Global navigation satellite systems (GNSS) allow estimating total electron content (TEC). However, it is still a problem to calculate absolute ionosphere parameters from GNSS data: negative TEC values could appear, and most of existing algorithms does not enable to estimate TEC spatial gradients and TEC time derivatives. We developed an algorithm to recover the absolute non-negative vertical and slant TEC, its derivatives and its gradients, as well as the GNSS equipment differential code biases (DCBs) by using the Taylor series expansion and bounded-variable least-squares. We termed this algorithm TuRBOTEC. Bounded-variable least-squares fitting ensures non-negative values of both slant TEC and vertical TEC. The second order Taylor series expansion could provide a relevant TEC spatial gradients and TEC time derivatives. The technique validation was performed by using independent experimental data over 2014 and the IRI-2012 and IRI-plas models. As a TEC source we used Madrigal maps, CODE (the Center for Orbit Determination in Europe) global ionosphere maps (GIM), the IONOLAB software, and the SEEMALA-TEC software developed by Dr. Seemala. For the Asian mid-latitudes TuRBOTEC results agree with the GIM and IONOLAB data (root-mean-square was < 3 TECU), but they disagree with the SEEMALA-TEC and Madrigal data (root-mean-square was >10 TECU). About 9% of vertical TECs from the TuRBOTEC estimates exceed (by more than 1 TECU) those from the same algorithm but without constraints. The analysis of TEC spatial gradients showed that as far as 10–15° on latitude, TEC estimation error exceeds 10 TECU. Longitudinal gradients produce smaller error for the same distance. Experimental GLObal Navigation Satellite System (GLONASS) DCB from TuRBOTEC and CODE peaked 15 TECU difference, while GPS DCB agrees. Slant TEC series indicate that the TuRBOTEC data for GLONASS are physically more plausible.

This study presents an analysis of the ground-based observations and model simulations of ionospheric electron density disturbances at three longitudinal sectors (eastern European, Siberian and American) during geomagnetic storms that occurred on 26–30 September 2011. We use the Global Self-consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP) to reveal the main mechanisms influencing the storm-time behavior of the total electron content (TEC) and the ionospheric F2 peak critical frequency (foF2) during different phases of geomagnetic storms. During the storm's main phase the long-lasting positive disturbances in TEC and foF2 at sunlit mid-latitudes are mainly explained by the storm-time equatorward neutral wind. The effects of eastward electric field can only explain the positive ionospheric storm in the first few hours of the initial storm phase. During the main phase the ionosphere was more changeable than the plasmasphere. The positive disturbances in the electron content at the plasmaspheric heights (800–20 000 km) at high latitudes can appear simultaneously with the negative disturbances in TEC and foF2. The daytime positive disturbances in foF2 and TEC occurred at middle and low latitudes and at the Equator due to n(O) ∕ n(N₂) enhancement during later stage of the main phase and during the recovery phase of the geomagnetic storm. The plasma tube diffusional depletion and negative disturbances in electron and neutral temperature were the main formation mechanisms of the simultaneous formation of the positive disturbances in foF2 and negative disturbances in TEC at low latitudes during the storm's recovery phase.

Global navigation satellite system signals are known to be an efficient tool to monitor the Earth ionosphere. We suggest Galileo E5 AltBOC phase and pseudorange observables—a single-frequency combination—to estimate the ionospheric total electron content (TEC). We performed a one-month campaign in September 2020 to compare the noise level for different TEC estimations based on single-frequency and dual-frequency data. Unlike GPS, GLONASS, or Galileo E5a and E5b single-frequency TEC estimations (involving signals with binary and quadrature phase-shift keying, such as BPSK and QPSK, or binary offset carrier (BOC) modulation), an extra wideband Galileo E5 AltBOC signal provided the smallest noise level, comparable to that of dual-frequency GPS. For elevation higher than 60 degrees, the 100 s root-mean-square (RMS) of TEC, an estimated TEC noise proxy, was as follows for different signals: ~0.05 TECU for Galileo E5 AltBOC, 0.09 TECU for GPS L5, ~0.1TECU for Galileo E5a/E5b BPSK, and 0.85 TECU for Galileo E1 CBOC. Dual-frequency phase combinations provided RMS values of 0.03 TECU for Galileo E1/E5, 0.03 and 0.07 TECU for GPS L1/L2 and L1/L5. At low elevations, E5 AltBOC provided at least twice less single-frequency TEC noise as compared with data obtained from E5a or E5b. The short dataset of our study could limit the obtained estimates; however, we expect that the AltBOC single-frequency TEC will still surpass the BPSK analogue in noise parameters when the solar cycle evolves and geomagnetic activity increases. Therefore, AltBOC signals could advance geoscience.

Monitoring the Earth’s ionosphere is an important, fundamental and applied problem. Global Navigation Satellite Systems (GNSS) provide a way of measuring the ionospheric total electron content (TEC), but real-time single-station absolute TEC measurements are still a problem. This study describes a single-station system to measure the absolute TEC, based on the GNSS–MITIGATOR (MonITorInG the Absolute TOtal electRon content) system. The latter enables real-time measurements for the absolute TEC and its derivatives in time and in space to be obtained. The system is implemented by using JAVAD receivers. The convergence time and the run-mode retention time is ~8 h. We provide potential methods for using the system to estimate the critical frequency of the ionosphere, foF2, at oblique paths in the Siberian region. The developed tool could be useful for supporting real-time multi-instrumental ionosphere monitoring or for compensating for the ionospheric errors of radio equipment.