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

arXiv: https://arxiv.org/abs/2608.11790 · HTML: https://mlsanity.com/paper/2608.11790/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 16 of 16)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy](https://mlsanity.com/paper/2110.02642/) (2021)
- [TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data](https://mlsanity.com/paper/2201.07284/) (2022)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Learning Graph Structures with Transformer for Multivariate Time Series Anomaly Detection in IoT](https://mlsanity.com/paper/2104.03466/) (2021)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)
- [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)
- [Security of GPS/INS based On-road Location Tracking Systems](https://mlsanity.com/paper/1808.03515/) (2018)
- [A Reinforcement Learning Approach for GNSS Spoofing Attack Detection of Autonomous Vehicles](https://mlsanity.com/paper/2108.08628/) (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)

## Abstract (arXiv)

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.