Geodetic Applications Research Articles

Observable-specific phase biases of Wuhan multi-GNSS experiment analysis center’s rapid satellite products

Precise Point Positioning (PPP) with Ambiguity Resolution (AR) is an important high-precision positioning technique that is gaining popularity in geodetic and geophysical applications. The implementation of PPP-AR requires precise products such as orbits, clocks, code, and phase biases. As one of the analysis centers of the International Global Navigation Satellite System (GNSS) Service (IGS), the Wuhan University Multi-GNSS experiment (WUM) Analysis Center (AC) has provided multi-GNSS Observable-Specific Bias (OSB) products with the associated orbit and clock products. In this article, we first introduce the models and generation strategies of WUM rapid phase clock/bias products and orbit-related products (with a latency of less than 16 h). Then, we assess the performance of these products by comparing them with those of other ACs and by testing the PPP-AR positioning precision, using data from Day of the Year (DOY) 047 to DOY 078 in 2022. It is found that the peak-to-peak value of phase OSBs is within 2 ns, and their fluctuations are caused by the clock day boundary discontinuities. The associated Global Positioning System (GPS) orbits have the best consistency with European Space Agency (ESA) products, and those of other systems rank in the medium place. GLObal NAvigation Satellite System (GLONASS) clocks show slightly inconsistency with other ACs’ due to the antenna thrust power adopted, while the phase clocks of other GNSSs show no distortion compared with legacy clocks. With well-estimated phase products for Precise Orbit Determination (POD), the intrinsic precision is improved by 14%, 17%, and 24% for GPS, Galileo navigation satellite system (Galileo), and BeiDou-3 Navigation Satellite System (BDS-3), respectively. The root mean square of PPP-AR using our products in static mode with respect to IGS weekly solutions can reach 0.16 cm, 0.16 cm, and 0.44 cm in the east, north, and up directions, respectively. The multi-GNSS wide-lane ambiguity fixing rates are all above 90%, while the narrow-lane fixing rates above 80%. In conclusion, the phase OSB products at WUM have good precision and performance, which will benefit multi-GNSS PPP-AR and POD.

Combination Strategy for the Geocentric Realization of Regional Epoch Reference Frames

AbstractFor high‐resolution regional geodetic applications, the International Terrestrial Reference Frame (ITRF) is complemented by regional densifications. These are realized either as multi‐year solutions related to a tectonic plate (e.g., EUREF for Europe) or as epoch reference frames (ERFs) to capture nonlinear geophysical station motions caused by, for example, earthquakes or non‐tidal loading (e.g., SIRGAS for Latin America). These Global Navigation Satellite Systems (GNSS)‐only based regional reference frames have in common that their geodetic datum is aligned with the ITRF datum at a specific epoch. The consequence is that their origin represents the Earth's center of figure and does not coincide with the instantaneous center of mass. Here, we present studies on a direct geocentric realization of regional ERFs. We propose to realize the geodetic datum for each epoch by combining global GNSS, Satellite Laser Ranging, and Very Long Baseline Interferometry networks via measured local ties at co‐located sites. A uniformly distributed global GNSS network is used to realize the orientation via a no‐net‐rotation constraint with respect to the ITRF and is densified by the stations of the regional subnetwork. The developed combination and filtering strategy aims to guarantee a stable datum realization for each epoch‐wise solution. Validating our results against global reference frames and geophysical loading models relating to the Earth's centers of mass and figure, we show that the realized displacement time series are geocentric and reflect seasonal geophysical processes. As the approach does not need to rely on co‐location sites in the region of interest, it is conceptually transferable to other regions on the globe.

Assessing the accuracy of online GNSS processing services and commercial software on short baselines

With the rapid establishment of free online processing services to provide users with reliable solutions, it is important to determine the reliability of using free online processing software for the Global Navigation Satellite System post-processing. The study aim at assessing the accuracy of two (2) free online processing software, AUSPOS, and CSRS-PPP and two (2) commercial software, compass post-processing, and GNSS solutions. Field observations were carried out on seven (7) control points using static GNSS observation techniques with an observation period of 1hr for three (3) consecutive days and conventional surveying using total station instruments to establish a closed traverse. The acquired data were post-processed using both online and commercial software. The co-ordinates generated from each software were then compared with the ones obtained using total station instruments to determine their relative discrepancies and accuracies. Root mean square error and T-test were used for the analysis of the result. The result obtained is (0.004m, 0.003m and 0.007m) for compass post-processing software and (0.015m, 0.012m and 0.016m) for GNSS solutions software and the online software had the Root Mean Square Error (RMSE) values of (0.025m, 0.023m and 0.027m) for AUSPOS and (0.034m, 0.037m and 0.041m) for CSRS-PPP both in X, Y, and Z direction i.e. UTM East, North and ellipsoidal height respectively. Analysis at a 5% level of significance shows no significant difference between the two methods. Online GNSS processing services are easy to use, do not require the knowledge of GNSS data processing and can be adopted for engineering and geodetic applications.

Development of GNSS software for Ghana Survey and Mapping Division

Processing of Global Navigational Satellite System (GNSS) data forms the basis for the usage of differential systems for obtaining spatial data. All open sources or commercial software packages developed for data processing give specific details to suit the intended purpose of the software. To obtain a uniform format for submitted survey data, Survey and Mapping Division (SMD) in various jurisdictions have specified formats for data submission for all kinds of surveys. In this regard, “GNSS Ghana” Software (GGS), a GNSS standalone Windows-based application with a modern user-friendly interface was developed for geodetic applications such as, projection and datum transformation worldwide, GNSS data post-processing of Receiver Independent Exchange Format (RINEX) files, and generating reports to meet Ghana SMD reporting standards including cadastral computations and reports for submission. To assess the developed software, GNSS data from two International GNSS Service (IGS) stations (BJCO and YKRO) were processed using GGS and three other commercial software such as GNSS Solution Software (GSS), Spectrum Survey Software (SSS), and Leica Geo Office (LGO), and the positional results compared against the existing coordinate. The results revealed that the GGS outperformed the remaining three commercial software packages with a sub-meter level of accuracy. Further assessment was conducted on datum transformation using the coordinates of 21 existing geodetic control points in Ghana. Utilizing the 7-transformation parameters of Ghana, the results gave uncertainties of [0.10ft. ± 0.99ft.] in the eastings and [0.02ft. ± 1.61ft.] in the northings with a 99% confidence level.

BeiDou Satellite Radiation Force Models for Precise Orbit Determination and Geodetic Applications

China's BeiDou satellite navigation system (BDS) has completed its full constellation in orbit since June 2020. Services have been evolved from regional (BDS-2) to global (BDS-3). This contribution evaluates the impact of solar radiation pressure (SRP) modeling on satellite orbits and geodetic parameters. To that end, we process 2 years of BDS observations (2019-2021), collected by a network of 100 ground stations. A physical a priori box-wing model based on the estimated optical properties is introduced. Various physical effects, such as radiator emission and thermal radiation of solar panels are considered. The ECOM (Empirical CODE orbit Model), ECOM+along-track and ECOM2 models are employed on top in the experiment. We show that without the use of the a priori box-wing model, the ECOM+along-track model shows clear better orbit solutions during eclipse seasons for BDS-3 satellites. This is proven to be mainly due to the thermal radiation of the solar panels. However, the along-track acceleration is highly correlated with LOD (length of day) and ECOM parameters. LOD estimates in this case are contaminated. When using the physical a priori box-wing model satellite orbital errors are greatly reduced for all the ECOM models. For instance, orbit misclosures of BDS-3 CAST (China Academy of Space Technology) satellites improve by a factor of two for the ECOM model during eclipse seasons. Furthermore, the use of the a priori box-wing model mitigates a great majority of the spurious signals in the geodetic parameters.

Probing a southern hemisphere VLBI Intensive baseline configuration for UT1 determination

The deviation of Universal Time from atomic time, expressed as UT1−UTC, reflects the irregularities of the Earth rotation speed and is key to precise geodetic applications which depend on the transformation between celestial and terrestrial reference frames. A rapidly varying quantity such as UT1−UTC demands observation scenarios enabling fast delivery of good results. These criteria are currently met only by the Very Long Baseline Interferometry (VLBI) Intensive sessions. Due to stringent requirements of a fast UT1−UTC turnaround, the observations are limited to a few baselines and a duration of one hour. Hence, the estimation of UT1−UTC from Intensives is liable to constraints and prone to errors introduced by inaccurate a priori information. One aspect in this context is that the regularly operated Intensive VLBI sessions organised by the International VLBI Service for Geodesy and Astrometry solely use stations in the northern hemisphere. Any potential systematic errors due to this northern hemisphere dominated geometry are so far unknown. Besides the general need for stimulating global geodetic measurements with southern observatories, this served as a powerful motivation to launch the SI (Southern Intensive) program in 2020. The SI sessions are observed using three VLBI antennas in the southern hemisphere: Ht (South Africa), Hb (Tasmania) and Yg (Western Australia). On the basis of UT1−UTC results from 53 sessions observed throughout 2020 and 2021, we demonstrate the competitiveness of the SI with routinely operated Intensive sessions in terms of operations and UT1−UTC accuracy. The UT1−UTC values of the SI reach an average agreement of 32 µs in terms of weighted standard deviation when compared with the conventional Intensives results of five independent analysis centers and of 27 µs compared with the 14C04 series. The mean scatter of all solutions of the considered northern hemisphere Intensives with respect to C04 is at a comparable level of 29 µs. The quality of the results is only slightly degraded if just the baseline HtHb is evaluated. In combination with the e-transfer capabilities from Ht to Hb, this facilitates continuation of the SI by ensuring rapid service UT1−UTC provision.Graphical

Assessment of ZTD Derived from COSMIC Occultation Data with ECWMF, Radiosondes, and GNSS.

Global Navigation Satellite System (GNSS) signals generate slant tropospheric delays when they pass through the atmosphere, which is recognized as the main source of error in many spatial geodetic applications. The zenith tropospheric delay (ZTD) derived from radio occultation data is of great significance to atmospheric research and meteorology and needs to be assessed in the use of precision positioning. Based on the atmPrf, sonPrf, and echPrf data from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) Data Analysis and Archiving Center (CDAAC) from 1 January to 31 December 2008 and 2012, we obtained the ZTDs of the radio occultation data (occZTD) and the corresponding radiosonde (sonZTD) and ECWMF data (echZTD). The ZTDs derived from ground-based global positioning system (GPS) observations from the International GNSS Service (IGS) were corrected to the lowest tangent point height of the matched radio occultation profile by the barometric height formula (gnsZTD). The statistical results show that the absolute values of the bias between occZTD and echZTD, sonZTD, or gnsZTD are less than 5 mm, and the standard deviations are approximately 20 mm or less, indicating that occZTD had significant accuracy in the GNSS positioning model even when the local spherical symmetry assumption error was introduced when the Abel inversion algorithm was used to obtain the refractive index profile of atmPrf. The effects of the horizontal/vertical matching resolution and the variation in the station height/latitude on the biases of occZTD and gnsZTD were analyzed. The results can be used to quantify the performance of radio occultation data for tropospheric delay error correction in dynamic high-precision positioning.

GNSS Tekniği ile Düşey Yöndeki Deformasyonların Araştırılması

Monitoring and analysis of deformations in the earth's crust and engineering structures are among the important issues of geodesy. In order to monitor the deformations, a geodetic network consisting of reference and object points is created in general. Deformation research is carried out by analyzing the movements at the network points. Measurements for the determination of these movements can be made with classical techniques as well as with GNSS techniques. The static relative positioning is a widely used method in such precise geodetic applications. In this study; the capacity of the GNSS technique to detect vertical deformations was investigated. For this purpose, a micro geodetic network was designed in the Selcuk University Campus area. A mechanism to create virtual deformations was placed on the object point in the designed network and periodic measurements were carried out by creating virtual deformations in the vertical direction. Measurements were processed with the Bernese v5.2 scientific GNSS software, analyzed by Iterative Weighted Similarity Transformation Method using the software developed to perform deformation analysis in GNSS networks, and the determined deformations were compared with the real deformation value, considering the ionospheric activities on the measurement days. As a result of the analyses, vectorial deformation amounts compatible with the real deformation value were obtained and it was seen that the motion amounts in the direction of the coordinate components were also compatible with the virtual deformation amount given on the mechanism.

Creating orthophotos with unmanned aerial vehicles and examining its accuracy and usability in geodetic applications

SummaryUnmanned aerial vehicles, one of the technologies that aim to produce data in many scientific studies, has widespread use in many engineering applications, especially in cartography applications. UAV, which can meet the high accuracy required in many studies, offer users the opportunity to produce point cloud and maps for various aims. It is aimed to produce a high‐resolution orthophoto map of the study area in this study. In addition, the accuracy of the orthophoto map produced for the areas classified according to topographic structures in the study area has been checked with GNSS measurements, and its compliance with the standards specified in the regulation has been examined. According to the results; Considering the root square mean error values of three axes, it has been searched whether the accuracy values of the products obtained are suitable according to the regulation and it has been determined that these values are within the limits. Then, the application of testing the accuracy of the orthophoto map has been started. When all checkpoints have been examined, the maximum error values in x, y, and h directions have been found to be 5.9, 4.5, and 4.9 cm, respectively.

Inclusion of data uncertainty in machine learning and its application in geodetic data science, with case studies for the prediction of Earth orientation parameters and GNSS station coordinate time series

Data uncertainty plays an important role in the field of geodesy. Even though deep learning is becoming increasingly important for geodetic applications due to its high accuracy, it typically does not consider the data uncertainty. As we demonstrate in this study, we propose to include the uncertainty of data in deep neural network architectures to achieve a better generalization. This is advantageous for big data applications as well as for small datasets. Inspired by weighted and total least squares, we formulate the problem for both input and target uncertainties, and combine it with the Bayesian learning method. This results in a new form of the loss function in machine learning. As an alternative approach, we consider data uncertainties by including them as additional features. For comparison purposes, we use models without the consideration of data uncertainty as a benchmark. To show the efficacy of the proposed method, we apply it to the prediction of Earth Orientation Parameters (EOPs, namely polar motion, dUT1, and LOD) and Global Navigation Satellite System (GNSS) station coordinate time series. We demonstrate that the least-squares-inspired method outperforms both the benchmark and the feature-inspired method for both the studies. In the EOPs study, the improvement can be more than 50% in the study interval. In the study of GNSS station coordinate time series, which is presented for 1000 stations across the globe, the improvement on an average basis is around 12%. The results demonstrate the advantage of using uncertainty information in the machine learning algorithms, when applied to geodetic time series.

Optimised gravity anomaly fields from along-track multi-mission satellite altimeter over Malaysian seas

Marine gravity anomalies are crucial parameters and elements for determining coastal and ocean geoid, tectonics and crustal structures, as well as offshore studies. This study aims to derive and develop a marine gravity anomaly model over Malaysian seas from multi-mission altimetry data. Universiti Teknologi Malaysia 2020 Mean Sea Surface Model is computed based on along-track data from nine satellite missions, incorporating TOPEX, Jason-1, Jason-2, ERS-2, Geosat Follow on (GFO), Envisat-1, CryoSat-2, SARAL/AltiKa, and Sentinel-3A. The data exploited are from 1993 to 2019 (27 years). Residual gravity anomaly is computed using Gravity Software, and two-dimensional planar Fast Fourier Transformation method is applied. The evaluation, selection, blunder detection, combination, and re-gridding of the altimetry-derived gravity anomalies and Global Geopotential Model data are demonstrated. Cross-validation procedure is employed for data cleaning and quality control using the Kriging interpolation method. Then, cross-validation procedure is applied to the tapering window width 200, which adopting the GECO model denotes the optimum gravity anomaly with root mean square errors in the range of ± 4.2472 mGal to ± 6.0202 mGal. The findings suggest that the estimated marine gravity anomaly is acceptable to be implemented in the marine geoid determination and bathymetry estimation over Malaysian seas. In addition, the results of this study are valuable for geodetic and geophysical applications in marine areas.

Forecasting global and multi-level thermospheric neutral density and ionospheric electron content by tuning models against satellite-based accelerometer measurements

Global estimation of thermospheric neutral density (TND) on various altitudes is important for geodetic and space weather applications. This is typically provided by models, however, the quality of these models is limited due to their imperfect structure and the sensitivity of their parameters to the calibration period. Here, we present an ensemble Kalman filter (EnKF)-based calibration and data assimilation (C/DA) technique that updates the model’s states and simultaneously calibrates its key parameters. Its application is demonstrated using the TND estimates from on-board accelerometer measurements, e.g., those of the Gravity Recovery and Climate Experiment (GRACE) mission (at sim 410 km altitude), as observation, and the frequently used empirical model NRLMSISE-00. The C/DA is applied here to re-calibrate the model parameters including those controlling the influence of solar radiation and geomagnetic activity as well as those related to the calculation of exospheric temperature. The resulting model, called here ‘C/DA-NRLMSISE-00’, is then used to now-cast TNDs and individual neutral mass compositions for 3 h, where the model with calibrated parameters is run again during the assimilation period. C/DA-NRLMSISE-00 is also used to forecast the next 21 h, where no new observations are introduced. These forecasts are unique because they are available globally and on various altitudes (300–600 km). To introduce the impact of the thermosphere on estimating ionospheric parameters, the coupled physics-based model TIE-GCM is run by replacing the O2, O1, He and neutral temperature estimates of the C/DA-NRLMSISE-00. Then, the non-assimilated outputs of electron density (Ne) and total electron content (TEC) are validated against independent measurements. Assessing the forecasts of TNDs with those along the Swarm-A (sim 467 km), -B (sim 521 km), and -C (sim 467 km) orbits shows that the root-mean-square error (RMSE) is considerably reduced by 51, 57 and 54%, respectively. We find improvement of 30.92% for forecasting Ne and 26.48% for TEC compared to the radio occulation and global ionosphere maps (GIM), respectively. The presented C/DA approach is recommended for the short-term global multi-level thermosphere and enhanced ionosphere forecasting applications.

On the computation of confidence regions and error ellipses: a critical appraisal

Customary confidence regions do not truly reflect in the majority of our geodetic applications the confidence one can have in one’s produced estimators. As it is common practice in our daily data analyses to combine methods of parameter estimation and hypothesis testing before the final estimator is produced, it is their combined uncertainty that has to be taken into account when constructing confidence regions. Ignoring the impact of testing on estimation will produce faulty confidence regions and therefore provide an incorrect description of estimator’s quality. In this contribution, we address the interplay between estimation and testing and show how their combined non-normal distribution can be used to construct truthful confidence regions. In doing so, our focus is on the designing phase prior to when the actual measurements are collected, where it is assumed that the working (null) hypothesis is true. We discuss two different approaches for constructing confidence regions: Approach I in which the region’s shape is user-fixed and only its size is determined by the distribution, and Approach II in which both the size and shape are simultaneously determined by the estimator’s non-normal distribution. We also prove and demonstrate that the estimation-only confidence regions have a poor coverage in the sense that they provide an optimistic picture. Next to the provided theory, we provide computational procedures, for both Approach I and Approach II, on how to compute confidence regions and confidence levels that truthfully reflect the combined uncertainty of estimation and testing.

On the Efficacy of Compact Radar Transponders for InSAR Geodesy: Results of Multiyear Field Tests

Compact and low-cost radar transponders are an attractive alternative to corner reflectors (CR) for SAR interferometric (InSAR) deformation monitoring, datum connection, and geodetic data integration. Recently, such transponders have become commercially available for C-band sensors, which poses relevant questions on their characteristics in terms of radiometric, geometric, and phase stability. Especially for extended time series and for high-precision geodetic applications, the impact of secular or seasonal effects, such as variations in temperature and humidity, has yet to be proven. Here we address these challenges using a multitude of short baseline experiments with four transponders and six corner reflectors deployed at test sites in the Netherlands and Slovakia. Combined together, we analyzed 980 transponder measurements in Sentinel-1 time series to a maximum extent of 21 months. We find an average Radar Cross Section (RCS) of over 42 dBm2 within a range of up to 15 degrees of elevation misalignment, which is comparable to a triangular trihedral corner reflector with a leg length of 2.0 m. Its RCS shows temporal variations of 0.3--0.7~dBm2 (standard deviation) which is partially correlated with surface temperature changes. The precision of the InSAR phase double-differences over short baselines between a transponder and a stable reference corner reflectors is found to be 0.5-1.2 mm (one sigma). We observe a correlation with surface temperature, leading to seasonal variations of up to +/-3 mm, which should be modeled and corrected for in high precision InSAR applications. For precise SAR positioning, we observe antenna-specific constant internal electronic delays of 1.2-2.1 m in slant-range, i.e., within the range resolution of the Sentinel-1 Interferometric Wide Swath (IW) product, with a temporal variability of less than 20~cm. Comparing similar transponders from the same series, we observe distinct differences in performance. Our main conclusion is that these characteristics are favorable for a wide range of geodetic applications. For particular demanding applications, individual calibration of single devices is strongly recommended.

An Adaptive Regularized Solution to Inverse Ill-Posed Models

The ill-posed models are widely encountered in various inversions of geodesy and remote sensing. The regularization approaches can significantly stabilize the solution to ill-posed models since the high-frequency noise is effectively suppressed. Although the famous Tikhonov regularization and truncated singular value decomposition (TSVD) regularization have been widely applied in various geodetic applications, there still remain theoretical drawbacks for either single regularization. For Tikhonov regularization, given a regularization parameter, the low-frequency terms are over regularized, and high-frequency terms are under regularized. For TSVD regularization, some medium-frequency terms will be mistaken for high-frequency terms to be truncated and the hidden signals will be lost. For this reason, we propose an adaptive regularized solution in spectral form, which adaptively divides the terms of different frequencies into three kinds: (i) the low-frequency terms are not regularized; (ii) the medium-frequency terms are regularized by the Tikhonov method; (iii) the high-frequency terms are regularized by TSVD method. The analytical conditions for determining the term sets are derived based on the criteria that the introduced biases should be smaller than the reduced errors, in other words, the mean squared error (MSE) should be reduced. The two examples are presented to demonstrate the performance of our adaptive regularization. The first numerical example is solving the Fredholm integral equation of the first kind, which is widely encountered in remote sensing inversions. The simulations clearly demonstrate that the adaptive regularized solution can improve the MSE of ordinary Tikhonov and TSVD regularized functions by 25.00% and 9.09%, respectively; In the second example, we apply the new method to investigate the mass variation of the Yangtze River Basin based on the Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field model. The Tongji-Grace 2018 monthly gravity field solutions from April 2002 to December 2016 are used to construct the mascon observation equation. The results show that our method also outperforms the ordinary Tikhonov and TSVD regularized solutions, with mean MSE reductions of about 13.40% and 11.69%, respectively. Furthermore, the spatial resolution of secular trend derived by our method are improved and the signal-to-noise ratio (SNR) of mass variation series is higher than the other two regularizations.

GNSS time and frequency transfers through national positioning, navigation and timing infrastructure

Abstract GNSS signals have been a practical time transfer tool to realise a Coordinated Universal Time (UTC) and set civilian clocks around the world with respect to this atomic time standard. UTC time scale is maintained by the International Bureau of Weights and Measurements (BIPM) adjusted to be close to a time scale based on the Earth’s rotation. In Thailand, the official atomic time clocks are maintained by the National Institute of Metrology Thailand (NIMT) to produce UTC(NIMT) and Thailand standard time which is always 7 hours ahead of UTC(NIMT) because of the time zone differences between Greenwich and Bangkok. National Positioning, Navigation and Timing (PNT) infrastructure comprises of GNSS geodetic receivers uniformly distributed to continually observe GNSS signals, mainly for geodetic survey applications both real-time and post-processing services. NIMT is involved in order to provide time link to UTC and to determine the characteristics of GNSS receiver internal clocks; namely, fractional frequency offset and frequency stabilities by applying the GNSS time transfer techniques of common-view algorithms. Monitored time differences with respect to UTC(NIMT) are achieved from selected 4 ground stations in different parts of the country with observations of 21 days in order to determine the frequency stability at 1-day and 7-day modes. GNSS standard log files; in RINEX format, at these receivers are transformed into a time transfer standard format; CGGTTS, used to compute the time differences between two stations, the fractional frequency offset and the frequency stability. Averaged fractional frequency offsets are 2.8 × 10 − 13 Hertz/Hertz 2.8\times {10^{-13}}\hspace{2.38387pt}\text{Hertz/Hertz} and computed Allan deviation is around 1.5 × 10 − 13 Hertz/Hertz 1.5\times {10^{-13}}\hspace{2.38387pt}\text{Hertz/Hertz} for an averaging time of 1 day. The comparison of the national time scale and receiver clock offsets of every receivers in this national GNSS PNT infrastructure could be accomplished through common-view time transfer using GNSS satellites to maintain the time link of geodetic active control points to UTC as well as to determine receiver internal clock characteristics.

Establishing a Marine Gravity Database around Egypt from Satellite Altimetry-Derived and Shipborne Gravity Data

For the purpose of marine geoid modeling and many other geodetic and geophysical applications, a marine gravity map around Egypt is established by the integration of gravity data provided by satellite altimetry and shipborne gravimetric observations. Firstly, the collected shipborne data were compared with GO_CONS_GCF_2_TIM_R6 and XGM2019e GGMs and with SSv29.1 and DTU17 altimetry models. Then, a pre-refinement of ship marine surveys was done with a rigorous condition, in which a number of 6525 points have been removed from the dataset. After that, 87709 points were deducted from the pre-filtered shipborne dataset to fit the study area and the cross-validation approach with the kriging interpolation algorithm were applied. A rigorous level of confidence was decided in this step where the points which have differences between the estimated and the observed values more than twice the STD of the residuals were removed until the STD reached a value less than 1 mGal. Finally, the filtered shipborne gravity data were combined with DTU17 (the best evaluation model) using the least-squares collocation technique (LSC). The final gravity map was tested using 8000 randomly chosen shipborne stations, which were not included when applying LSC, revealing the significant enhancement gained after the integration process.

Some Remarks on Registration Techniques of Point Clouds Obtained from Terrestrial Laser Scanning

Terrestrial laser scanning (TLS) is a measurement technique used for many geodetic applications (such as determination of displacement and deformation of building objects or monitoring of engineering structures) as well as for non-geodetic applications (for example in forestry, archeology or geotechnics). Despite the high level of automation, the measurement with a laser scanner and the processing of the results consist of many stages and depend on many factors. The most important factors are: the features of measurement object (size, material, availability), required accuracy, speed of scanning, required scan density, type of reference frame, registration method, planned visualization, and 3D modelling method. In this article, the authors focused on the type of registration technique of point clouds obtained from TLS. The most popular strategies of registration were discussed. The practical application of the selected technique was presented on the example of measurement of the railway gauge of the viaduct. Due to the characteristic object (narrow and long railway line) and considering the local reference frame of point clouds as well as the need of minimization of the measurement time, the hybrid registration method in the nested variant was selected.

Application of the nonlinear optimisation in regional gravity field modelling using spherical radial base functions

The gravity field is a signature of the mass distribution and interior structure of the Earth, in addition to all its geodetic applications especially geoid determination and vertical datum unification. Determination of a regional gravity field model is an important subject and needs to be investigated and developed. Here, the spherical radial basis functions (SBFs) are applied in two scenarios for this purpose: interpolating the gravity anomalies and solving the fundamental equation of physical geodesy for geoid or disturbing potential determination, which has the possibility of being verified by the Global Navigation Satellite Systems (GNSS)/levelling data. Proper selections of the number of SBFs and optimal location of the applied SBFs are important factors to increase the accuracy of estimation. In this study, the gravity anomaly interpolation based on the SBFs is performed by Gauss-Newton optimisation with truncated singular value decomposition, and a Quasi-Newton method based on line search to solve the minimisation problems with a small number of iterations is developed. In order to solve the fundamental equation of physical geodesy by the SBFs, the truncated Newton optimisation is applied as the Hessian matrix of the objective function is not always positive definite. These two scenarios are applied on the terrestrial free-air gravity anomalies over the topographically rough area of Auvergne. The obtained accuracy for the interpolated gravity anomaly model is 1.7 mGal with the number of point-masses about 30% of the number of observations, and 1.5 mGal in the second scenario where the number of used kernels is also 30%. These accuracies are root mean square errors (RMSE) of the differences between predicted and observed gravity anomalies at check points. Moreover, utilising the optimal constructed model from the second scenario, the RMSE of 9 cm is achieved for the differences between the gravimetric height anomalies derived from the model and the geometric height anomalies from GNSS/levelling points.

Determination of Tropospheric Parameters from ERA Surface Data for Space Geodetic Techniques

This study investigates methods of deriving meteorological parameters needed in space geodetic applications, from the surface data of the numerical weather model (NWM). It is more efficient than pressure level data in terms of storage and transmission. Based on more realistic assumptions for the structure of the troposphere, formulas for accurate vertical reduction of pressure (P) and precipitable water vapor (PWV) are deduced, and they are applied with the gridded lapse rate data provided by the GPT2w model. The new method achieves better accuracy especially when a large height difference between the grid point and station exists. Validation with global radiosonde observations shows that the RMS errors of P, temperature (T), and water vapor pressure (e) derived from 2.5° × 2.5° ERA surface data are 1.16 hPa, 1.95 K, and 1.76 hPa respectively; zenith tropospheric delays (ZTDs) calculated from derived P, T, and e values have a mean RMS error of 3.26 cm, comparable to that obtained from in situ measurements; adding PWV will increase ZTD estimation accuracy to 1.52 cm, comparable to that obtained from NWM pressure level data. Validations with Global Navigation Satellite System estimated ZTDs from global and regional station networks display similar results on the globe, as well as features for localized regions. Using higher spatial resolution NWM seems to have little effect on the accuracy of ZTDs calculated from P, T, and e, while it apparently improves the accuracy of ZTDs calculated from P, T, e, and PWV.