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Research ArticleOriginal Article
Open Access

SBAS Protection Levels with Gauss-Markov K-Factors for Any Integrity Target

Julie Antic, Odile Maliet, and Sébastien Trilles
NAVIGATION: Journal of the Institute of Navigation September 2023, 70 (3) navi.594; DOI: https://doi.org/10.33012/navi.594
Julie Antic
THALES ALENIA SPACE, Toulouse, France
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  • For correspondence: [email protected] [email protected] [email protected]
Odile Maliet,
THALES ALENIA SPACE, Toulouse, France
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  • For correspondence: [email protected] [email protected] [email protected]
Sébastien Trilles
THALES ALENIA SPACE, Toulouse, France
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  • For correspondence: [email protected] [email protected] [email protected]
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  • FIGURE 1
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    FIGURE 1

    Illustration of the auto-correlation function of SFI real data, MOPS, and Gauss-Markov (GM) models

  • FIGURE 2
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    FIGURE 2

    Ilustration of PSD overbounding of SFI by Gauss-Markov (GM) processes with different correlation times (τ)

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    FIGURE 3

    Validation of the exact formula for the GMK-factor.

  • FIGURE 4
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    FIGURE 4

    Comparison of the exact and asymptotic formulae used for GMK-factors with T/τ equals 1.

  • FIGURE 5
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    FIGURE 5

    GMK-factors and MOPS K-factors versus the correlation time τ. The explicit formula was used in the independent case (i.e., τ = 0).

  • FIGURE 6
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    FIGURE 6

    GMK-factors for new SBAS uses versus the correlation time. The explicit formula was used in the independent case (i.e., τ = 0).

  • FIGURE 7
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    FIGURE 7

    GMK-factors evaluated for vertical IR between 10−4/h and 10−9/h with respect to correlation time τ

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    FIGURE 8

    GMK-factors evaluated for horizontal IR between 10−4 and 10−7 with respect to correlation time τ

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    TABLE 1

    Integrity Requirements of Aviation Approaches Supported by SBAS

    Typical operationIR in fault-free conditionsTime interval T(sec)Component
    APV I, APV II, CAT I10−7150Vertical
    APV I, APV II, CAT I10−9150Horizontal
    En-Route, Terminal, NPA5 x 10−83600Horizontal
    • Note: APV I: approach with vertical guidance; CAT: category; NPA: non precision approach.

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NAVIGATION: Journal of the Institute of Navigation: 70 (3)
NAVIGATION: Journal of the Institute of Navigation
Vol. 70, Issue 3
Fall 2023
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SBAS Protection Levels with Gauss-Markov K-Factors for Any Integrity Target
Julie Antic, Odile Maliet,, Sébastien Trilles
NAVIGATION: Journal of the Institute of Navigation Sep 2023, 70 (3) navi.594; DOI: 10.33012/navi.594

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SBAS Protection Levels with Gauss-Markov K-Factors for Any Integrity Target
Julie Antic, Odile Maliet,, Sébastien Trilles
NAVIGATION: Journal of the Institute of Navigation Sep 2023, 70 (3) navi.594; DOI: 10.33012/navi.594
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  • Article
    • Abstract
    • 1 INTRODUCTION
    • 2 STATE OF THE ART: MOPS K-FACTORS
    • 3 GMK METHOD: GAUSS-MARKOV FOR K-FACTOR DETERMINATION
    • 4 APPLICATIONS
    • 5 CONCLUSION AND PERSPECTIVES
    • HOW TO CITE THIS ARTICLE
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Keywords

  • GNSS augmentation
  • integrity risk
  • K-factor
  • protection level
  • SBAS

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