Moment-Matching Probabilistic Data Association for Optimization-Based SLAM

Probabilistic data association (PDA) improves semantic SLAM in perceptually aliased scenes, but existing methods often assume a fixed landmark set, recompute association weights as the map grows, or rely on hand-tuned null-hypothesis weights. To address these limitations, we propose BPDA-GMM, an online Bayesian PDA framework for semantic SLAM with a growing object-level map. BPDA-GMM uses a Dirichlet-process prior to induce a Chinese Restaurant Process (CRP) association model, where accumulated evidence favors existing landmarks, and the concentration parameter assigns probability mass to new landmarks. For each semantic detection, plausible candidates are selected by a joint semantic-geometric gate, CRP-weighted association probabilities are computed, and object landmarks are updated as semantic Gaussians in closed form. The resulting landmark set forms a Gaussian mixture model, and its dominant component is passed to the back-end as a max-mixture semantic factor. When association weights are inconclusive, an ambiguity-triggered $α$-divergence tempering step improves discrimination. Finally, a decoupled back-end zeroes the pose Jacobian of semantic factors, allowing noisy detections to refine landmarks without directly perturbing the trajectory. Experiments in simulation and on a real indoor dataset demonstrate improved trajectory accuracy, semantic mapping quality, and robustness to perceptual aliasing and classifier errors over state-of-the-art baselines. Code and video are publicly available at https://github.com/thanhnguyencanh/BPDA-SLAM.

Data association between landmark measurements and landmark variables has long been a central challenge in SLAM, as estimation accuracy depends critically on associating measurements with the correct landmark variables. Recent advances in deep learning have created new opportunities for the problem; data association can now leverage not only positional measurements but also semantic information about object landmarks, such as class labels from neural object detectors and feature vectors from visual foundation models. In this paper, we present a generalized data-association-free SLAM framework that jointly estimates data associations, robot poses, landmark positions, and landmark semantics from odometry, and positional and semantic measurements of landmarks. The proposed framework (i) creates a synergy between data association and landmark semantics estimation; (ii) adopts a semi-incremental estimation scheme for improved accuracy and computational efficiency; and (iii) provides a principled justification, guidelines, and heuristics for landmark-number estimation, improving the interpretability and practical usability of the framework. The proposed framework and algorithms are evaluated on synthetic and real-world datasets with two types of semantic information, class labels and real-valued feature vectors, and demonstrate superior performance compared to strong baselines.

Simultaneous localization and mapping (SLAM) is a foundational state estimation problem in robotics in which a robot accurately constructs a map of its environment while also localizing itself within this construction. We study the active SLAM problem through the lens of optimal stochastic control, thereby recasting it as a decision-making problem under partial information. After reviewing several commonly studied models, we present a general stochastic control formulation of active SLAM together with a rigorous treatment of motion, sensing, and map representation. We introduce a new exploration stage cost that encodes the geometry of the state when evaluating information-gathering actions. This formulation, constructed as a nonstandard partially observable Markov decision process (POMDP), is then analyzed to derive rigorously justified approximate solutions that are near-optimal. To enable this analysis, the associated regularity conditions are studied under general assumptions that apply to a wide range of robotics applications. For a particular case, we conduct an extensive numerical study in which standard learning algorithms are used to learn near-optimal policies.