Eren Erdogan

This paper characterizes, with static and roving GNSS receivers in the context of precision agriculture research, the hybrid ionospheric-geodetic GNSS model Wide-Area Real-Time Kinematics (WARTK), which computes and broadcasts real-time corrections for high-precision GNSS positioning and navigation within sparse GNSS receiver networks. This research is motivated by the potential benefits of the low-cost precise WARTK technique on mass-market applications such as precision agriculture. The results from two experiments summarized in this work, the second one involving a working spraying tractor, show, firstly, that the corrections from the model are in good agreement with the corrections provided by IGS (International GNSS Services) analysis centers computed in post-processing from global GNSS data. Moreover, secondly and most importantly, we have shown that WARTK provides navigation solutions at decimeter-level accuracy, and the ionospheric corrections significantly reduce the computational time for ambiguity estimation: up to convergence times for the 50%, 75% and 95% of cases equal or below 30 s (single-epoch), 150 s and 600 s approximately, vs. 1000 s, 2750 s and 4850 s without ionospheric corrections, everything for a roving receiver at more than 100 km far away from the nearest permanent receiver. The real-time horizontal position errors reach up to 3 cm, 5 cm and 12 cm for 50%, 75% and 95% of cases, respectively, by constraining and continuously updating the ambiguities without updating the permanent receiver coordinates, vs. the 6 cm, 12 cm and 32 cm, respectively, in the same conditions but without WARTK ionospheric corrections.

In the last decades, advances in satellite technologies, data analysis techniques, and models, and a growing number of analysis centers allow modeling the ionospheric electron content with unprecedented accuracy. International GNSS Service (IGS) Ionosphere Associated Analysis Centers (IAAC) continuously provide global ionospheric maps (GIMs) based on processing GNSS data from the ground IGS network. It is a great advantage that these GIMs are often based on very different modeling techniques and thus, are also characterized by different accuracy levels. Due to the dynamic nature of the ionosphere, there is a permanent need to improve the modeling techniques of ionospheric key parameters such as the vertical total electron content (vTEC).In this presentation, we evaluate a new ionosphere model from DGFI-TUM denoted OTHG, which is a candidate for a new IGS IAAC product. The OTHG model is based on tensor products of trigonometric B-spline functions in longitude and polynomial B-spline functions in latitude for a global representation (Goss et al. 2019). Here, we complement our earlier investigations of the seven analysis center models (Wielgosz et al. 2021) with new results for the OTHG GIMs. For these investigations, we use our own validation methodology presented in Krypiak-Gregorczyk et al. (2017), which is based on GIM-derived slant TEC (sTEC) comparison with carrier phase geometry-free combination of GNSS signals. In the presented study, we use one year of GNSS data collected by 25 globally distributed stations. The overall yearly RMS value is calculated for each product based on all 365 days of continuous observations from all stations. The results show that the overall RMS of the tested GIMs ranges from 0.93 TECU to 1.29 TECU. The OTHG GIMs performed as one of the best. In addition, GIM vTEC comparisons to Jason-2 and Jason - 3 altimetry data are studied. In these analyses, the OTHG GIMs also showed a good performance. Therefore, it can be concluded that  DGFI-TUM is a valuable ionospheric product for the research community. Goss A., Schmidt M., Erdogan E., Görres B., Seitz F. (2019) High-resolution vertical total electron content maps based on multi-scale B-spline representations. Annales Geophysicae, 37(4), 10.5194/angeo-37-699-2019Krypiak-Gregorczyk A., Wielgosz P., Borkowski A. (2017) Ionosphere Model for European Region Based on Multi-GNSS Data and TPS Interpolation, Remote Sensing, 9(12), 1221,  DOI:10.3390/rs9121221Wielgosz P., Milanowska B., Krypiak-Gregorczyk A., Jarmołowski W. (2021) Validation of GNSS‑derived global ionosphere maps for different solar activity levels: case studies for years 2014 and 2018. GPS Solutions 25, 103. https://doi.org/10.1007/s10291-021-01142-x

Monitoring the Vertical Total Electron Content (VTEC) of the ionosphere is important for applications ranging from navigation to detection of space weather events. Therefore, emerging efforts have been made by several analysis centers to estimate the VTEC using different approaches in real‐time. Global Navigation Satellite Systems (GNSS) is a crucial technology for ionosphere modeling due to its worldwide distributed receivers, high temporal resolution, and low latency data dissemination capability. The selection of a convenient approach to extract ionosphere information from GNSS and the representation of VTEC by an appropriate mathematical model are essential factors for providing fast and accurate ionosphere products. Contrarily to the widespread phase‐leveling method, which uses noisy and erroneous code measurements, the modeling concept in this paper utilizes pure carrier‐phase measurements. Measurements acquired through the International GNSS Service (IGS) real‐time service in Radio Technical Commission for Maritime Services format are from GPS, GLONASS, and GALILEO. The measurement biases, including the ambiguity of carrier‐phase measurements, are simultaneously estimated along with VTEC model parameters. In our approach, VTEC is represented by B‐spline expansions embedded into a Kalman filter. Due to their localizing feature, B‐splines form a highly sparse structure in the filter measurement model. Thus, matrix operations for large‐scale problems can be performed fast using sparse matrix operations, as is done in this study. The differential slant total electron content (dSTEC) analysis and the comparison with Jason‐3 altimetry VTEC were performed for validation within selected periods in 2019. The dSTEC analysis shows that the quality of the generated real‐time VTEC maps slightly outperforms those provided by the other IGS analysis centers.

The main objective of the ESA-funded project COSTO (Contribution of Swarm data to the prompt detection of Tsunamis and other natural hazards) is to better characterize, understand and discover coupling processes and interactions between the ionosphere, the lower atmosphere and the Earth’s surface as well as sea level vertical displacements. Together with our project partners from the University of Warmia and Mazury (UWM), the National Observatory of Athens (NOA) and the Universitat Politecnica de Catalunya (UPC) we focus in COSTO to tsunamis that are the result of earthquakes (EQ), volcano eruptions or landslides.In the scope of COSTO a roadmap was developed to detect the vertical and horizontal propagation of Travelling Ionospheric Disturbances (TID) in the observations of Low Earth Orbiting (LEO) satellites. Under the assumption that the TIDs triggered by tsunamis behave in approximately the same way for different EQ / tsunami events, this roadmap can be applied also to other events. In this regard, the Tohoku-Oki EQ in 2011 and the Chile EQ in 2015 were studied in detail. The aim of investigating these events is to detect the TIDs in the near vicinity of the propagating tsunami. Thereby, given tsunami propagation models serve as a rough orientation to determine the moments in time and positions for which there is co-location with selected LEO satellites/missions, namely GRACE, GOCE and Swarm. GOCE with an altitude of around 280km and the GRACE satellites with an altitude of around 450km flew over the region where the Tohoku-Oki tsunami was located, about 2.5 hours after the EQ. Using wavelet transform, similar signatures with periods of 10-30 seconds could be detected in the top-side STEC observations of GOCE as well as in the Ka-band observations of GRACE at the time of the overflight. These signatures can be related to the gravity wave originating from the tsunami. Similar signatures were detected in the signals from the GRACE Ka-band observations and in the Swarm Langmuir Probe measurements at an altitude of 450 km for the 2015 Chile tsunami. These roadmap studies provided the first opportunity to observe the vertical and horizontal tsunami induced gravity waves in the ionosphere.

The ionospheric signal delay is one of the largest error sources in GNSS applications and may cause in case of a single-frequency receiver a positioning error of up to several meters. To avoid such an inaccuracy some of the Ionosphere Associated Analysis Centers (IAAC) of the International GNSS Service (IGS) provide the user the Vertical Total Electron Content (VTEC) as Real-Time Global Ionosphere Maps (RT-GIM) via streaming formats. Currently, the only data format used for the dissemination of these ionospheric corrections is based on the State Space Representation (SSR) message and the RTCM standards.Mathematically most of the RT-GIMs are based on modeling VTEC as series expansions in spherical harmonics (SH) up to a highest degree of n = 15 which corresponds to a spatial resolution of 12° in latitude and longitude and is therefore, too low for modern GNSS applications such as autonomous driving. However, the SSR VTEC message allows the dissemination of SH coefficients only up to a maximum degree of n = 16.To avoid the drawbacks of expanding VTEC in SHs other approaches such as a voxel representation or a B-spline series expansion have been proven to be appropriate candidates for global and regional modelling with an enhanced resolution. In order to provide in these cases the significant model parameters to the user, the application of the SSR VTEC message requires a transformation of the model parameters into SH coefficients. In this contribution a methodology will be presented which describes a fast transformation of the B-spline approach into a SH representation with high accuracy by minimizing the information loss.To test the method, a high-resolution VTEC GIM modeled as a series expansion in B-splines is transformed into SH representations of different highest degree values; the results are validated via dSTEC analysis as well as via an example of single frequency positioning and show a significantly improved accuracy compared to the IGS GIMs.

The project OPTIMAP is at the current stage a joint initiative of BGIC, GSSAC and DGFI-TUM. The development of an operational tool for ionospheric mapping and prediction is the main goal of the project.The ionosphere is a dispersive medium. Therefore, GNSS signals are refracted while they pass through the ionosphere. The magnitude of the refraction rate depends on the frequencies of the transmitted GNSS signals. The ionospheric disturbance on the GNSS signals paves the way of extracting Vertical Total Electron Content (VTEC) information of the ionosphere.In OPTIMAP, the representation of the global and regional VTEC signal is based on localizing B-spline basis functions. For global VTEC modeling, polynomial B-splines are employed to represent the latitudinal variations, whereas trigonometric B-splines are used for the longitudinal variations. The regional modeling in OPTIMAP relies on a polynomial B-spline representation for both latitude and longitude.The VTEC modeling in this study relies on both a global and a regional sequential estimator (Kalman filter) running in a parallel mode. The global VTEC estimator produces VTEC maps based on data from GNSS receiver stations which are mainly part of the global real-time IGS network. The global estimator relies on additional VTEC information obtained from a forecast procedure using ultra-rapid VTEC products. The regional estimator makes use of the VTEC product of the real-time global estimator as background information and generates high-resolution VTEC maps using real-time data from the EUREF Permanent GNSS Network. EUREF provides a network of very dense GNSS receivers distributed alongside Europe.Carrier phase observations acquired from GPS and GLONASS, which are transmitted in accordance with RTCM standard, are used for real-time regional VTEC modeling. After the acquisition of GNSS data, cycle slips for each satellite-receiver pair are detected, and ionosphere observations are constructed via the linear combination of carrier-phase observations in the data pre-processing step. The unknown B-spline coefficients, as well as the biases for each phase-continuous arc belonging to each receiver-satellite pair, are simultaneously estimated in the Kalman filter.Within this study, we compare the performance of regional and global VTEC products generated in real-time using the well-known dSTEC analysis.

The accuracy and availability of satellite-based applications, like Global Navigation Satellite System (GNSS) positioning and remote sensing, crucially depend on the knowledge of the ionospheric electron density distribution. The tomography of the ionosphere is one of the major tools for providing links to specific ionospheric corrections and studying and monitoring physical processes in the ionosphere and plasmasphere. In this work, we apply an ensemble Kalman filter (EnKF) approach for the 4D electron density reconstruction of the topside ionosphere and plasmasphere, with the focus on the investigation of different propagation models, and compare them with the iterative reconstruction technique of simultaneous multiplicative column normalized method plus (SMART+). The slant total electron content (STEC) measurements of 11 low earth orbit (LEO) satellites are assimilated into the reconstructions. We conduct a case study on a global grid with altitudes between 430 and 20 200 km, for two periods of the year 2015, covering quiet to perturbed ionospheric conditions. Particularly the performance of the methods for estimating independent STEC and electron density measurements from the three Swarm satellites is analysed. The results indicate that the methods of EnKF, with exponential decay as the propagation model, and SMART+ perform best, providing, in summary, the lowest residuals.

The accuracy and availability of satellite-based applications like GNSS positioning and remote sensing crucially depends on the knowledge of the ionospheric electron density distribution. The tomography of the ionosphere is one of the major tools to provide link specific ionospheric corrections as well as to study and monitor physical processes in the ionosphere and plasmasphere. In this work, we apply an Ensemble Kalman Filter (EnKF) approach for the 4D electron density reconstruction of the topside ionosphere and plasmasphere with the focus on the investigation of different propagation models and compare them with the iterative reconstruction technique SMART+. The STEC measurements of eleven LEO satellites are assimilated into the reconstructions. We conduct a case study on a global grid with altitudes between 430 and 20200 km, for two periods of the year 2015 covering quiet to perturbed ionospheric conditions. Particularly, the performance of the methods to estimate independent STEC and electron density measurements from the three Swarm satellites is analysed. The results indicate that the methods EnKF with Exponential decay as the propagation model and SMART+ perform best, providing in summary the lowest residuals.

The Kalman filter (KF) is widely applied in (ultra) rapid and (near) real-time ionosphere modeling to meet the demand on ionosphere products required in many applications extending from navigation and positioning to monitoring space weather events and naturals disasters. The requirement of a prior definition of the stochastic models attached to the measurements and the dynamic models of the KF is a drawback associated with its standard implementation since model uncertainties can exhibit temporal variations or the time span of a given test data set would not be large enough. Adaptive methods can mitigate these problems by tuning the stochastic model parameters during the filter run-time. Accordingly, one of the primary objectives of our study is to apply an adaptive KF based on variance component estimation to compute the global Vertical Total Electron Content (VTEC) of the ionosphere by assimilating different ionospheric GNSS measurements. Secondly, the derived VTEC representation is based on a series expansion in terms of compactly supported B-spline functions. We highlight the morphological similarity of the spatial distributions and the magnitudes between VTEC values and the corresponding estimated B-spline coefficients. This similarity allows for deducing physical interpretations from the coefficients. In this context, an empirical adaptive model to account for the dynamic model uncertainties, representing the temporal variations of VTEC errors, is developed in this work according to the structure of B-spline coefficients. For the validation, the differential slant total electron content (dSTEC) analysis and a comparison with Jason-2/3 altimetry data are performed. Assessments show that the quality of the VTEC products derived by the presented algorithm is in good agreement, or even more accurate, with the products provided by IGS ionosphere analysis centers within the selected periods in 2015 and 2017. Furthermore, we show that the presented approach can be applied to different ionosphere conditions ranging from very high to low solar activity without concerning time-variable model uncertainties, including measurement error and process noise of the KF because the associated covariance matrices are computed in a self-adaptive manner during run-time.