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Jackknife ARAIM: Efficient GNSS Integrity Monitoring for Simultaneous Faults under Non-Gaussian Errors

Penggao Yan, Ronghe Jin, Junyi Zhang, Cheng-Wei Wang, Li-Ta Hsu

Abstract

Legacy and advanced receiver autonomous integrity monitoring (RAIM/ARAIM) rely on Gaussian error models that can be overly conservative for real-world non-Gaussian errors. This paper proposes an extended jackknife detector capable of detecting multiple simultaneous faults with non-Gaussian nominal errors. Furthermore, an integrity monitoring algorithm, jackknife ARAIM, is developed by systematically exploiting the properties of the jackknife detector in the range domain. We prove that the proposed method has equivalent monitoring performance with the solution separation (SS) ARAIM, but is significantly computationally efficient for single-fault cases with non-Gaussian nominal errors, while maintaining similar efficiency to SS ARAIM for multiple-fault cases. 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 50 m VPL produced by the ARAIM algorithm using Gaussian nominal error models. In GPS-Galileo dual-constellation setting, while these Gaussian-based ARAIM algorithms suffer 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. Moreover, we tentatively implement the SS ARAIM using non-Gaussian overbounds and compare it with the proposed Jackknife ARAIM method regarding computation efficiency. The proposed method achieves up to 59.4% reduction in median processing time compared to SS ARAIM in single-constellation scenarios.

Jackknife ARAIM: Efficient GNSS Integrity Monitoring for Simultaneous Faults under Non-Gaussian Errors

Abstract

Legacy and advanced receiver autonomous integrity monitoring (RAIM/ARAIM) rely on Gaussian error models that can be overly conservative for real-world non-Gaussian errors. This paper proposes an extended jackknife detector capable of detecting multiple simultaneous faults with non-Gaussian nominal errors. Furthermore, an integrity monitoring algorithm, jackknife ARAIM, is developed by systematically exploiting the properties of the jackknife detector in the range domain. We prove that the proposed method has equivalent monitoring performance with the solution separation (SS) ARAIM, but is significantly computationally efficient for single-fault cases with non-Gaussian nominal errors, while maintaining similar efficiency to SS ARAIM for multiple-fault cases. 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 50 m VPL produced by the ARAIM algorithm using Gaussian nominal error models. In GPS-Galileo dual-constellation setting, while these Gaussian-based ARAIM algorithms suffer 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. Moreover, we tentatively implement the SS ARAIM using non-Gaussian overbounds and compare it with the proposed Jackknife ARAIM method regarding computation efficiency. The proposed method achieves up to 59.4% reduction in median processing time compared to SS ARAIM in single-constellation scenarios.

Paper Structure

This paper contains 29 sections, 92 equations, 10 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Jackknife Detector for Simultaneous Faults
  3. Jackknife Detector for Single Fault
  4. Threat Model
  5. Reconstruction of Jackknife Residual
  6. Combination of Jackknife Residuals
  7. Reconstruction of Hypothesis Tests
  8. Jackknife RAIM with non-Gaussian Nominal Errors
  9. Determine the Threshold of Monitors
  10. Integrity Risk Evaluation
  11. Bound on the probability of HMI under $H_0$
  12. Bound on the probability of HMI under $H_k$
  13. Finalized bound of integrity risk
  14. Protection Level Derivation
  15. Consideration of Constellation Faults
  16. ...and 14 more sections

Figures (10)

  • Figure 1: 99.5 percentile of the VPL over the course of the day yielded by (a) the SS ARAIM and (b) the proposed JK-Gaussian ARAIM for the single constellation; and the triangular chart of (c) the SS ARAIM and (d) the proposed JK-Gaussian ARAIM regarding the vertical performance for the single constellation. "NO" represents normal operation, "MI" represents misleading information, "SU" represents system unavailable, "SU&MI" represents system unavailable and misleading information, and "HMI" represents hazardously misleading information.
  • Figure 2: (a) 99.5 percentile of the VPL over the course of the day yielded by the proposed JK-non-Gaussian ARAIM for the single constellation; (b) The triangular chart of the proposed JK-non-Gaussian ARAIM regarding the vertical performance for the single constellation.
  • Figure 3: 99.5 percentile of the VPL over the course of the day yielded by (a) the SS ARAIM and (b) the proposed JK-Gaussian ARAIM for the dual constellation; and the triangular chart of (c) the SS ARAIM and (d) the proposed JK-Gaussian ARAIM regarding the vertical performance for the dual constellation.
  • Figure 4: (a) 99.5 percentile of the VPL over the course of the day yielded by the proposed JK-non-Gaussian ARAIM for the dual constellation; (b) The triangular chart of the proposed JK-non-Gaussian ARAIM regarding the vertical performance for the dual constellation.
  • Figure 5: Computation time comparison for GPS-only constellation: (a) Trajectories of GPS satellites over a 24-hour period; (b) The box plot of computation times for jackknife and SS ARAIM methods both with non-Gaussian overbounds.
  • ...and 5 more figures