PAIRS Lab

RA-L 2026 IEEE Robotics and Automation Letters · Vol. 11, No. 10

BPDA-GMM

Bayesian Probabilistic Data Association via Gaussian Mixture Models for Semantic SLAM

Thanh Nguyen Canh1, Haolan Zhang1, Antonio Sgorbissa2, Xiem HoangVan3, Nak Young Chong1,4

1Japan Advanced Institute of Science and Technology   2DIBRIS, University of Genoa   3VNU University of Engineering and Technology   4Hanyang University

Paper arXiv Code Video
Outdoor Loop: BPDA-GMM (cyan) stays on the ground-truth loop while baselines drift.

01 · Abstract

Is this an object already in the map, or a new one?

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.

We propose BPDA-GMM, an online Bayesian PDA framework for semantic SLAM with a growing object-level map. A Dirichlet-process prior induces a Chinese Restaurant Process (CRP) association model: accumulated evidence favors existing landmarks, and the concentration parameter reserves probability for new ones. Each detection is gated semantically and geometrically, assigned CRP-weighted association probabilities, and fused into semantic Gaussian landmarks in closed form. The landmarks form a Gaussian mixture whose dominant component enters the back-end as a max-mixture factor. When weights are inconclusive, ambiguity-triggered α-divergence tempering sharpens them, and a decoupled back-end lets noisy detections refine landmarks without perturbing the trajectory.

Experiments in simulation and on a real indoor dataset show better trajectory accuracy, semantic mapping quality and robustness to perceptual aliasing and classifier errors than state-of-the-art baselines.

02 · Video

BPDA-GMM in five minutes

03 · Method

From one detection to a consistent object map

BPDA-GMM system overview: each semantic detection passes a semantic-geometric gate, receives CRP-weighted association probabilities, updates semantic Gaussian landmarks, and the dominant component is added to a decoupled pose-landmark back-end.
Fig. 1: BPDA-GMM system overview.
  1. 1

    Semantic–geometric gate

    Only landmarks that are close in space and plausible in class survive as candidates for a detection.

  2. 2

    CRP association weights

    A Dirichlet-process prior weighs existing landmarks by accumulated evidence and keeps a principled chance for a new landmark, with no hand-tuned null weight.

  3. 3

    Semantic Gaussian update

    Each landmark is a Gaussian over position and class, updated in closed form; together they form a Gaussian mixture map.

  4. 4

    Tempering when ambiguous

    If association weights are inconclusive, α-divergence tempering sharpens them instead of committing to a guess.

  5. 5

    Decoupled back-end

    The dominant component becomes a max-mixture factor whose pose Jacobian is zeroed, so noisy detections refine landmarks without bending the trajectory.

  6. 6

    CRP loop closure

    Re-identifying landmarks with the same CRP model closes semantic loops on revisits.

04 · Simulation benchmark

Five scenarios, seven methods

From a small figure-eight to Victoria Park with 151 landmarks. Pick a scenario and a metric; the chart and table update together.

Trajectory estimates on the benchmark scenarios over time.
Estimated trajectories of BPDA-GMM and baselines on all benchmark scenarios; BPDA-GMM stays close to ground truth.
Fig. 3: Estimated trajectories on all benchmark scenarios.

05 · Real indoor dataset

Fewer duplicate objects, more correct ones

Object-level map quality on a real indoor sequence with 84 ground-truth objects in five classes (chair, table, monitor, fridge, plant).

Object-map F1 scoreoverall, all classes · higher is better
Qualitative object-map comparison on the real indoor sequence: BPDA-GMM produces a compact semantic map with fewer duplicate landmarks.
Fig. 5: Qualitative object-map comparison on the real indoor sequence.

06 · Analysis

Fast, and every part matters

Processing time per keyframemean, ms · lower is better
Ablation on City10000ATE · lower is better

07 · Cite

Citation

@article{canh2026bpdagmm,
  title   = {Bayesian Probabilistic Data Association via Gaussian Mixture Models for Semantic SLAM},
  author  = {Canh, Thanh Nguyen and Zhang, Haolan and Sgorbissa, Antonio and HoangVan, Xiem and Chong, Nak Young},
  journal = {IEEE Robotics and Automation Letters},
  volume  = {11},
  number  = {10},
  pages   = {11378--11385},
  year    = {2026},
  doi     = {10.1109/LRA.2026.3726389}
}