pith. sign in

arxiv: 2606.31473 · v1 · pith:4QK3HQ55new · submitted 2026-06-30 · 📡 eess.SP · cs.AI· math.PR

Von Mises Based Uncertainty Quantification for Closely Spaced Automotive Radar Targets

Vinay Kulkarni , V. V. Reddy This is my paper

Pith reviewed 2026-07-01 03:52 UTC · model grok-4.3

classification 📡 eess.SP cs.AImath.PR
keywords von Mises distributionuncertainty quantificationdirection of arrivalautomotive radarevidential deep learningtarget associationprobabilistic tracking
0
0 comments X

The pith

Von Mises ensemble for radar DOA produces parameters that integrate directly into tracking via closed-form likelihoods.

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

The paper compares a circular von Mises ensemble against an evidential deep learning method for producing uncertainty-aware direction-of-arrival estimates in automotive radar. The ensemble outputs a mean direction and concentration parameter that respects angular geometry, while the alternative yields a Student-t distribution in Euclidean space. Under nominal and perturbed conditions the ensemble shows lower nominal uncertainty and sharper response to severe shifts, yet the key advance is that its representation supplies closed-form von Mises likelihoods for immediate use in association steps. This setup supports a single probabilistic pipeline from detection through tracking rather than separate uncertainty handling stages.

Core claim

The ENS framework produces angular predictions parameterized by (mu, kappa), enabling interpretable uncertainty aligned with directional geometry. Performance is evaluated under in-distribution and multiple out-of-distribution conditions using risk coverage and ROC or AUROC analyses. Results indicate that ENS achieves lower uncertainty under nominal conditions and exhibits stronger sensitivity to severe perturbations, whereas EDL provides smoother uncertainty variation and slightly improved ranking consistency. Importantly, the ENS representation enables direct probabilistic integration into association modules via closed form VM likelihoods, facilitating a unified detection tracking pipelin

What carries the argument

Von Mises ensemble (ENS) that outputs direction-of-arrival predictions as a mean angle mu and concentration kappa.

If this is right

  • ENS yields lower uncertainty values than EDL under nominal operating conditions.
  • ENS uncertainty responds more strongly to severe distribution shifts than EDL.
  • EDL uncertainty varies more smoothly across conditions and ranks detections slightly more consistently.
  • Closed-form VM likelihoods allow association modules to consume ENS outputs without additional approximation steps.

Where Pith is reading between the lines

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

  • The same (mu, kappa) outputs could be fed into multi-hypothesis trackers to maintain angular separation hypotheses without discretizing the circle.
  • Because likelihoods are analytic, the approach may reduce the need for Monte-Carlo sampling inside downstream fusion filters.
  • The geometric consistency of the representation suggests it could be paired with other circular statistics modules such as circular filtering for ego-motion compensation.

Load-bearing premise

The von Mises distribution faithfully represents the angular uncertainty that arises when radar targets are closely spaced.

What would settle it

A collection of measured angular residuals from real closely spaced targets whose histogram deviates markedly from the von Mises density at the fitted kappa values.

Figures

Figures reproduced from arXiv: 2606.31473 by Vinay Kulkarni, V. V. Reddy.

Figure 1
Figure 1. Figure 1: Closely spaced extended targets and their localized ROI representa [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Architecture of the proposed probabilistic neural network. The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: In-distribution performance evaluation using [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Risk coverage analysis for OOD samples at a range of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Sensor failure / partial array degradation OOD evaluation. ROC curves [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

This work investigates uncertainty-aware deep learning approaches for direction of arrival (DOA) estimation in automotive radar, focusing on probabilistic modeling and downstream integration. A circular-statistics-based von Mises (VM) ensemble (ENS) is compared with an evidential deep learning (EDL) framework based on a normal inverse gamma formulation, yielding a Student t predictive distribution in the Euclidean domain. The ENS framework produces angular predictions parameterized by (mu, kappa), enabling interpretable uncertainty aligned with directional geometry. Performance is evaluated under in distribution and multiple out-of-distribution conditions using risk coverage and ROC or AUROC analyses. Results indicate that ENS achieves lower uncertainty under nominal conditions and exhibits stronger sensitivity to severe perturbations, whereas EDL provides smoother uncertainty variation and slightly improved ranking consistency. Importantly, the ENS representation enables direct probabilistic integration into association modules via closed form VM likelihoods, facilitating a unified detection tracking pipeline. These findings highlight a trade-off between geometric consistency and statistical generality in uncertainty-aware DOA estimation.

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

2 major / 1 minor

Summary. The paper compares a von Mises ensemble (ENS) model, which outputs angular DOA predictions parameterized by (μ, κ), against an evidential deep learning (EDL) approach yielding Student-t predictive distributions for uncertainty-aware direction-of-arrival estimation in automotive radar. It reports that ENS achieves lower uncertainty under nominal (in-distribution) conditions and greater sensitivity to severe out-of-distribution perturbations via risk-coverage curves and AUROC analyses, while EDL offers smoother uncertainty variation and slightly better ranking consistency. The manuscript highlights that the ENS (μ, κ) representation permits direct probabilistic integration into association modules through closed-form von Mises likelihoods, thereby facilitating a unified detection-tracking pipeline.

Significance. If the empirical comparisons are reproducible and the modeling assumptions hold, the work contributes a geometrically consistent alternative to Euclidean uncertainty quantification for circular DOA problems and surfaces a concrete trade-off between directional fidelity and statistical flexibility. The closed-form VM likelihood property is mathematically attractive for downstream fusion, but its practical benefit for tracking remains an assertion rather than a demonstrated outcome.

major comments (2)
  1. [Abstract] Abstract: The claim that 'the ENS representation enables direct probabilistic integration into association modules via closed form VM likelihoods, facilitating a unified detection tracking pipeline' is presented as an important finding, yet the manuscript reports only upstream DOA uncertainty metrics (risk-coverage and AUROC) under ID/OOD conditions; no JPDA-style association filter, multi-target tracking metrics (e.g., MOTA, OSPA), or end-to-end pipeline results are provided to substantiate the facilitation benefit.
  2. [Evaluation] Evaluation sections: Performance differences between ENS and EDL are stated without accompanying equations for the ENS loss, the precise definition of the von Mises parameters, dataset sizes, training procedures, or statistical significance tests, making it impossible to verify whether the reported advantages are load-bearing or could be explained by implementation details.
minor comments (1)
  1. Notation for the concentration parameter κ and its mapping to uncertainty should be clarified with an explicit equation relating κ to angular variance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will revise the manuscript accordingly to improve clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract] The claim that 'the ENS representation enables direct probabilistic integration into association modules via closed form VM likelihoods, facilitating a unified detection tracking pipeline' is presented as an important finding, yet the manuscript reports only upstream DOA uncertainty metrics (risk-coverage and AUROC) under ID/OOD conditions; no JPDA-style association filter, multi-target tracking metrics (e.g., MOTA, OSPA), or end-to-end pipeline results are provided to substantiate the facilitation benefit.

    Authors: We agree that the manuscript provides no end-to-end tracking experiments or association-filter results to empirically substantiate the facilitation claim. The statement rests on the mathematical property that the von Mises (μ, κ) output admits a closed-form likelihood for use in probabilistic association. In revision we will rephrase the abstract to present this as a theoretical advantage of the representation rather than a demonstrated outcome of the current work. revision: yes

  2. Referee: [Evaluation] Performance differences between ENS and EDL are stated without accompanying equations for the ENS loss, the precise definition of the von Mises parameters, dataset sizes, training procedures, or statistical significance tests, making it impossible to verify whether the reported advantages are load-bearing or could be explained by implementation details.

    Authors: We acknowledge the need for these details to ensure reproducibility. The revised manuscript will add the explicit ENS loss function, the definition of the von Mises parameters (μ, κ), dataset sizes and splits, training hyperparameters and procedures, and any statistical significance tests performed on the reported metrics. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The manuscript compares a von Mises ensemble (ENS) producing (mu, kappa) parameters against an evidential deep learning baseline, evaluating both via risk-coverage curves and AUROC on ID/OOD radar data. The central assertion that ENS 'enables direct probabilistic integration into association modules via closed form VM likelihoods' rests on the known closed-form properties of the von Mises distribution itself rather than any fitted parameter or self-referential derivation within the paper. No equations, self-citations, or ansatzes are presented that reduce a reported prediction or uniqueness claim to the same inputs by construction. The evaluation metrics are independent of the modeling choice, leaving the framework self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the central comparison rests on unstated modeling assumptions about angular error distributions.

pith-pipeline@v0.9.1-grok · 5701 in / 1010 out tokens · 36793 ms · 2026-07-01T03:52:54.135135+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

43 extracted references · 3 canonical work pages

  1. [1]

    S. M. Kay,Fundamentals of statistical signal processing: detection theory. Prentice-Hall, Inc., 1993

    1993

  2. [2]

    M. A. Richards,Fundamentals of radar signal processing. McGraw- Hill Education, 2014

    2014

  3. [3]

    MIMO radar for advanced driver-assistance systems and autonomous driving: Advantages and challenges,

    S. Sun, A. P. Petropulu, and H. V . Poor, “MIMO radar for advanced driver-assistance systems and autonomous driving: Advantages and challenges,”IEEE Signal Process. Magazine, vol. 37, no. 4, pp. 98– 117, 2020

    2020

  4. [4]

    Introduction to radar systems,

    M. I. Skolnik, “Introduction to radar systems,”New York, 1980

    1980

  5. [5]

    Spatial diversity 24- GHz FMCW radar with ground effect compensation for automotive applications,

    H.-N. Wang, Y .-W. Huang, and S.-J. Chung, “Spatial diversity 24- GHz FMCW radar with ground effect compensation for automotive applications,”IEEE Trans. Veh. Techn., vol. 66(2), pp. 965–973, 2016

    2016

  6. [6]

    Radar technology encyclopedia, artech house,

    D. K. Barton and S. Leonov, “Radar technology encyclopedia, artech house,”Inc., Ed., Norwood, MA (USA), 1997

    1997

  7. [7]

    Systems characteristics of automotive radars operating in the frequency band 76–81 ghz for intelligent transport. systems applications,

    M. Series, “Systems characteristics of automotive radars operating in the frequency band 76–81 ghz for intelligent transport. systems applications,”Recommendation ITU-R, M, pp. 2057–1, 2014

    2057

  8. [8]

    A review of multi-sensor fusion in autonomous driving,

    H. Qian, M. Wang, M. Zhu, and H. Wang, “A review of multi-sensor fusion in autonomous driving,”Sensors, vol. 25, no. 19, p. 6033, 2025

    2025

  9. [9]

    How centralized radar processing enables safer, smarter autonomous driving,

    L. Dowling, N. Shigihalli, S. Murray, and B. Fathi, “How centralized radar processing enables safer, smarter autonomous driving,”NVIDIA Developer Technical Blog, 2026

    2026

  10. [10]

    A survey of uncertainty quantification in deep learning,

    J. Gawlikowski, F. Kahl, M. Heine, and et al., “A survey of uncertainty quantification in deep learning,”IEEE Transactions on Neural Networks and Learning Systems, 2023

    2023

  11. [11]

    RD-CFAR: Fast and accurate constant false alarm rate algorithm for automotive radar ap- plications,

    J. Kazazi, M. Kamarei, and M. Fakharzadeh, “RD-CFAR: Fast and accurate constant false alarm rate algorithm for automotive radar ap- plications,”IEEE Signal Processing Letters, 2025

    2025

  12. [12]

    Comparison of cfar algorithms in real-time target detec- tion for automotive radar,

    A. Unknown, “Comparison of cfar algorithms in real-time target detec- tion for automotive radar,”IEEE Access, 2025

    2025

  13. [13]

    Adaptive two-dimensional cfar detection for automotive radar in nonhomogeneous environments,

    Y . Wang, H. Liu, and X. Li, “Adaptive two-dimensional cfar detection for automotive radar in nonhomogeneous environments,”IEEE Transactions on Vehicular Technology, 2023

    2023

  14. [14]

    Knowledge-aided cfar detection for automotive radar applications,

    H. Rohling and M. M ¨unster, “Knowledge-aided cfar detection for automotive radar applications,”IEEE Transactions on Aerospace and Electronic Systems, 2024

    2024

  15. [15]

    Bar-Shalom, X

    Y . Bar-Shalom, X. R. Li, and T. Kirubarajan,Estimation with Applica- tions to Tracking and Navigation. Wiley, 2001

    2001

  16. [16]

    Mahler,Statistical Multisource-Multitarget Information Fusion

    R. Mahler,Statistical Multisource-Multitarget Information Fusion. Artech House, 2007

    2007

  17. [17]

    Closely spaced multi- target association and localization using br and aoa measurements in distributed MIMO radar systems,

    Z. Yu, Z. Jin, T. Sun, J. Ding, J. Li, and Q. Guo, “Closely spaced multi- target association and localization using br and aoa measurements in distributed MIMO radar systems,”Remote Sensing, vol. 17, no. 6, 2025

    2025

  18. [18]

    Deep learning-based estimation for multitarget radar detection,

    M. Delamou, A. Bazzi, and M. Chafii, “Deep learning-based estimation for multitarget radar detection,”arXiv preprint arXiv:2305.05621, 2023

    work page arXiv 2023

  19. [19]

    See further than cfar: A data-driven radar detector trained by lidar,

    I. R. Montero, A. Palffy, J. F. P. Kooij, D. M. Gavrila, F. Fioranelli, and A. Yarovoy, “See further than cfar: A data-driven radar detector trained by lidar,” inProceedings of the IEEE Radar Conference (RadarConf), 2024

    2024

  20. [20]

    Detecting radar targets in range profiles with partially complex-valued neural networks,

    M. Bauw, “Detecting radar targets in range profiles with partially complex-valued neural networks,”arXiv preprint arXiv:2602.09597, 2026

    work page arXiv 2026

  21. [21]

    Complex-valued neural networks for millimeter-wave fmcw radar angle estimation,

    K. Kaiser, J. Daugalas, J. L ´opez-Randulfe, A. Knoll, R. Weigel, and F. Lurz, “Complex-valued neural networks for millimeter-wave fmcw radar angle estimation,” inEuropean Radar Conference, 2021

    2021

  22. [22]

    Kan-powered large-target detection for automotive radar,

    V . Kulkarni, V . Reddy, and N. Maheshwari, “Kan-powered large-target detection for automotive radar,”IEEE Transactions on Radar Systems, 2025

    2025

  23. [23]

    Gamma-based statistical modeling for extended target detection in mmwave automotive radar,

    V . Kulkarni and V . Reddy, “Gamma-based statistical modeling for extended target detection in mmwave automotive radar,”arXiv preprint arXiv:2509.26573, 2025

    work page arXiv 2025

  24. [24]

    Area-based CFAR target detection for automotive millimeter-wave radar,

    Z. Wei, B. Li, T. Feng, Y . Tao, and C. Zhao, “Area-based CFAR target detection for automotive millimeter-wave radar,”IEEE Trans. Vehicular Technology, vol. 72, no. 3, pp. 2891–2906, 2022. 12

    2022

  25. [25]

    Detection of close-proximity automotive targets using lstm,

    V . Kulkarni, V . Reddy, and A. Dixit, “Detection of close-proximity automotive targets using lstm,” inIEEE Radar Conf., 2023, pp. 1–6

    2023

  26. [26]

    Noise integral-based sparse bayesian learning for doa estimation using grid pruning and adaptation,

    Y . Liang, X. Zheng, W. Meng, and J. Li, “Noise integral-based sparse bayesian learning for doa estimation using grid pruning and adaptation,” IET Electronics Letters, 2025

    2025

  27. [27]

    A bayesian deep un- folded network for off-grid direction-of-arrival estimation,

    N. Li, X. Zhang, F. Lv, B. Zong, and W. Feng, “A bayesian deep un- folded network for off-grid direction-of-arrival estimation,”Electronics, vol. 13, no. 11, 2024

    2024

  28. [28]

    A sparse bayesian learning- based doa estimation method with the kalman filter in mimo radar,

    S. Liu, L. Tang, Y . Bai, and X. Zhang, “A sparse bayesian learning- based doa estimation method with the kalman filter in mimo radar,” Electronics, vol. 9, no. 2, p. 347, 2020

    2020

  29. [29]

    Evidential deep learning to quantify classification uncertainty,

    M. Sensoy, L. Kaplan, and M. Kandemir, “Evidential deep learning to quantify classification uncertainty,”Advances in Neural Information Processing Systems (NeurIPS), 2018

    2018

  30. [30]

    Deep eviden- tial regression,

    A. Amini, W. Schwarting, A. Soleimany, and D. Rus, “Deep eviden- tial regression,”Advances in Neural Information Processing Systems (NeurIPS), 2020

    2020

  31. [31]

    Dropout as a bayesian approximation: Representing model uncertainty in deep learning,

    Y . Gal and Z. Ghahramani, “Dropout as a bayesian approximation: Representing model uncertainty in deep learning,” inProceedings of the International Conference on Machine Learning (ICML), 2016

    2016

  32. [32]

    Simple and scalable predictive uncertainty estimation using deep ensembles,

    B. Lakshminarayanan, A. Pritzel, and C. Blundell, “Simple and scalable predictive uncertainty estimation using deep ensembles,”Advances in neural information processing systems, vol. 30, 2017

    2017

  33. [33]

    Bayesian deep learning and a proba- bilistic perspective of generalization,

    A. G. Wilson and P. Izmailov, “Bayesian deep learning and a proba- bilistic perspective of generalization,”Advances in neural information processing systems, vol. 33, pp. 4697–4708, 2020

    2020

  34. [34]

    K. V . Mardia and P. E. Jupp,Directional Statistics. Wiley, 2000

    2000

  35. [35]

    Training products of experts by minimizing contrastive divergence,

    G. E. Hinton, “Training products of experts by minimizing contrastive divergence,”Neural computation, vol. 14, no. 8, pp. 1771–1800, 2002

    2002

  36. [36]

    Cbam: Convolutional block attention module,

    S. Woo, J. Park, J.-Y . Lee, and I. S. Kweon, “Cbam: Convolutional block attention module,” inProceedings of the European Conference on Computer Vision (ECCV), 2018, pp. 3–19

    2018

  37. [37]

    The hungarian method for the assignment problem,

    H. W. Kuhn, “The hungarian method for the assignment problem,”Naval research logistics quarterly, vol. 2, no. 1-2, pp. 83–97, 1955

    1955

  38. [38]

    Deep evidential regression (nig) implemen- tation,

    A. Amini and Contributors, “Deep evidential regression (nig) implemen- tation,” https://github.com/aamini/evidential-deep-learning

  39. [39]

    K. V . Mardia and P. E. Jupp,Directional Statistics. John Wiley & Sons, 2000

    2000

  40. [40]

    Selective classification for deep neural networks,

    Y . Geifman and R. El-Yaniv, “Selective classification for deep neural networks,” inNeurIPS, 2017

    2017

  41. [41]

    An introduction to roc analysis,

    T. Fawcett, “An introduction to roc analysis,”Pattern Recognition Letters, vol. 27, no. 8, pp. 861–874, 2006

    2006

  42. [42]

    The meaning and use of the area under a receiver operating characteristic (roc) curve,

    J. A. Hanley and B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (roc) curve,”Radiology, vol. 143, no. 1, pp. 29–36, 1982

    1982

  43. [43]

    The use of the area under the roc curve in the evaluation of machine learning algorithms,

    A. P. Bradley, “The use of the area under the roc curve in the evaluation of machine learning algorithms,”Pattern Recognition, vol. 30, no. 7, pp. 1145–1159, 1997

    1997