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

arXiv: https://arxiv.org/abs/2609.26231 · HTML: https://mlsanity.com/paper/2609.26231/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 17 of 17)

- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [Graph Neural Network-Based Anomaly Detection in Multivariate Time Series](https://mlsanity.com/paper/2106.06947/) (2021)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Drift with Devil: Security of Multi-Sensor Fusion based Localization in High-Level Autonomous Driving under GPS Spoofing (Extended Version)](https://mlsanity.com/paper/2006.10318/) (2020)
- [A GPS spoofing detection and classification correlator-based technique using the LASSO](https://mlsanity.com/paper/2004.13900/) (2020)
- [Sensor Fusion-based GNSS Spoofing Attack Detection Framework for Autonomous Vehicles](https://mlsanity.com/paper/2106.02982/) (2021)
- [Prediction-Based GNSS Spoofing Attack Detection for Autonomous Vehicles](https://mlsanity.com/paper/2010.11722/) (2020)
- [Quickest Change Detection with Non-Stationary Post-Change Observations](https://mlsanity.com/paper/2110.01581/) (2021)
- [Infrastructure-enabled GPS Spoofing Detection and Correction](https://mlsanity.com/paper/2202.05463/) (2022)
- [GPS-IDS: An Anomaly-based GPS Spoofing Attack Detection Framework for Autonomous Vehicles](https://mlsanity.com/paper/2405.08359/) (2024)
- [Carrier-phase and IMU based GNSS Spoofing Detection for Ground Vehicles](https://mlsanity.com/paper/2203.00140/) (2022)
- [Sequential Detection of a Temporary Change in Multivariate Time Series](https://mlsanity.com/paper/2110.15935/) (2021)
- [GPS Attack Detection and Mitigation for Safe Autonomous Driving using Image and Map based Lateral Direction Localization](https://mlsanity.com/paper/2310.05407/) (2023)
- [Extending RAIM with a Gaussian Mixture of Opportunistic Information](https://mlsanity.com/paper/2402.03449/) (2024)

## Abstract (arXiv)

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.