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arxiv: 2603.03559 · v2 · pith:52DBO4PTnew · submitted 2026-03-03 · 📡 eess.SP

Probabilistic Occupancy Grid for Radio-Based SLAM

Xuhong Li , Erik Leitinger , Fredrik Tufvesson , Florian Meyer This is my paper

Pith reviewed 2026-05-21 11:15 UTC · model grok-4.3

classification 📡 eess.SP
keywords probabilistic occupancy gridradio-based SLAMmultipath measurementssimultaneous localization and mappingRF sensingreflection coefficients6G sensing
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The pith

A probabilistic occupancy grid framework enables joint radio-based localization and mapping of extended objects with complex geometries.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a new map representation for radio sensing that uses occupancy grids instead of simple point or plane models. The grid cells track occupancy probabilities and connect to radio measurements via a surface model for reflections. Material properties are encoded as reflection coefficients within the grid. When embedded in a SLAM algorithm, the method jointly estimates agent position and builds the map from multipath signals. Simulation results confirm that geometry and properties are recovered accurately alongside precise localization.

Core claim

The proposed occupancy grid map representation is integrated into a multipath-based SLAM formulation to enable simultaneous mobile-agent localization and environment mapping using multipath measurements. To connect RF measurements with the grid map, a surface model is employed to describe candidate reflection paths, while occupancy grid cell states capture measurement uncertainties and fine-grained geometric details. RF-related object properties are represented through reflection coefficients. The framework offers a principled approach to physically interpretable radio-based mapping.

What carries the argument

Probabilistic occupancy grid integrated with multipath-based SLAM, using a surface model for reflection paths and reflection coefficients for RF properties.

If this is right

  • Simulations demonstrate accurate reconstruction of geometry and material properties.
  • High-accuracy localization is achieved simultaneously with mapping.
  • Prior occupancy maps from other devices or sensors can extend and refine the map.
  • Complex extended objects can be represented beyond simplified geometric assumptions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This approach could support more robust environmental perception in future wireless systems by handling realistic object shapes.
  • Combining radio maps with data from other sensors might further improve accuracy in challenging environments.
  • Extensions to dynamic environments could test the framework's scalability.

Load-bearing premise

The surface model for candidate reflection paths accurately links RF measurements to specific occupancy grid cells without large unmodeled errors or biases.

What would settle it

A test case with known complex object geometry where the estimated occupancy probabilities or reflection coefficients show systematic mismatches with the true surface properties under varying multipath conditions.

Figures

Figures reproduced from arXiv: 2603.03559 by Erik Leitinger, Florian Meyer, Fredrik Tufvesson, Xuhong Li.

Figure 1
Figure 1. Figure 1: (a) Geometrical depiction of a distributed multiple-input [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Factor graph representation of the joint posterior PDF (3). (a) shows the message propagation between the subgraphs, as well as [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Performance results using synthetic D-MIMO measurements. (a) Geometrical depiction of the simulation environment and setup. (b) [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Results of a simulation run for agent 1. The estimated surfaces, propagation paths and agent track are shown for time n = 173. The estimated surfaces are computed using the MMSE estimates of the detected SFVs. Estimated propagation paths are obtained by connecting the MMSE estimates of the agent position, interaction points on the estimated surfaces and PAs, and compared with the true visible paths. The co… view at source ↗
read the original abstract

Sensing is an integral part of 6G and beyond systems, providing exceptional environmental perception along with communication. Radio frequency (RF)-based sensing often relies on simplified geometric assumptions (e.g., point scatterers or planar surfaces) to model specular multipath and keep inference tractable. However, such representations are limited in their ability to capture extended objects with complex geometries and properties. This paper presents a probabilistic occupancy grid framework for radio-based simultaneous localization and mapping (SLAM), jointly reconstructing geometric structures and their RF-related properties. The proposed occupancy grid map representation is integrated into a multipath-based SLAM formulation to enable simultaneous mobile-agent localization and environment mapping using multipath measurements. To connect RF measurements with the grid map, a surface model is employed to describe candidate reflection paths, while occupancy grid cell states capture measurement uncertainties and fine-grained geometric details. RF-related object properties are represented through reflection coefficients. The proposed framework offers a principled, proof-of-concept approach to physically interpretable radio-based mapping, and simulation results demonstrate accurate reconstruction of geometry and material properties, as well as high-accuracy localization. In addition, the results highlight the potential to use prior occupancy maps obtained from other radio devices or complementary sensors for subsequent map extension and refinement.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper proposes a probabilistic occupancy grid framework for radio-based SLAM that integrates a surface model to connect multipath RF measurements to grid cells, enabling joint localization of a mobile agent and mapping of geometric structures along with their RF properties such as reflection coefficients. The approach is presented as a proof-of-concept with simulation results showing accurate reconstruction of geometry and material properties as well as high-accuracy localization, and it discusses the use of prior occupancy maps for map extension.

Significance. If the central claims hold, the work provides a more expressive map representation than point scatterers or planar surfaces for capturing extended objects with complex geometries in RF sensing. This could meaningfully advance integrated sensing and communication in 6G systems by enabling physically interpretable joint inference of occupancy, geometry, and material properties from multipath measurements. The simulation-based demonstration offers initial evidence of feasibility, and the potential for incorporating prior maps from other sensors is a practical strength.

major comments (1)
  1. [Surface model and measurement likelihood sections] The surface model used to associate candidate reflection paths with grid-cell states (occupancy and reflection coefficient) is load-bearing for the joint inference claim. If this model implicitly assumes locally planar or point-like reflectors and neglects effects such as diffraction, diffuse scattering, or intra-cell geometry variation, the measurement likelihoods become mis-specified; the manuscript should include an explicit analysis or ablation of sensitivity to such model mismatch, as the reported simulations appear to employ the same surface model.
minor comments (2)
  1. [Abstract] The abstract states that simulation results demonstrate accurate reconstruction but omits details on error bars, comparison baselines, or data exclusion rules; adding these would allow better evaluation of the quantitative support for the joint mapping and localization claims.
  2. Notation for grid-cell states and reflection coefficients should be defined consistently when first introduced to improve readability for readers unfamiliar with occupancy grid literature.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive review. The major comment raises a valid point about the assumptions underlying the surface model. We address it below and will revise the manuscript to incorporate an explicit sensitivity analysis.

read point-by-point responses

  1. Referee: [Surface model and measurement likelihood sections] The surface model used to associate candidate reflection paths with grid-cell states (occupancy and reflection coefficient) is load-bearing for the joint inference claim. If this model implicitly assumes locally planar or point-like reflectors and neglects effects such as diffraction, diffuse scattering, or intra-cell geometry variation, the measurement likelihoods become mis-specified; the manuscript should include an explicit analysis or ablation of sensitivity to such model mismatch, as the reported simulations appear to employ the same surface model.

    Authors: The surface model is based on geometric ray-tracing principles to associate specular multipath components with candidate reflection locations on the occupancy grid, enabling the joint estimation of cell occupancy and reflection coefficients. The probabilistic formulation of the grid is designed to absorb some model uncertainties through the occupancy probabilities and per-cell material parameters. We acknowledge, however, that the current simulations generate and process data under the identical surface model, and that an explicit robustness study against mismatches such as diffraction, diffuse scattering, or sub-cell geometric variation is absent. In the revised manuscript we will add a dedicated subsection under Numerical Results that performs controlled mismatch experiments (e.g., injecting diffuse scattering components and perturbing intra-cell geometry) and reports the resulting degradation in localization and mapping accuracy. revision: yes

Circularity Check

0 steps flagged

No significant circularity; framework introduces independent map representation and inference structure.

full rationale

The paper proposes a new probabilistic occupancy grid for radio-based SLAM that integrates a surface model to link multipath RF measurements to grid-cell states (occupancy and reflection coefficients). The derivation chain consists of defining this representation, embedding it in a joint localization-mapping posterior, and validating via simulation; none of these steps reduce by construction to fitted parameters, prior self-citations, or renamed known results. The central claim rests on the proposed surface-to-grid connection and the resulting joint inference, which are presented as novel and are not shown to be equivalent to their inputs. This is the most common honest outcome for a paper that supplies its own modeling assumptions and empirical checks rather than deriving predictions solely from previously fitted quantities.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach relies on standard domain assumptions from SLAM and radio propagation modeling rather than introducing many new free parameters or invented entities; the surface model is treated as a connecting mechanism rather than a fitted construct.

axioms (1)
  • domain assumption Surface model describes candidate reflection paths that connect RF measurements to grid cells
    Invoked to link measurements with the occupancy grid representation.

pith-pipeline@v0.9.0 · 5753 in / 1224 out tokens · 53562 ms · 2026-05-21T11:15:56.218933+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Coherent Direct Multipath SLAM

    eess.SP 2026-04 unverdicted novelty 7.0

    A scalable coherent MP-SLAM method uses a phase-preserving nonzero-mean Type-II likelihood with shared complex mean across arrays plus an SFV model to achieve robust localization and mapping directly from raw signals,...

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages · cited by 1 Pith paper

  1. [1]

    The integrated sensing and communication revolution for 6G: Vision, techniques, and applications,

    N. Gonz ´alez-Prelcicet al., “The integrated sensing and communication revolution for 6G: Vision, techniques, and applications,”Proc. IEEE, vol. 112, no. 7, pp. 676–723, May 2024

    work page 2024

  2. [2]

    PMBM-based SLAM filters in 5G mmWave vehicular networks,

    H. Kim, K. Granstrom, L. Svensson, S. Kim, and H. Wymeersch, “PMBM-based SLAM filters in 5G mmWave vehicular networks,”IEEE Trans. V eh. Technol., pp. 1–1, May 2022

    work page 2022

  3. [3]

    A belief propagation algorithm for multipath-based SLAM with multiple map features: A mmWave MIMO application,

    X. Li, X. Cai, E. Leitinger, and F. Tufvesson, “A belief propagation algorithm for multipath-based SLAM with multiple map features: A mmWave MIMO application,” inProc. IEEE ICC 2024, Aug. 2024, pp. 269–275

    work page 2024

  4. [4]

    Batch SLAM with PMBM data association sampling and graph-based optimization,

    Y . Ge, O. Kaltiokallio, Y . Xia, A. F. Garc ´ıa-Fern´andez, H. Kim, J. Talvitie, M. Valkama, H. Wymeersch, and L. Svensson, “Batch SLAM with PMBM data association sampling and graph-based optimization,” IEEE Trans. Signal Process., vol. 73, pp. 2139–2153, May 2025

    work page 2025

  5. [5]

    Direct multipath-based SLAM,

    M. Liang, E. Leitinger, and F. Meyer, “Direct multipath-based SLAM,” IEEE Trans. Signal Process., vol. 74, Mar. 2025

    work page 2025

  6. [6]

    Learning occupancy grid maps with forward sensor models,

    S. Thrun, “Learning occupancy grid maps with forward sensor models,” Autonomous Robots, vol. 15, pp. 111–127, Sept. 2003

    work page 2003

  7. [7]

    Modern MAP inference methods for accurate and fast occupancy grid mapping on higher order factor graphs,

    V . Dhiman, A. Kundu, F. Dellaert, and J. J. Corso, “Modern MAP inference methods for accurate and fast occupancy grid mapping on higher order factor graphs,” inIEEE Int. Conf. Robot. Autom. (ICRA), Sept. 2014, pp. 2037–2044

    work page 2014

  8. [8]

    A random finite set approach for dynamic occupancy grid maps with real-time application,

    D. Nuss, S. Reuter, M. Thom, T. Yuan, G. Krehl, M. Maile, A. Gern, and K. Dietmayer, “A random finite set approach for dynamic occupancy grid maps with real-time application,”Int. J. Robot. Res., vol. 37, pp. 841–866, Jul. 2018

    work page 2018

  9. [9]

    Super rays and culling region for real-time updates on grid-based occupancy maps,

    Y . Kwon, D. Kim, I. An, and S.-e. Yoon, “Super rays and culling region for real-time updates on grid-based occupancy maps,”IEEE Trans. Robot., vol. 35, no. 2, pp. 482–497, Apr. 2019

    work page 2019

  10. [10]

    MRFMap: Online probabilistic 3D mapping using forward ray sensor models,

    K. S. Shankar and N. Michael, “MRFMap: Online probabilistic 3D mapping using forward ray sensor models,” inRobotics: Science and Systems, Jul. 2020

    work page 2020

  11. [11]

    Bayesian learning of occupancy grids,

    C. Robbiano, E. K. P. Chong, M. R. Azimi-Sadjadi, L. L. Scharf, and A. Pezeshki, “Bayesian learning of occupancy grids,”IEEE Trans. Intell. Transp. Syst., vol. 23, no. 2, pp. 1073–1084, Sept. 2022

    work page 2022

  12. [12]

    Belief propagation based localization and mapping using sparsely sampled GNSS SNR measurements,

    A. T. Irish, J. T. Isaacs, F. Quitin, J. a. P. Hespanha, and U. Madhow, “Belief propagation based localization and mapping using sparsely sampled GNSS SNR measurements,” inProc. IEEE Int. Conf. Robot. Autom. (ICRA), Sept. 2014, pp. 1977–1982

    work page 2014

  13. [13]

    Hybrid model for reverberant indoor radio channels using rays and graphs,

    G. Steinb ¨ocket al., “Hybrid model for reverberant indoor radio channels using rays and graphs,”IEEE Trans. Antennas Propag., vol. 64, no. 9, pp. 4036–4048, Sept. 2016

    work page 2016

  14. [14]

    An iterative 5G positioning and synchronization algorithm in NLOS environments with multi- bounce paths,

    Z. Li, F. Jiang, H. Wymeersch, and F. Wen, “An iterative 5G positioning and synchronization algorithm in NLOS environments with multi- bounce paths,”IEEE Wireless Commun. Lett., vol. 12, no. 5, pp. 804– 808, Feb. 2023

    work page 2023

  15. [15]

    A belief propagation algorithm for multipath-based SLAM,

    E. Leitinger, F. Meyer, F. Hlawatsch, K. Witrisal, F. Tufvesson, and M. Z. Win, “A belief propagation algorithm for multipath-based SLAM,” IEEE Trans. Wireless Commun., vol. 18, no. 12, pp. 5613–5629, Dec. 2019

    work page 2019

  16. [16]

    Data fusion for multipath-based SLAM: Combining information from multiple propa- gation paths,

    E. Leitinger, A. Venus, B. Teague, and F. Meyer, “Data fusion for multipath-based SLAM: Combining information from multiple propa- gation paths,”IEEE Trans. Signal Process., vol. 71, pp. 4011–4028, Sep. 2023

    work page 2023

  17. [17]

    Adaptive multipath-based SLAM for distributed MIMO systems,

    X. Li, B. Deutschmann, E. Leitinger, and F. Meyer, “Adaptive multipath-based SLAM for distributed MIMO systems,” 2025, arXiv. [Online]. Available: https://arxiv.org/abs/2506.21798

    work page arXiv 2025

  18. [18]

    Factor graphs and the sum-product algorithm,

    F. Kschischang, B. Frey, and H.-A. Loeliger, “Factor graphs and the sum-product algorithm,”IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 498–519, Feb. 2001

    work page 2001

  19. [19]

    An introduction to factor graphs,

    H.-A. Loeliger, “An introduction to factor graphs,”IEEE Signal Process. Mag., vol. 21, no. 1, pp. 28–41, Feb. 2004

    work page 2004

  20. [20]

    Fingerprinting-based positioning in dis- tributed massive MIMO systems,

    V . Savic and E. G. Larsson, “Fingerprinting-based positioning in dis- tributed massive MIMO systems,” inProc. IEEE VTC 2015, Sept. 2015, pp. 1–5

    work page 2015

  21. [21]

    Uplink joint positioning and synchronization in cell-free deployments with Radio Stripes,

    A. Fascista, B. J. B. Deutschmann, M. F. Keskin, T. Wilding, A. Coluc- cia, K. Witrisal, E. Leitinger, G. Seco-Granados, and H. Wymeersch, “Uplink joint positioning and synchronization in cell-free deployments with Radio Stripes,” inProc. IEEE ICC 2023, Rome, Italy, May 2023

    work page 2023

  22. [22]

    Joint localization, synchronization and mapping via phase- coherent distributed arrays,

    ——, “Joint localization, synchronization and mapping via phase- coherent distributed arrays,”IEEE J. Sel. Top. Signal Process., vol. 19, no. 2, pp. 412–429, Mar. 2025

    work page 2025

  23. [23]

    Phase- coherent D-MIMO ISAC: Multi-target estimation and spectral efficiency trade-offs,

    V . Tentu, H. Wymeersch, M. F. Keskin, S. Dey, and T. Svensson, “Phase- coherent D-MIMO ISAC: Multi-target estimation and spectral efficiency trade-offs,” inProc. IEEE JC&S 2026, Feb. 2026

    work page 2026

  24. [24]

    Estimation of radio channel parameters: models and algo- rithms,

    A. Richter, “Estimation of radio channel parameters: models and algo- rithms,” Ph.D. dissertation, Ilmenau University of Technology, 2005

    work page 2005

  25. [25]

    Superfast line spectral estimation,

    T. L. Hansen, B. H. Fleury, and B. D. Rao, “Superfast line spectral estimation,”IEEE Trans. Signal Process., vol. PP, no. 99, 2018

    work page 2018

  26. [26]

    Super-resolution estimation of UWB channels including the dense component–an SBL- inspired approach,

    S. Grebien, E. Leitinger, K. Witrisal, and B. H. Fleury, “Super-resolution estimation of UWB channels including the dense component–an SBL- inspired approach,”IEEE Trans. Wirel. Commun., pp. 10 301 – 10 318, Feb. 2024

    work page 2024

  27. [27]

    Message passing algorithms for scalable multitarget tracking,

    F. Meyer, T. Kropfreiter, J. L. Williams, R. Lau, F. Hlawatsch, P. Braca, and M. Z. Win, “Message passing algorithms for scalable multitarget tracking,”Proc. IEEE, vol. 106, no. 2, pp. 221–259, Feb. 2018

    work page 2018

  28. [28]

    Bar-Shalom, P

    Y . Bar-Shalom, P. K. Willett, and X. Tian,Tracking and Data Fusion: a Handbook of Algorithms. Storrs, CT, USA: Yaakov Bar-Shalom, 2011

    work page 2011

  29. [29]

    Single-anchor, multipath-assisted indoor positioning with aliased an- tenna arrays,

    T. Wilding, S. Grebien, E. Leitinger, U. M ¨uhlmann, and K. Witrisal, “Single-anchor, multipath-assisted indoor positioning with aliased an- tenna arrays,” inAsilomar-18, Pacifc Grove, CA, USA, Oct. 2018, pp. 525–531

    work page 2018

  30. [30]

    Multipath-based SLAM exploiting AoA and amplitude information,

    E. Leitinger, S. Grebien, and K. Witrisal, “Multipath-based SLAM exploiting AoA and amplitude information,” inProc. IEEE ICCW-19, Shanghai, China, May 2019

    work page 2019

  31. [31]

    Sequential detection and estimation of multipath channel parameters using belief propaga- tion,

    X. Li, E. Leitinger, A. Venus, and F. Tufvesson, “Sequential detection and estimation of multipath channel parameters using belief propaga- tion,”IEEE Trans. Wirel. Commun., vol. 21, no. 10, pp. 8385–8402, Apr. 2022

    work page 2022

  32. [32]

    Taichi Lang, https://github.com/taichi-dev/taichi, gitHub repository

    work page