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)

Abstract

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.

Estimation and analysis of multi-GNSS differential code biases using a hardware signal simulator

“…The first group models vertical TEC (VTEC) as a polynomial that is a function of ionospheric pierce point coordinates in a coordinate system referenced to the earth-sun axis. Both the satellite and receiver DCBs are considered as unknowns along with other coefficients and are solved for in a least squares (LSQ) solution (Lanyi and Roth 1988;Sardón et al 1994;Jakowski et al 1996;Lin 2001;Otsuka et al 2002, Rao 2007Yuan et al 2007;Mayer et al 2011;Durmaz and Karslioglu 2015). The second group uses the method of minimization of the standard deviation of VTEC using different receiver trial biases and the one that minimizes the standard deviation of computed VTEC is chosen as the receiver bias for that particular station (Ma and Maruyama 2003;Zhang et al 2003;Komjathy et al 2005;Arikan et al 2008, Montenbruck et al 2014.…”

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

“…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).…”

Observed TEC Anomalies by GNSS Sites Preceding the Aegean Sea Earthquake of 2014

“…In order to monitor anomalous days, the VTEC values at IPP points should be utilized to get daily VTEC variation over each ground station. In this study, during a 24-hour run, the hourly VTEC over each station is represented by a second-order polynomial surface model (Durmaz and Karslioglu 2014 …”