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arxiv: 2509.14000 · v4 · submitted 2025-09-17 · 💻 cs.LG

JaGuard: Position Error Correction of GNSS Jamming with Deep Temporal Graphs

Ivana Kesi\'c , Alja\v{z} Blatnik , Carolina Fortuna , Bla\v{z} Bertalani\v{c} This is my paper

Pith reviewed 2026-05-18 15:56 UTC · model grok-4.3

classification 💻 cs.LG
keywords GNSSjamming mitigationposition error correctiontemporal graph neural networksheterogeneous graphssatellite constellationsinterference resilience
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The pith

A deep temporal graph network on satellite star graphs corrects jamming-induced GNSS position errors to a few centimeters.

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

The paper establishes that GNSS jamming mitigation can be solved by recasting it as a dynamic graph regression task on heterogeneous star graphs representing satellite constellations at each time epoch. It introduces JaGuard, which uses a Heterogeneous Graph ConvLSTM to combine spatial features like signal-to-noise ratio, azimuth, and elevation with temporal dynamics to predict 2D positional deviations. A reader would care because intentional jamming threatens precise positioning in critical infrastructure, and existing methods overlook the structured deterioration in satellite signals. If correct, this enables resilient correction at fixed receivers even when interference is severe or training data is limited.

Core claim

The central discovery is that dynamically modeling the physical deterioration of the satellite constellation as a heterogeneous star graph and processing it with a deep temporal graph network allows accurate estimation of jamming-induced positional drift. JaGuard fuses spatial context from satellite signals with short-term temporal dynamics at 1 Hz epochs to predict and correct 2D position errors, outperforming baselines under various jamming powers and data scarcity conditions.

What carries the argument

The Heterogeneous Graph ConvLSTM applied to 1 Hz heterogeneous star graphs of the satellite-receiver scene, which integrates SNR, azimuth, and elevation features with temporal coherence to regress positional deviation.

Load-bearing premise

The assumption that the synthesized jammer signals and the fixed star-graph structure at 1 Hz fully capture the real-world spatio-temporal effects of intentional GNSS jamming.

What would settle it

Deploying the system in a real environment with live jammers and measuring if the corrected positions match independent high-precision references within the reported error bounds.

Figures

Figures reproduced from arXiv: 2509.14000 by Alja\v{z} Blatnik, Bla\v{z} Bertalani\v{c}, Carolina Fortuna, Ivana Kesi\'c.

Figure 1
Figure 1. Figure 1: From physical constellation to graph snapshot [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Temporal graph sequence [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 3D surfaces of MAE (cm) as a function of input window size and hidden dimension for both receivers (GP01, Ublox10) under [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of Average MAE by train–test split. [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
read the original abstract

Global Navigation Satellite Systems (GNSS) face growing disruption from intentional jamming, undermining critical infrastructure where precise positioning and timing are essential. Current position error correction (PEC) methods mainly focus on multi-path propagation errors and fail to exploit the spatio-temporal coherence of satellite constellations. We recast jamming mitigation as a dynamic graph regression problem. We propose Jamming Guardian (JaGuard), a receiver-centric deep temporal graph network that estimates and corrects jamming-induced positional drift at fixed locations like roadside units. Modeling the satellite-receiver scene as a heterogeneous star graph at each 1 Hz epoch, our Heterogeneous Graph ConvLSTM fuses spatial context (SNR, azimuth, elevation) with short-term temporal dynamics to predict 2D positional deviation. Evaluated on a real-world dataset from two commercial receivers under synthesized RF interference (three jammer types, -45 to -70 dBm), JaGuard consistently yields the lowest Mean Absolute Error (MAE) compared to advanced baselines. Under severe jamming (-45 dBm), it maintains an MAE of 2.85-5.92 cm, improving to sub-2 cm at lower interference. On mixed-power datasets, JaGuard surpasses all baselines with MAEs of 2.26 cm (GP01) and 2.61 cm (U-blox 10). Even under extreme data starvation (10% training data), JaGuard remains stable, bounding error at 15-20 cm and preventing the massive variance increase seen in baselines. This confirms that dynamically modeling the physical deterioration of the constellation graph is strictly necessary for resilient interference correction.

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

3 major / 2 minor

Summary. The manuscript introduces JaGuard, a receiver-centric deep temporal graph network for GNSS position error correction under jamming. It recasts the problem as dynamic graph regression by modeling the satellite-receiver scene as a heterogeneous star graph at each 1 Hz epoch, incorporating spatial features (SNR, azimuth, elevation) and using a Heterogeneous Graph ConvLSTM to fuse spatial context with short-term temporal dynamics for predicting 2D positional deviations. Evaluations on real commercial receivers (GP01 and U-blox 10) under synthesized RF interference from three jammer types at -45 to -70 dBm report that JaGuard achieves the lowest MAE (e.g., 2.85-5.92 cm at -45 dBm, 2.26 cm and 2.61 cm on mixed-power sets) and remains stable under 10% training data (error bounded at 15-20 cm), outperforming baselines and supporting the necessity of graph modeling for resilient correction.

Significance. If the results hold under more rigorous validation, the work could contribute to ML-based GNSS resilience techniques by demonstrating the value of spatio-temporal graph modeling for jamming-induced error correction. The reported robustness to data starvation is a strength that could inform practical deployments at fixed locations. However, significance is limited by the reliance on synthesized interference, which may not generalize to real intentional jamming with variable characteristics.

major comments (3)
  1. [Evaluation] The experimental section provides no details on baseline implementations, exact train/test splits, error bars, or statistical significance tests for the MAE claims (e.g., 2.85-5.92 cm at -45 dBm or 2.26 cm on mixed-power GP01). This makes it impossible to assess whether the consistent outperformance is robust or reproducible.
  2. [Abstract and Conclusion] The claim that dynamically modeling the physical deterioration of the constellation graph is 'strictly necessary' rests only on the same empirical comparisons used to tune the model; no ablation studies isolating the graph component or theoretical arguments are provided to support necessity beyond performance gains on this dataset.
  3. [Dataset and Experiments] The dataset uses synthesized RF interference (three jammer types at fixed power levels) and a 1 Hz heterogeneous star-graph representation. This setup may fail to capture non-stationary spectra, adaptive power, or multipath interactions in real jamming, risking that the ConvLSTM overfits synthetic artifacts rather than learning generalizable corrections.
minor comments (2)
  1. [Method] Provide the full hyperparameter settings for the Heterogeneous Graph ConvLSTM and any preprocessing steps for SNR/azimuth/elevation features to improve reproducibility.
  2. [Results] Add error bars or variance measures to all reported MAE values and figures to substantiate the stability claims under data starvation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript arXiv:2509.14000. We address each of the major comments point-by-point below, indicating where revisions will be made to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Evaluation] The experimental section provides no details on baseline implementations, exact train/test splits, error bars, or statistical significance tests for the MAE claims (e.g., 2.85-5.92 cm at -45 dBm or 2.26 cm on mixed-power GP01). This makes it impossible to assess whether the consistent outperformance is robust or reproducible.

    Authors: We agree with this observation and will enhance the experimental section for better reproducibility. In the revised manuscript, we will add: detailed descriptions of how each baseline was implemented and tuned; the precise train/test split methodology, including the proportion of data used for training and any temporal or scenario-based partitioning; error bars (e.g., standard deviations from multiple random seeds or cross-validation); and statistical significance tests (such as paired t-tests) comparing JaGuard's MAE to baselines. These details will be incorporated into Section 4 (Experiments). revision: yes

  2. Referee: [Abstract and Conclusion] The claim that dynamically modeling the physical deterioration of the constellation graph is 'strictly necessary' rests only on the same empirical comparisons used to tune the model; no ablation studies isolating the graph component or theoretical arguments are provided to support necessity beyond performance gains on this dataset.

    Authors: The referee is correct that our use of 'strictly necessary' is supported only by empirical evidence from model comparisons. We do not provide a theoretical proof of necessity. To address this, we will revise the abstract and conclusion to state that the results 'highlight the importance' of dynamic graph modeling rather than claiming strict necessity. Furthermore, we will include an ablation study in the experiments section that compares the full model against a non-graph variant to isolate the contribution of the graph component. revision: yes

  3. Referee: [Dataset and Experiments] The dataset uses synthesized RF interference (three jammer types at fixed power levels) and a 1 Hz heterogeneous star-graph representation. This setup may fail to capture non-stationary spectra, adaptive power, or multipath interactions in real jamming, risking that the ConvLSTM overfits synthetic artifacts rather than learning generalizable corrections.

    Authors: We acknowledge the limitations inherent in using synthesized RF interference, as it provides controlled and repeatable conditions but cannot fully emulate the dynamic and adaptive nature of real intentional jamming scenarios, including variable spectra and multipath effects. Our study is positioned as an initial investigation into graph-based correction at fixed receiver locations under known interference types. In the revised version, we will add a dedicated paragraph in the Discussion section to explicitly discuss these constraints and outline plans for future validation on real jamming data. We maintain that the current setup allows for rigorous evaluation of the proposed method's potential. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical ML evaluation is self-contained

full rationale

The paper recasts GNSS jamming mitigation as a dynamic graph regression task and introduces the JaGuard Heterogeneous Graph ConvLSTM architecture to predict positional deviations from SNR, azimuth, and elevation features on a star-graph representation. All performance claims (MAE values under varying jamming powers and data-starvation regimes) are obtained by training the model on portions of a collected dataset with synthesized RF interference and evaluating against baselines on held-out or mixed-power splits. No equation or step reduces by construction to a fitted constant or input; the 'strictly necessary' conclusion for graph modeling follows directly from comparative empirical results rather than algebraic identity or self-citation chains. The derivation remains independent of the target metrics and does not rely on any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the modeling choice that satellite-receiver scenes form heterogeneous star graphs whose spatio-temporal evolution can be learned from SNR/azimuth/elevation features, plus the assumption that synthesized jamming data distribution matches real interference sufficiently for generalization.

free parameters (1)
  • Heterogeneous Graph ConvLSTM hyperparameters
    Network weights, learning rate, and graph convolution parameters are fitted to the collected receiver dataset to minimize positional MAE.
axioms (1)
  • domain assumption Spatio-temporal coherence of satellite constellations can be captured by a heterogeneous star graph at each 1 Hz epoch using SNR, azimuth, and elevation features
    Invoked when recasting the problem as dynamic graph regression and when designing the input representation.

pith-pipeline@v0.9.0 · 5833 in / 1474 out tokens · 93155 ms · 2026-05-18T15:56:37.131238+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

  1. [1]

    Hamza, B

    V . Hamza, B. Stopar, O. Sterle, P. Pavlovˇciˇc-Preˇseren, Recent advances and applications of low-cost gnss receivers: a review, GPS solutions 29 (1) (2025) 56

    work page 2025

  2. [2]

    J. Li, K. K. Nagalapur, E. Stare, S. Dwivedi, S. A. Ashraf, P.-E. Eriksson, U. Engstr¨om, W.-H. Lee, T. Lohmar, 5g new radio for public safety mission critical communications, IEEE Communications Standards Magazine 6 (4) (2023) 48–55

    work page 2023

  3. [3]

    Biswas, Cyber security in power grid networks, at the crossover domain intersection, in: 2024 IEEE 5th India Council International Subsections Conference (INDISCON), IEEE, 2024, pp

    H. Biswas, Cyber security in power grid networks, at the crossover domain intersection, in: 2024 IEEE 5th India Council International Subsections Conference (INDISCON), IEEE, 2024, pp. 1–6

    work page 2024

  4. [4]

    Gerrard, A

    N. Gerrard, A. Rødningsby, A. Morrison, N. Sokolova, C. Rost, Exploration of unintentional gnss rfi sources: Causes, occurrence rates, and predicted future impact, in: Proceedings of the 35th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+2022), 2022, pp. 3925–3934

    work page 2022

  5. [5]

    Morong, P

    T. Morong, P. Puri ˇcer, P. Kov´aˇr, Study of the gnss jamming in real environment, International Journal of Electronics and Telecommunication 65 (1) (2019) 65–70

    work page 2019

  6. [6]

    Workgroup, Gps spoofing: Final report of the gps spoofing workgroup, GPS Spoofing WorkGroup: London, UK (2024)

    G. Workgroup, Gps spoofing: Final report of the gps spoofing workgroup, GPS Spoofing WorkGroup: London, UK (2024)

    work page 2024

  7. [7]

    H. Li, Y . Xie, X. Meng, S. Wu, J. Xu, X. Wang, A novel method for anomaly detection and correction of gnss time series, Measurement Science and Technology 36 (1) (2024) 016330. 19

    work page 2024

  8. [8]

    Q. Liu, C. Gao, R. Shang, Z. Peng, R. Zhang, L. Gan, W. Gao, Nlos signal detection and correction for smartphone using convolutional neural network and variational mode decomposition in urban environment, GPS Solutions 27 (1) (2023) 31

    work page 2023

  9. [9]

    Y . Xia, S. Pan, X. Meng, W. Gao, F. Ye, Q. Zhao, X. Zhao, Anomaly detection for urban vehicle gnss observation with a hybrid machine learning system, Remote sensing 12 (6) (2020) 971

    work page 2020

  10. [10]

    I. E. Mehr, F. Dovis, A deep neural network approach for classification of gnss interference and jammer, IEEE Transactions on Aerospace and Electronic Systems (2024)

    work page 2024

  11. [11]

    Ivanov, R

    V . Ivanov, R. C. Wilson, M. Scaramuzza, Towards simple machine learning baselines for gnss rfi detection, arXiv preprint arXiv:2504.07993 (2025)

    work page arXiv 2025

  12. [12]

    Y . Zhou, X. He, S. Wang, S. Hu, X. Sun, J. Huang, Hybrid gnss time-series prediction method based on ensemble empirical mode decompo- sition with long short-term memory, Discover Applied Sciences 7 (1) (2025) 61

    work page 2025

  13. [13]

    Chen, et al., An improved vmd-lstm model for time-varying gnss time series prediction with temporally correlated noise [j]

    H. Chen, et al., An improved vmd-lstm model for time-varying gnss time series prediction with temporally correlated noise [j]. remote sens. 15 (14) (2023)

    work page 2023

  14. [14]

    W. Gao, Z. Li, Q. Chen, W. Jiang, Y . Feng, Modelling and prediction of gnss time series using gbdt, lstm and svm machine learning approaches., Journal of Geodesy 96 (10) (2022)

    work page 2022

  15. [15]

    Michail, An introduction to temporal graphs: An algorithmic perspective, Internet Mathematics 12 (4) (2016) 239–280

    O. Michail, An introduction to temporal graphs: An algorithmic perspective, Internet Mathematics 12 (4) (2016) 239–280

    work page 2016

  16. [16]

    S. M. Kazemi, R. Goel, K. Jain, I. Kobyzev, A. Sethi, P. Forsyth, P. Poupart, Representation learning for dynamic graphs: A survey, Journal of Machine Learning Research 21 (70) (2020) 1–73

    work page 2020

  17. [17]

    H. Gao, F. Yang, Y . Yang, Y . Xu, Y . Su, Adaptive receptive field graph neural networks, Neural Networks (2025) 107658

    work page 2025

  18. [18]

    Chen, C.-L

    S.-A. Chen, C.-L. Li, N. Yoder, S. O. Arik, T. Pfister, Tsmixer: An all-mlp architecture for time series forecasting, arXiv preprint arXiv:2303.06053 (2023)

    work page arXiv 2023

  19. [19]

    Zhang, M

    C. Zhang, M. Zhong, Z. Wang, N. Goddard, C. Sutton, Sequence-to-point learning with neural networks for non-intrusive load monitoring, in: Proceedings of the AAAI conference on artificial intelligence, V ol. 32, 2018. 20

    work page 2018