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This study demonstrates a rich complexity of the time–frequency ionospheric signal spectrum, dependent on the measurement type and platform. Different phenomena contributing to satellite-derived and ground-derived geophysical data that only selected signal bands can be potentially sensitive to seismicity over time, and they are applicable in lithosphere–atmosphere–ionosphere coupling (LAIC) studies. In this study, satellite-derived and ground-derived ionospheric observations are filtered by a Fourier-based band-pass filter, and an experimental selection of potentially sensitive frequency bands has been carried out. This work focuses on band-pass filtered ionospheric observations and seismic activity in the region of the Aegean Sea over a two-year time period (2020–2021), with particular focus on the entire system of tectonic plate junctions, which are suspected to be a potential source of ionospheric disturbances distributed over hundreds of kilometers. The temporal evolution of seismicity power in the Aegean region is represented by the record of earthquakes characterized by M ≥ 4.5, used for the estimation of cumulative seismic energy. The ionospheric response to LAIC is explored in three data types: short inspections of in situ electron density (Ne) over a tectonic plate boundary by Swarm satellites, stationary determination of three Ne density profile parameters by the Athens Digisonde station AT138 (maximum frequency of the F2 layer: foF2; maximum frequency of the sporadic E layer: foEs; and frequency spread: ff), and stationary measure of vertical total electron content (VTEC) interpolated from a UPC-IonSAT Quarter-of-an-hour time resolution Rapid Global ionospheric map (UQRG) near Athens. The spectrograms are made with the use of short-term Fourier transform (STFT). These frequency bands in the spectrograms, which show a notable coincidence with seismicity, are filtered out and compared to cumulative seismic energy in the Aegean Sea, to the geomagnetic Dst index, to sunspot number (SN), and to the solar radio flux (F10.7). In the case of Swarm, STFT allows for precise removal of long-wavelength Ne signals related to specific latitudes. The application of STFT to time series of ionospheric parameters from the Digisonde station and GIM VTEC is crucial in the removal of seasonal signals and strong diurnal and semi-diurnal signal components. The time series formed from experimentally selected wavebands of different ionospheric observations reveal a moderate but notable correlation with the seismic activity, higher than with any solar radiation parameter in 8 out of 12 cases. The correlation coefficient must be treated relatively and with caution here, as we have not determined the shift between seismic and ionospheric events, as this process requires more data. However, it can be observed from the spectrograms that some weak signals from selected frequencies are candidates to be related to seismic processes.

This paper reviews the key studies concerning GNSS positioning and applications conducted at leading Polish research institutions from 2019 until 2022. The review also constitutes a contribution to the national report of Poland for the International Union of Geodesy and Geodynamics (IUGG) presented at the 28th General Assembly of IUGG held in 2023 in Berlin, Germany. In particular, we discuss the advances in theory and applications of relative and absolute positioning, troposphere and ionosphere sounding, smartphone and low-cost GNSS data processing, and other specific studies such as those on satellite antenna calibration and clock stability. In light of these recent advances by the Polish scientific community, continuous progress in GNSS theory and processing algorithms is thought to be maintained in the future, and GNSS applications are expected to continue to proliferate.

Swarm electron density (Ne) observations from the Langmuir probe (LP) can detect ionospheric disturbances at the altitude of a satellite. Along-track satellite observations provide a large number of very short observations of different places in the ionosphere, where Ne is disturbed. Moreover, different perturbations occupy various Ne signal frequencies. Therefore, such short signals are more recognizable in two dimensions, where aside from their change in time, we can observe their diversity in the frequency domain. Spectral analysis is an essential tool applied here, as it enables signal decomposition and the recognition of composite patterns of Ne disturbances that occupy different frequencies. This study shows a high-resolution application of short-term Fourier transform (STFT) to Swarm Ne observations in the Papua New Guinea region in the vicinity of earthquakes, tsunamis, and related general seismic activity. The system of tectonic plate junctions, including the Pacific–Australian boundary, is located orthogonally to Swarm track footprints. The selected wavelengths of seismically induced ionospheric disturbances detected via Swarm are compared with the three sets of three-month records of seismic activity: in the winter solstice of 2016/2017, when seismic activity was highest, and in the summer solstice and vernal equinox of 2016, which were calmer. Moreover, more Swarm data records are analyzed at the same latitudes for validation purposes, in a place where there are no tectonic plate boundaries that are orthogonal to the Swarm orbital footprint. Additional validation is supplied through Swarm Ne observations from completely different latitudes, where the Swarm orbital footprint orthogonally crosses a different subducting plate boundary. Aside from the seismic energy, the solar radio flux (F10.7), equatorial plasma bubbles (EPBs), and geomagnetic ap and Dst indices are also reviewed here. Their influence on the ionospheric Ne is also found in Swarm observations. Finally, the Pearson correlation coefficient (PCC), applied to the pairs of 3-month time series created from Swarm Ne variations, seismic energy, ap, Dst, and F10.7, summarizes the graphical inspection of mutual correlations. It points to the predominant correlation of Swarm Ne disturbances with seismicity, especially during nighttime. We show that most of the Ne disturbances at a selected wavelength of 300 km correlate more with seismicity than with geomagnetic and solar indices. Therefore, Swarm LP can be assessed as being capable of observing the lithosphere–atmosphere–ionosphere coupling (LAIC) from the orbit.

This review paper presents research results on geodetic positioning and applications carried out in Poland, and related to the activities of the International Association of Geodesy (IAG) Commission 4 “Positioning and Applications” and its working groups. It also constitutes the chapter 4 of the national report of Poland for the International Union of Geodesy and Geodynamics (IUGG) covering the period of 2015-2018. The paper presents selected research, reviewed and summarized here, that were carried out at leading Polish research institutions, and is concerned with the precise multi-GNSS (Global Navigation Satellite Systems) satellite positioning and also GNSS-based ionosphere and troposphere modelling and studies. The research, primarily carried out within working groups of the IAG Commission 4, resulted in important advancements that were published in leading scientific journals. During the review period, Polish research groups carried out studies on multi-GNSS functional positioning models for both relative and absolute solutions, stochastic positioning models, new carrier phase integer ambiguity resolution methods, inter system bias calibration, high-rate GNSS applications, monitoring terrestrial reference frames with GNSS, assessment of the real-time precise satellite orbits and clocks, advances in troposphere and ionosphere GNSS remote sensing methods and models, and also their applications to weather, space weather and climate studies.

Global ionosphere maps (GIMs) representing ionospheric total electron content (TEC) are applicable in many scientific and engineering applications. However, the GIMs provided by seven Ionosphere Associated Analysis Centers (IAACs) are generated with different temporal resolutions and using different modeling techniques. In this study, we focused on the influence of map time interval on the empirical accuracy of these ionospheric products. We investigated performance of the high-resolution GIMs during high (2014) and low (2018) solar activity periods as well as under geomagnetic storms (19 February 2014 and 17 March 2015). In each of the analyzed periods, GIMs were also assessed over different geomagnetic latitudes. For the evaluation, we used direct comparison of GIM-derived slant TEC (STEC) with dual-frequency GNSS observations obtained from 18 globally distributed stations. In order to perform a comprehensive study, we also evaluated GIMs with respect to altimetry-derived vertical TEC (VTEC) obtained from the Jason-2 and Jason-3 satellites. The study confirmed the influence of GIMs time interval on the provided TEC accuracy, which was particularly evident during high solar activity, geomagnetic storms, and also at low latitudes. The results show that 120-min interval contributes significantly to the accuracy degradation, whereas 60-min one is sufficient to maintain TEC accuracy.

In 2019, the University of Warmia and Mazury in Olsztyn, in cooperation with Astri Polska, started a European Space Agency (ESA) project. The purpose of the project is the development and implementation of a field calibration procedure for a multi-frequency and multi-system global navigation satellite system (GNSS). The methodology and algorithms proposed in the project are inspired by the “Hannover” concept of absolute field receiver antenna calibration; however, some innovations are introduced. In our approach, the antenna rotation point is close to the nominal mean phase center (MPC) of the antenna, although it does not coincide with it. Additionally, a National Marine Electronics Association local time zone (NMEA ZDA) message is used to synchronize the robot with the GNSS time. We also propose some modifications in robot arm movement scenarios. Our first test results demonstrate consistent performance for the calibration strategy and calibration procedure. For the global positioning system (GPS) L1 frequency, the calibration results show good agreement with the IGS-type mean values. For high satellite elevations (20°–90°), the differences do not exceed 1.5 mm. For low elevation angles (0°–20°), the consistency of the results is worse and the differences exceed a 3 mm level in some cases.

There is a noticeable number of studies carried out on both the operational parameters of Global Navigation Satellite System (GNSS) and the satellite signal itself. Researchers look for, inter alia, proven sources of errors affecting the integrity of the satellite signal because this parameter determines the approval of the system’s operational use. It also seems of key importance that the atmospheric conditions, in any area of satellite signal usage, should not be underestimated due to their extensive impact. As the ionospheric refraction seriously limits the operational use of the satellite navigation signal, in this article, the authors attempted to quantify the effect of solar activity (expressed by sunspots) on the signal integrity using fuzzy logic. Fuzzy reasoning is used when information is inaccurate or incomplete and necessitates making decisions under conditions of uncertainty. Thanks to fuzzy sets, there are no obstacles to characterize the degree of intensity of a given phenomenon. In order to look at the problem more broadly, attention was also paid to the tropospheric conditions, and it was verified whether, against the background of cloudiness, precipitation, humidity, pressure and temperature, solar activity affects the integrity to the greatest extent. The integrity measurements from the EGNOS system (PRN120 and PRN126) collected at the monitoring station in Warsaw, Poland in 2014 were used.

Geostatistical Analyst is a set of advanced tools for analysing spatial data and generating surface models using statistical and deterministic methods available in ESRI ArcMap software. It enables interpolation models to be created on the basis of data measured at chosen points. The software also provides tools that enable analyses of the data variability, setting data limits and checking global trends, as well as creating forecast maps, estimating standard error and probability, making various surface visualisations, and analysing spatial autocorrelation and correlation between multiple data sets. The data can be interpolated using deterministic methods providing surface continuity, and also by stochastic techniques like kriging, based on a statistical model considering data autocorrelation and providing expected interpolation errors. These properties of Geostatistical Analyst make it a valuable tool for modelling and analysing the Earth’s ionosphere. Our research aims to test its applicability for studying the ionosphere, and ionospheric disturbances in particular. As raw source data, we use Global Navigation Satellite Systems (GNSS)-derived ionospheric total electron content. This paper compares ionosphere models (maps) developed using various interpolation methods available in Geostatistical Analyst. The comparison is based on several indicators that can provide the statistical characteristics of an interpolation error. In this contribution, we use our own method, the parametric assessment of the quality of estimation (MPQE). Here, we present analyses and a discussion of the modelling results for various states of the ionosphere: On the disturbed day of the St Patrick’s Day geomagnetic storm of 2015, one quiet day before the storm and one day after its occurrence, reflecting the ionosphere recovery phase. Finally, the optimal interpolation method is selected and presented.

Precise real-time kinematic (RTK) Global Navigation Satellite System (GNSS) positioning requires fixing integer ambiguities after a short initialization time. Originally, it was assumed that it was only possible at a relatively short distance from a reference station (

This article describes an implementation of precise point positioning (PPP) and the least-squares collocation (LSC) method in the modeling of total electron content (TEC) in Southeast Asia, which is characterized by relatively homogeneous Global Navigation Satellite Systems (GNSS) data from International GNSS Service (IGS) stations and the occurrence of the highest TEC anomalies. A homogeneous coverage of the data in this region provides an opportunity for the testing of different spatial modeling methods applied to TEC data. The spherical harmonic expansion (SHE) and spherical splines (SS) have been the most popular mathematical tools for the interpolation of TEC in the ionosphere over the last decades. The developed stochastic model (PPPLSC) is compared with the well-known stochastic global UQRG model, which is interpolated by the ordinary kriging (OK) and CODG global TEC model based on spherical harmonics (SH), and also the IGSG model, which is a combination of several models developed by the IGS Ionosphere Associate Analysis Centers. These four models derived from different approaches are assessed together using self-consistency analysis based on a geometry-free combination of carrier-phase observations, and also using external validation employing dual-frequency altimeter TEC from three low-Earth-orbit satellites. The study implements the LSC modeling technique, which is quite new for TEC and is a valuable step towards increasing the accuracy and resolution of ionosphere models. LSC, similarly to OK, is a stochastic parametric technique, applying the covariance based on data properties. Therefore LSC restores the fullest possible signal in the interpolated model in terms of spatial resolution. Leave-one-out (LOO) validation of the covariance parameters assures optimal interpolation results in the least-squares sense. The covariance matrices of LSC parametrized by LOO validation enable estimation with reliable internal precision for the model. The self-consistency analysis of TEC models with the use of carrier-phase observations proves a better consistency of stochastic models in relation to TEC models based on SHE. The set of statistical values of external comparisons with three altimetry-derived trajectories of TEC observations additionally confirms the advantage of stochastic PPPLSC and UQRG models. The validation results all together indicate a better quality of stochastic models in relation to those based on the summation of spherical functions. The factor that is suspected to decrease the accuracy of the latter models is the loss of the higher frequency signal due to the spectral limitation coming from the low order of SHE applied in IGSG and CODG. [ABSTRACT FROM AUTHOR]

This study addresses the potential contribution of the first pair of Galileo FOC satellites sent into incorrect highly eccentric orbits for geodetic and surveying applications. We began with an analysis of the carrier to noise density ratio and the stochastic properties of GNSS measurements. The investigations revealed that the signal power of E14 & E18 satellites is higher than for regular Galileo satellites, what is related to their lower altitude over the experiment area. With regard to the noise of the observables, there are no significant differences between all Galileo satellites. Furthermore, the study confirmed that the precision of Galileo data is higher than that of GPS, especially in the case of code measurements. Next analysis considered selected domains of precise instantaneous medium-range positioning: ambiguity resolution and coordinate accuracy as well as observable residuals. On the basis of test solutions, with and without E14 & E18 data, we found that these satellites did not noticeably influence the ambiguity resolution process. The discrepancy in ambiguity success rate between test solutions did not exceed 2%. The differences between standard deviations of the fixed coordinates did not exceed 1 mm for horizontal components. The standard deviation of the L1/E1 phase residuals, corresponding to regular GPS and Galileo, and E14 & E18 satellite signals, was at a comparable level, in the range of 6.5–8.7 mm. The study revealed that the Galileo satellites with incorrect orbits were fully usable in most geodetic, surveying and many other post-processed applications and may be beneficial especially for positioning during obstructed visibility of satellites. This claim holds true when providing precise ephemeris of satellites.

The ionosphere is still considered one of the most significant error sources in precise Global Navigation Satellite Systems (GNSS) positioning. On the other hand, new satellite signals and data processing methods allow for a continuous increase in the accuracy of the available ionosphere models derived from GNSS observables. Therefore, many research groups around the world are conducting research on the development of precise ionosphere products. This is also reflected in the establishment of several ionosphere-related working groups by the International Association of Geodesy. Whilst a number of available global ionosphere maps exist today, dense regional GNSS networks often offer the possibility of higher accuracy regional solutions. In this contribution, we propose an approach for regional ionosphere modelling based on un-differenced multi-GNSS carrier phase data for total electron content (TEC) estimation, and thin plate splines for TEC interpolation. In addition, we propose a methodology for ionospheric products self-consistency analysis based on calibrated slant TEC. The results of the presented approach are compared to well-established global ionosphere maps during varied ionospheric conditions. The initial results show that the accuracy of our regional ionospheric vertical TEC maps is well below 1 TEC unit, and that it is at least a factor of 2 better than the global products.

The ionosphere plays a crucial role in space weather that affects satellite navigation as the ionospheric delay is one of the major errors in GNSS. On the other hand, GNSS observations are widely used to determine the amount of ionospheric total electron content (TEC). An important aspect in the electron content estimation at regional and global scale is adopting the appropriate interpolation strategy. In this paper we propose and validate a new method for regional TEC modeling based on least squares collocation (LSC) with noise variance estimation. This method allows for providing accurate TEC maps with high spatial and temporal resolution. Such maps may be used to support precise GNSS positioning and navigation, e.g. in RTK mode and also in the ionosphere studies. To test applicability of new TEC maps to positioning, double-difference ionospheric corrections were derived from the maps and their accuracy was analyzed. In addition, the corrections were applied to GNSS positioning and validated in ambiguity resolution domain. The tests were carried out during a strong ionospheric storm when the ionosphere is particularly difficult to model. The performance of the new approach was compared to IGS and UPC global, and CODE regional TEC maps. The results showed an advantage of our solution with resulting accuracy of the relative ionospheric corrections usually better than 10 cm, even during the ionospheric disturbances. This proves suitability of our regional TEC maps for, e.g. supporting fast ambiguity resolution in kinematic GNSS positioning. [ABSTRACT FROM AUTHOR]

Two overlapping frequencies—L1/E1 and L5/E5a—in GPS and Galileo systems support the creation of mixed double-differences in a tightly combined relative positioning model. On the other hand, a tightly combined model makes it necessary to take into account receiver intersystem bias, which is the difference in receiver hardware delays. This bias is present in both carrier-phase and pseudorange observations. Earlier research showed that using a priori knowledge of earlier-calibrated ISB to correct GNSS observations has significant impact on ambiguity resolution and, therefore, precise positioning results. In previous research concerning ISB estimation conducted by the authors, small oscillations in phase ISB time series were detected. This paper investigates this effect present in the GPS–Galileo-IOV ISB time series. In particular, ISB short-term temporal stability and its dependence on the number of Galileo satellites used in the ISB estimation was examined. In this contribution we investigate the amplitude and frequency of the detected ISB time series oscillations as well as their potential source. The presented results are based on real observational data collected on a zero baseline with the use of different sets of GNSS receivers. [ABSTRACT FROM AUTHOR]