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Conservative Estimation of Inertial Sensor Errors Using Allan Variance Data

Kyle A. Lethander and Clark N. Taylor
NAVIGATION: Journal of the Institute of Navigation September 2023, 70 (3) navi.563; DOI: https://doi.org/10.33012/navi.563

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  • TABLE 1

    Sources of Noise With Associated Allan Variance (AV) Slopes

    Error MechanismAV effectEmbedded Image slopeUnits
    (gyro.)    		Units
    (accel.)    		τread
    QuantizationEmbedded Image−2deg2m2s−2Embedded Image
    Random walkβrwτ−1/2−1deg2 s−1m2 s−31
    Bias instabilityEmbedded Image0deg2 s−2m2 s−4argmin Embedded Image
    Rate random walkEmbedded Image+1deg2 s−3m2 s−53
    Rate rampEmbedded Image+2deg2 s−4m2 s−6Embedded Image
  • TABLE 2

    χ2 Simulation Results

    Number of trials1001001,0001,00010,00010,000
    Percent overbound94.6294.3494.5994.8694.9794.97
  • TABLE 3

    Noise Coefficients Selected for Monte-Carlo Simulation

    Error MechanismMagnitudeUnits
    Quantization, σq1.0 × 10−7deg
    Random walk, σrw4.0 × 10−3deg s−1/2
    Bias instability, σb1.0 × 10−3deg s−1
    Rate random walk, σrrw2.0 × 10−4deg s−3/2
    Rate ramp, σrr1.0 × 10−8deg s−2
  • TABLE 4

    A Quantitative Comparison Between ARMAV and GMWM

    1 hour3 hours5 hours
    Method% belowRMSE log% belowRMSE log% belowRMSE log
    ARMAV weighted74.34 %0.0982.38 %0.0983.88 %0.08
    Constrained ARMAV15.02 %0.3517.66 %0.2918.91 %0.28
    C-ARMAV w/ χ20.39 %0.390.51 %0.520.42 %0.44
    GMWM weighted75.98 %0.1083.14 %0.1084.37 %0.09
    Constrained GMWM16.34 %0.1716.78 %0.1117.01 %0.13
    C-GMWM w/ χ20.58 %0.280.38 %0.270.43 %0.19
  • TABLE 5

    ADIS16470 Calculated Noise Coefficient Statistics: Random Walk, Bias Instability, and Rate Random Walk

    Measured SignalNoise CoefficientDatasheetGMWMCGMWMCGMWM w/ χ2 upper bound
    Embedded ImagesEmbedded ImagesEmbedded Images
    x-axis gyroσrw (deg s−1/2)5.67 × 10−33.66 × 10−31.30 × 10−53.77 × 10−32.97 × 10−53.77 × 10−35.96 × 10−5
    σb (deg s−1)2.22 × 10−35.03 × 10−41.64 × 10−42.11 × 10−42.05 × 10−45.01 × 10−42.12 × 10−3
    σrrw (deg s−3/2)–4.02 × 10−45.62 × 10−54.94 × 10−43.31 × 10−57.42 × 10−45.21 × 10−4
    y-axis gyroσrw5.67 × 10−32.73 × 10−31.16 × 10−52.73 × 10−31.52 × 10−52.73 × 10−31.41 × 10−5
    σb2.22 × 10−31.30 × 10−37.39 × 10−52.20 × 10−37.09 × 10−42.14 × 10−35.67 × 10−4
    σrrw–1.29 × 10−42.73 × 10−54.89 × 10−41.93 × 10−45.74 × 10−41.65 × 10−4
    z-axis gyroσrw5.67 × 10−33.90 × 10−34.68 × 10−63.91 × 10−31.40 × 10−53.93 × 10−32.13 × 10−5
    σb2.22 × 10−31.11 × 10−36.01 × 10−51.33 × 10−32.39 × 10−41.30 × 10−31.72 × 10−4
    σrrw–2.61 × 10−44.15 × 10−53.13 × 10−41.81 × 10−54.94 × 10−42.44 × 10−4
  • TABLE 6

    Percent Overbound Between Models Generated From and the Allan Variance for 20 Data Collects of a Single Sensor

    AxisGMWM Overbound %CGMWM + χ2 overbound %
    x43.59%98.13%
    y51.34%90.13%
    z47.28%99.12%

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Conservative Estimation of Inertial Sensor Errors Using Allan Variance Data
Kyle A. Lethander, Clark N. Taylor
NAVIGATION: Journal of the Institute of Navigation Sep 2023, 70 (3) navi.563; DOI: 10.33012/navi.563
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