Regional VTEC modeling with multivariate adaptive regression splines

Durmaz, Murat; Karslıoğlu, Mahmut Onur; Nohutçu, Metin

doi:10.1016/j.asr.2010.02.030

Cited by 29 publications

(21 citation statements)

References 16 publications

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“…Alongside the parametric approaches, other methods are also presented for VTEC modeling, such as neuralnetworks (Hernández-Pajares et al 1997), kriging (Wielgosz et al 2003) and multivariate adaptive regression splines (MARS) (Durmaz et al 2010). Later, Durmaz and Karslioglu (2011) introduced a multivariate adaptive regression B-splines (BMARS) algorithm for VTEC modeling, which is derived from MARS with a scale-by-scale model building strategy using compactly supported B-splines (Bakin and Hegland 1997;Bakin et al 2000a, b).…”

Section: Introductionmentioning

confidence: 99%

Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS)

Durmaz

Karslıoğlu

2014

J Geod

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There are various global and regional methods that have been proposed for the modeling of ionospheric vertical total electron content (VTEC). Global distribution of VTEC is usually modeled by spherical harmonic expansions, while tensor products of compactly supported univariate Bsplines can be used for regional modeling. In these empirical parametric models, the coefficients of the basis functions as well as differential code biases (DCBs) of satellites and receivers can be treated as unknown parameters which can be estimated from geometry-free linear combinations of global positioning system observables. In this work we propose a new semi-parametric multivariate adaptive regression B-splines (SP-BMARS) method for the regional modeling of VTEC together with satellite and receiver DCBs, where the parametric part of the model is related to the DCBs as fixed parameters and the non-parametric part adaptively models the spatio-temporal distribution of VTEC. The latter is based on multivariate adaptive regression B-splines which is a non-parametric modeling technique making use of compactly supported B-spline basis functions that are generated from the observations automatically. This algorithm takes advantage of an adaptive scale-by-scale model building strategy that searches for best-fitting B-splines to the data at each scale. The VTEC maps generated from the proposed method are compared numerically and visually with the global ionosphere maps (GIMs) which are provided by the Center for Orbit Determination in Europe (CODE). The VTEC values from SP-BMARS and CODE GIMs are also compared with VTEC values obtained through calibration using local ionospheric model. The estimated satellite and receiver DCBs from the SP-BMARS model are compared with the CODE distributed DCBs. The results show that the SP-BMARS algorithm can be used to estimate satellite and receiver DCBs while adaptively and flexibly modeling the daily regional VTEC.

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Section: Introductionmentioning

confidence: 99%

Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS)

Durmaz

Karslıoğlu

2014

J Geod

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“…Several research groups have provided GNSS-based solutions regarding the TEC modeling with appropriate approaches for quality assessment; for example, see Rovira-Garcia et al (2015), Li et al (2015), Brunini et al (2011) and Orus et al (2007). In the context of quality assessment, through a GPS phase-continuous arc, differential STEC, i.e., dSTEC values, can be obtained with an accuracy of less than 0.1 TECU (Feltens et al, 2011). Note that 1 TECU is equivalent to 10 16 electrons m −2 .…”

Section: Self-consistency Analysismentioning

confidence: 99%

“…A common approach, generally denoted as single-layer model (SLM), is based on the assumption that the electrons in the ionosphere are concentrated within a thin shell at a fixed altitude above the Earth (Mannucci et al, 1998;Komjathy and Langley, 1996). The spatial variations of electron content in this single layer are represented by a proper mathematical model such as spherical harmonics (Schaer, 1999), B-splines (Schmidt, 2007;Schmidt et al, 2008), spatially defined total electron content (TEC) grids (Skone, 1999), polynomials (Komjathy and Langley, 1996;Komjathy, 1997), wavelets (Schmidt, 2007), or the MARS (Durmaz et al, 2010) and BMARS approaches (Durmaz and Karslioglu, 2015). Furthermore, three-dimensional models that consider the variation with altitude were also studied (Hernández-Pajares et al, 1999;Mitchell and Spencer, 2003;Liu, 2004;Zeilhofer et al, 2009;Limberger et al, 2013).…”

Section: E Erdogan Et Al: Near Real-time Estimation Of Ionosphere Vtecmentioning

confidence: 99%

Near real-time estimation of ionosphere vertical total electron content from GNSS satellites using B-splines in a Kalman filter

Erdogan¹,

Schmidt²,

Seitz³

et al. 2017

Ann. Geophys.

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Abstract. Although the number of terrestrial global navigation satellite system (GNSS) receivers supported by the International GNSS Service (IGS) is rapidly growing, the worldwide rather inhomogeneously distributed observation sites do not allow the generation of high-resolution global ionosphere products. Conversely, with the regionally enormous increase in highly precise GNSS data, the demands on (near) real-time ionosphere products, necessary in many applications such as navigation, are growing very fast. Consequently, many analysis centers accepted the responsibility of generating such products. In this regard, the primary objective of our work is to develop a near real-time processing framework for the estimation of the vertical total electron content (VTEC) of the ionosphere using proper models that are capable of a global representation adapted to the real data distribution.The global VTEC representation developed in this work is based on a series expansion in terms of compactly supported B-spline functions, which allow for an appropriate handling of the heterogeneous data distribution, including data gaps. The corresponding series coefficients and additional parameters such as differential code biases of the GNSS satellites and receivers constitute the set of unknown parameters. The Kalman filter (KF), as a popular recursive estimator, allows processing of the data immediately after acquisition and paves the way of sequential (near) real-time estimation of the unknown parameters. To exploit the advantages of the chosen data representation and the estimation procedure, the Bspline model is incorporated into the KF under the consideration of necessary constraints. Based on a preprocessing strategy, the developed approach utilizes hourly batches of GPS and GLONASS observations provided by the IGS data centers with a latency of 1 h in its current realization.Two methods for validation of the results are performed, namely the self consistency analysis and a comparison with Jason-2 altimetry data. The highly promising validation results allow the conclusion that under the investigated conditions our derived near real-time product is of the same accuracy level as the so-called final post-processed products provided by the IGS with a latency of several days or even weeks.

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“…MARS is an adaptive method requiring no gridding of the input space. Durmaz et al (2010) applied MARS to regional VTEC modeling over a large part of Europe successfully. Subsequently Multivariate Adaptive Regression B-Splines (BMARS) was presented by Durmaz and Karslioglu (2011) with tensor product B-splines as basis functions obtained from observation locations.…”

Section: Introductionmentioning

confidence: 99%

Regional spatio - temporal modeling of the ionospheric Vertical Total Electron Content (VTEC) using Multivariate Adaptive Regression B‒Splines (BMARS)

Karslıoğlu¹,

Durmaz²

2012

J Geod Geoinf

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Regional VTEC modeling with multivariate adaptive regression splines

Cited by 29 publications

References 16 publications

Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS)

Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS)

Near real-time estimation of ionosphere vertical total electron content from GNSS satellites using B-splines in a Kalman filter

Regional spatio - temporal modeling of the ionospheric Vertical Total Electron Content (VTEC) using Multivariate Adaptive Regression B‒Splines (BMARS)

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