Moment-Matching Probabilistic Data Association for Optimization-Based SLAM

Khoa Nguyen; Mitchell Turton; Florian Meyer

cs.ROSep 5, 2026

Moment-Matching Probabilistic Data Association for Optimization-Based SLAM

Authors: Khoa Nguyen, Mitchell Turton, Florian Meyer

Organizations: Department of Electrical and Computer Engineering, University of California San Diego, USA · Georgia Institute of Technology, Atlanta, GA

Abstract

Optimization-based simultaneous localization and mapping (SLAM) makes it possible to reduce accumulated navigation errors of sensing platforms by returning to known areas (loop closure). In this paper, we present an approach to combine probabilistic data association (PDA) with optimization-based SLAM. Instead of associating a single measurement with each landmark, we follow the PDA paradigm from the multiobject tracking community. In particular, in a processing stage performed in addition to the nonlinear least-squares solver of optimization-based SLAM, our method (i) assigns multiple measurements to landmarks probabilistically, (ii) computes the mean and covariance of landmark distributions via moment matching by taking multiple measurement-to-landmark associations into account, and (iii) establishes a virtual landmark measurement and a corresponding linear-Gaussian measurement model that leads to the mean and covariance matrix as moment-matching PDA in (ii). By converting the PDA update step into an equivalent linear-Gaussian measurement update step, PDA can be performed effectively within any optimization-based SLAM method. Our preliminary numerical evaluation in a scenario with false negatives and false positives indicates that incremental smoothing and mapping 2 (iSAM2), combined with the proposed PDA approach, can improve agent localization performance compared to conventional iSAM2.

Figures & tables

Fig. 1 : Flow diagram showing the proposed pipeline for integrating PDA with optimization-based SLAM.

Panel of Figure 2 — Fig. 2 : Comparison of agent state estimation results using different association strategies. The agent follows a repeated figure-eight trajectory. Ground truth is shown in black. Estimated trajectories are shown in green for oracle batch SLAM, blue for DA + iSAM2, and red for PDA + iSAM2. Landmark estimates are shown as dots with uncertainty ellipses.

Fig. 3 : Comparison of mean absolute error for different association strategies for different FP and FN settings, parameterized by the probability of detection

p_{\mathrm{d}}

and mean number of FPs

\mu_{\mathrm{fp}}

$(p_{\mathrm{d}},\mu_{\mathrm{fp}})$	PDA + iSAM2	DA + iSAM2	Batch (Oracle)
$(0.9,0.02)$	1.182 m	5.643 m	0.536 m
$(0.8,0.05)$	1.595 m	7.688 m	0.539m
$(0.7,0.10)$	1.887 m	9.761 m	0.572 m
$(0.6,0.20)$	2.515 m	11.961 m	0.513 m

TABLE I : Mean absolute error (in meters) for different

(p_{\mathrm{d}},\mu_{\mathrm{fp}})

parameter settings.

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BPDA-GMM: Bayesian Probabilistic Data Association via Gaussian Mixture Models for Semantic SLAM

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School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa, 923-1211, Japan · University of Engineering and Technology, Vietnam National University, Hanoi, 10000, Vietnam

Simultaneous Localization and Mapping Dirichlet Process Mixture Models

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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.

Abstract

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