Abstract
Ionospheric models are applied for computing the Total Electron Content (TEC) in ionosphere to reduce its effects on the Global Navigation Satellite System (GNSS)-based Standard Point Positioning (SPP) applications. However, the accuracy of these models is limited due to the simplified model structures and their dependency on the calibration period. In this study, we present a sequential Calibration approach based on the Ensemble Kalman Filter (C-EnKF) to improve TEC estimations. The advantage of C-EnKF, over the frequently implemented state-of-the-art, is that a short period of GNSS network measurements is needed to calibrate model parameters. To demonstrate the results, the International Reference Ionosphere (IRI)-2016 model is used as reference and the Vertical TEC (VTEC) estimates from 53 IGS (the International GNSS Service) stations in Europe are applied as observation. The C-EnKF is applied to calibrate four selected model parameters (i.e., \(IG_{12}\), URSI(771), URSI(1327) and URSI(1752) related to the ionospheric activity as well as height and density peak-modelling in the F2 layer), which are identified by performing a sensitivity analysis. The calibrated model, called ‘C-EnKF-IRI’, is localized within Europe and can be used for near-real time TEC estimations and forecasting of the next day (at least). Validation against the dual frequency GNSS measurements of three IGS stations indicates that during September 2017, the accuracy of forecasting VTECs is improved up to 64.87% compared to IRI-2016. The electron density (Ne) profiles of C-EnKF-IRI are validated against those of COSMIC products, which indicates \(\sim \)38.1% improvement during days with low (\(Kp=3\)) and high (\(Kp=8\)) geomagnetic activity. Applying the forecasts of VTECs in SPP experiments shows similar performance as the 11-days delayed IONEX data, i.e., 51%, 52% and 79%, improvements in estimating ionospheric contributions compared to the usage of the original IRI-2016, Klobuchar and NeQuick-G models, respectively. The TEC forecasts of C-EnKF-IRI are found to be of the same quality of the IONEX final TEC products in SPP applications.
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Data availability
The GPS data, final precise GPS satellite orbit and clock products that support the findings of this study are available in the Crustal Dynamics Data Information System which can be accessed from ftp://cddis.gsfc.nasa.gov/. The Differential Code Bias (DCB) product are available from http://ftp.aiub.unibe.ch/BSWUSER52/ORB/. The COSMIC data are available from http://www.cosmic.ucar.edu. The Ionosonde data in Europe are available from https://www.ukssdc.ac.uk/cgi-bin/digisondes/cost_database.pl. The localized TEC estimates within Europe for the entire September 2017 will be provided by efo@plan.aau.dk per request.
References
Ahluwalia HS (2000) Ap time variations and interplanetary magnetic field intensity. J Geophys Res Space Phys 105(A12):27481–27487. https://doi.org/10.1029/2000JA900124
Allen J (2004) The ap* index of maximum 24-hour disturbance for storm events
An X, Meng X, Chen H, Jiang W, Xi R, Chen Q (2020) Modelling global ionosphere based on multi-frequency, multi-constellation GNSS observations and IRI model. Remote Sens 12(3):439. https://doi.org/10.3390/rs12030439
Andersen OB, Knudsen P, Berry PA (2010) The DNSC08GRA global marine gravity field from double retracked satellite altimetry. J Geodesy 84(3):191–199. https://doi.org/10.1007/s00190-009-0355-9
Aragon-Angel A, Zürn M, Rovira-Garcia A (2019) Galileo ionospheric correction algorithm: an optimization study of NeQuick-G. Radio Sci 54(11):1156–1169. https://doi.org/10.1029/2019RS006875
Bilitza D (2001) International reference ionosphere 2000. Radio Sci 36(2):261–275. https://doi.org/10.1029/2000RS002432
Bilitza D (2018) IRI the international standard for the ionosphere. Adv Radio Sci 16. https://doi.org/10.5194/ars-16-1-2018
Bilitza D, Altadill D, Truhlik V, Shubin V, Galkin I, Reinisch B, Huang X (2017) International reference ionosphere 2016: from ionospheric climate to real-time weather predictions. Space Weather 15(2):418–429. https://doi.org/10.1002/2016SW001593
Boehm J, Niell A, Tregoning P, Schuh H (2006) Global mapping function (GMF): a new empirical mapping function based on numerical weather model data. Geophys Res Lett 33(7). https://doi.org/10.1029/2005GL025546
Borries C, Jakowski N, Jacobi C, Hoffmann P, Pogoreltsev A (2007) Spectral analysis of planetary waves seen in ionospheric total electron content (TEC): first results using GPS differential TEC and stratospheric reanalyses. J Atmos Solar Terr Phys 69(17–18):2442–2451. https://doi.org/10.1016/j.jastp.2007.02.004
Boulic R, Thalmann NM, Thalmann D (1990) A global human walking model with real-time kinematic personification. Vis Comput 6(6):344–358. https://doi.org/10.1007/BF01901021
Bouya Z, Terkildsen, M, Neudegg D (2010) Regional GPS-based ionospheric TEC model over australia using spherical cap harmonic analysis, cosp, 38, 4
Brown S, Bilitza D, Yigit E (2018) Ionosonde-based indices for improved representation of solar cycle variation in the international reference ionosphere model. J Atmospheric Solar-Terrestrial Phys 171:137–146. https://doi.org/10.1016/j.jastp.2017.08.022
Brown S, Bilitza D, Yiğit E (2018) Ionosonde-based indices for improved representation of solar cycle variation in the international reference ionosphere model. J Atmos Solar Terr Phys 171:137–146. https://doi.org/10.1016/j.jastp.2017.08.022
Bust G, Datta-Barua S (2014) Scientific investigations using IDA4D and EMPIRE, Modeling the Ionosphere-Thermosphere System, pp 283–297. https://doi.org/10.1002/9781118704417.ch23
Bust G, Garner T, Gaussiran T (2004) Ionospheric data assimilation three-dimensional (IDA3D): A global, multisensor, electron density specification algorithm. J Geophys Res: Space Phys 109(A11). https://doi.org/10.1029/2003JA010234
CCIR C (1967) Atlas of ionospheric characteristics
COSMIC Program Office (2013) http://cdaac-www.cosmic.ucar.edu/cdaac/products.html
Daniell RE, Brown L, Anderson D, Fox M, Doherty PH, Decker D, Sojka JJ, Schunk RW (1995) Parameterized ionospheric model: a global ionospheric parameterization based on first principles models. Radio Sci 30(5):1499–1510. https://doi.org/10.1029/95RS01826
Dubey S, Wahi R, Gwal A (2006) Ionospheric effects on GPS positioning. Adv Space Res 38(11):2478–2484. https://doi.org/10.1016/j.asr.2005.07.030
Engfeldt A (2005) Network RTK in northern and central Europe, Lantmäteriet
Erdogan E, Schmidt M, Goss A, Görres B, Seitz F (2020) Adaptive modeling of the global ionosphere vertical total electron content. Remote Sens 12(11):1822. https://doi.org/10.3390/rs12111822
Evensen G (2003) The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn 53(4):343–367. https://doi.org/10.1007/s10236-003-0036-9
Evensen G (2009) The Ensemble Kalman filter for combined state and parameter estimation. IEEE Control Syst Mag 29(3):83–104. https://doi.org/10.1109/MCS.2009.932223
Farzaneh S, Forootan E (2018) Reconstructing regional ionospheric electron density: a combined spherical slepian function and empirical orthogonal function approach. Surv Geophys 39(2):289–309. https://doi.org/10.1007/s10712-017-9446-y
Farzaneh S, Forootan E (2020) A least squares solution to regionalize VTEC estimates for positioning applications. Remote Sens. 12(21):3545. https://doi.org/10.3390/rs12213545
Feltens J, Schaer S (1998) IGS products for the ionosphere. In: Proceedings of the 1998 IGS Analysis Center Workshop Darmstadt, Germany, pp 3–5
Forootan E, Farzaneh S, Kosary M, Schmidt M, Schumacher M (2020) A simultaneous calibration and data assimilation (C/DA) to improve nrlmsise00 using thermospheric neutral density (TND) from space-borne accelerometer measurements. Geophys J Int 224(2):1096–1115. https://doi.org/10.1093/gji/ggaa507
Forootan E, Kosary M, Farzaneh S, Kodikara T, Vielberg K, Fernandez-Gomez I, Borries C, Schumacher M (2022) Forecasting global and multi-level thermospheric neutral density and ionospheric electron content by tuning models against satellite-based accelerometer measurements. Sci Rep 12:2095. https://doi.org/10.1038/s41598-022-05952-y
Gan Y, Duan Q, Gong W, Tong C, Sun Y, Chu W, Ye A, Miao C, Di Z (2014) A comprehensive evaluation of various sensitivity analysis methods: a case study with a hydrological model. Environ Model Softw 51:269–285. https://doi.org/10.1016/j.envsoft.2013.09.031
Goncharenko L, Chau J, Condor P, Coster A, Benkevitch L (2013) Ionospheric effects of sudden stratospheric warming during moderate-to-high solar activity: case study of January 2013. Geophys Res Lett 40(19):4982–4986. https://doi.org/10.1002/grl.50980
Gonzalez WD, Tsurutani BT, De Gonzalez ALC (1999) Interplanetary origin of geomagnetic storms. Space Sci Rev 88(3):529–562. https://doi.org/10.1023/A:1005160129098
Goss A, Schmidt M, Erdogan E, Seitz F (2020) Global and regional high-resolution VTEC modelling using a two-step B-spline approach. Remote Sens 12(7):1198. https://doi.org/10.3390/rs12071198
Groves PD (2015) Principles of GNSS, inertial, and multisensor integrated navigation systems, 2nd edition [book review]. IEEE Aerosp Electron Syst Mag 30(2):26–27. https://doi.org/10.1109/MAES.2014.14110
He J, Yue X, Le H, Ren Z, Wan W (2020) Evaluation on the quasi-realistic ionospheric prediction using an ensemble Kalman filter data assimilation algorithm Space Weather 18(3):e2019SW002,410. https://doi.org/10.1029/2019SW002410
Hernández-Pajares M, Juan J, Sanz J, Orus R, Garcia-Rigo A, Feltens J, Komjathy A, Schaer S, Krankowski A (2009) The IGS VTEC maps: a reliable source of ionospheric information since 1998. J Geodesy 83(3–4):263–275. https://doi.org/10.1007/s00190-008-0266-1
Hoque MM, Jakowski N, Cahuasquí JA (2020) Fast ionospheric correction algorithm for Galileo single frequency users, In: 2020 European navigation conference (ENC), pp 1–10. https://doi.org/10.23919/ENC48637.2020.9317502
Håkansson M (2020) Nadir-dependent GNSS code biases and their effect on 2D and 3D ionosphere modeling. Remote Sens 12(6). https://doi.org/10.3390/rs12060995
ICD (2017a) BeiDou navigation satellite system signal in space interface control document open service signal B1C (Version 1.0), China Satellite Navigation Office, http://www.beidou.gov.cn/xt/gfxz/201712/P020171226741342013031.pdf
ICD (2017b) BeiDou navigation satellite system signal in space interface control document open service signal B2a (Version 1.0). China Satellite Navigation Office, http://www.beidou.gov.cn/xt/gfxz/201712/P020171226742357364174.pdf
ICD (2020) BeiDou navigation satellite system signal in space interface control document open service signal B2b (Version 1.0), China Satellite Navigation Office. http://en.beidou.gov.cn/SYSTEMS/ICD/202008/P020200803539206360377.pdf
Jakowski N, Mayer C, Hoque M, Wilken V (2011) Total electron content models and their use in ionosphere monitoring. Radio Sci 46(06):1–11. https://doi.org/10.1029/2010RS004620
Jee G, Lee H.-B., Kim Y. H., Chung J.-K., Cho J (2010) Assessment of GPS global ionosphere maps (GIM) by comparison between CODE GIM and TOPEX/Jason TEC data: ionospheric perspective. J Geophys Res: Space Phys 115(A10). https://doi.org/10.1029/2010JA015432
Johnston G, Riddell A, Hausler G (2017) The international GNSS service. Springer, Cham, pp 967–982. https://doi.org/10.1007/978-3-319-42928-1_33
Jones WB, Gallet RM (1962) Representation of diurnal and geographic variations of ionospheric data by numerical methods. Telecommun J 29(5):129–147
Katamzi Z, Smith N, Mitchell C, Spalla P, Materassi M (2012) Statistical analysis of travelling ionospheric disturbances using TEC observations from geostationary satellites. J Atmos Solar Terr Phys 74:64–80. https://doi.org/10.1016/j.jastp.2011.10.006
Kedar S, Hajj GA, Wilson BD, Heflin MB (2003) The effect of the second order GPS ionospheric correction on receiver positions. Geophys Res Lett 30(16). https://doi.org/10.1029/2003GL017639
Kelley MC (2009) The earth’s ionosphere: plasma physics and electrodynamics. Academic Press
Klobuchar JA (1987) Ionospheric time-delay algorithm for single frequency GPS users. IEEE Trans Aerospace Electron Syst AES-23(3), 325–331. https://doi.org/10.1109/TAES.1987.310829
Krypiak-Gregorczyk A, Wielgosz P, Jarmołowski W (2017) A new TEC interpolation method based on the least squares collocation for high accuracy regional ionospheric maps. Measur Sci Technol 28(4):045801. https://doi.org/10.1088/1361-6501/aa58ae
Kursinski ER, Hajj GA, Schofield JT, Linfield RP, Hardy KR (1997) Observing earth’s atmosphere with radio occultation measurements using the global positioning system. J Geophys Res: Atmospheres 102(D19):23429–23465. https://doi.org/10.1029/97JD01569
Lei J, Syndergaard S, Burns AG, Solomon SC, Wang W, Zeng Z, Roble RG, Wu Q, Kuo Y-H, Holt JM, et al.(2007) Comparison of COSMIC ionospheric measurements with ground-based observations and model predictions: preliminary results. J Geophys Res: Space Phys 112(A7). https://doi.org/10.1029/2006JA012240
Li X, Guo D (2010) Modeling and prediction of ionospheric total electron content by time series analysis. In: 2010 2nd International Conference on Advanced Computer Control, vol 2, pp. 375–379. IEEE, https://doi.org/10.1109/ICACC.2010.5486653
Li Z, Yuan Y, Wang N, Hernandez-Pajares M, Huo X (2015) SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions. J Geodesy 89(4):331–345. https://doi.org/10.1007/s00190-014-0778-9
Liou Y-A, Pavelyev AG, Liu S-F, Pavelyev AA, Yen N, Huang C-Y, Fong C-J (2007) FORMOSAT-3/COSMIC GPS radio occultation mission: preliminary results. IEEE Trans Geosci Remote Sens 45(11):3813–3826. https://doi.org/10.1109/TGRS.2007.903365
Liu L, Yao Y, Zou S, Kong J, Shan L, Zhai C, Zhao C, Wang Y (2019) Ingestion of GIM-derived TEC data for updating IRI-2016 driven by effective IG indices over the European region. J Geodesy 93(10):1911–1930. https://doi.org/10.1007/s00190-019-01291-5
Liu RY, Smith PA, King JW (1983) A new solar index which leads to improved foF2 predictions using the CCIR atlas., Telecommun J 50(8):408–414
Liu W (2016) Positioning performance of single-frequency GNSS receiver using Australian regional ionospheric corrections, Master’s thesis, Queensland University of Technology
McNamara LF, Thompson DC (2015) Validation of COSMIC values of foF2 and M(3000)F2 using ground-based ionosondes. Adv Space Res 55(1):163–169. https://doi.org/10.1016/j.asr.2014.07.015
Mengist CK, Ssessanga N, Jeong S-H, Kim J-H, Kim YH, Kwak Y-S (2019) Assimilation of multiple data types to a regional ionosphere model with a 3D-Var algorithm (IDA4D). Space Weather 17(7):1018–1039. https://doi.org/10.1029/2019SW002159
Mukhtarov P, Andonov B, Pancheva D (2013) Global empirical model of TEC response to geomagnetic activity. J Geophys Res Space Phys 118(10):6666–6685. https://doi.org/10.1002/jgra.50576
Mulassano P, Dovis F, Collomb F (2004) European projects for innovative GNSS-related applications. GPS Solut 7(4):268–270. https://doi.org/10.1007/s10291-003-0071-5
Nava B, Coisson P, Radicella S (2008) A new version of the NeQuick ionosphere electron density model. J Atmos Solar Terr Phys 70(15):1856–1862. https://doi.org/10.1016/j.jastp.2008.01.015
Nohutcu M, Karslioglu M, Schmidt M (2010) B-spline modeling of VTEC over Turkey using GPS observations. J Atmos Solar Terr Phys 72(7–8):617–624. https://doi.org/10.1016/j.jastp.2010.02.022
Nossent J, Elsen P, Bauwens W (2011) Sobol’ sensitivity analysis of a complex environmental model. Environ Model Softw 26(12):1515–1525. https://doi.org/10.1016/j.envsoft.2011.08.010
Øvstedal O (2002) Absolute positioning with single-frequency GPS receivers. GPS Solut 5(4):33–44. https://doi.org/10.1007/PL00012910
Pedatella N, Yue X, Schreiner W (2015) Comparison between GPS radio occultation electron densities and in situ satellite observations. Radio Sci 50(6):518–525. https://doi.org/10.1002/2015RS005677
Pignalberi A (2019) A three-dimensional regional assimilative model of the ionospheric electron density, Ph.D. thesis, alma
Rawer K, Bilitza D, Ramakrishnan S (1978) Goals and status of the international reference ionosphere. Rev Geophys 16(2):177–181. https://doi.org/10.1029/RG016i002p00177
Reinisch BW, Huang X, Galkin I, Bilitza D (2013) Real time assimilative foF2 maps for IRI. In: 2013 US National Committee of URSI National Radio Science Meeting (USNC-URSI NRSM), pp 1–1, IEEE
Rishbeth H (1998) How the thermospheric circulation affects the ionospheric F2-layer. J Atmos Solar Terr Phys 60(14):1385–1402. https://doi.org/10.1016/S1364-6826(98)00062-5
Rose JA, Watson RJ, Allain DJ, Mitchell CN (2014) Ionospheric corrections for GPS time transfer. Radio Sci 49(3):196–206. https://doi.org/10.1002/2013RS005212
Rovira-Garcia A, Juan JM, Sanz J, González-Casado G (2015) A worldwide ionospheric model for fast precise point positioning. IEEE Trans Geosci Remote Sens 53(8):4596–4604. https://doi.org/10.1109/TGRS.2015.2402598
Rovira-Garcia A, Ibanez-Segura D, Orus-Perez R, Juan JM, Sanz J, Gonzalez-Casado G (2020) Assessing the quality of ionospheric models through GNSS positioning error: methodology and results. GPS Solut 24(1):1–12. https://doi.org/10.1007/s10291-019-0918-z
Saastamoinen J (1972) Atmospheric correction for the troposphere and stratosphere in radio ranging satellites, pp 247–251. American Geophysical Union (AGU). https://doi.org/10.1029/GM015p0247
Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comput Phys Commun 145(2):280–297. https://doi.org/10.1016/S0010-4655(02)00280-1
Saltelli A (2002) Sensitivity analysis for importance assessment. Risk Anal 22(3):579–590. https://doi.org/10.1111/0272-4332.00040
Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. design and estimator for the total sensitivity index. Comput Phys Commun 181(2):259–270. https://doi.org/10.1016/j.cpc.2009.09.018
Sanz SJ, Juan ZJ, Hernández-Pajares M (2013) GNSS data processing book, vol. I: fundamentals and algorithms, Tech. rep., TM-23/1. Noordwijk: ESA Communications
Schaer S, helvétique des sciences naturelles. Commission géodésique S (1999) Mapping and predicting the Earth’s ionosphere using the Global Positioning System, vol 59, Institut für Geodäsie und Photogrammetrie, Eidg. Technische Hochschule\(\ldots \)
Schaer S, Beutler G, Mervart L, Rothacher M, Wild U (1996a) Global and regional ionosphere models using the GPS double difference phase observable. In: Proceedings of the IGS workshop“ Special Topics and New Directions”
Schaer S, Beutler G, Rothacher M, Springer TA (1996b) Daily global ionosphere maps based on GPS carrier phase data routinely produced by the CODE analysis center. In: Proceedings of the IGS Analysis Center Workshop 1996
Scherliess L, Schunk RW, Sojka JJ, Thompson DC (2004) Development of a physics-based reduced state Kalman filter for the ionosphere. Radio Sci 39(1):1–12. https://doi.org/10.1029/2002RS002797
Schumacher M (2016) Methods for assimilating remotely-sensed water storage changes into hydrological models, Ph.D. thesis, Rheinische Friedrich-Wilhelms-Universität Bonn
Schumacher M, Eicker A, Kusche J, Schmied HM, Döll P (2015) Covariance analysis and sensitivity studies for GRACE assimilation into WGHM. In: IAG 150 Years. Springer. pp 241–247. https://doi.org/10.1007/1345_2015_119
Schunk RW, Scherliess L, Sojka JJ, Thompson DC, Anderson DN, Codrescu M, Minter C, Fuller-Rowell TJ, Heelis RA, Hairston M, et al (2004) Global assimilation of ionospheric measurements (GAIM). Radio Sci 39(1). https://doi.org/10.1029/2002RS002794
Sobol I (2001) Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates. Math Comput Simul 55(1):271–280. https://doi.org/10.1016/S0378-4754(00)00270-6
Sobol IM (1990) On sensitivity estimation for nonlinear mathematical models. Matematicheskoe Modelirovanie 2(1):112–118
Spalla P, Cairolo L (1994) TEC and foF2 comparison Ann Geophys 37(5). https://doi.org/10.4401/ag-4182
Su K, Jin S, Hoque M (2019) Evaluation of ionospheric delay effects on multi-GNSS positioning performance. Remote Sens 11(2):171. https://doi.org/10.3390/rs11020171
Su K, Jin S, Hoque MM (2019b) Evaluation of ionospheric delay effects on multi-GNSS positioning performance. Remote Sens 11(2). https://doi.org/10.3390/rs11020171
Tapping KF (2013) The 10.7cm solar radio flux (F10.7), Space Weather 11(7):394–406. https://doi.org/10.1002/swe.20064
Union-Radiocommunication IT (2009) ITU-R reference ionospheric characteristics. International Telecommunication Union Geneva
Verhagen S, Odijk D, Teunissen P, Huisman L (2010) Performance improvement with low-cost multi-GNSS receivers, In: Proceedings of the 2010 5th ESA workshop on satellite navigation technologies and European workshop on GNSS signals and signal processing (NAVITEC), Noordwijk, The Netherlands, 8–10 December 2010, pp 1–8
Wan W, Ding F, Ren Z, Zhang M, Liu L, Ning B (2012) Modeling the global ionospheric total electron content with empirical orthogonal function analysis. Sci China Technol Sci 55(5):1161–1168. https://doi.org/10.1007/s11431-012-4823-8
Webb DF, Howard RA (1994) The solar cycle variation of coronal mass ejections and the solar wind mass flux. J Geophys Res Space Phys 99(A3):4201–4220. https://doi.org/10.1029/93JA02742
Wu M, Guo P, Xu T, Fu N, Xu X, Jin H, Hu X (2015) Data assimilation of plasmasphere and upper ionosphere using COSMIC/GPS slant TEC measurements. Radio Sci 50(11):1131–1140. https://doi.org/10.1002/2015RS005732
Wu X, Hu X, Wang G, Zhong H, Tang C (2013) Evaluation of COMPASS ionospheric model in GNSS positioning. Adv Space Res 51(6):959–968. https://doi.org/10.1016/j.asr.2012.09.039
Wübbena G, Schmitz M, Bagge A (2005) PPP-RTK: precise point positioning using state-space representation in RTK networks. Proc ION GNSS 5:13–16
Yang K-F, Chu Y-H, Su C-L, Ko H-T, Wang C-Y (2009) An examination of FORMOSAT-3/COSMIC ionospheric electron density profile: data quality criteria and comparisons with the IRI model. Terrestrial Atmospheric Oceanic Sci 20(1):193. https://doi.org/10.3319/TAO.2007.10.05.01(F3C)
Yuan Y, Ou J (2001) Auto-covariance estimation of variable samples (ACEVS) and its application for monitoring random ionospheric disturbances using GPS. J Geodesy 75:438–447. https://doi.org/10.1007/s001900100197
Yuan Y, Ou J (2001) An improvement to ionospheric delay correction for single-frequency GPS users-the APR-I scheme. J Geodesy 75(5–6):331–336. https://doi.org/10.1007/s001900100182
Yuan Y, Huo X, Ou J, Zhang K, Chai Y, Wen D, Grenfell R (2008) Refining the Klobuchar ionospheric coefficients based on GPS observations. IEEE Trans Aerosp Electron Syst 44(4):1498–1510. https://doi.org/10.1109/TAES.2008.4667725
Yuan Y, Tscherning C, Knudsen P, Xu G, Ou J (2008) The ionospheric eclipse factor method (IEFM) and its application to determining the ionospheric delay for GPS. J Geodesy 82(1):1–8. https://doi.org/10.1007/s00190-007-0152-2
Yuan Y, Wang N, Li Z, Huo X (2019) The BeiDou global broadcast ionospheric delay correction model (BDGIM) and its preliminary performance evaluation results. Navigation 66(1):55–69. https://doi.org/10.1002/navi.292
Yue X, Schreiner W. S., Rocken C, Kuo Y-H (2011) Evaluation of the orbit altitude electron density estimation and its effect on the abel inversion from radio occultation measurements. Radio Sci 46(1). https://doi.org/10.1029/2010RS004514
Zhang B, Teunissen PJ, Yuan Y, Zhang X, Li M (2019) A modified carrier-to-code leveling method for retrieving ionospheric observables and detecting short-term temporal variability of receiver differential code biases. J Geodesy 93(1):19–28. https://doi.org/10.1007/s00190-018-1135-1
Zhang C, Chu J, Fu G (2013) Sobol’s sensitivity analysis for a distributed hydrological model of Vichun River Basin, China. J Hydrol 480:58–68. https://doi.org/10.1016/j.jhydrol.2012.12.005
Zhang J, Gao J, Yu B, Sheng C, Gan X (2020) Research on remote GPS common-view precise time transfer based on different ionosphere disturbances. Sensors 20(8):2290. https://doi.org/10.3390/s20082290
Zumberge J, Heflin M, Jefferson D, Watkins M, Webb FH (1997) Precise point positioning for the efficient and robust analysis of GPS data from large networks. J Geophys Res: Solid Earth 102(B3):5005–5017. https://doi.org/10.1029/96JB03860
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Mona Kosary: developing the software, testing the methodology on real data, writing the first draft, and performing the validations. Ehsan Forootan: conceptualising the main idea of the research, supervision, adding discussions and suggestions during the development, and benchmarking the methodology. Saeed Farzaneh: writing the first draft and revisions, contributing in developing the software and performing the validations, and supervision. Maike Schumacher: contributing on conceptual developments, advising, proof reading the drafts, and controlling the computations.
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Kosary, M., Forootan, E., Farzaneh, S. et al. A sequential calibration approach based on the ensemble Kalman filter (C-EnKF) for forecasting total electron content (TEC). J Geod 96, 29 (2022). https://doi.org/10.1007/s00190-022-01623-y
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DOI: https://doi.org/10.1007/s00190-022-01623-y