Abstract
The provision of accurate ionospheric corrections in PPP-RTK enormously improves the performance of single-receiver user integer ambiguity resolution (IAR), thus enabling fast high precision positioning. While an external provider can disseminate such corrections to the user with a time delay, it is the task of the user to accurately time-predict the corrections so that they become applicable to the user positioning time. Accurate time prediction of the corrections requires a dynamic model in which the process noise of the corrections has to be correctly specified. In this contribution, we present an estimation method to determine the process noise variance of PPP-RTK corrections using single-receiver GNSS data. Our focus is on variance estimation of the first-order slant ionospheric delays, which allows one to analyze how the ionospheric process noise changes as a function of the solar activity, receiver local time, and receiver geographic latitude. By analyzing 11-year GNSS datasets, it is illustrated that estimates of the ionospheric process noise are strongly correlated with the solar flux index F10.7. These estimates also indicate a seasonal variation, with the highest level of variation observed during the spring and autumn equinoxes.
Similar content being viewed by others
Data availability
The GNSS data are accessible from https://cddis.nasa.gov/archive/gnss/data/ and https://data.gnss.ga.gov.au/. Likewise, the orbit products are accessible through https://cddis.nasa.gov/archive/gnss/products/mgex/. The solar flux index F10.7 data are available at https://omniweb.gsfc.nasa.gov.
References
Adebiyi S, Adimula I, Oladipo O (2014) Seasonal variations of GPS derived TEC at three different latitudes of the southern hemisphere during geomagnetic storms. Adv Space Res 53(8):1246–1254
Amiri-Simkooei A (2007) Least-squares variance component estimation: theory and GPS applications. Dissertation, Delft University of Technology
Amiri-Simkooei A, Tiberius C (2007) Assessing receiver noise using GPS short baseline time series. GPS Solut 11:21–35
Araujo-Pradere E, Fuller-Rowell T, Codrescu M, Bilitza D (2005) Characteristics of the ionospheric variability as a function of season, latitude, local time, and geomagnetic activity. Radio Sci 40(05):1–15
Carlin L, Hauschild A, Montenbruck O (2021) Precise point positioning with GPS and Galileo broadcast ephemerides. GPS Solut 25(2):77
Chen Y, Liu L, Le H (2008) Solar activity variations of nighttime ionospheric peak electron density. J Geophys Res 113(A11).
Collins P, Lahaye F, Bisnath S (2012) External ionospheric constraints for improved PPP-AR initialisation and a generalised local augmentation concept. In: Proceedings of ION GNSS 2012, Institute of Navigation, Tennessee, USA. 17–21 September, pp 3055–3065
de Bakker P, Tiberius C, Van Der Marel H, van Bree R (2012) Short and zero baseline analysis of GPS L1 C/A, L5Q, GIOVE E1B, and E5aQ signals. GPS Solut 16:53–64
Galav P, Dashora N, Sharma S, Pandey R (2010) Characterization of low latitude GPS-TEC during very low solar activity phase. J Atmos Sol-Terr Phys 72(17):1309–1317
Hernández-Pajares M, Juan JM, Sanz J, Aragón-Àngel À, García-Rigo A, Salazar D, Escudero M (2011) The ionosphere: effects, GPS modeling and the benefits for space geodetic techniques. J Geod 85:887–907
Khodabandeh A (2021) Single-station PPP-RTK: correction latency and ambiguity resolution performance. J Geod 95(4):42
Khodabandeh A, Teunissen P, Psychas D (2023) On the problem of double-filtering in PPP-RTK. Sensors 23(1):229
King J, Papitashvili N (2005) Solar wind spatial scales in and comparisons of hourly Wind and ACE plasma and magnetic field data. J Geophys Res 110(A2).
Leick A, Rapoport L, Tatarnikov D (2015) GPS satellite surveying. Wiley, Hoboken
Odijk D, Zhang B, Khodabandeh A, Odolinski R, Teunissen P (2016) On the estimability of parameters in undifferenced, uncombined GNSS network and PPP-RTK user models by means of S-system theory. J Geod 90(1):15–44
Psychas D, Khodabandeh A, Teunissen P (2022) Impact and mitigation of neglecting PPP-RTK correctional uncertainty. GPS Solut 26(1):33
Rastogi R (1960) Abnormal features of the F2 region of the ionosphere at some southern high-latitude stations. J Geophys Res 65(2):585–592
Ratovsky KG, Shi JK, Oinats AV, Romanova EB (2014) Comparative study of high-latitude, mid-latitude and low-latitude ionosphere on basis of local empirical models. Adv Space Res 54(3):509–516
Tapping K (1987) Recent solar radio astronomy at centimeter wavelengths: The temporal variability of the 10.7-cm flux. J Geophys Res 92(1):829–838
Teunissen P, de Bakker P (2013) Single-receiver single-channel multi-frequency GNSS integrity: outliers, slips, and ionospheric disturbances. J Geod 87:161–177
Teunissen P (2000) Adjustment theory: an introduction. Delf University Press, Delft
Teunissen P, Amiri-Simkooei A (2008) Least-Squares Variance Component Estimation. J Geod 82:65–82
Wübbena G, Schmitz M, Bagge A (2005) PPP-RTK: precise point positioning using state-space representation in RTK networks. In: Proceedings of ION GNSS 2005, Institute of Navigation, Long Beach, CA, USA, pp 2584–2594
Wang K, Khodabandeh A, Teunissen P (2017) A study on predicting network corrections in PPP-RTK processing. Adv Space Res 60(7):1463–1477
Zha J, Zhang B, Liu T, Hou P (2021) Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results. GPS Solut 25(4):135
Zhang B, Teunissen P, Yuan Y (2017) On the short-term temporal variations of GNSS receiver differential phase biases. J Geod 91:563–572
Acknowledgements
The GNSS data/products are made available by the International GNSS Service (IGS) and Geoscience Australia. The solar flux index F10.7 data is supplied by the GSFC/SPDF OMNIWeb interface. All this support is gratefully acknowledged.
Author information
Authors and Affiliations
Contributions
PSN and AK initiated the concept and the framework. PSN conducted the analysis and wrote the main manuscript text. All the authors reviewed and edited the manuscript.
Corresponding author
Ethics declarations
Conflict of interests
The authors declare no competing interests.
Consent to participate
Not applicable.
Consent for publication
Not applicable.
Ethics approval
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Sadegh Nojehdeh, P., Khodabandeh, A., Khoshelham, K. et al. Estimating process noise variance of PPP-RTK corrections: a means for sensing the ionospheric time-variability. GPS Solut 28, 43 (2024). https://doi.org/10.1007/s10291-023-01577-4
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10291-023-01577-4