Geodetic Applications Research Articles

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares (WTLS) have been regarded as the standard tool for the errors-in-variables (EIV) model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors. However, in many geodetic applications, some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix. It is called the linear structured EIV (LSEIV) model. Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications. On the one hand, the functional part of the LSEIV model is modified into the errors-in-observations (EIO) model. On the other hand, the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix. The algorithms are derived through the Lagrange multipliers method and linear approximation. The estimation principles and iterative formula of the parameters are proven to be consistent. The first-order approximate variance-covariance matrix (VCM) of the parameters is also derived. A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach. Afterwards, the least squares (LS), total least squares (TLS) and linear structured weighted total least squares (LSWTLS) solutions are compared and the accuracy evaluation formula is proven to be feasible and effective. Finally, the LSWTLS is applied to the field of deformation analysis, which yields a better result than the traditional LS and TLS estimations.

Geophysically Informed Machine Learning for Improving Rapid Estimation and Short‐Term Prediction of Earth Orientation Parameters

AbstractRapid provision of Earth orientation parameters (EOPs, here polar motion and dUT1) is indispensable in many geodetic applications and also for spacecraft navigation. There are, however, discrepancies between the rapid EOPs and the final EOPs that have a higher latency but the highest accuracy. To reduce these discrepancies, we focus on a data‐driven approach, present a novel method named ResLearner, and use it in the context of deep ensemble learning. Furthermore, we introduce a geophysically constrained approach for ResLearner. We show that the most important geophysical information to improve the rapid EOPs is the effective angular momentum functions of atmosphere, ocean, land hydrology, and sea level. In addition, semidiurnal, diurnal, and long‐period tides coupled with prograde and retrograde tidal excitations are important features. The influence of some climatic indices on the prediction accuracy of dUT1 is discussed, and El Niño Southern Oscillation is found to be influential. We developed an operational framework, providing the improved EOPs on a daily basis with a prediction window of 63 days to fully cover the latency of final EOPs. We show that under the operational conditions and using the rapid EOPs of the International Earth Rotation and Reference Systems Service (IERS), we achieve improvements as high as 60%, thus significantly reducing the differences between rapid and final EOPs. Furthermore, we discuss how the new final series IERS 20 C04 is preferred over 14 C04. Finally, we compare against EOP hindcast experiments of the European Space Agency, on which ResLearner presents comparable improvements.

First Observations With a GNSS Antenna to Radio Telescope Interferometer

AbstractWe describe the design of a radio interferometer composed of a Global Navigation Satellite Systems (GNSS) antenna and a Very Long Baseline Interferometry radio telescope. Our eventual goal is to use this interferometer for geodetic applications including local tie measurements. The GNSS element of the interferometer uses a unique software‐defined receiving system and modified commercial geodetic‐quality GNSS antenna. We ran three observing sessions in 2022 between a 25 m radio telescope in Fort Davis, Texas (FD‐VLBA), a transportable GNSS antenna placed within 100 m, and a GNSS antenna placed at a distance of about 9 km. We have detected a strong interferometric response with a Signal‐to‐Noise Ratio (SNR) of over 1,000 from Global Positioning System and Galileo satellites. We also observed natural radio sources including Galactic supernova remnants and Active Galactic Nuclei located as far as one gigaparsec, thus extending the range of sources that can be referenced to a GNSS antenna by 18 orders of magnitude. These detections represent the first observations made with a GNSS antenna to radio telescope interferometer. We have developed a novel technique based on a Precise Point Positioning solution of the recorded GNSS signal that allows us to extend integration time at 1.5 GHz to at least 20 min without any noticeable SNR degradation when a rubidium frequency standard is used.

SARAL/AltiKa measurements for geodetic applications: Impact of drifting and mispointing phase data

The Indo-French SARAL/AltiKa mission in Ka band has provided valuable information on global oceans to cater the needs of oceanographic community. The SARAL/AltiKa has been operating in three different orbital configurations, viz. Exact Repeat Mission (ERM, March 2013 – July 2016), Drifting Phase (DP, July 2016 – February 2019) and Mispointing Phase (MP, February 2019 – till date). We investigate the utility of the SARAL/AltiKa data for geodetic applications. Global crossover analysis of Sea Surface Height (SSH) measurements from SARAL/AltiKa suggests a stable performance throughout its life with similar range of standard deviations during ERM (5.8 cm), DP (5.9 cm) and MP (5.9 cm) configurations. Two separate Mean Sea Surface (MSS) models were retrieved by adding DP and MP data from SARAL/AltiKa to the ERM stacks of SARAL/AltiKa and Jason satellite series. The quality of MSS models were evaluated based on the crossover differences with the ERM database. It is observed that the crossover adjustments have reduced the deviations in SSH errors by ∼30% for both DP-MSS and MP-MSS models. Analysis of along-track sea surface slopes suggests that 99.9% of data in ERM and DP phases and 93.8% of data in MP phase are well within 1 μrad bound corresponding to an accuracy of ∼1 mGal in free-air gravity anomaly. Further, time-series analysis of Sea Level Anomaly (SLA) from SARAL/AltiKa showed a stable performance with no significant drifts throughout its phases. Deviations in daily SLA for SARAL/AltiKa DP (10 cm) is considerably lower than that of Jason-3 (10.2 cm) and CryoSat-2 (10.2 cm) satellites. However, daily SLA for the MP phase showed slightly larger deviation (10.4 cm), owing to the larger number of outliers, which could be easily removed using a simple median filter. The present study reveals the usefulness of MP data from SARAL/AltiKa for geodetic applications.

Millimeter accuracy SLR bias determination using independent multi-LEO DORIS and GPS-based precise orbits

Satellite Laser Ranging (SLR) has become an invaluable core technique in numerous geodetic applications. SLR measurements to passive spherical satellites essentially contribute to the determination of geocenter coordinates and global scale in the International Terrestrial Reference Frame (ITRF) realizations. In addition, SLR measurements to active satellites in Low Earth Orbit (LEO) are up to now mostly used for an independent validation of orbit solutions, usually derived by microwave tracking techniques based on Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) or Global Navigation Satellite Systems (GNSS). This allows for the analysis of systematic orbit errors (e.g., originating from poorly known non-gravitational perturbations or sensor offsets) not only in the radial direction (key to satellite altimetry missions), but in three dimensions.Major obstacles to reach the millimeter accuracy and stability goals of 0.1mm/y (at decadal time scales) of the Global Geodetic Observing System (GGOS) are station-satellite measurement biases and on-ground/board coordinate offsets. Among the observatories of the International Laser Ranging Service (ILRS) a large diversity of measurement qualities exists, and the calibration of station-dependent errors is now necessary to further exploit SLR data for present and future climate-driven needs.We demonstrate that the analysis of SLR data to active LEO satellites equipped with DORIS or GNSS receivers is a promising means to characterize SLR biases and their stability. Using two independent selections of Earth observation missions in LEOs (consisting of six altimetry, three magnetic field and two gravity field satellites) with three different analysis software packages (Bernese, ZOOM, Napeos), we estimate SLR range biases for all involved tracking stations on a yearly basis. We find that for many of the stations independently estimated sets of biases agree on a few-mm level and that the inclusion of satellites from multiple missions allows rendering the bias estimation more robust and in particular less prone to geographically correlated orbit errors. This shows that microwave-derived orbits of active LEO satellites, nowadays of very high quality due to numerous advances in modeling and analysis techniques, can serve as interesting sources for SLR station calibration in demanding climate applications.

Monitoring of the Vertical Settlement In Heavy Structures By Precise Levelling

Monitoring and analysing of the vertical deformations or the settlements of the structures is one of the main research fields in geodetic applications, which is considered a precise periodic measurement, made at different epochs to investigate these deformations on heavy structures.In this research, the deformation measurements were carried out on one of Baghdad University buildings,” Building of Computers Department” of dimensions (70.0 * 81.3 m.). Due to some cracks observed in their walls, it was necessary to monitor the vertical displacement of this building at some particular monitoring points by constructing a vertical network and measured in different epochs. The first epoch (zero epoch) was carried out in April 2006, the second in July 2006, the third in October 2006 and the last one in October 2012.These four epochs include precise levelling measurements were adjusted by Least Squares Adjustment with the aim of investigating the settlement of this building. The two approaches “the Global Congruency test” and “the simple test” are carried out to detect if there any deformation. These two approaches were employed in the analysis and found the difference in elevations between two epochs most be ensured and found that if the monitoring points (P1 to P4) stayed really stable, when compared with the time interval or not?Then according to the analysis procedure to determine the localization of settlement at specific points in the case may change in elevation must be applied. The results showed in two different statistical techniques a significant settlement in four selected corner points on building (P1, P2, P3 and P4). The statistics are based on the probability 95% test and the congruency test with Fisher distribution table

Editorial: Advances on upper-atmosphere characterization for geodetic space weather research and applications

Editorial: Advances on upper-atmosphere characterization for geodetic space weather research and applications

A Multi-GNSS/IMU Data Fusion Algorithm Based on the Mixed Norms for Land Vehicle Applications

As a typical application of geodesy, the GNSS/INS (Global Navigation Satellite System and Inertial Navigation System) integrated navigation technique was developed and has been applied for decades. For the integrated systems with multiple sensors, data fusion is one of the key problems. As a well-known data fusion algorithm, the Kalman filter can provide optimal estimates with known parameters of the models and noises. In the literature, however, the data fusion algorithm of the GNSS/INS integrated navigation and positioning systems is performed under a certain norm, and performance of the conventional filtering algorithms are improved only under this fixed and limited frame. The mixed norm-based data fusion algorithm is rarely discussed. In this paper, a mixed norm-based data fusion algorithm is proposed, and the hypothesis test statistics are constructed and adopted based on the chi-square distribution. Using the land vehicle data collected through the multi-GNSS and the IMU (Inertial Measurement Unit), the proposed algorithm is tested and compared with the conventional filtering algorithms. Results show that the influences of the outlying measurements and the uncertain noises are weakened with the proposed data fusion algorithm, and the precision of the estimates is further improved. Meanwhile, the proposed algorithm provides an open issue for geodetic applications with mixed norms.

Ultra-short-term prediction of LOD using LSTM neural networks

Earth orientation parameters (EOPs) are essential in geodesy, linking the terrestrial and celestial reference frames. Due to the time needed for data processing and combining different space geodetic techniques, EOPs of the highest quality suffer latencies from several days to several weeks. However, real-time EOPs are needed for multiple geodetic and geophysical applications. Predictions of EOPs in the ultra-short term can overcome the latency of EOP products to a certain extent. Traditionally, predictions are performed using statistical methods. With the rapid expansion of computing capacity and data volume, the application of deep learning in geodesy has become increasingly promising in recent years. In particular, the Long Short-Term Memory (LSTM) neural networks, one of the most popular Recurrent Neural Network varieties, are promising for geodetic time series prediction. In this study, we investigate the potential of using LSTM to predict daily length of day (LOD) variations up to ten days in advance, accounting for the contribution of effective angular momentum (EAM). The data are first preprocessed to obtain residuals by combining physical and statistical models. Then, we employ LSTM networks to predict the LOD residuals using both LOD and EAM residuals as input features. Our methods outperform all other state-of-the-art methods in the first eight days with an improvement of up to 43% under the first EOP Prediction Comparison Campaign conditions. In addition, we assess the performance of LOD predictions using more extended time series to consider the improvements of EOP products over the last decade. The results show that extending data volume significantly increases the performance of the methods.

DinSAR coseismic deformation measurements of the Mw 8.3 Illapel earthquake (Chile)

Abstract The beginning of radars goes back to the 1930s where its main boost was related to the second world war. Nowadays, the techniques associated with radars are focused around a vast variety of civil, geodetic, and military applications. The development of the synthetic aperture principle, in the 1950s and 1960s, gave birth to a lot of new applications, and together with the technological progress of the last decades, the technique of interferometry with synthetic aperture radar (SAR) data became one of the most powerful ones for sensing remotely, with high quality and a vast spatial coverage. We used Sentinel-1 data and the differential interferometry SAR (DinSAR) technique to map and measure the surface deformation related to the 2015 Mw 8.3 Illapel earthquake (Chile). We also validated the results, by analysing the temporal variation of coordinates acquired from global navigation satellite system observations and projecting them in the geometry of the SAR system. Using this application we prove the DinSAR technique to be useful and powerful for the observation and analysis of surface deformation caused by the release of stress during the Mw 8.3 Illapel earthquake. It proved to be an efficient tool to detect and map the surface deformation with high spatial resolution in an approximate area of 20,000 km2.

Comparison of PPPH MATLAB based program vs Online GNSS Services

The modernization of GNSS provides promising improvements to satellite navigation users across the world, it is important to determine the reliability of using free online processing software for the Global Navigation Satellite System post-processing. The study aims at assessing the accuracy of two free online processing software, GAPS, and CSRS-PPP and Open-source software, PPPH MATLAB based software, and GNSS solutions. Field observations were carried out on data from three stations using GNSS observation from IGS with an observation period of 30 seconds the acquired data were post-processed using both online and open-source software. The coordinates generated from each software were then compared with the ones obtained from station to determine their relative discrepancies and accuracies. for GAPS and CSRS-PPP both in X, Y, and Z direction in ITRF14 reference. 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. Initial time must be checked for better resolution.

An assessment of the implications of gravity reduction methods on local geoid modelling over Ado Ekiti

There are several gravity reduction approaches that are available for use in geodetic applications. More so, with the rapid rate at which gravimetric geoid models are being incorporated into Global Navigation Satellite System (GNSS) solutions, the need for precise regional models is becoming increasingly relevant. The two chosen gravity reduction approaches (Bouguer and Residual Terrain Model (RTM)) were used to reduce gravity anomalies over Ado town. The reduced anomalies were then used to compute a local geoid for the study area using the conventional Stokes integral in the Remove Compute Restore (RCR) technique. Comparison of the computed geoid by both methods with GNSS Levelling data at selected locations show that the RTM reduced anomalies produce a better geoid model than the Bouguer reduced anomalies over the study area with a RMSE of 83.2cm and 83.5cm respectively.

A methodology for transformation between geodetic datums used in Syria

The Global Navigation Satellite System (GNSS) provides geodetic coordinates referenced to the world ellipsoid WGS84, whereas positions are computed on the local ellipsoid adopted for geodetic computation in various countries. Thus, to take advantage of GNSS in geodetic applications, the need arises to transform coordinates from the global ellipsoid to the local ellipsoid. This is usually carried out by applying geometric transformation models to convert coordinates from The Global Geodetic System WGS84 into the local systems used in each country of the world and into the grid coordinates of local systems. Over the past years, with the increase in the utilization of GNSS in several geodetic projects, numerous methodologies are available for the solution of transformation issues. These methods can be classified into three categories, the first is based on direct mathematical formulas, the second on iteration approaches, and the last category depends on direct transformation from the global system to the local system based on the calculation of transformation parameters (three, seven, nine …etc.). In this study, a methodology has been proposed for direct transformation from global geodetic coordinates to local geodetic coordinates for a limited area in Syria. It is based on the properties of the ratio and proportion between the geometric elements of points on global and local ellipsoids without the calculation of transformation parameters. The results are compared with some studied methods (Bursa-Wolf, Molodensky Abridge, and Cassini). The resulting accuracy is about ± 3.5 cm. The main conclusion drawn is that the proposed method provides a promising alternative approach in coordinates transformation. Therefore, the capability of the suggested methodology as a powerful method for converting geodetic coordinates from one referenced frame to another has been demonstrated in this present study.

Global geopotential models evaluation based on terrestrial gravity data over Ethiopia

Abstract The availability of high-degree and recent global geopotential models is a crucial resource for different geodetic and geophysical applications such as modelling of geoid and quasi-geoid and establishing global reference and height systems, estimating Moho depth, gravity anomaly and tectonics, other geopotential functional, and oceanography, which emphasizes the importance for model evaluation. We have therefore estimated complete Bouguer anomalies and Moho whose results are evaluated with the terrestrial values. We validate the recently released satellite-only and high-degree combined GGMs over Ethiopia using terrestrial gravity data based on a statistical comparison of the Bouguer anomaly, its residual and Moho depth. The terrestrial-derived gravity anomaly is more accurately estimated by EIGEN6C4. The assessment against a recently conducted high resolution (∼3 km) terrestrial and airborne gravimetric survey over Ethiopia shows that EIGEN6C4/SGG_UGM_1 and 2 have the highest accuracy (∼3.28/3.27 mGal). However, the comparison with such data hardly discriminates the qualities of other GGMs that have or are truncated to the same degree and order. Whereas, the validation results of GGMs against terrestrial and airborne data are identical. EIGEN6C4, SGG_UGM_2, XGM2016, XGM2019e_2159/SGG_UGM_1 have the best quality, and the accuracy of associated Moho is 4.89/4.90 km, and this value changes to 4.98/4.91/5.51 km when the EGM08/ITSG_Grace2018s/GOCO06S are assessed.

Refinement of global gridded ray-traced Zenith tropospheric delay over Nigeria based on local GNSS network observations

• Application of deep structured supervised neural network modelling technique. • Data derived from the local GNSS observation within the study area. • A refinement model is developed to predict ZTD parameters at user-defined points. • Improvement in the accuracy of the local refine VMF1-ZTD estimates. Recent studies on the application of Zenith Tropospheric Delay (ZTD) in meteorology and geodesy have shown improved accuracy with the use of locally estimated ZTD compared to Global ZTD. This paper focuses on the refinement of global gridded ray-traced Vienna Mapping Functions 1 (VMF1) ZTD over Nigeria, using ZTD estimates derived from local GNSS Continuously Operating Reference Stations (CORS) observations. Three (3) years of GNSS observations collected at 13 CORS located within the study area were post-processed using GNSS Analysis and Processing Software (GAPS) to derive the local GNSS-ZTD estimates. The global VMF1-ZTD were interpolated at the locations of the local GNSS-CORS. An optimal deep structured supervised Neural Network (NN) was derived by training feedforward networks using the Levenberg-Marquardt backpropagation algorithm, with spatiotemporal variables and VMF1-ZTD as inputs and the GNSS-ZTD as the target. The outputs from the NN model were assessed using internal and external data. Results from internal data evaluations indicated a robust and accurate model output with optimum network performances indicating MSE of ∼7.22 × 10 −6 m and ∼4.56 × 10 −4 m for hydrostatic and wet ZTD networks respectively. The external data evaluations performed using the International GNSS Services (IGS) Zenith Path Delay (ZPD), indicated an RMSE range of ∼0.041 m to 0.095 m for global-VMF1 and ∼0.030 m to 0.037 m for the Local Refine (LR)-VMF1. The results suggest that the application of ZTD estimates derived from local GNSS observations in the refinement of global gridded VMF1-ZTD yields an improved accuracy over Nigeria. Consequently, the LR-VMF1 ZTD estimates are recommended for improved accuracy, required for geodetic and meteorological applications in and around Nigeria :

Object Recognition of a GCP Design in UAS Imagery Using Deep Learning and Image Processing—Proof of Concept Study

Image-based unmanned aircraft systems (UASs) are used in a variety of geodetic applications. Precise 3D terrain surface mapping requires ground control points (GCPs) for scaling and (indirect) georeferencing. In image analysis software (e.g., Agisoft Metashape), the images can be generated to a 3D point cloud using Structure-from-Motion (SfM). In general, the conventional GCP design for UAS flights is a checkerboard pattern, which is provided in the software and used for automatic marker detection in each image. When changing the pattern, manual work would be required by picking the GCP individually by hand. To increase the level of automation in the evaluation, this article aims to present a workflow that automatically detects a new edge-based GCP design pattern in the images, calculates their center points, and provides this information to the SfM software. Using the proposed workflow based on deep learning (DL) and image processing, the quality of the resulting 3D model can be equated to the result with GCP center points picked by human evaluator. Consequently, the workload can be accelerated with this approach.

Image-Based Baseline Correction Method for Spaceborne InSAR With External DEM

An accurate baseline of synthetic aperture radar (SAR) interferometry (InSAR) is an important parameter for the geodetic application of the InSAR data. Although some advanced SAR satellites have precise orbit determination, there are still many SAR satellites suffering from baseline inaccuracies, such as GF-3. In this article, an image-based estimator for baseline correction is proposed, which requires only the external digital elevation model (DEM) data. The idea of the method is to project the orbit error phase onto the phase components carrying the baseline error information, which is called orbit error phase bases in this article, and to correct the baseline according to the projection coefficients. Since the pure orbit error phase is unavailable, the residual phase of the interferogram is used to approximate the orbit error phase, and a series of processes are introduced to weaken the effect of this approximation. Both the simulated and real data from GF-3 SAR are used to validate the proposed method, and a comparison with the conventional nonlinear least-square and the latest proposed flat-Earth phase-based baseline refinement methods are made. The results indicated the superior accuracy and robustness of our method, especially in areas with higher relief and wider coverage.

Recent Advances in Modelling Geodetic Time Series and Applications for Earth Science and Environmental Monitoring

Geodesy is the science of accurately measuring the topography of the earth (geometric shape and size), its orientation in space, and its gravity field. With the advances in our knowledge and technology, this scientific field has extended to the understanding of geodynamical phenomena such as crustal motion, tides, and polar motion. This Special Issue is dedicated to the recent advances in modelling geodetic time series recorded using various instruments. Due to the stochastic noise properties inherent in each of the time series, careful modelling is necessary in order to extract accurate geophysical information with realistic associated uncertainties (statistically sufficient). The analyzed data have been recorded with various space missions or ground-based instruments. It is impossible to be comprehensive in the vast and dynamic field that is Geodesy, particularly so-called “Environmental Geodesy”, which intends to understand the Earth’s geodynamics by monitoring any changes in our environment. This field has gained much attention in the past two decades due to the need by the international community to understand how climate change modifies our environment. Therefore, this Special Issue collects some articles which emphasize the recent development of specific algorithms or methodologies to study particular natural phenomena related to the geodynamics of the earth’s crust and climate change.

Accuracy Assessment for GNSS Precise Point Position Using Online Service and Offline Software

There are many applications of Global Navigation Satellite System (GNSS) (GPS, GLONASS, Galileo, and BeiDou) such as civilian (agriculture, mapping, road and traffic safety) and military services. Precise point positioning (PPP) solution is considered as a main geodetic surveying task in post processing of GNSS observations. In last years (PPP) solution package are developed as online services and offline software’s. This study aims to introduce a comparative study between solutions of post processing free online processing (CSRS-PPP) and free offline software (PPPH). Field observations were carried out on 9 IGS stations utilizing a static GNSS observation method and an observation RINEX 3 format for period of 24hr for 3 consecutive days in January and 3 consecutive days in March 2022. Post-processing of the obtained data was done using online and offline software. The coordinates from online and offline compared with coordinates from IGS station to assess their respective differences and accuracy. The minimum difference 0 cm for both solutions and the maximum difference 1.568 cm for online and 1.404 cm for offline. Online GNSS processing services can be used for engineering and geodetic applications since they are simple to use like PPPH, and are easy to execute.

Precise orbit determination for a large LEO constellation with inter-satellite links and the measurements from different ground networks: a simulation study

Geodetic applications of Low Earth Orbit (LEO) satellites requires accurate satellite orbits. Instead of using onboard Global Navigation Satellite System observations, this contribution treats the LEO satellite constellation independently, using Inter-Satellite Links and the measurements of different ground networks. Due to geopolitical and geographical reasons, a ground station network cannot be well distributed. We compute the impact of different ground networks (i.e., global networks with different numbers of stations and regional networks in different areas and latitudes) on LEO satellite orbit determination with and without the inter-satellite links. The results are based on a simulated constellation of 90 LEO satellites. We find that the orbits determined using a high latitude network is worse than using a middle or low latitude network. This is because the high latitude network has a poorer geometry even if the availability of satellite measurements is higher than for the other two cases. Also, adding more stations in a regional network shows almost no improvements on the satellite orbits if the number of stations is more than 16. With the help of ISL observations, however, the satellite orbits determined with a small regional network can reach the same accuracy as that with the global network of 60 stations. Furthermore, satellite biases can be well estimated (less than 0.6 mm) and have nearly no impact on satellite orbits. It does thus not matter if they are not physically calibrated for estimating precise orbits.