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Research ArticleRegular Papers
Open Access

Detecting Slowly Accumulating Faults Using a Bank of Cumulative Innovations Monitors in Kalman Filters

John D. Quartararo, and Steven E. Langel
NAVIGATION: Journal of the Institute of Navigation March 2022, 69 (1) navi.507; DOI: https://doi.org/10.33012/navi.507
John D. Quartararo,
Electronic Systems Innovation Center, The MITRE Corporation, Bedford, MA, USA
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  • For correspondence: [email protected]
Steven E. Langel
Electronic Systems Innovation Center, The MITRE Corporation, Bedford, MA, USA
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  • FIGURE 1
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    FIGURE 1

    Effect of model uncertainty on the true probability of false alarm for a cumulative chi-square monitor

  • FIGURE 2
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    FIGURE 2

    Minimum detectable error for a cumulative chi-square monitor

  • FIGURE 3
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    FIGURE 3

    One example of a FIND configuration

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    FIGURE 4

    Performance analysis flowchart for cumulative innovations monitor

  • FIGURE 5
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    FIGURE 5

    Probability of detection as a function of time for a tightly coupled GPS/inertial EKF equipped with a tactical grade IMU (CAIEV)

  • FIGURE 6
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    FIGURE 6

    Best case Pmd for snapshot, IH, and FIND monitors (CAIEV analysis)

  • FIGURE 7
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    FIGURE 7

    Monte Carlo detection rate example for three fault detection algorithms with an aviation-grade IMU, 750-meter pulloff fault, 100 runs

  • FIGURE A1
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    FIGURE A1

    FIND false alarm rate as a function of the detection threshold

Tables

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    TABLE 1

    Extended Kalman filter algorithm

    Time UpdateMeasurement Update
    Embedded ImageEmbedded Image
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    TABLE 2

    IMU model parameters

    Accelerometers (per-axis)Gyroscopes (per-axis)
    Bias (m/s2)Noise Root PSDBias (rad/s)Noise Root PSD
    Turn-OnIn-RunEmbedded ImageTurn-OnIn-RunEmbedded Image
    Tactical0.9 × 1e-20.1 × 1e-2Embedded Image0.9 × 5e-50.1 × 5e-5Embedded Image
    Aviation0.9 × 1e-30.1 × 1e-3Embedded Image0.9 × 5e-80.1 × 5e-8Embedded Image
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    TABLE 3

    Maximum (best) detection rate over time (Rmax, as percentage of 100 runs) for various configurations and algorithms (across 0–30 minute span where faults start at 20-minute mark)

    TacticalAviation
    SnapshotIHFINDSnapshotIHFIND
    Fault Magnitude (m)250288
    500No Data28100
    7501948100
    1,00000184100100
    1,250115099100100
    1,50027100
    2,00086100
    2,500400100No Data
    3,000903100
    3,5001002100
    4,000100100100
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    TABLE 4

    Time to 99% detection rate (since fault onset in sec) from Monte Carlo runs for various configurations and algorithms; dashes indicate where 99% detection rates were not achieved.

    TacticalAviation
    SnapshotIHFINDSnapshotIHFIND
    Fault Magnitude (m)250---
    500No Data--130
    750--62
    1,000----19741
    1,250---12314427
    1,500--44
    2,000--21
    2,500--16No Data
    3,000--13
    3,50021-11
    4,0001411110
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    TABLE 5

    Accumulated position fault (in m) at the 99% detection time from Monte Carlo runs for various configurations and algorithms; dashes indicate where 99% detection rates were not achieved.

    TacticalAviation
    SnapshotIHFINDSnapshotIHFIND
    Fault Magnitude (m)250---
    500No Data--23
    750--8
    1,000----1085
    1,250---53723
    1,500--8
    2,000--2
    2,500--2No Data
    3,000--1
    3,5004-1
    4,00021371

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NAVIGATION: Journal of the Institute of Navigation: 69 (1)
NAVIGATION: Journal of the Institute of Navigation
Vol. 69, Issue 1
Spring 2022
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Detecting Slowly Accumulating Faults Using a Bank of Cumulative Innovations Monitors in Kalman Filters
John D. Quartararo,, Steven E. Langel
NAVIGATION: Journal of the Institute of Navigation Mar 2022, 69 (1) navi.507; DOI: 10.33012/navi.507

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Detecting Slowly Accumulating Faults Using a Bank of Cumulative Innovations Monitors in Kalman Filters
John D. Quartararo,, Steven E. Langel
NAVIGATION: Journal of the Institute of Navigation Mar 2022, 69 (1) navi.507; DOI: 10.33012/navi.507
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  • Article
    • Summary
    • 1 INTRODUCTION
    • 2 MOTIVATION FOR MULTI-MONITOR APPROACH
    • 3 ALGORITHM DESCRIPTIONS
    • 4 IMPLEMENTATION DETAILS
    • 5 ANALYSIS METHODS
    • 6 RESULTS
    • 7 SUMMARY
    • 8 FUTURE WORK
    • HOW TO CITE THIS ARTICLE
    • APPENDIX A: EFFECT OF MONITOR CROSS-CORRELATION ON FALSE ALARM RATE
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Keywords

  • anti-spoofing
  • fault detection
  • GNSS
  • GPS
  • inertial
  • innovations monitoring
  • Kalman filtering
  • sensor fusion

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