Combination of Ground- and Space-Based GPS Data for the Determination of a Multi-scale Regional 4-D Ionosphere Model

Abstract

In this paper, we present a four-dimensional (4-D) electron density model. The vertical distribution of the electron density is described by a F2-layer Chapman function combined with a plasmasphere layer function. The F2-layer peak density NmF2 and the peak height hmF2 are spatially and temporally modeled as 3-D series expansions in terms of localized B-spline functions depending on geographical longitude, latitude and time. The corresponding unknown series coefficients are estimated by a linearized model through an appropriate parameter estimation procedure. The input data are ground-based GPS data combined with electron density profiles retrieved from ionospheric GPS radio occultation measurements onboard the FORMOSAT-3/COSMIC, GRACE and CHAMP satellites, in order to compensate the insensitivity of the ground-based GPS data to the height parameter hmF2 as well as benefit from their different spatiotemporal resolutions. We verify our approach by measurements exemplarily over South and Central America for a selected time span during a solar minimum day 2008-07-01. Based on the B-spline method, we demonstrate an effective data compression by applying a multi-scale representation for the estimated coefficients derived from wavelet analysis. IntroductionIt is well known that the ionospheric delay is the most important error source for Global Navigation Satellite Systems (GNSS) such as the Global Positioning System (GPS). In contrast to dual-frequency GPS users, single frequency

Correlation studies for B-spline modeled F2 Chapman parameters obtained from FORMOSAT-3/COSMIC data

“…The stochastic model effectively causes a decorrelation by suppressing key parameter correlations and enables the reliable estimation of the key parameters by increasing the prior information weight by means of the VCE as a consequence of the sparse F3/C measurement distribution. However, there are enough F3/C input data to correct the background information, as shown by Limberger et al (2013) and Liang et al (2014). Another important point in this context concerns the incomplete stochastic model where no covariances between key parameters have been considered so far.…”

“…The validity of B-splines for ionospheric VTEC modeling, in particular when dealing with inhomogeneously distributed observations, has been successfully demonstrated in Schmidt et al (2011) through comparison with spherical harmonics series expansions. Moreover, an exemplary approach for regional VTEC modeling has been published by and later enhanced by Limberger et al (2013) and Liang et al (2014) to determine F2 Chapman key parameters, based on Eq. (1), aiming for regional 4-D N e representation.…”

“…Various model approaches have already been proposed, and recently published papers will be mentioned here: Altadill et al (2012) modeled hmF2 from globally distributed ionosonde measurements by means of a spherical harmonic analytical model for quiet solar conditions, Hoque and Jakowski (2012) proposed the operational Neustrelitz peak height model based on 13 coefficients with only a few empirically fixed parameters and driven by ionosonde data plus IRO measurements, and Brunini et al (2013) studied and compared different techniques to estimate hmF2. Moreover, Alizadeh (2013) used spherical harmonic expansions to model the N e distribution globally from the combination of different satellite-based observation techniques and Limberger et al (2013) dealt with the estimation of the three F2 Chapman parameters NmF2, hmF2 and H F2 in terms of a polynomial B-spline representation from IRO-derived electron density profiles (EDPs), which was further extended by Liang et al (2014) for the usage of EDPs together with ground-based GPS data.…”

“…On most of the current RA missions such as Jason-2, SARAL, Cyosat and HY-2A, a DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) receiver that is active for orbit determination purposes can also be considered to derive STEC from the signals transmitted by DORIS ground beacons (Dettmering et al, 2014). The total electron content (TEC) is commonly considered as the backbone of ionosphere models, but its integral characteristic (TEC is defined as the integral of the N e along any specific signal path) makes the TEC observable insensitive for the description of the N e distribution, especially with respect to height.…”

Analysis of different propagation models for the estimation of the topside ionosphere and plasmasphere with an ensemble Kalman filter

“…Moreover, there are approaches based on physical models which combine the estimation of the electron density with physically related variables, such as neutral winds or the oxygen / nitrogen ratio (see Wang, et al, 2004;Scherliess et al, 2009;Lee et al, 2012;Lomidze et al, 2015;Schunk et al, 2004Schunk et al, , 2016Elvidge and Angling, 2019).…”