=Paper=
{{Paper
|id=Vol-2880/paper12
|storemode=property
|title=Performance Testing and Runtime Optimisation of an Independent NeQuick-G Implementation
|pdfUrl=https://ceur-ws.org/Vol-2880/paper12.pdf
|volume=Vol-2880
|authors=Nikki de Kleer,Hein Zelle
|dblpUrl=https://dblp.org/rec/conf/icl-gnss/KleerZ21
}}
==Performance Testing and Runtime Optimisation of an Independent NeQuick-G Implementation==
<pdf width="1500px">https://ceur-ws.org/Vol-2880/paper12.pdf</pdf>
<pre>
Performance Testing and Runtime Optimisation of an
Independent NeQuick-G Implementation
N.M. (Nikki) de Kleera , M.J. (Rien) Lagerwerfa and H.D. (Hein) Zellea
a
    NLR - Royal Netherlands Aerospace Centre, Anthony Fokkerweg 2, Amsterdam, 1059 CM, The Netherlands


                                           Abstract
                                           Single frequency GNSS observations require an ionospheric correction model to eliminate ranging
                                           errors caused by the ionospheric delay. The NeQuick-G algorithm is an algorithm prescribed by
                                           the Galileo GNSS system to eliminate ranging errors caused by the ionospheric delay. Compared to
                                           the Klobuchar algorithm, which is prescribed by the GPS, the NeQuick-G algorithm provides more
                                           accurate ionospheric delay estimates, at the cost of increased computational effort.
                                               In this research we propose, implement, and test an independent, runtime optimised version of
                                           the NeQuick-G algorithm. The implementation is performed in C, with the goal of running on
                                           embedded hardware. The main optimisation applied is caching of intermediate results, to avoid
                                           repeated integral computations.
                                               The NeQuick-G implementation is compared to two independent reference implementations [1] [2],
                                           both following the Galileo NeQuick-G algorithm specification [3]. The ionospheric delay estimates are
                                           shown to be identical to those of the reference implementations to within 10−10 TECU. This difference
                                           is attributed to rounding errors at machine level. The impact of result caching on the ionospheric
                                           correction quality is determined to be negligible: the average difference between non-caching and
                                           caching (30 s) TEC delay estimates is approximately 1 cm. Finally, the runtime performance of the
                                           implementation is compared to the reference implementation on modern PC hardware as well as for
                                           representative embedded hardware (Cyclone5).
                                               The independent implementation shows comparable performance to the reference algorithms.
                                           A significant runtime reduction is achieved with 30 s caching as specified in the Galileo NeQuick-
                                           G documentation. The performance measured on Cyclone5 embedded hardware suggests that the
                                           caching algorithm can be run without issues up to 50 Hz or beyond. More aggressive optimisation
                                           and caching, allowing for minor degradation of the results, is in progress and will be presented.

                                           Keywords
                                           Galileo, Ionospheric correction, NeQuick-G, Optimisation




Acknowledgments
We acknowledge the European Union and the European GNSS Agency (GSA) for supporting
the cooperation of the Galileo Reference Center (GRC) with Member States within the GRC
Grant project (Grant agreement nr. GSA/GRANT/04/2016), in support of an independent
monitoring of the Galileo system performance.




ICL-GNSS 2021 WiP Proceedings, June 01–03, 2021, Tampere, Finland
" nikki.de.kleer@nlr.nl (N.M.(.d. Kleer); rien.lagerwerf@nlr.nl (M.J.(. Lagerwerf); hein.zelle@nlr.nl (H.D.(.
Zelle)
 0000-0002-4641-110X (N.M.(.d. Kleer); 0000-0003-1916-4665 (M.J.(. Lagerwerf); 0000-0002-2690-1689
(H.D.(. Zelle)
                                       ©  2021 Copyright for this paper by its authors.
                                       Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
    CEUR
    Workshop
    Proceedings
                  http://ceur-ws.org
                  ISSN 1613-0073       CEUR Workshop Proceedings (CEUR-WS.org)
References
[1] ESA, NeQuick Galileo Ionospheric Correction Model, 2021. https://essr.esa.int/project/
    nequickg-galileo-ionospheric-correction-mode.
[2] M. A. Angel, M. Zürn, A. R. Garcia, Galileo ionospheric correction algorithm: An opti-
    mization study of nequick-g, RADIO SCIENCE (2019). doi:10.1029/2019RS006875.
[3] Ionospheric correction algorithm for galileo single frequency users, volume Issue 1.2, Euro-
    pean Commission, 2016.

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