical usability. The code is open-sourced at https://github.com/LIAS-CUHKSZ/Polytopic-SLAM-Uncertainty-Quantification.
Neural-rendering-based SLAM relies on rendered RGB-D residuals for camera tracking and map optimization, but the reliability of these predictions can vary substantially because of sensor noise, limited observation coverage, and incomplete map representations. Without an explicit reliability estimate, unreliable residuals may adversely affect pose optimization, while frames already well explained by the current map may trigger redundant mapping updates. In this paper, we present BayesianGS-SLAM, an uncertainty-aware 3D Gaussian Splatting SLAM framework that estimates predictive color and depth uncertainty during mapping and consistently reuses it across the SLAM pipeline. Our tractable probabilistic formulation combines a sensor-noise uncertainty component with an opacity-induced map-representation component propagated through the rendering process. The resulting predictive uncertainty is used to augment mapping, normalize tracking residuals through a robust pose objective, and evaluate incoming frames using a predictive-surprise-based keyframe criterion. Unlike prior uncertainty-aware neural-rendering SLAM methods that primarily consider color uncertainty or use uncertainty only during mapping, our framework estimates predictive uncertainty for both color and depth and integrates it into mapping, tracking, and keyframe selection. Evaluations on real-world RGB-D datasets demonstrate substantially improved depth uncertainty-error ranking compared with existing uncertainty-aware SLAM methods. Moreover, the proposed keyframe-selection strategy reduces the number of selected keyframes and mapping calls while maintaining competitive tracking and rendering performance.
Monocular SLAM historically suffers from scale ambiguity and tracking failure in dynamic environments. While recent vision foundation models (VFMs) provide remarkable zero-shot depth priors, naively integrating these deterministic predictions ignores predictive uncertainty and frame-to-frame scale inconsistencies. We propose PRISM-SLAM, a real-time framework that rigorously integrates VFM priors into a structured Bayesian factor graph to achieve scale-aware, metric-consistent localization and mapping. Specifically, we introduce a Plücker Ray-Distance Factor to anchor monocular observations in absolute space within a globally consistent metric coordinate system, mathematically resolving scale drift by making the metric scale Fisher-identifiable. To handle environmental dynamics, we derive an epistemic uncertainty proxy from temporal depth consistency and formulate a Dynamic Scene Uncertainty Gating (DSUG) mechanism. This soft-gating approach probabilistically down-weights dynamic distractors without incurring the heavy computational overhead associated with traditional semantic segmentation masks. By employing a multi-process architecture that asynchronously processes VFM inference and geometric tracking, PRISM-SLAM provides verified metric output at 30 FPS using solely RGB input, bridging the gap between foundation models and real-world robotic applications. Evaluated on the TUM RGB-D and 7-Scenes benchmarks, PRISM-SLAM achieves a metric SE(3) Absolute Trajectory Error (ATE) nearly identical to its oracle-aligned Sim(3) error. This demonstrates that our system can produce deployment-ready metric trajectories by delivering robust metric SLAM solutions without any post-hoc scale correction. Project page: https://prismslam-cmd.github.io/prismslam_pr/
Visual Place Recognition (VPR) in lifelong deployment requires continuous adaptation to new environments without catastrophic forgetting. In this paper, we propose SLAM, a Structured and Localized Analytic Manifold adaptation framework. Our framework elegantly unifies uncertainty-aware smoothing via Unscented transformation, topological space partitioning through a Gaussian Mixture Model (GMM), and H∞ robust bound optimization into a singular, unified closed-form analytical recursion. Exhaustive ablation studies demonstrate that while the synergistic combination of uncertainty smoothing and localized mapping (U+G configuration) achieves the state-of-the-art nominal accuracy of 27.5%, the full deployment of the H∞ bound does not require an architectural split; rather, it introduces a mathematically guaranteed minimax robust bound. This formulation enables the system to seamlessly modulate the intrinsic trade-off between nominal placement precision and worst-case disturbance attenuation through a single regularization parameter.