Search

The EUREF Permanent Network (EPN) currently consists of more than 300 evenly distributed continuously operating Global Navigation Satellite System (GNSS) reference stations. As a result of the continuous modernization of GNSS systems, the equipment of reference stations is subject to changes and upgrades. Changes relating to GNSS receiver antenna replacement are considered the main reason for discontinuities noticed in station position time series. It is assumed that resulting offsets are primarily caused by changes in carrier phase multipath effects after antenna replacement. However, the observed position shifts may also indicate the deficiency in the antenna phase center corrections (PCC) models. In this paper, we identified and interpreted the coordinate shifts caused by antenna/radome changes at selected EPN stations. The main objective was to investigate the correlation between the offset occurrence and PCC model type (type mean, individual robot-derived, individual chamber-derived) as well as multipath changes after antenna replacement. For the study, GNSS data from 12 EPN stations covering the years 2017–2019 were analyzed. The results proved that the antenna replacement is critical in the context of station coordinates stability and, in most cases, results in visible shifts in the position component time series. For GPS-only solutions, the most stable results were achieved using robot-derived individual PCC models. On the other hand, in the case of GPS + Galileo processing, the most stable results were obtained using chamber-derived individual PCC models. Furthermore, discontinuities due to the antenna change were noticed in the position time series in 75% of GPS + Galileo solutions. On the other hand, multipath changes arising as the result of antenna replacement were responsible, depending on solution type, for 21–42% of variations in the coordinates.

In this manuscript, we introduce the Ionospheric Tomographic Common Clock (ITCC) model of undifferenced uncombined GNSS measurements. It is intended for improving the Wide Area precise positioning in a consistent and simple way in the multi-GNSS context, and without the need of external precise real-time products. This is the case, in particular, of the satellite clocks, which are estimated at the Wide Area GNSS network Central Processing Facility (CPF) referred to the reference receiver one; and the precise realtime ionospheric corrections, simultaneously computed under a voxel-based tomographic model with satellite clocks and other geodetic unknowns, from the uncombined and undifferenced pseudoranges and carrier phase measurements at the CPF from the Wide Area GNSS network area. The model, without fixing the carrier phase ambiguities for the time being (just constraining them by the simultaneous solution of both ionospheric and geometric components of the uncombined GNSS model), has been successfully applied and assessed against previous precise positioning techniques. This has been done by emulating real-time conditions for Wide Area GPS users during 2018 in Poland., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The research has been performed under the support of ATOMIC ESA funded project and the manuscript has been written under PYTHIA EC project support. The ground GNSS network data was provided by Leica in Poland and the position of the GPS transmitters from IGS.

Ionosphere Associate Analysis Centers (IAACs) of the International GNSS Service (IGS) independently produce global ionosphere maps (GIMs) of the total electron content (TEC). The GIMs are based on different modeling techniques, resulting in different TEC levels and accuracies. In this study, we evaluated the accuracy and consistency of the IAAC GIMs during high (2014) and low (2018) solar activity periods of the 24th solar cycle. In our study, we applied two different evaluation methods. First, we carried out a comparison of the GIM-derived slant TEC (STEC) with carrier phase geometry-free combination of GNSS signals obtained from 25 globally distributed stations. Second, vertical TEC (VTEC) from GIMs was compared to altimetry-derived VTEC obtained from the Jason-2 and Jason-3 satellites and complemented for plasmaspheric TEC. The analyzed GIMs obtained STEC RMS values reaching from 1.98 to 3.00 TECU and from 0.96 to 1.29 TECU during 2014 and 2018, respectively. The comparison to altimetry data resulted in VTEC STD values that varied from 3.61 to 5.97 TECU and from 1.92 to 2.78 TECU during 2014 and 2018, respectively. The results show that among the IAACs, the Center for Orbit Determination in Europe global maps performed best in low and high solar activity periods. However, the highest accuracy was obtained by a non-IGS product—UQRG GIMs provided by Universitat Politècnica de Catalunya. It was also shown that the best results were obtained using a modified single layer model mapping function and that the map time interval has a relatively small influence on the resulting map accuracy.

The study intercompares three stochastic interpolation methods originating from the same geostatistical family: least-squares collocation (LSC) known from geodesy, as well as ordinary kriging (OKR) and universal kriging (UKR) known from geology and other geosciences. The objective of this work is to assess advantages and drawbacks of fundamental differences in modeling between these methods in imperfect data conditions. These differences primarily refer to the treatment of the reference field, commonly called ‘mean value’ or ‘trend’ in geostatistical language. The trend in LSC is determined globally before the interpolation, whereas OKR and UKR detrend the observations during the modeling process. The approach to detrending leads to the evident differences between LSC, OKR and UKR, especially in severe conditions such as far from the optimal data distribution. The theoretical comparisons of LSC, OKR and UKR often miss the numerical proof, while numerical prediction examples do not apply cross-validation of the estimates, which is proven to be a reliable measure of the prediction precision and a validation of empirical covariances. Our study completes the investigations with precise parametrization of all these methods by leave-one-out validation. It finds the key importance of the detrending schemes and shows the advantage of LSC prior global detrending scheme in unfavorable conditions of sparse data, data gaps and outlier occurrence. The test case is the modeling of vertical total electron content (VTEC) derived from GNSS station data. This kind of data is a challenge for precise covariance modeling due to weak signal at higher frequencies and existing outliers. The computation of daily set of VTEC maps using the three techniques reveals the weakness of UKR solutions with a local detrending type in imperfect data conditions.

In recent years, the Global Navigation Satellite Systems (GNSS) have been intensively modernized, resulting in the introduction of new carrier frequencies for GPS and GLONASS and the development of new satellite systems such as Galileo and BeiDou (BDS). For this reason, the absolute field antenna calibrations performed so far for the two legacy carrier frequencies, the GPS and GLONASS, seem to be insufficient. Hence, all antennas will require a re-calibration of their phase center variations for the new signals to ensure the highest measurement accuracy. Currently, two absolute calibration methods are used to calibrate GNSS antennas: field calibration using a robot and calibration in an anechoic chamber. Unfortunately, differences in these methodologies also result in a disparity in the obtained antenna phase center corrections (PCC). Therefore, we analyze the differences between individual PCC obtained with these two methods, specifically for the Leica AR-25 antenna model (LEIAR25). In addition, the influence of PCC differences on the GNSS-derived position time series for 19 EUREF Permanent GNSS Network (EPN) stations was also assessed. The results show that the calibration method has a noticeable impact on PCC models. PCC differences determined for the ionosphere-free combination may reach up over 20 mm and can be transferred to the position domain. Further tests concerning the positioning accuracy showed that for horizontal coordinates differences between solutions were mostly below 1 mm, exceeding 2 mm only at two stations for the GLONASS solution. However, the height component differences exceeded 5 mm for four, six and six stations out of 19 for the GPS, GLONASS and Galileo solutions, respectively. These differences are strongly dependent on large L2 calibration differences.

GNSS antenna electrical phase center variability is a source of errors in precise geodetic measurements, particularly in reference frame maintenance, satellite precise levelling, deformation monitoring, the establishment of geodetic control networks, geodynamic research, etc. It has a considerable influence on the precision and accuracy of the resulting coordinates. Previous research shows that changing the antenna on the monitored point often results in a considerable bias in the derived height coordinate component. In theory, if electrical phase center is sufficiently modeled, antenna changes should have negligible effect on coordinates. We present the analysis of the influence of the GPS antenna models on the resulting marker position. Numerical tests are based on field measurements. The GPS data collected at the test baseline were processed using Bernese GPS Software Version 5.0. The research shows that the IGS and NGS phase center variation models for some types of the surveying (rover) antennas are still imperfect and are contaminated by constant errors, which may exceed even ± 5 mm for horizontal coordinates components and ± 25 mm for vertical ones.

The ionosphere can be modeled and studied using multi-frequency GNSS signals and their geometry-free linear combination. Therefore, a number of GNSS-derived ionospheric models have been developed and applied in a broad range of applications. However, due to the complexity of estimating the carrier phase ambiguities, most of these models are based on low-accuracy carrier phase smoothed pseudorange data. This, in turn, critically limits their accuracy and applicability. Therefore, we present a new methodology of estimating the phase bias of the scaled L1 and L2 carrier phase difference which is a function of the ambiguities, the ionospheric delay, and hardware delays. This methodology is suitable for ionospheric modeling at regional and continental scales. In addition, we present its evaluation under varying ionospheric conditions. The test results show that the carrier phase bias of geometry-free linear combination can be estimated with a very high accuracy, which consequently allows for calculating ionospheric TEC with the uncertainty lower than 1.0 TECU. This high accuracy makes the resulting ionosphere model suitable for improving GNSS positioning for high-precision applications in geosciences.

Availability of two overlapping frequencies L1/E1 and L5/E5a of the signals transmitted by GPS and Galileo systems offers the possibility of tightly combining observations from both systems in a single observational model. A tightly combined observational model assumes a single reference satellite for all observations from both Galileo and GPS systems. However, when inter-system double-differenced observations are created, receiver inter-system bias is introduced. This study presents the results and the methodology for estimation and accounting for phase and code GPS-Galileo inter-system bias in precise relative positioning. The research investigates the size and temporal stability of the estimated bias for different receiver pairs as well as examines the influence of accounting for the inter-system bias on the user position solution. The obtained numerical results are based on four experiments carried out at different locations and time periods using both real and simulated GNSS data.

GPS measurements obtained by the global IGS network were used to study the occurrence of TEC fluctuations in the northern and southern high-latitude ionosphere during severe geomagnetic storms. In the northern hemisphere, GPS stations located higher than 55N Corrected Geomagnetic Latitude (CGL) at different longitudes were selected. In the southern hemisphere, Antarctic permanent GPS stations were used. Dual-frequency GPS measurements for individual satellite passes served as raw data. As a measure of fluctuation activity the rate of TEC (ROT) was used, and the fluctuation intensity was evaluated using the ROTI index. Using daily GPS measurements from all selected stations, images of the spatial and temporal behavior of TEC fluctuations were formed (in Corrected Geomagnetic Coordinates—CGC and geomagnetic local time—GLT). Similarly to the auroral oval, these images demonstrate an irregularity oval. The occurrence of the irregularity oval relates to the auroral oval, cusp and polar cap. During a storm, the intensity of TEC fluctuations essentially increased. The irregularity oval expands equatorward with an increase of magnetic activity. The study showed that the existing high-latitude GPS stations can provide a permanent monitoring tool for the irregularity oval in near real-time. In this paper, the features of the development of phase fluctuations at the geomagnetic conjugate points, and inter-hemispheric differences and similarities during winter and summer conditions, are discussed.

In many surveying applications, determination of accurate heights is of significant interest. The delay caused by the neutral atmosphere is one of the main factors limiting the accuracy of GPS positioning and affecting mainly the height coordinate component rather than horizontal ones. Estimation of the zenith total delay is a commonly used technique for accounting for the tropospheric delay in static positioning. However, in the rapid static positioning mode the estimation of the zenith total delay may fail, since for its reliable estimation longer observing sessions are required. In this paper, several troposphere modeling techniques were applied and tested with three processing scenarios: a single baseline solution with various height differences and a multi-baseline solution. In specific, we introduced external zenith total delays obtained from Modified Hopfield troposphere model with standard atmosphere parameters, UNB3m model, COAMPS numerical weather prediction model and zenith total delays interpolated from a reference network solution. The best results were obtained when tropospheric delays derived from the reference network were applied.

This research is motivated by the recent IGS Ionosphere Working Group recommendation issued at the IGS 2010 Workshop held in Newcastle, UK. This recommendation encourages studies on the evaluation of the application of COSMIC radio occultation profiles for additional IGS global ionosphere map (GIM) validation. This is because the reliability of GIMs is crucial to many geodetic applications. On the other hand, radio occultation using GPS signals has been proven to be a promising technique to retrieve accurate profiles of the ionospheric electron density with high vertical resolution on a global scale. However, systematic validation work is still needed before using this powerful technique for sounding the ionosphere on a routine basis. In this paper, we analyze the properties of the ionospheric electron density profiling retrieved from COSMIC radio occultation measurements. A comparison of radio occultation data with ground-based measurements indicates that COSMIC profiles are usually in good agreement with ionosonde profiles, both in the F2 layer peak electron density and the bottom side of the profiles. For this comparison, ionograms recorded by European ionospheric stations (DIAS network) in 2008 were used.

Precise GPS positioning requires the processing of carrier-phase observations and fixing integer ambiguities. With increasing distance between receivers, ambiguity fixing becomes more difficult because ionospheric and tropospheric effects do not cancel sufficiently in double differencing. A popular procedure in static positioning is to increase the length of the observing session and/or to apply atmospheric (ionospheric) models and corrections. We investigate the methodology for GPS rapid static positioning that requires just a few minutes of dual-frequency GPS observations for medium-length baselines. Ionospheric corrections are not required, but the ionospheric delays are treated as pseudo-observations having a priori values and respective weights. The tropospheric delays are reduced by using well-established troposphere models, and satellite orbital and clock errors are eliminated by using IGS rapid products. Several numerical tests based on actual GPS data are presented. It is shown that the proposed methodology is suitable for rapid static positioning within 50---70 km from the closest reference network station and that centimeter-level precision in positioning is feasible when using just 1 min of dual-frequency GPS data.

This paper presents a new strategy for GPS carrier phase data processing. The classic approach generally consists of three steps: a float solution, a search for integer ambiguities, and a fixed solution. The new approach is based on certain properties of ambiguity function method and ensures the condition of integer ambiguities without the necessity of the additional step of the integer search. The ambiguities are not computed explicitly, although the condition of “integerness” of the ambiguities is ensured in the results through the least squares adjustment with condition equations in the functional model. An appropriate function for the condition equations is proposed and presented. The presented methodology, modified ambiguity function approach, currently uses a cascade adjustment with successive linear combinations of L1 and L2 carrier phase observations to ensure a correct solution. This paper presents the new methodology and compares it to the three-stage classic approach which includes ambiguity search. A numerical example is provided for 25 km baseline surveyed with dual-frequency receivers. All tests were performed using an in-house developed GINPOS software and it has been shown that the positioning results from both approaches are equivalent. It has also been proved that the new approach is robust to adverse effects of cycle slips. In our opinion, the proposed approach may be successfully used for carrier phase GPS data processing in geodetic applications.

Real Time Kinematic (RTK) GPS positioning over longer distances requires a support of atmospheric (ionospheric and tropospheric) corrections, since the atmospheric errors decorrelate with the growing distances and cannot be completely eliminated by double differencing of the satellite observations. Currently, the most commonly used approach is to derive the atmospheric corrections at the reference station network and provide them in real time to the roving receiver. Another solution, proposed here, is to use predictive atmospheric models in order to derive the atmospheric corrections. This paper presents the test results of the performance assessment of the predictive ionosphere model (UWM-IPM) application to medium-range RTK positioning. The rover data collected within 25 to 67 km from the closest reference station were processed in the kinematic mode with the support of the ionospheric corrections derived from the UWM-IPM model. The RTK solution was derived in both single-and multi-baseline modes, and compared to the two reference solutions obtained without the ionospheric corrections. All numerical tests were carried out using the MPGPS software developed in cooperation with The Ohio State University; a recent extension to the software, developed at the University of Warmia and Mazury in Olsztyn, introduces the predictive ionosphere model to the RTK solution. The test results are very promising, and indicate that predicted ionosphere corrections can effectively support medium-range RTK positioning, and allow for fast ambiguity resolution over distances of several tens of kilometers under moderate ionospheric conditions.

The network-based GPS technique provides a broad spectrum of corrections to support RTK (real-time kinematic) surveying and geodetic applications. The most important among them are the ionospheric corrections generated in the reference network. The accuracy of these corrections depends upon the ionospheric conditions and may not always be sufficient to support ambiguity resolution (AR), and hence accurate GPS positioning. This paper presents the analyses of the network-derived ionospheric correction accuracy under extremely varying – quiet and stormy – geomagnetic and ionospheric conditions. In addition, the influence of the correction accuracy on the instantaneous (single-epoch) and on-the-fly (OTF) AR in long-range RTK GPS positioning is investigated, and the results, based on post-processed GPS data, are provided. The network used here to generate the ionospheric corrections consists of three permanent stations selected from the Ohio Continuously Operating Reference Stations (CORS) network. The average separation between the reference stations was ∼200 km and the test baseline was 121 km long. The results show that, during the severe ionospheric storm, the correction accuracy deteriorates to the point when the instantaneous AR is no longer possible, and the OTF AR requires much more time to fix the integers. The analyses presented here also outline the importance of the correct selection of the stochastic constraints in the rover solution applied to the network-derived ionospheric corrections.

The network-based approach to kinematic GPS positioning significantly increases the distance, over which carrier-phase ambiguity resolution can be performed. This can be achieved either by introducing geometric conditions based on the fixed reference locations, and/or through the use of reference network data to estimate the corrections to GPS observations that can be broadcast to the users. The Multi Purpose GPS Processing Software (MPGPS) developed at The Ohio State University uses the multiple reference station approach for wide area and regional differential kinematic GPS positioning. The primary processing algorithm uses the weighted free-net (WFN) approach with the distance-dependent weighting scheme to derive optimal estimates of the user coordinates and realistic accuracy measures. The WFN approach, combined with the single epoch (instantaneous) ambiguity resolution algorithm is presented here as one approach to real-time kinematic (RTK) GPS. Since for baselines exceeding ~100 km, the instantaneous ambiguity resolution may not always be possible due to the increasing observation noise and insufficient number of observations to verify the integer selection, an alternative approach, based on a single- (or multiple-) baseline solution, supported by a double-difference (DD) ionospheric delay propagated from the previous epoch is also presented. In this approach, some data accumulation, supported by the network-derived atmospheric corrections, is required at the beginning of the rover data processing to obtain the integer ambiguities; after this initialization period, the processing switches to the instantaneous RTK positioning mode. This paper presents a discussion on the effects of the network geometry, station separation and the data reduction technique on the final quality and reliability of the rover positioning solution. A 24-h data set of August 31, 2003, collected by the Ohio Continuously Operating Reference Station (CORS) network was processed by both techniques under different network geometry and reference station separation. Various solutions, such as (1) single-baseline solution for varying base-rover separation, (2) multi-baseline solution with medium-range base separation (over 100 km), and (3) multi-baseline solution with long-range base separation (up to 377 km), were obtained and compared for accuracy and consistency. The horizontal positioning accuracy achieved in these tests, expressed as the difference between the estimated coordinates and the known rover coordinates, is at the sub-decimeter level for the first approach, and at the centimeter-level for the second method, for baselines over 100 km. In the vertical coordinate, decimeter- and sub-decimeter levels were achieved for the two approaches, respectively. Even though all the results presented here were obtained in post-processing, both algorithms are suitable for real-time applications.

The primary objective of this paper is to test several methods of modeling the ionospheric corrections derived from a reference GPS network, and to study the impact of the models’ accuracy on the user positioning results. The five ionospheric models that are discussed here are: (1) network RTK (NR) carrier phase-based model — MPGPS-NR, (2) absolute, smoothed pseudorange-based model — MPGPS-P4, (3) IGS Global Ionosphere Model — GIM, (4) absolute model based on undifferenced dual-frequency ambiguous carrier phase data — ICON, and (5) carrier phase-based data assimilation method — MAGIC. Methods 1–4 assume that the ionosphere is an infinitesimal single layer, while method (5) considers the ionosphere as a 3D medium.The test data set was collected at the Ohio Continuously Operating Reference Stations (CORS) network on August 31, 2003. A 24-hour data set, representing moderate ionospheric conditions (maximum Kp = 2o), was processed. The ionospheric reference “truth” in doubledifference (DD) form was generated from the dualfrequency carrier phase data for two selected baselines, ~60 and ~100 km long, where one station was considered as a user receiver at an unknown location (simulated rover). The five ionospheric models were used to generate the DD ionospheric corrections for the rover, and were compared to the reference “truth.” The quality statistics were generated and discussed. Examples of instantaneous ambiguity resolution and RTK positioning are presented, together with the accuracy requirements for the ionospheric corrections, to assure integer ambiguity fixing.

This paper presents the multiple reference station approach to wide area (and regional) instantaneous RTK GPS, implemented in the MPGPSTM (Multi Purpose GPS Processing Software) software, developed at the Ohio State University. A weighted free-net approach (WFN) was applied in the instantaneous RTK software module, which enabled optimal estimation of the rover coordinates, properly reflecting the accuracies of the observations and the coordinates of the CORS stations. The effect of using the distance-dependent weighting scheme in the WFN approach on the final rover solution is analyzed. The influence of the different weights was studied by introducing the distance-dependent weights as a function of the CORS station separation L to the rover (1/L2). The results show that almost 100% of the differences between the computed horizontal rover coordinates and the known reference coordinates are below a decimeter, and 95% of the differences in the vertical coordinate are below 20 cm, when using the suggested approach. In addition, the accuracy analysis of two other solutions, with different datum definition (minimum constraint and over-constrained), is presented. This analysis verifies the suitability of the stochastic models used in the RTK module and the rigorous approach, taking into account inter-baseline correlation as well as the correlation in-between each baseline component.

This paper presents the analyses connected with reduction of errors from ionospheric refraction using GPS data from local satellite networks. This is particularly essential during rising solar activity. The Bernese GPS Software v. 4.2 was used, as an analytical tool. The test data included measurements from a geodynamic network SUDETES situated in the Sudety Mountains across the border between the Czech Republic and Poland. A local ionospheric activity model developed from a regional model augmented with data from a local network has been tested at three levels. The criteria included comparison with a global model, the success rate of ambiguity determination using the quasi-ionosphere free and wide-lane/narrow-lane strategies, and in the position domain through analysis of residuals. The results show that the local model increases the success rate for ambiguity determination for the wide-lane/narrow-lane strategy and is available sooner than the global models. The output of the SUDETES network processing including the models of local ionospheric and tropospheric activity have been used to process data from a number of relatively small networks situated in the Sudety mountains.

This paper demonstrates the concept and practical examples of instantaneous mapping of regional ionosphere, based on GPS observations from the State of Ohio continuously operating reference stations (CORS) network. Interpolation/prediction techniques, such as kriging (KR) and the Multiquadric Model (MQ), which are suitable for handling multi-scale phenomena and unevenly distributed data, were used to create total electron content (TEC) maps. Their computational efficiency (especially the MQ technique) and the ability to handle undersampled data (especially kriging) are particularly attractive. Presented here are the preliminary results based on GPS observations collected at five Ohio CORS stations (~100 km sta-tion separation and 1-second sampling rate). Dual frequency carrier phase and code GPS observations were used. A zero-difference approach was used for absolute TEC recovery. The quality of the ionosphere rep-resentation was tested by comparison to the International GPS Service (IGS) Global Ionosphere Maps (GIMs), which were used as a reference.