Skip to main content

Main menu

  • Home
  • Current Issue
  • Archive
  • About Us
    • About NAVIGATION
    • Editorial Board
    • Peer Review Statement
    • Open Access
  • More
    • Email Alerts
    • Info for Authors
    • Info for Subscribers
  • Other Publications
    • ion

User menu

  • My alerts

Search

  • Advanced search
NAVIGATION: Journal of the Institute of Navigation
  • Other Publications
    • ion
  • My alerts
NAVIGATION: Journal of the Institute of Navigation

Advanced Search

  • Home
  • Current Issue
  • Archive
  • About Us
    • About NAVIGATION
    • Editorial Board
    • Peer Review Statement
    • Open Access
  • More
    • Email Alerts
    • Info for Authors
    • Info for Subscribers
  • Follow ion on Twitter
  • Visit ion on Facebook
  • Follow ion on Instagram
  • Visit ion on YouTube
Research ArticleOriginal Article
Open Access

Robust Modeling of GNSS Orbit and Clock Error Dynamics

Elisa Gallon, Mathieu Joerger, and Boris Pervan
NAVIGATION: Journal of the Institute of Navigation December 2022, 69 (4) navi.539; DOI: https://doi.org/10.33012/navi.539
Elisa Gallon
1Navigation Laboratory, Mechanical, Material and Aerospace Engineering Department, Illinois Institute of Technology, IL, U.S.A.
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: [email protected]
Mathieu Joerger,
2NAViTi Laboratory, Department of Aerospace and Ocean Engineering, Virginia Tech, VA, U.S.A.
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
Boris Pervan
1Navigation Laboratory, Mechanical, Material and Aerospace Engineering Department, Illinois Institute of Technology, IL, U.S.A.
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • Article
  • Figures & Data
  • Supplemental
  • References
  • Info & Metrics
  • PDF
Loading

Article Figures & Data

Figures

  • Tables
  • Additional Files
  • FIGURE 1
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 1

    Error generation diagram

  • FIGURE 2
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 2

    Projection of radial, along-track, and cross-track errors onto the user’s line of sight

  • FIGURE 3
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 3

    Orbit and clock errors for all GPS and Galileo satellites in all three cases at 30-s intervals in December 2018

  • FIGURE 4
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 4

    Example ephemerides interpolation (radial errors) of GPS PRN07 in December 2018 (upper), as well as its impact on radial+clock error ACF (lower)

  • FIGURE 5
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 5

    GPS and Galileo orbit and clock errors over December 2018

  • FIGURE 6
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 6

    Upper bound on standard deviation of ACF estimate (τ = 6 h, σ = 1.5 m)

  • FIGURE 7
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 7

    Statistics of the 2018 GPS/GAL orbit and clock errors

  • FIGURE 8
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 8

    Tapering window and its impact on an ACF

  • FIGURE 9
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 9

    PSDs of orbit and clock errors for (a) GPS and (b) Galileo

  • FIGURE 10
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE 10

    PSD bounding of (a) GPS Rb, (b) GAL RAFS, (c) GPS Cs, and (d) GAL PHM

  • FIGURE A2
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE A2

    GPS and Galileo ephemerides interpolation diagram

  • FIGURE A1
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE A1

    GPS PRN07 ephemerides interpolation

  • FIGURE C1
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE C1

    Example of tapering windows used in the PSD estimation process

  • FIGURE C2
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE C2

    Impact of tapering window on PSD estimate of FOGMRP in terms of spectral leakage in (a) original figure and (b) the zoomed figure

  • FIGURE C3
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE C3

    Impact of a tapering window on PSD estimate of FOGMRP in terms of data noise in (a) the original figure and (b) a zoomed-in version

  • FIGURE C4
    • Download figure
    • Open in new tab
    • Download powerpoint
    FIGURE C4

    (a) Tapered ACF and (b) PSD estimates for GPS PRN 01 orbit+clock errors

Tables

  • Figures
  • Additional Files
    • View popup
    TABLE 1

    Clocks and Blocks of Each GPS Satellite (2018–2020)

    PRN01020305060708091011121314151617
    ClockRbRbRbRbRbRbCsRbRbRbRbRbRbRbRbRb
    BlockIIFIIRIIFIIRIIFIIRIIFIIFIIFIIRIIRIIRIIRIIRIIRIIR
    PRN181920212223242526272829303132
    ClockRbRbRbRbRbRbCsRbRbRbRbRbRbRbRb
    BlockIIAIIRIIRIIRIIRIIRIIFIIFIIFIIFIIRIIRIIFIIRIIF
    • View popup
    TABLE 2

    Clocks and Blocks of Each Galileo Satellite (2018–2020)

    PRN01020305070809111213141518
    ClockPHMPHMPHMPHMPHMPHMPHMRAFSPHMPHMPHMPHMPHM
    PRN192021222425262730313336
    ClockPHMRAFSPHMRAFSPHMPHMPHMPHMPHMPHMPHMPHM
    • View popup
    TABLE 3

    PSD Bounding Summary: FOGMRP Parameters

    τb (h)σb (m)
    GPS Rb51.6
    GPS Cs51.8
    GPS All51.8
    GAL RAFS20.55
    GAL PHM20.65
    GAL All20.65
    • View popup
    TABLE D1

    GPS Radial+Clock Means Over Stationary Data Sets From 2018

    GPS PRNMean [m]Std. Dev. [m]Length [mths]
    10.151810.52102≤12
    20.2110.31693≤12
    3−0.595620.41451≤3
    30.193690.35442≤3
    30.0320220.2914≤3
    3−0.337540.28413≤9
    50.225660.33265≤12
    60.0427760.30049≤12
    70.0237680.47918≤12
    8−0.0293571.1326≤12
    90.0648820.36227≤12
    10−0.109170.2902≤12
    11−0.049910.46482≤12
    12−0.0955590.30714≤12
    13−0.0703580.44447≤12
    14−0.00537350.33284≤12
    150.124530.26539≤12
    160.188510.30236≤12
    17−0.0116780.74955≤12
    18−0.109580.79282≤9
    190.243240.27517≤12
    200.167950.27282≤12
    210.165030.38677≤12
    220.248050.2823≤9
    220.0443980.27601≤3
    220.354080.27412≤3
    23−0.109550.27479≤12
    24−0.116471.4026≤12
    25−0.159570.30715≤9
    25−0.20880.26378≤6
    26−0.276040.37371≤3
    260.126750.24348≤3
    26−0.226160.31531≤9
    27−0.162670.18802≤3
    270.0171110.23106≤6
    270.190580.29172≤3
    27−0.0463870.32942≤3
    270.192490.26256≤3
    28−0.00592121.0776≤12
    290.158550.61683≤12
    30−0.0802410.29056≤12
    300.185930.26506≤3
    31−0.158510.48574≤12
    32−0.0433640.28695≤12
    • View popup
    TABLE D2

    GAL Radial+Clock Means Over Stationary Data Sets from 2018

    GAL PRNMean [m]Std. Dev. [m]Length [mths]
    10.0912140.24568≤6
    10.0785550.21544≤3
    1−0.422040.22004≤3
    1−0.0388230.21709≤3
    1−0.425190.23084≤3
    1−0.0197010.23685≤3
    20.0154090.2775≤3
    20.0126960.21544≤6
    2−0.122530.22308≤9
    3−0.0260170.22428≤6
    3−0.188050.18314≤9
    4−0.0178090.23644≤6
    4−0.186040.18491≤9
    5−0.0723060.24484≤6
    5−0.25840.1949≤9
    70.0487840.21218≤12
    8−0.12010.22493≤12
    9−0.0215830.24177≤6
    9−0.155460.2156≤9
    110.0751130.28793≤12
    12−0.00313220.25776≤6
    12−0.118560.23787≤9
    190.0363880.2193≤12
    21−0.376970.25023≤3
    240.058250.23793≤6
    24−0.0614140.21475≤9
    25−0.229880.23432≤6
    26−0.0456810.31476≤6
    26−0.258120.22305≤9
    27−0.126510.24678≤6
    300.0618760.28908≤6
    30−0.0542810.25925≤9
    31−0.163860.23093≤6

Additional Files

  • Figures
  • Tables
  • Video Abstract

PreviousNext
Back to top

In this issue

NAVIGATION: Journal of the Institute of Navigation: 69 (4)
NAVIGATION: Journal of the Institute of Navigation
Vol. 69, Issue 4
Winter 2022
  • Table of Contents
  • Index by author
Print
Download PDF
Article Alerts
Sign In to Email Alerts with your Email Address
Email Article

Thank you for your interest in spreading the word on NAVIGATION: Journal of the Institute of Navigation.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
Robust Modeling of GNSS Orbit and Clock Error Dynamics
(Your Name) has sent you a message from NAVIGATION: Journal of the Institute of Navigation
(Your Name) thought you would like to see the NAVIGATION: Journal of the Institute of Navigation web site.
Citation Tools
Robust Modeling of GNSS Orbit and Clock Error Dynamics
Elisa Gallon, Mathieu Joerger,, Boris Pervan
NAVIGATION: Journal of the Institute of Navigation Dec 2022, 69 (4) navi.539; DOI: 10.33012/navi.539

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Share
Robust Modeling of GNSS Orbit and Clock Error Dynamics
Elisa Gallon, Mathieu Joerger,, Boris Pervan
NAVIGATION: Journal of the Institute of Navigation Dec 2022, 69 (4) navi.539; DOI: 10.33012/navi.539
Twitter logo Facebook logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Google Plus One
Bookmark this article

Jump to section

  • Article
    • Abstract
    • 1 INTRODUCTION
    • 2 ORBIT AND CLOCK ERROR CHARACTERIZATION OVER TIME
    • 3 ERROR STATIONARITY ANALYSIS
    • 4 ROBUST MODELING OF ORBIT AND CLOCK ERRORS
    • 5 CONCLUSION
    • HOW TO CITE THIS ARTICLE
    • ACKNOWLEDGMENTS
    • APPENDIX A EPHEMERIS INTERPOLATION
    • APPENDIX B VARIANCE OF AUTOCORRELATION ESTIMATES
    • APPENDIX C SENSITIVITY OF PSD ESTIMATION TO PARAMETER SELECTION
    • APPENDIX D GPS AND GALILEO ORBIT AND CLOCK MEAN ERRORS
    • REFERENCES
  • Figures & Data
  • Supplemental
  • References
  • Info & Metrics
  • PDF

Related Articles

  • Google Scholar

Cited By...

  • No citing articles found.
  • Google Scholar

More in this TOC Section

  • GNSS L5/E5a Code Properties in the Presence of a Blanker
  • Robust Interference Mitigation in GNSS Snapshot Receivers
  • Identification of Authentic GNSS Signals in Time-Differenced Carrier-Phase Measurements with a Software-Defined Radio Receiver
Show more Original Article

Similar Articles

Keywords

  • ARAIM
  • error modeling
  • GNSS
  • INS
  • integrity
  • Kalman filter
  • orbit error

Unless otherwise noted, NAVIGATION content is licensed under a Creative Commons CC BY 4.0 License.

© 2025 The Institute of Navigation, Inc.

Powered by HighWire