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Research ArticleOriginal Article
Open Access

Case study of Bayesian RAIM algorithm integrated with Spatial Feature Constraint and Fault Detection and Exclusion algorithms for multi-sensor positioning

Jelena Gabela, Allison Kealy, Mark Hedley and Bill Moran
NAVIGATION: Journal of the Institute of Navigation June 2021, 68 (2) 333-351; DOI: https://doi.org/10.1002/navi.433
Jelena Gabela
1Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, Australia
2Department of Geospatial Science, Royal Melbourne Institute of Technology, Victoria, Australia
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  • For correspondence: [email protected]
Allison Kealy
2Department of Geospatial Science, Royal Melbourne Institute of Technology, Victoria, Australia
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Mark Hedley
3Data 61, Commonwealth Scientific and Industrial Research Organisation, New South Wales, Australia
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Bill Moran
1Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, Australia
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Article Figures & Data

Figures

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  • ALGORITHM 1
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    ALGORITHM 1

    Pseudocode for BRAIM

  • ALGORITHM 2
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    ALGORITHM 2

    Pseudocode for FDE+BRAIM

  • FIGURE 1
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    FIGURE 1

    Example of how BRAIM works. Weights of particles within AL (green) are summarized

  • ALGORITHM 3
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    ALGORITHM 3

    Pseudocode for SFC+BRAIM

  • FIGURE 2
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    FIGURE 2

    Example of how SFC+BRAIM works. Weights of particles within AL and the road feature are summarized

  • FIGURE 3
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    FIGURE 3

    Dynamic node (i.e., user) equipped with GNSS receiver and WASP sensor

  • FIGURE 4
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    FIGURE 4

    Data collection area with anchor nodes set up around the improvised road

  • FIGURE 5
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    FIGURE 5

    The trajectory of the dynamic node (red) and the locations of the anchor nodes (white pins)

  • FIGURE 6
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    FIGURE 6

    The velocity of the dynamic node during the data collection, as seen in Gabela et al., 2019

  • FIGURE 7
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    FIGURE 7

    Integrity estimation for GPS+WASP data depending on the applied integrity monitoring algorithm

  • FIGURE 8
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    FIGURE 8

    Integrity estimation for GPS+WASP(GMM) data for road-level positioning depending on the applied algorithm

  • FIGURE 9
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    FIGURE 9

    Integrity availability assessment for GPS+WASP data set for road-level positioning depending on the applied integrity monitoring algorithm

  • FIGURE 10
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    FIGURE 10

    Integrity availability assessment for GPS+WASP(GMM) data for road-level positioning depending on the applied algorithm

Tables

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    TABLE 1

    Three-component Gaussian Mixture Model (GMM)

    Parameters/Component number123
    μ[m]0.0111-0.50850.0776
    σ2[m2]0.0176 0.53350.0171
    ω0.4321 0.04140.5265
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    TABLE 2

    Positioning performance results

    DataAlgorithmAvg HPE [m]Std [m]Max [m]
    GBa4.323.8521.14
    FDE+B2.961.4119.26
    SFC+B map+ 1m3.032.0216.89
    SFC+B2.911.8015.83
    FDE+SFC+B map+ 1m2.621.129.42
    FDE+SFC+B2.631.199.44
    G+W GaussianB0.250.171.74
    SFC+B map+lm0.240.140.91
    SFC+B0.270.151.52
    FDE+SFC+B map+ 1m0.250.161.18
    FDE+SFC+B0.280.171.60
    G+W GMMB0.260.284.31
    FDE+B0.310.445.46
    SFC+B map+ 1m0.240.203.43
    SFC+B0.260.264.68
    FDE+SFC+B map+ 1m0.290.355.33
    FDE+SFC+B0.310.425.99
    • ↵a BRAIM (B).

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    TABLE 3

    Estimated integrity for HAL = 5 m

    DataAlgorithmMed PMIAvg PMIMax PMI
    GBa2.59e-013.18e-010.92
    FDE+B2.53e-013.05e-010.71
    SFC+B map+ 1m1.26e-011.64e-010.76
    SFC+B1.09e-011.47e-010.68
    FDE+SFC+B map+ 1m1.23e-011.55e-010.56
    FDE+SFC+B1.06e-011.34e-010.58
    G+W GaussianB3.31e-105.24e-058.26e-03
    FDE+B2.68e-102.81e-081.84e-06
    SFC+B map+ 1m5.71e-124.89e-061.22e-03
    SFC+B1.325e-5.07e-064.49e-03
    12
    FDE+SFC+B map+ 1m5.48e-129.06e-102.97e-07
    FDE+SFC+B1.326e-1.86e-091.52e-06
    12
    G+W GMMB6.97e-071.08e-030.15
    FDE+B9.67e-073.90e-030.98
    SFC+B map+ 1m5.81e-082.05e-040.10
    SFC+B2.94e-084.29e-040.37
    FDE+SFC+B map+ 1m9.68e-088.94e-040.20
    FDE+SFC+B3.39e-087.40e-040.21
    • ↵a BRAIM (B).

    • View popup
    TABLE 4

    Estimated integrity for HAL = 1.1 m

    DataAlgorithmMed PMIAvg PMIMax PMI
    G+W GaussianBa4.08e-027.09e-020.78
    FDE+B3.94e-026.31e-020.65
    SFC+B map+ 1m4.03e-026.91e-020.73
    SFC+B2.95e-024.82e-020.70
    FDE+SFC+B map+ 1m3.96e-026.19e-020.28
    FDE+SFC+B2.86e-024.34e-020.9999998
    G+W GMMB5.40e-034.02e-020.999995
    FDE+B5.73e-034.48e-020.9993
    SFC+B map+ 1m4.71e-033.51e-020.99995
    SFC+B3.40e-032.57e-020.99
    FDE+SFC+B map+ 1m5.79e-034.03e-020.998
    FDE+SFC+B3.80e-033.41e-021.00
    • ↵a BRAIM (B).

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NAVIGATION: Journal of the Institute of Navigation: 68 (2)
NAVIGATION: Journal of the Institute of Navigation
Vol. 68, Issue 2
Summer 2021
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Case study of Bayesian RAIM algorithm integrated with Spatial Feature Constraint and Fault Detection and Exclusion algorithms for multi-sensor positioning
Jelena Gabela, Allison Kealy, Mark Hedley, Bill Moran
NAVIGATION: Journal of the Institute of Navigation Jun 2021, 68 (2) 333-351; DOI: 10.1002/navi.433

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Case study of Bayesian RAIM algorithm integrated with Spatial Feature Constraint and Fault Detection and Exclusion algorithms for multi-sensor positioning
Jelena Gabela, Allison Kealy, Mark Hedley, Bill Moran
NAVIGATION: Journal of the Institute of Navigation Jun 2021, 68 (2) 333-351; DOI: 10.1002/navi.433
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    • Abstract
    • 1 INTRODUCTION
    • 2 MATHEMATICAL FRAMEWORK
    • 3 EXPERIMENTAL VALIDATION AND PERFORMANCE EVALUATION METRICS
    • 4 RESULTS
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Keywords

  • Bayesian Receiver Autonomous Integrity Monitoring
  • GNSS
  • Local Positioning System
  • multi-sensor positioning
  • particle filter
  • Spatial Feature Constraint

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