Regional GNSS Networks Research Articles

Improvement and Comparison of Multi-Reference Station Regional Tropospheric Delay Modeling Method Considering the Effect of Height Difference

Tropospheric delay information is particularly important for network RTK (Network Real-time Kinematic) positioning. Conventionally, tropospheric delay information at a virtual reference station (VRS) is obtained using the linear interpolation method (LIM). However, the conventional LIM cannot work well when there is a substantial height difference between the rover station and the reference station. Consequently, we propose a modified linear interpolation method (MLIM) by carefully handling the height difference between the rover station and the reference station. The new MLIM method first corrects the systematic error of the double-difference (DD) tropospheric delay in the elevation direction caused by the height difference, and then utilizes the linear interpolation algorithm to obtain the tropospheric delay of the VRS station. To determine the parameters of the low-order surface model (LSM), we also propose a modified LSM (MLSM) interpolation method in the triangular network and evaluate it in the positioning domains. The two new interpolation methods are evaluated using two regional GNSS networks with obvious height disparities. Results show that the DD tropospheric delay interpolation accuracy obtained by the new MLIM and MLSM is improved by 56.5% and 78.7% on average in the two experiments compared to the conventional method. The new MLIM and MLSM are more accurate than the traditional LIM (TLIM) in cases with low elevation satellites. Additionally, the positioning accuracies are improved by using the MLIM and MLSM methods. The MLIM and MLSM outperform TLIM in the up-component by an average of 72.8% and 80.7%, respectively.

Rigorous and fast constraints transformations at the solution level: case studies for regional and global GNSS networks

Rigorous and fast constraints transformations at the solution level: case studies for regional and global GNSS networks

Performance improvement of real-time PPP ambiguity resolution using a regional integer clock

Obtaining reliable GNSS uncalibrated phase delay (UPD) or integer clock products is the key to achieving ambiguity-fixed solutions for real-time (RT) precise point positioning (PPP) users. However, due to the influence of RT orbit errors, the quality of UPD/integer clock products estimated with a globally distributed GNSS network is difficult to ensure, thereby affecting the ambiguity resolution (AR) performance of RT-PPP. In this contribution, by fully utilising the consistency of orbital errors in regional GNSS network coverage areas, a method is proposed for estimating regional integer clock products to compensate for RT orbit errors. Based on Centre National d’Études Spatiales (CNES) RT precise products, the regional GPS/BDS integer clock was estimated with a CORS network in the west of China. Results showed that the difference between the estimated regional and CNES global integer clock/bias products was generally less than 5 cm for GPS, whereas clock differences of greater than 10 cm were observed for BDS due to the large RT orbit error. Compared with PPP using global integer clock/bias products, the AR performance of PPP using the regional integer clock was obviously improved for four rover stations. For single GPS, the horizontal and vertical accuracies of ambiguity-fixed PPP solutions were improved by 56.2% and 45.3% on average, respectively, whereas improvements of 67.5% and 50.5% in the horizontal and vertical directions, respectively, were observed for the combined GPS/BDS situation. Based on a regional integer clock, the RMS error of a kinematic ambiguity-fixed PPP solution in the horizontal direction could reach 0.5 cm. In terms of initialisation time, the average time to first fix (TTFF) in combined GPS/BDS PPP was shortened from 18.2 min to 12.7 min. In view of the high AR performance realised with the use of regional integer clocks, this method can be applied to scenarios that require high positioning accuracy, such as deformation monitoring.

A Least Squares Solution to Regionalize VTEC Estimates for Positioning Applications

A new approach is presented to improve the spatial and temporal resolution of the Vertical Total Electron Content (VTEC) estimates for regional positioning applications. The proposed technique utilises a priori information from the Global Ionosphere Maps (GIMs) of the Center for Orbit Determination in Europe (CODE), provided in terms of Spherical Harmonic (SH) coefficients of up to degree and order 15. Then, it updates the VTEC estimates using a new set of base-functions (with better resolution than SHs) while using the measurements of a regional GNSS network. To achieve the highest accuracy possible, our implementation is based on a transformation of the GIM/CODE VTECs to their equivalent coefficients in terms of (spherical) Slepian functions. These functions are band-limited and reflect the majority of signal energy inside an arbitrarily defined region, yet their orthogonal property is remained. Then, new dual-frequency GNSS measurements are introduced to a Least Squares (LS) updating step that modifies the Slepian VTEC coefficients within the region of interest. Numerical application of this study is demonstrated using a synthetic example and ground-based GPS data in South America. The results are also validated against the VTEC estimations derived from independent GPS stations (that are not used in the modelling), and the VTEC products of international centres. Our results indicate that, by using 62 GPS stations in South America, the ionospheric delay estimation can be considerably improved. For example, using the new VTEC estimates in a Precise Point Positioning (PPP) experiment improved the positioning accuracy compared to the usage of GIM/CODE and Klobuchar models. The reductions in the root mean squared of errors were ∼23% and 25% for a day with moderate solar activity while 26% and ∼35% for a day with high solar activity, respectively.

Regional integration of long-term national dense GNSS network solutions

The EUREF Permanent Network Densification is a collaborative effort of 26 European GNSS analysis centers providing series of daily or weekly station position estimates of dense national and regional GNSS networks, in order to combine them into one homogenized set of station positions and velocities. During the combination, the station meta-data, including station names, DOMES numbers, and position offset definitions were carefully homogenized, position outliers were efficiently eliminated, and the results were cross-checked for any remaining inconsistencies. The results cover the period from March 1999 to January 2017 (GPS week 1000-1933) and include 31 networks with positions and velocities for 3192 stations, well covering Europe. The positions and velocities are expressed in ITRF2014 and ETRF2014 reference frames based on the Minimum Constraint approach using a selected set of ITRF2014 reference stations. The position alignment with the ITRF2014 is at the level of 1.5, 1.2, and 3.2 mm RMS for the East, North, Up components, respectively, while the velocity RMS values are 0.17, 0.14, and 0.38 mm/year for the East, North, and Up components, respectively. The high quality of the combined solution is also reflected by the 1.1, 1.1, and 3.5 mm weighted RMS values for the East, North, and Up components, respectively.

Investigation of Deformations of the Earth Crust on the Territory of Ukraine Using a Gnss Observations

Abstract A regional GNSS network consisting of 202 permanent GNSS stations established to study the recent crustal strain deformation in the Ukrainian territory. The GNSS observations (from December 7, 1997 to January 28, 2017) collected and processed using Bernese GNSS Software ver. 5.2 in accordance with the recommendations of the Central Bureau of the EUREF Permanent GNSS Network. Based on the above results the velocity vectors were estimated using Bernese GNSS Software ver. 5.2 for the future calculation of deformation. In particular, ellipses of distortion, rotation, maximum shear strain, and deformation area are obtained. Due to the differences in rate of the horizontal extension and rotation the area is divided in two main blocks. The first block shows compression that prevails in the North-East direction. Stretch in both directions is prevailing on second block. The obtained results can indicate the presence of some force which could effect on the study area.

Assessing a new velocity field in Greece towards a new semi-kinematic datum

Greece has always been an interesting study area for the geodesists due to its intense geodynamic behaviour. Especially, the exploitation of a modern geodetic velocity field using GNSS becomes a crucial requirement for geodetic purposes. The main aim of the present study is the assessment of a modern geodetic velocity model. This procedure is based on the unification of various reference frames, implemented from individual extended GNSS campaigns in different epochs with the effective involvement of the Hellenic Military Geographic Service. The implementation of geodetic velocities in the inhomogeneous Greek velocity field improves significantly the reliability of transformations, more than 60% with respect to the horizontal component, applying a vice versa time shift to a common epoch. We also emphasise the necessity to adopt a velocity model in order to process regional GNSS networks and therefore to establish a modern semi-kinematic reference frame in Greece.

Detection of water vapor time variations associated with heavy rain in northern Italy by geodetic and low-cost GNSS receivers

GNSS atmospheric water vapor monitoring is not yet routinely performed in Italy, particularly at the regional scale. However, in order to support the activities of regional environmental protection agencies, there is a widespread need to improve forecasting of heavy rainfall events. Localized convective rain forecasts are often misplaced in space and/or time, causing inefficiencies in risk mitigation activities. Water vapor information can be used to improve these forecasts. In collaboration with the environmental protection agencies of the Lombardy and Piedmont regions in northern Italy, we have collected and processed GNSS and weather station datasets for two heavy rain events: one which was spatially widespread, and another which was limited to few square kilometers. The time variations in water vapor derived from a regional GNSS network with inter-station distances on the order of 50 km were analyzed, and the relationship between the time variations and the evolution of the rain events was evaluated. Results showed a signature associated with the passage of the widespread rain front over each GNSS station within the area of interest. There was a peak in the precipitable water vapor value when the heavier precipitation area surrounded the station, followed by a steep decrease (5–10 mm in about 1 h) as the rainclouds moved past the station. The smaller-scale event, a convective storm a few kilometers in extent, was not detected by the regional GNSS network, but strong fluctuations in water vapor were detected by a low-cost station located near the area of interest.

Observations of the Weddell Sea Anomaly in the ground-based and space-borne TEC measurements

The Weddell Sea Anomaly (WSA) is a summer ionospheric anomaly, which is characterized by a greater nighttime ionospheric density than that in daytime in the region near the Weddell Sea. We investigate the WSA signatures in the ground-based TEC (vertical total electron content) by using GPS and GLONASS measurements of the dense regional GNSS networks in South America. We constructed the high-resolution regional TEC maps for December 2014–January 2015. The WSA effects of the TEC exceed the noontime values are registered starting from 17 LT, it reaches its maximum at 01–05 LT and starts to disappear after 09 LT. Maximal TEC enhancements were as large as a factor of 2.5–3.5 and were registered at 03–04 LT. This effect was mainly localized in the geographical region of 55°S-75°S latitude and 80°W-30°W longitude, close to the Antarctic Peninsula. Further, we examined the WSA occurrence in the topside ionosphere by using GPS measurements from a zenith-looking GPS antenna on board three Swarm satellites to determine topside TEC (above ∼500 km altitude) at the topside ionosphere-plasmasphere system. Global maps of the topside TEC indicated that the zone with significant WSA effect in the topside TEC (TEC increase ∼2–4 times the noontime level) had a large spatial extent over southern Pacific and Atlantic Ocean. It was observed around 150°W-20°W and between 40°S and 70°S during 23 LT - 06 LT. For the first time, the WSA signatures were shown in the topside TEC data derived from the GPS measurements onboard the Swarm constellation. Independently, two other instruments - FORMOSAT-3/COSMIC radio occultation electron density profiles and in situ measurements by the Langmuir Probe instrument onboard Swarm satellites – were able to confirm: (1) the same location of the WSA zone as revealed in Swarm TEC; (2) the most-pronounced WSA effect, as a maximal electron density exceed over the noontime values, corresponds to altitudes above 400–500 km.

On the Convergence of Ionospheric Constrained Precise Point Positioning (IC-PPP) Based on Undifferential Uncombined Raw GNSS Observations

Precise Point Positioning (PPP) has become a very hot topic in GNSS research and applications. However, it usually takes about several tens of minutes in order to obtain positions with better than 10 cm accuracy. This prevents PPP from being widely used in real-time kinematic positioning services, therefore, a large effort has been made to tackle the convergence problem. One of the recent approaches is the ionospheric delay constrained precise point positioning (IC-PPP) that uses the spatial and temporal characteristics of ionospheric delays and also delays from an a priori model. In this paper, the impact of the quality of ionospheric models on the convergence of IC-PPP is evaluated using the IGS global ionospheric map (GIM) updated every two hours and a regional satellite-specific correction model. Furthermore, the effect of the receiver differential code bias (DCB) is investigated by comparing the convergence time for IC-PPP with and without estimation of the DCB parameter. From the result of processing a large amount of data, on the one hand, the quality of the a priori ionosphere delays plays a very important role in IC-PPP convergence. Generally, regional dense GNSS networks can provide more precise ionosphere delays than GIM and can consequently reduce the convergence time. On the other hand, ignoring the receiver DCB may considerably extend its convergence, and the larger the DCB, the longer the convergence time. Estimating receiver DCB in IC-PPP is a proper way to overcome this problem. Therefore, current IC-PPP should be enhanced by estimating receiver DCB and employing regional satellite-specific ionospheric correction models in order to speed up its convergence for more practical applications.

Spatiotemporal filtering of regional GNSS network’s position time series with missing data using principle component analysis

The existing spatiotemporal analysis methods suppose that the involved time series are complete and have the same data interval. However missing data inevitably occur in the position time series of Global Navigation Satellite Systems networks for many reasons. In this paper, we develop a modified principal component analysis to extract the Common Mode Error (CME) from the incomplete position time series. The principle of the proposed method is that a time series can be reproduced from its principle components. The method is equivalent to the method of Dong et al. (J Geophys Res 111:3405–3421, 2006) in case of no missing data in the time series and to the extended ‘stacking’ approach under the assumption of a uniformly spatial response. The new method is first applied to extract the CME from the position time series of the Crustal Movement Observation Network of China (CMONOC) over the period of 1999–2009 where the missing data occur in all stations with the different gaps. The results show that the CMEs are significant in CMONOC. The size of the first principle components for the North, East and Up coordinates are as large as 40, 41 and 37 % of total principle components and their spatial responses are not uniform. The minimum amplitudes of the first eigenvectors are only 41, 15 and 29 % for the North, East and Up coordinate components, respectively. The extracted CMEs of our method are close to the data filling method, and the Root Mean Squared error (RMS) values computed from the differences of maximum CMEs between two methods are only 0.31, 0.52 and 1.55 mm for North, East and Up coordinates, respectively. The RMS of the position time series is greatly reduced after filtering out the CMEs. The accuracies of the reconstructed missing data using the two methods are also comparable. To further comprehensively test the efficiency of our method, the repeated experiments are then carried out by randomly deleting different percentages of data at some stations. The results show that the CMEs can be extracted with high accuracy at the non missing-data epochs. And at the missing-data epochs, the accuracy of extracted CMEs has a strong dependence on the number of stations with missing data.