Session A2: Future Augmentation Systems, Correction Services and Integrity 1

Enhancing Availability of GNSS Integrity Monitoring: An Efficient Jackknife Approach in Non-Gaussian Environments
Penggao Yan, Weisong Wen, and Li-Ta Hsu, Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University
Location: Johnson (First Floor)
Date/Time: Wednesday, Sep. 10, 4:46 p.m.

1. Background
Global Navigation Satellite Systems (GNSS) play a critical role in positioning and navigation, particularly in safety-sensitive domains such as aviation, where stringent integrity requirements must be upheld (Brown, 1992; Perea et al., 2017). Ensuring integrity involves continuously monitoring errors in GNSS positioning and alerting users when inaccuracies exceed acceptable thresholds, thereby mitigating the risk of misleading navigation information (Blanch et al., 2022). Traditionally, this has been accomplished using Receiver Autonomous Integrity Monitoring (RAIM), a technique that utilizes redundant pseudorange measurements to identify inconsistencies and detect satellite faults (Parkinson & Axelrad, 1988). The widespread adoption of RAIM stems from its ability to autonomously provide integrity alerts directly at the receiver level. However, conventional RAIM methods possess inherent limitations. They generally assume the presence of only one faulty satellite at a time, operate within a single satellite constellation, and primarily offer horizontal-plane protection without ensuring vertical navigation accuracy (Angus, 2006; Pervan et al., 1998). These constraints can render legacy RAIM ineffective in complex scenarios, such as multiple simultaneous satellite failures or poor satellite geometry, necessitating the development of more sophisticated integrity solutions (Blanch et al., 2015).
To address these limitations, the Advanced RAIM (ARAIM) framework has been introduced, which leverages multi-constellation and dual-frequency GNSS data (Blanch et al., 2013). By incorporating signals from multiple satellite systems and employing more robust fault detection algorithms, ARAIM enhances system resilience against simultaneous satellite anomalies, though at the cost of increased computational demands. This advancement significantly improves GNSS availability and enables vertical navigation integrity within a multi-GNSS setting (Joerger et al., 2014). ARAIM is particularly promising for facilitating precision approach operations worldwide, such as Localizer Performance with Vertical Guidance (LPV) at a decision height of 200 feet, without requiring ground-based augmentation systems.
Despite these advancements, a common assumption has been made in developing RAIM and ARAIM algorithms that the nominal measurement error is Gaussian distributed. While this assumption simplifies calculations and reduces computational complexity, real-world nominal range errors often exhibit non-Gaussian and heavy-tailed characteristics (Rife et al., 2004; Braff & Shively, 2005). Notably, key contributors to range errors, such as orbital and clock inaccuracies, exhibit pronounced heavy-tailed distributions, rendering the Gaussian overbounding approach excessively conservative (Wang et al., 2021). This over-conservatism propagates to the positioning domain, enlarging the Protection Level (PL) within the standard ARAIM framework, which in turn constrains the system’s practical availability under stringent navigation requirements, such as LPV-200 operations (International Civil Aviation Organization, 2006). Consequently, overcoming the limitations of Gaussian overbounding has driven research into more advanced fault detection strategies capable of accurately identifying non-Gaussian measurement anomalies.
2. Addressing Non-Gaussian Errors in GNSS Integrity Monitoring
Several methodologies have been explored to account for non-Gaussian errors in GNSS integrity monitoring. One approach involves refining statistical error models to better represent empirical error distributions (Rife et al., 2012; Yan et al., 2025). Instead of relying on a single Gaussian distribution, researchers have applied mixture models or extreme value theory to capture the statistical properties of GNSS errors (Larson et al., 2019). A notable contribution in this area is the Principal Gaussian Overbound method, which employs Gaussian mixture modeling to characterize the tails of the error distribution while maintaining analytically tractable integrity bounds (Yan et al., 2025). However, these overbounding techniques, while effective in constraining error magnitudes, do not inherently identify which measurements are faulty; rather, they primarily ensure that integrity risk remains within acceptable limits.
Another research direction focuses on robust estimation and detection techniques (Pfeifer & Protzel, 2019; Yang & Xu, 2016). Statistical estimators, such as M-estimators, have been introduced to mitigate the impact of outliers in positioning solutions by assigning lower weights to anomalous measurements or completely excluding them from computations (Crespillo et al., 2020). These methods improve positioning performance under heavy-tailed error conditions; however, a critical challenge remains in guaranteeing rigorous integrity performance. Specifically, many robust statistical approaches lack well-defined probability bounds for missed detections and false alarms, making it difficult to quantify their effectiveness in integrity-sensitive applications.
In our previous work (Yan, Song, et?al., 2025), we proposed a jackknife?based GNSS fault detector to accommodate non?Gaussian measurement errors. The method systematically excludes one measurement at a time and tests the inconsistency between each observed value and its prediction from subset solutions. In contrast to conservative bound?inflation approaches (B.?Pervan et?al., 2000) and black-box robust algorithms (Crespillo et?al., 2018; Pfeifer & Protzel, 2019), the jackknife detector is derived from a linearized GNSS model and provides a provably sensitive and reliable test (Yan, Song, et?al., 2025). We have established its theoretical equivalence to solution separation: the solution?separation statistic is the projection of the jackknife test along the derivative of the solution with respect to the suspected measurement. Owing to its scalar form, the jackknife test achieves roughly a fourfold computational speed?up over solution separation. However, the method assumes at most one faulty measurement per epoch—consistent with legacy RAIM—which restricts applicability when multiple simultaneous faults can occur.
3. Proposed Method: Jackknife ARAIM
In this study, the jackknife-based fault detection technique is extended to accommodate multiple simultaneous faults with non-Gaussian errors. The enhanced fault detection method is further integrated into a multiple-hypothesis-based integrity monitoring algorithm, termed Jackknife ARAIM, which is designed to function effectively under both Gaussian and non-Gaussian error assumptions. This integration enables efficient handling of both Gaussian and non-Gaussian nominal error bounds while effectively managing the computational complexity inherent in multi-fault scenarios. While the baseline ARAIM algorithm can accommodate non-Gaussian errors (Perea et al., 2019), our approach recasts the fault detection problem through the jackknife statistic, enabling more computationally efficient simultaneous-fault monitoring compared to baseline ARAIM.
The effectiveness of the proposed method is examined in worldwide simulations, with the nominal measurement error simulated based on authentic experimental data, which reveals different findings in existing research. In a single Global Positioning System (GPS) constellation setting, the proposed method can reduce the 99.5 percentile vertical protection level (VPL) below 45 m, outperforming baseline ARAIM’s 50 m VPL. In GPS-Galileo dual-constellation setting, while baseline ARAIM suffers VPL inflation over 60 m due to Galileo’s heavy-tailed errors, the proposed method maintains VPL below 40 m, achieving over 92 % normal operations for 35 m Vertical Alert Limit. For computational context, we implemented a baseline ARAIM variant with non?Gaussian overbounds; relative to this baseline, Jackknife?ARAIM reduces median processing time by up to 62.7% in dual?constellation cases. These findings suggest feasibility for localizer performance with vertical guidance (LPV-200) operations, thereby improving integrity and computation efficiency in multi?constellation GNSS applications.
4. Contributions and Meanings of This Research
This research presents three key contributions:
- This research expands the jackknife resampling-based fault detection framework to handle multiple simultaneous faults in GNSS positioning. This contribution establishes a rigorous theoretical foundation for detecting faults in linearized pseudorange-based navigation systems affected by non-Gaussian nominal errors.
- This research introduces the jackknife ARAIM method, which provides an efficient approach for multi-hypothesis integrity monitoring, capable of handling both Gaussian and non-Gaussian nominal errors.
- A series of experimental simulations using real-world measurement error distributions validate the proposed algorithm's effectiveness. Results suggest that integrating non-Gaussian overbounding into Jackknife ARAIM significantly improves system performance, making it viable for LPV-200 precision approach operations.

Reference:
- Angus, J. E. (2006). RAIM with multiple faults. *NAVIGATION*, 53(4), 249–257.
- Blanch, J., Walker, T., Enge, P., Lee, Y., Pervan, B., Rippl, M., Spletter A., & Kropp, V. (2015). Baseline advanced RAIM user algorithm and possible improvements. *IEEE Transactions on Aerospace and Electronic Systems*, *51*(1), 713-732.
- Blanch, J., Walter, T., Milner, C., Joerger, M., Pervan, B., & Bouvet, D. (2022, January). Baseline advanced RAIM user algorithm: proposed updates. In *Proceedings of the 2022 International Technical Meeting of The Institute of Navigation* (pp. 229-251).
- Blanch, J., Walter, T., Enge, P., Wallner, S., Amarillo Fernandez, F., Dellago, R., Ioannides, R., Fernandez Hernandez, I., Belabbas, B., Spletter, A., & Rippl, M. (2013). Critical Elements for a Multi-Constellation Advanced RAIM: Critical Elements for Multi-Constellation ARAIM. *NAVIGATION*, *60*(1), 53–69.
- Braff, R., & Shively, C. (2005). A method of over bounding ground based augmentation system (GBAS) heavy tail error distributions. *The Journal of Navigation*, *58*(1), 83-103.
- Brown, R. G. (1992). A baseline GPS RAIM scheme and a note on the equivalence of three RAIM methods. *NAVIGATION*, *39*(3), 301-316.
- Crespillo, O. G., Medina, D., Skaloud, J., & Meurer, M. (2018, April). Tightly coupled GNSS/INS integration based on robust M-estimators. In *2018 IEEE/ION Position, Location and Navigation Symposium (PLANS)* (pp. 1554-1561). IEEE.
- Garcia Crespillo, O., Andreetti, A., & Grosch, A. (2020). Design and evaluation of robust m-estimators for gnss positioning in urban environments. In *Institute of Navigation International Technical Meeting 2020, ITM 2020*.
- International Civil Aviation Organization. (2006). *Annex 10, Aeronautical Telecommunications, Volume I (Radio Navigational Aids)*.
- Joerger, M., Chan, F. C., & Pervan, B. (2014). Solution separation versus residual?based RAIM. *NAVIGATION*, *61*(4), 273-291.
- Larson, J. D., Gebre?Egziabher, D., & Rife, J. H. (2019). Gaussian?Pareto overbounding of DGNSS pseudoranges from CORS. *NAVIGATION*, *66*(1), 139-150.
- Parkinson, B. W., & Axelrad, P. (1988). Autonomous GPS integrity monitoring using the pseudorange residual. *NAVIGATION*, *35*(2), 255-274.
- Perea, S., Meurer, M., Rippl, M., Belabbas, B., & Joerger, M. (2017). URA/SISA analysis for GPS and Galileo to support ARAIM. *NAVIGATION*, *64*(2), 237-254.
- Pfeifer, T., & Protzel, P. (2019, May). Expectation-maximization for adaptive mixture models in graph optimization. In *2019 international conference on robotics and automation (ICRA)* (pp. 3151-3157). IEEE.
- Pervan, B. S., Pullen, S. P., & Christie, J. R. (1998). A multiple hypothesis approach to satellite navigation integrity. *NAVIGATION*, *45*(1), 61-71.
- Rife, J., Pullen, S., & Pervan, B. (2004, September). Core overbounding and its implications for LAAS integrity. In *Proceedings of the 17th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2004)* (pp. 2810-2821).
- Rife, J., & Pervan, B. (2012). Overbounding revisited: Discrete error-distribution modeling for safety-critical GPS navigation. *IEEE Transactions on Aerospace and Electronic Systems*, *48*(2), 1537-1551.
- Wang, S., Zhai, Y., & Zhan, X. (2021). Characterizing BDS signal?in?space performance from integrity perspective. *NAVIGATION*, *68*(1), 157-183.
- Yan, P., Song, B., Xia, X., Wen, W., & Hsu, L.-T. (2025). An efficient detector for faulty GNSS measurements detection with non-Gaussian noises. arXiv preprint arXiv:2507.03987.
- Yan, P., Zhong, Y., & Hsu, L. T. (2024). Principal gaussian overbound for heavy-tailed error bounding. *IEEE Transactions on Aerospace and Electronic Systems*.
- Yang, Y., & Xu, J. (2016). GNSS receiver autonomous integrity monitoring (RAIM) algorithm based on robust estimation. *Geodesy and geodynamics*, *7*(2), 117-123.