Article Figures & Data
Figures
- FIGURE 1
Effect of model uncertainty on the true probability of false alarm for a cumulative chi-square monitor
- FIGURE 2
Minimum detectable error for a cumulative chi-square monitor
- FIGURE 3
One example of a FIND configuration
- FIGURE 4
Performance analysis flowchart for cumulative innovations monitor
- 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
Best case Pmd for snapshot, IH, and FIND monitors (CAIEV analysis)
- 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
FIND false alarm rate as a function of the detection threshold
Tables
Time Update Measurement Update 
Accelerometers (per-axis) Gyroscopes (per-axis) Bias (m/s2) Noise Root PSD Bias (rad/s) Noise Root PSD Turn-On In-Run Turn-On In-Run Tactical 0.9 × 1e-2 0.1 × 1e-2 0.9 × 5e-5 0.1 × 5e-5 Aviation 0.9 × 1e-3 0.1 × 1e-3 0.9 × 5e-8 0.1 × 5e-8 - 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)
Tactical Aviation Snapshot IH FIND Snapshot IH FIND Fault Magnitude (m) 250 2 8 8 500 No Data 2 8 100 750 19 48 100 1,000 0 0 1 84 100 100 1,250 1 1 50 99 100 100 1,500 2 7 100 2,000 8 6 100 2,500 40 0 100 No Data 3,000 90 3 100 3,500 100 2 100 4,000 100 100 100 - 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.
Tactical Aviation Snapshot IH FIND Snapshot IH FIND Fault Magnitude (m) 250 - - - 500 No Data - - 130 750 - - 62 1,000 - - - - 197 41 1,250 - - - 123 144 27 1,500 - - 44 2,000 - - 21 2,500 - - 16 No Data 3,000 - - 13 3,500 21 - 11 4,000 14 111 10 - 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.
Tactical Aviation Snapshot IH FIND Snapshot IH FIND Fault Magnitude (m) 250 - - - 500 No Data - - 23 750 - - 8 1,000 - - - - 108 5 1,250 - - - 53 72 3 1,500 - - 8 2,000 - - 2 2,500 - - 2 No Data 3,000 - - 1 3,500 4 - 1 4,000 2 137 1
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