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Research ArticleOriginal Article
Open Access

Navigation Safety Assurance of a KF-Based GNSS/IMU System: Protection Levels Against IMU Failure

Jinsil Lee, Minchan Kim, Dongchan Min, Sam Pullen, and Jiyun Lee
NAVIGATION: Journal of the Institute of Navigation December 2023, 70 (4) navi.612; DOI: https://doi.org/10.33012/navi.612
Jinsil Lee
1Korea Advanced Institute of Science and Technology (KAIST)
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  • For correspondence: [email protected]
Minchan Kim
1Korea Advanced Institute of Science and Technology (KAIST)
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Dongchan Min
1Korea Advanced Institute of Science and Technology (KAIST)
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Sam Pullen,
2Stanford University
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Jiyun Lee
1Korea Advanced Institute of Science and Technology (KAIST)
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  • FIGURE 1
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    FIGURE 1

    State errors of an EKF-based GNSS/IMU navigation system when an IMU step fault (0.5 m/s2 on each axis of the accelerometer) is injected

  • FIGURE 2
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    FIGURE 2

    Illustration of the integrity and continuity architecture of a KF-based GNSS/IMU navigation system with an emphasis on the IMU fault hypothesis

  • FIGURE 3
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    FIGURE 3

    GNSS/IMU navigation system integrity and continuity requirements

  • FIGURE 4
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    FIGURE 4

    Illustration of KF innovation-based IMU fault monitoring concept

    PDF: Probability density function

  • FIGURE 5
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    FIGURE 5

    Example result of the KF innovation-based IMU fault monitor

    Two KF innovations exceed their thresholds, and the system declares an IMU fault.

  • FIGURE 6
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    FIGURE 6

    Two types of PLKF,IMU: Real-time and predictive PLKF,IMU

  • FIGURE 7
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    FIGURE 7

    Simulation results for the real-time VPLKF, IMU

  • FIGURE 8
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    FIGURE 8

    Simulation results for the predictive VPLKF,IMU

  • FIGURE 9
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    FIGURE 9

    Simulation results for the predictive VPLKF,IMU under an accelerometer ramp fault

  • FIGURE 10
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    FIGURE 10

    Simulation results for the predictive VPLKF,IMU under a gyroscope step fault

  • FIGURE 11
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    FIGURE 11

    Simulation results for the predictive VPLKF,IMU under a gyroscope ramp fault

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    TABLE 1

    Simulation Conditions

    Navigation requirementsIntegrity requirements allocated to the IMU fault hypothesis, IIMU3.3 × 10−8 /hour = IGNSS/IMU /3 = (10−7/hour)/3 (IGNSS/IMU is equally allocated among the three hypotheses, as defined in Figure 3)

    Continuity requirements allocated to the false alert event under the IMU fault hypothesis, CIMU (= Pfa,IMU*)

    *Only the continuity requirement due to a false alert is considered

    0.5 × 10−6 / hour = *CGNSS/IMU /2 = (10−6/hour)/2 (*CGNSS/IMU is equally allocated among the two fault monitors, as defined in Figure 3)
    GNSS constellation31 GPS constellations
    GNSSGNSS error model
    • -Satellite clock/ephemeris error: 2.4 m (1σ)

    • -Ionospheric error: 0 m (removed using dual-frequency measurements)

    • -Tropospheric error: WAAS tropospheric model (RTCA, 2001)

    • -Multipath error: *2.6 × WAAS airborne multipath model (RTCA, 2001)

    • *2.6 is the multipath inflation factor caused by using L1/L5 dual-frequency measurements (Walter et al., 2010)

    GNSS measurement update rate2 Hz
    Prior probability of GNSS faults10−5
    IMUIMU error model
    • -Tactical-grade IMU noise level (Groves, 2007)

    • -Gyroscope noise (power spectral density [PSD]): 3.4 × 10−11 rad2/s

    • -Accelerometer noise PSD: 3.8 × 10−6 m2/s3

    • -Gyroscope bias PSD: 2 × 10−12 rad2/s3

    • -Accelerometer bias PSD: 1 × 10−7 m2/s5

    IMU measurement update rate100 Hz
    Prior probability of IMU sensor faults10−5
    Flight trajectoryHovering scenario (static)
    • Note: WAAS: Wide area augmentation system.

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NAVIGATION: Journal of the Institute of Navigation: 70 (4)
NAVIGATION: Journal of the Institute of Navigation
Vol. 70, Issue 4
Winter 2023
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Navigation Safety Assurance of a KF-Based GNSS/IMU System: Protection Levels Against IMU Failure
Jinsil Lee, Minchan Kim, Dongchan Min, Sam Pullen,, Jiyun Lee
NAVIGATION: Journal of the Institute of Navigation Dec 2023, 70 (4) navi.612; DOI: 10.33012/navi.612

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Navigation Safety Assurance of a KF-Based GNSS/IMU System: Protection Levels Against IMU Failure
Jinsil Lee, Minchan Kim, Dongchan Min, Sam Pullen,, Jiyun Lee
NAVIGATION: Journal of the Institute of Navigation Dec 2023, 70 (4) navi.612; DOI: 10.33012/navi.612
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  • Article
    • Abstract
    • 1 INTRODUCTION
    • 2 IMPACT OF IMU SENSOR FAULTS ON A KF-BASED GNSS/IMU NAVIGATION SYSTEM
    • 3 INTEGRITY AND CONTINUITY ALGORITHMS OF A KF-BASED GNSS/IMU NAVIGATION SYSTEM
    • 4 SUMMARY
    • HOW TO CITE THIS ARTICLE
    • ACKNOWLEDGMENTS
    • APPENDIX A
    • APPENDIX B
    • APPENDIX C
    • REFERENCES
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Keywords

  • GNSS/IMU integration
  • IMU failure
  • integrity
  • kalman filter
  • protection level

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