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

Abstract

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.

Reconstructing Regional Ionospheric Electron Density: A Combined Spherical Slepian Function and Empirical Orthogonal Function Approach

“…The number of dominant base-functions can be related to N in Eq. (14) using the approach presented inSimons (2010), from which N = 21 is found to be most of the time an optimum value and a trade-off between the resolution level and the computational load (see similar arguments inErdogan et al, 2017). The number of EOFs (K) in Eq.…”

Using Support Vector Machine (SVM) and Ionospheric Total Electron Content (TEC) Data for Solar Flare Predictions

“…Since these signals must propagate through the Earth's troposphere and the ionosphere, they are considerably affected by the physical characteristics of these layers. When electromagnetic signals propagate through the troposphere they are delayed, and the speed of propagation is decreased [35]. The amount of delay depends mainly on the pressure, temperature and water vapor (WV) content, which vary significantly both in space and time [36].…”

Global and Regional High-Resolution VTEC Modelling Using a Two-Step B-Spline Approach

“…for details see [28]. Once the prediction of the state vector from time t s−1 to time t s is given, the predicted state vector and its covariance matrix are updated with the new allocated measurements at time t s by…”

“…Since the estimation is performed for both model parts separately, we need to decompose the matrices Σ y and Σ w in the KF Equations (17) to (21) as well. The matrices Σ y,glob and Σ y,reg are set up in accordance to [28] and consist of two diagonal block matrices related to GPS and GLONASS observations of the data sets D 1 and D 2 . The relative weighting between the blocks is performed by adaptively defined variance factors, details can be found by [31].…”

“…During the storm time on March 17, the number of significant coefficients increases to 80, because of the stronger signal variations during that time. For the example in Figure 8, we applied the Equations (27) and (28) to calculate ∆VTEC and their corresponding standard deviations on a grid as Product type 2b introduced in Section 2.3. We chose the output sampling intervals ∆Φ = 1 • in latitude and ∆Λ = 1 • in longitude.…”