High-Order Liquid Evidence Modeling for Continuous and Subtle GNSS Spoofing Detection in Autonomous Driving

Muhammad Ayub Sabir; Junbiao Pang; Fatima Ashraf

cs.LGAug 12, 2026

High-Order Liquid Evidence Modeling for Continuous and Subtle GNSS Spoofing Detection in Autonomous Driving

Authors: Muhammad Ayub Sabir, Junbiao Pang, Fatima Ashraf

Organizations: Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China

Abstract

Continuous and subtle GNSS spoofing poses a serious threat to autonomous vehicles because forged positions may remain locally plausible while gradually becoming inconsistent with vehicle motion observed by non-GNSS onboard sensors. Existing AV-oriented detectors commonly rely on residual thresholds or feature-level classification and provide limited modeling of how weak GNSS--motion inconsistency develops and persists over time. This paper formulates subtle GNSS spoofing detection as a causal sequential evidence-modeling problem and proposes a high-order liquid evidence detector. The method first compares the displacement implied by consecutive GNSS positions with that inferred from independent onboard motion observations and converts their difference into uncertainty-normalized residual evidence. It then represents the current inconsistency, its local evolution, excess above the normal level, accumulated persistence, and displacement validity as causal weak evidence. These cues are mapped into instantaneous, evolutionary, and persistent latent states, aligned through a bounded Kirchhoff-inspired symmetric exchange, and combined through an explicit third-order interaction to capture their coordinated support for spoofing. To model how this coordinated evidence develops over time, second-order liquid dynamics track its memory and evolution to estimate causal spoofing probabilities, which are converted into confirmed alarms using validation-selected threshold and persistence parameters. Experiments on the AV--GPS dataset family demonstrate strong controlled and external generalization, together with clear sequential alarm behavior. On Dataset-1, the proposed detector achieves an AUROC of 0.9932 and an AUPRC of 0.9843, while obtaining the lowest false-positive rate among the learning-based baselines. Code: https://github.com/pangjunbiao/HO-LLN-Spoofing.

Figures & tables

Fig. 1: Overview of the proposed causal high-order liquid evidence framework for continuous and subtle GNSS spoofing detection.

Symbol	Description
$g_{t},\;u_{t},\;\mathcal{H}_{t}$	GNSS observation, non-GNSS onboard motion observation, and causal history up to time $t$
$\Delta p_{t}^{g},\;\Delta p_{t}^{u}$	GNSS-implied and onboard-motion-implied planar displacements
$r_{t},\;\Sigma_{t},\;\eta_{t}$	GNSS–motion displacement residual, residual uncertainty matrix, and uncertainty-normalized residual evidence
$\nu_{t}$	Displacement-validity indicator
$q_{t},\;\tilde{a}_{t}$	Above-normal residual evidence and compressed accumulated evidence
$\xi_{t}$	Causal evidence vector combining the current residual, its evolution, persistence, and validity

TABLE I: Key notation used in the proposed framework.

Scenario	Samples	segments	Normal	Spoofed	Role in this paper
Dataset-1	62,042	27	46,287	15,755	Model development and controlled comparison.
Dataset-2	6,890	6	5,184	1,706	External generalization evaluation.
Dataset-3	636	1	231	405	Causal sequential case study.

TABLE II: Dataset statistics and experimental roles of the AV–GPS scenarios.

Model	AUROC $\uparrow$	AUPRC $\uparrow$	F1 $\uparrow$	Prec. $\uparrow$	Recall $\uparrow$	FPR $\downarrow$	Delay $\downarrow$
Proposed	0.9932	0.9843	0.9139	0.9909	0.8480	0.0027	3.5
XGBoost	0.9605	0.9514	0.9296	0.9835	0.8813	0.0052	14.5
MLP	0.9832	0.9650	0.8883	0.9667	0.8217	0.0099	8.5
LSTM	0.9466	0.9220	0.8704	0.9191	0.8266	0.0254	0.0
GRU	0.9627	0.9224	0.8467	0.9237	0.7814	0.0226	0.5

TABLE III: Dataset-1 controlled test comparison of learning-based detectors.

Scenario	Evaluation role	AUROC $\uparrow$	AUPRC $\uparrow$	F1 $\uparrow$	Prec. $\uparrow$	Recall $\uparrow$	FPR $\downarrow$	ADR $\uparrow$	Delay $\downarrow$
Dataset-1	Controlled held-out test	0.9932	0.9843	0.9139	0.9909	0.8480	0.0027	1.00	3.5
Dataset-2	External generalization	0.9899	0.9872	0.9567	0.9598	0.9536	0.0131	0.75	19.0
Dataset-3	Causal sequential case study	0.9233	0.9661	0.8727	0.9205	0.8296	0.1266	1.00	35.0

TABLE IV: Cross-scenario performance of the finalized proposed detector.

Fig. 2: Dataset-3 causal case study comparing the proposed detector and the EKF Detector during spoofing events.

Method	Attack-1 Delay $\downarrow$	Attack-2 Delay $\downarrow$	Mean Delay $\downarrow$	ADR $\uparrow$	False Alarm Rows $\downarrow$	False Alarm Events $\downarrow$
Proposed	16.0	54.0	35.0	1.0	29	2
EKF Detector	22.0	29.0	25.5	1.0	0	0

TABLE V: Dataset-3 event-level comparison with the EKF Detector.

Evidence-role setting	AUROC $\uparrow$	AUPRC $\uparrow$	F1 $\uparrow$	Prec. $\uparrow$	Recall $\uparrow$	FPR $\downarrow$	ADR $\uparrow$	Delay (s) $\downarrow$
Complete evidence	0.9932	0.9843	0.9139	0.9909	0.8480	0.0027	1.00	3.5
Accumulation removed	0.8814	0.7624	0.2137	0.9766	0.1200	0.0010	0.50	166.0
Residual evolution removed	0.9876	0.9765	0.6743	0.5126	0.9848	0.3274	1.00	3.5
Evolution– $q_{t}$ removed	0.9830	0.9723	0.6141	0.4462	0.9848	0.4274	1.00	3.5
Low-order evidence only	0.7284	0.4663	0.5154	0.3996	0.7256	0.3811	1.00	3.5
Validity evidence only	0.5018	0.2565	0.4105	0.2593	0.9840	0.9826	1.00	3.5

TABLE VI: Dataset-1 evidence-role analysis of the causal representation.

Evidence-role setting	D1 F1 $\uparrow$	D1 FPR $\downarrow$	D2 F1 $\uparrow$	D2 FPR $\downarrow$	D3 F1 $\uparrow$	D3 FPR $\downarrow$
Complete evidence	0.9139	0.0027	0.9567	0.0131	0.8727	0.1266
Accumulation removed	0.2137	0.0010	0.8977	0.0023	0.5081	0.0393
Residual evolution removed	0.6743	0.3274	0.5517	0.5031	0.7646	0.8210
Evolution– $q_{t}$ removed	0.6141	0.4274	0.4986	0.6226	0.7400	0.8559
Low-order evidence only	0.5154	0.3811	0.5515	0.4959	0.7785	0.6157
Validity evidence only	0.4105	0.9826	0.3927	0.9817	0.7910	0.9345

TABLE VII: Cross-scenario evidence-role analysis of the causal representation.

Setting	Model-side mechanism	D1 F1 $\uparrow$	D1 FPR $\downarrow$	D2 F1 $\uparrow$	D2 FPR $\downarrow$	D3 F1 $\uparrow$	D3 FPR $\downarrow$
H0	Recurrent-only variant	0.9120	0.0474	0.7631	0.1809	0.7641	0.9083
H1	Kirchhoff-inspired symmetric exchange	0.9345	0.0405	0.7136	0.2398	0.7796	1.0000
H2	Exchange + third-order feature	0.9461	0.0167	0.9209	0.0454	0.8650	0.2140
H3	Full proposed	0.9139	0.0027	0.9567	0.0131	0.8727	0.1266

TABLE VIII: Architectural role analysis using the common causal evidence input.

Model	Mean AUPRC	Mean AUROC	Mean F1	Worst F1	Mean FPR $\downarrow$	Worst FPR $\downarrow$	Mean ADR
Proposed second-order liquid	0.9792	0.9688	0.9144	0.8727	0.0475	0.1266	0.9167
GPS-IDS–AdaBoost	0.9580	0.9335	0.7907	0.5630	0.3783	0.6407	0.7500
GPS-IDS–MLP	0.7194	0.7248	0.7385	0.4426	0.5493	0.8230	0.8333
GPS-IDS–Random Forest	0.6270	0.6899	0.7157	0.3970	0.6728	1.0000	0.6667
GPS-IDS–Gradient Boosting	0.8406	0.8453	0.7091	0.3965	0.6763	0.9992	0.6667
GPS-IDS–Decision Tree	0.5949	0.6265	0.6819	0.3831	0.6693	0.9985	0.8333

TABLE IX: Cross-Scenario Aggregate Comparison with Selected GPS-IDS Classifier Variants

Variant	Value	F1 $\uparrow$	FPR $\downarrow$	Delay (s) $\downarrow$
$\theta$	0.50	0.9231	0.0045	3.5
$\theta$	0.60	0.9139	0.0027	3.5
$\theta$	0.90	0.8876	0.0000	15.5
$N_{\mathrm{p}}$	3	0.9231	0.0075	1.0
$N_{\mathrm{p}}$	8	0.9139	0.0027	3.5
$N_{\mathrm{p}}$	11	0.9079	0.0013	5.5

TABLE X: Parameter sensitivity around the selected Dataset-1 configuration.

Metric	Dataset-1 Test	Dataset-2 External	Dataset-3 Sequential
Seeds	5	5	5
AUROC $\uparrow$	$0.9929{\pm}0.0025$	$0.9883{\pm}0.0019$	$0.9127{\pm}0.0194$
AUPRC $\uparrow$	$0.9833{\pm}0.0059$	$0.9862{\pm}0.0018$	$0.9630{\pm}0.0065$
F1 $\uparrow$	$0.9160{\pm}0.0073$	$0.9489{\pm}0.0315$	$0.8875{\pm}0.0142$
Prec. $\uparrow$	$0.9790{\pm}0.0178$	$0.9375{\pm}0.0626$	$0.9373{\pm}0.0236$
Recall $\uparrow$	$0.8607{\pm}0.0092$	$0.9625{\pm}0.0060$	$0.8430{\pm}0.0137$

TABLE XI: Multi-seed robustness of the finalized proposed detector.

Autonomous Driving

Autonomous driving develops vehicles that perceive road scenes, predict interactions, and plan and control safe movement with limited or no human input.

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High-Order Liquid Evidence Encoding for Gradual GNSS Spoofing Detection in Autonomous Driving

Muhammad Ayub Sabir, Junbiao Pang, Fatima Ashraf

Faculty of Information Technology, Beijing University of Technology, Beijing 100124, China

Autonomous Driving

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Accurate Global Navigation Satellite System (GNSS)-based localization is essential for safe and reliable autonomous driving. However, spoofing attacks can manipulate vehicle position estimates. Continuous and subtle attacks are particularly difficult to detect because individual GNSS observations may remain plausible while the inconsistency between GNSS-implied displacement and onboard vehicle motion gradually increases. Existing methods often rely on static vehicle-behavior features or a single residual signal and do not explicitly model this evolution. To address this problem, we propose a causal high-order liquid evidence framework for GNSS spoofing detection. The method first constructs a physics-guided GNSS--motion inconsistency residual by comparing GNSS-implied displacement with onboard-motion-derived displacement. It then forms separate evidence streams for the residual level and its first- and second-order discrete variations, with relevant contextual cues selected according to the evidence order. Each stream is processed by a separate adaptive liquid encoder, and the resulting temporal states are hierarchically coupled to predict spoofing at the window endpoint using only current and past observations. Experiments on three subsets of the real-world AV-GPS dataset show that the proposed method achieves the highest F1-scores among the evaluated temporal models on Dataset~~1 and Dataset~~3, reaching 0.9535 and 0.9777, respectively. On Dataset~3, it detects both labeled normal-to-attack transitions within four sampling steps. Code and datasets are publicly available at: https://github.com/pangjunbiao/GNSS_Spoofing.git.

Abstract

Autonomous Driving

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