GNSS Measurements Research Articles

On the applicability of low-cost GNSS antennas to precise surveying applications

Abstract This study addresses the scientific question of the applicability of low-cost antennas to the most precise GNSS applications. First of all, we inspect the implications of the availability and quality of low-cost antenna PCC models for precise positioning. From this point of view, we analyze the selected performance indicators of multi-constellation positioning with the representative set of low-cost mass-market GNSS receiver antennas. The processing strategy was based on the relative positioning model, considered the most reliable and precise one. To isolate the antenna-related errors from atmospheric propagation ones, we conducted an experiment based on an ultra-short baseline. As the main indications of low-cost antenna performance, we considered distance and height residuals, defined as the difference between benchmarks and the retrieved from GNSS measurements. We found that the low-cost antenna's PCV effect may significantly affect the final results. On the other hand, the results obtained using certain configurations of low-cost antennas were characterized by only slightly higher standard deviations and discrepancies with respect to benchmark values than those obtained with surveying or geodetic equipment. We identify several sets of low-cost antennas where distance residuals do not exceed 4 mm and height residuals do not exceed 6 mm, which shows the low-cost antenna performance comparable to those achieved using high-grade antennas. On this basis, we conclude that selected low-cost antennas can meet the requirements of high-precision surveying applications.

Simulation case study of precise orbit determination for IGSO satellites using onboard Ka/GNSS observations

Abstract Inter-satellite links can provide a more accurate space reference for IGSO satellites than onboard GNSS side-lobe signals. In this study, POD quality is analyzed based on onboard Ka/GNSS observations by utilizing a simulated IGSO satellite orbit. Considering the similar orbit altitude, we first select three IGSO satellites from BDS-3 as target satellites. These satellites have actual Ka-band measurements available, along with other BDS-3 satellites and ground anchor stations, allowing us to assess the POD performance. The Ka-band availability of these IGSO satellites can serve as a means to evaluate the maximum utilization of BDS Ka-band resources. In terms of the POD results, the root mean square (RMS) of the Ka-band residuals can reach 10.9 cm, and the orbit consistency in the 3D direction is better than 0.35 m. In addition, simulations are conducted for onboard GNSS, inter-satellite link (ISL), and ground anchor-satellite link (GSL), considering the different constraints on the Ka-band resources. With only GNSS measurements, the 3D orbit accuracy is approximately 1.5 m, but when additional ISL and GSL measurements are considered, the POD accuracy can surpass 0.28 m. These results illustrate that incorporating Ka-band measurements can effectively enhance the POD accuracy for high-orbit satellites.

Tree detection and in-row localization for autonomous precision orchard management

This work presents a framework for localizing ground robots within fruit tree orchards. The standard practice of managing orchards at the large block-level does not maximize the potential of farms — individual plants have different needs due to variations in soil, pests, disease, irrigation, etc. In order to make selective management decisions for individual trees, such as precision fertilization, a robot must be able to accurately localize itself within the row. This is a challenge since in high density, modern orchard systems it is often difficult to obtain accurate GNSS measurements. Our algorithm begins by using deep learning to segment a tree trunk in an RGB-D image and then estimate its width. We then use the trunk segmentations and widths to calculate particle weights in a particle filter-based localization system. We show that integrating trunk width into the particle update step led to a 45% decrease in the distance traveled before convergence, and a 31% decrease in convergence time, alongside a marginal increase in the rate of correct convergence. We also demonstrate autonomous tree-level localization with a large ground robot in realistic field experiments in a commercial apple orchard.

A Robust Factor Graph Optimization Method of GNSS/INS/ODO Integrated Navigation System for Autonomous Vehicle

Abstract The GNSS/INS/ODO integrated navigation system provides accurate positioning for autonomous vehicles. However, the observation quality of GNSS and ODO can decrease in complex environments and various driving conditions, leading to a decline in the accuracy and robustness of the integrated navigation system. An FGO-Robust method is proposed to resolve this challenge by fusing the INS/ODO-Slip factor and adaptive GNSS factor. The INS/ODO-Slip factor compensates for ODO measurement values by estimating the wheel slip ratio in real-time during optimization, thereby reducing ODO measurement errors' impact on factor graph optimization. Additionally, the adaptive GNSS factor minimizes the impact of GNSS outliers in the optimization process by designing a dynamic observation weight function. The vehicle experiments are conducted to evaluate the performance of the proposed method in different simulated conditions with ODO and GNSS measurement failures. The experimental results demonstrate that the FGO-Robust method can effectively improve the positioning accuracy of the integrated navigation system under various measurement failure conditions, with improvements of 83.4%, 66.1%, and 68.1% relative to FGO. Moreover, the FGO-Robust method improves the robustness of the integrated navigation system in complex environments and various driving conditions.

Statistics of precipitable water vapour, optical thickness and cloud cover within the Northern part of Eurasia

One of the most important tasks in astroclimatic studies of possible locations for the Eurasian Submillimeter Telescopes is estimating statistics of precipitable water vapour, optical thickness and cloud cover. In this paper, the statistics of precipitable water vapour and total cloud cover within Northern part of Eurasia are studied using ERA-5 reanalysis. Optical thickness statistics at a wavelength of 3 mm were obtained using the Liebe model from the ERA-5 reanalysis for the region where the BTA is located. The most favorable astroclimatic zones of Eurasia include Tibet and the Eastern Pamirs, certain regions of the Sayan Mountains, Altai and Mts within Dagestan. Also we verified the ERA-5 reanalysis data using radiosonde data, GNSS measurement data and radiometric measurements for 2021.

Decimeter-Level Accuracy for Smartphone Real-Time Kinematic Positioning Implementing a Robust Kalman Filter Approach and Inertial Navigation System Infusion in Complex Urban Environments.

New smartphones provide real-time access to GNSS pseudorange, Doppler, or carrier-phase measurement data at 1 Hz. Simultaneously, they can receive corrections broadcast by GNSS reference stations to perform real-time kinematic (RTK) positioning. This study aims at the real-time positioning capabilities of smartphones using raw GNSS measurements as a conventional method and proposes an improvement to the positioning through the integration of Inertial Navigation System (INS) measurements. A U-Blox GNSS receiver, model ZED-F9R, was used as a benchmark for comparison. We propose an enhanced ambiguity resolution algorithm that integrates the traditional LAMBDA method with an adaptive thresholding mechanism based on real-time quality metrics. The RTK/INS fusion method integrates RTK and INS measurements using an extended Kalman filter (EKF), where the state vector x includes the position, velocity, orientation, and their respective biases. The innovation here is the inclusion of a real-time weighting scheme that adjusts the contribution of the RTK and INS measurements based on their current estimated accuracy. Also, we use the tightly coupled (TC) RTK/INS fusion framework. By leveraging INS data, the system can maintain accurate positioning even when the GNSS data are unreliable, allowing for the detection and exclusion of abnormal GNSS measurements. However, in complex urban areas such as Qazvin City in Iran, the fusion method achieved positioning accuracies of approximately 0.380 m and 0.415 m for the Xiaomi Mi 8 and Samsung Galaxy S21 Ultra smartphones, respectively. The subsequent detailed analysis across different urban streets emphasized the significance of choosing the right positioning method based on the environmental conditions. In most cases, RTK positioning outperformed Single-Point Positioning (SPP), offering decimeter-level precision, while the fusion method bridged the gap between the two, showcasing improved stability accuracy. The comparative performance between the Samsung Galaxy S21 Ultra and Xiaomi Mi 8 revealed minor differences, likely attributed to variations in the hardware design and software algorithms. The fusion method emerged as a valuable alternative when the RTK signals were unavailable or impractical. This demonstrates the potential of integrating RTK and INS measurements for enhanced real-time smartphone positioning, particularly in challenging urban environments.

Co-seismic and post-seismic slip associated with the 2021 Mw5.9 Arkalochori, Central Crete (Greece) earthquake constrained by geodetic data and aftershocks

The co-seismic and post-seismic deformation field associated with the Mw5.9 Arkalochori main shock that occurred in central Crete (Greece) on 27 September 2021 is analyzed using Copernicus Sentinel-1A & 1B images, GNSS measurements and seismological data. The fault geometry is constrained through the joint inversion of multiple datasets and the slip distribution for the co-seismic and post-seismic period is obtained using a homogeneous half-space elastic model and the Steepest Descent Method. The results indicate a blind normal fault striking 215° with a 55° dip to the northwest and the co-seismic slip model suggests a nearly circular main slip patch (8 × 6 km2) with a maximum slip of 0.98 m. Post-seismic displacements started rapidly after the main shock followed by a gradual decay as highlighted by the calculated InSAR time series. The temporal evolution of post-seismic slip is described by a simple logarithmic function, decaying faster at the southwest part of the fault. The cumulative afterslip model suggests that the maximum post-seismic slip of 0.23 m occurred within a similar depth range compared to the co-seismic one, yet with a shift towards the southwest. Post-seismic slip inside the main shock rupture area is sustained, highlighting the slow recovery of locking in the co-seismic slip region. Afterslip (seismic or aseismic) played a dominant role in the early post-seismic period acting complementarily to the main rupture. Indications suggest that the spatiotemporal evolution of the productive aftershock sequence may be driven afterslip, alongside other potential factors.

The surface deformation of permafrost and active layer thickness in the upper reaches of the Black River basin, revealed by InSAR observations and independent component analysis

The Heihe River Basin, located in the northeastern part of the Qinghai-Tibetan Plateau, is part of the perennial permafrost belt of the Qilian Mountains. Recent observations indicate ongoing permafrost degradation in this region. This study utilizes data from 255 observations provided by Sentinel-1 satellites, MODIS Land Surface Temperature, SMAP-L4 soil moisture data, GNSS measurements, and in situ measurement. We introduced Variational Bayesian independent Component Analysis (VB-ICA) in multi-temporal Interferometric Synthetic Aperture Radar (MT-InSAR) processing to investigate the spatial-temporal characteristics of surface deformation and permafrost active layer thickness (ALT) variations. The analysis demonstrates strong agreement with borehole data and offers improvements over traditional methodologies. The maximum value of ALT in the basin is found to be 5.7 m. VB-ICA effectively delineates seasonal deformations related to the freeze-thaw cycles, with a peak seasonal deformation amplitude of 60 mm. Moreover, the seasonal permafrost's lower boundary reaches an elevation of 3700 m, revealing that permafrost is experiencing widespread degradation and associated soil erosion in the high elevation region of The Heihe River Basin. The paper also explores the efficacy of reference point selection and baseline network establishment for employing the InSAR method in monitoring freeze-thaw deformations. The study underscores the InSAR method's adaptability and its importance for interpreting permafrost deformation and related parameters.

ОПТИМИЗАЦИЯ МЕТОДИКИ СОЗДАНИЯ КАРКАСНЫХ ГЕОДЕЗИЧЕСКИХ СЕТЕЙ ГНСС-ОБОРУДОВАНИЕМ С ЦЕЛЬЮ НАПОЛНЕНИЯ ЕДИНОЙ ЭЛЕКТРОННОЙ КАРТОГРАФИЧЕСКОЙ ОСНОВЫ (ЕЭКО) ПЛАНОВО-КАРТОГРАФИЧЕСКИМИ МАТЕРИАЛАМИ

The article reflects the main directions of reforming the sphere of spatial data turnover in Russia. The essence of the Federal Information System, the unified digital platform "National Spatial Data System" is revealed. The objectives of its creation and its connection with other state information systems and state information resources of the country are defined. The content of the Unified Electronic Cartographic Framework as an integral part of the National Spatial Data System is reflected. The requirements for the composition of the metric and semantic information of the EEC are given. The analysis of the national reports of Rosreestr "On the state and use of lands" was carried out, on the basis of which a conclusion was made about the relevance of mapping the territory of Russia. A description of the frame geodetic networks, methods and regulatory requirements for their construction is given. The substantiation of the possibility of optimizing the methodology for the production of satellite measurements in the "static" mode when creating networks of this class is given. The features of field and desk work within the framework of the study are reflected. Based on the results obtained, the duration of GNSS measurement sessions was determined, which allows to ensure the accuracy of the relative position of points of the frame geodetic network set by regulatory requirements.

PrNet: A Neural Network for Correcting Pseudoranges to Improve Positioning With Android Raw GNSS Measurements

PrNet: A Neural Network for Correcting Pseudoranges to Improve Positioning With Android Raw GNSS Measurements

Interactive planning of GNSS monitoring applications with virtual reality

In conventional GNSS planning software, the local circumstances at the antenna locations are hardly covered. Due to uniform cut-off angles in the elevation of the satellite orbits, the quality investigations are often not representative at inhomogeneous areas (e.g. vicinity of mountains or buildings). An experimental software was developed in Unity with ray-tracing approaches to evaluate the satellite constellation on the basis of actual on-site geometry with virtual reality. The software has been tested in a real-life use case for the simulation of GNSS measurements at an Austrian water dam. Furthermore, the results have been validated by actual GNSS measurements on-site.

Drive-by Structural Monitoring using GNSS measurements at alpine bridges

Most bridges in Europe were built in the 1960s and 1970s and are now reaching the end of their design life. It is therefore important to monitor these bridges to ensure a safe operation for many years to come. Load tests are a common way of checking the health of an infrastructure. Such a test was carried out on a ~560m long motorway bridge (7 spans) in Austria. Previous studies have shown that geodetic GNSS (Global Navigation Satellite System) receivers with a data rate of 20Hz can be used for vibration monitoring. Therefore, for the load test, geodetic GNSS receivers were mounted on the moving load (2 trucks of 50 tons each) to test the capability of drive-by GNSS measurements for structural monitoring of bridges. Additional sensors (accelerometers, fibre optic cables) were mounted on one span and data was collected during the load tests. The frequency analysis performed with the GNSS measurements agrees well with the frequency analysis performed with the data from the other sensors, where the main frequencies occurred between 2-3Hz with amplitudes in the millimetre range. The advantage of drive-by GNSS measurements is the acquisition of data from the entire bridge. Therefore, the shape of the bridge (slack span of each span) and the dynamic behaviour (frequency response, mode shapes) can be derived from the same data at the same time.

Benefit of classical leveling for geoid-based vertical reference frames

Classically, vertical reference frames were realized as national or continent-wide networks of geopotential differences derived from geodetic leveling, i.e., from the combination of spirit leveling and gravimetry. Those networks are affected by systematic errors in leveling, leading to tilts in the order of decimeter to meter in larger networks. Today, there opens the possibility to establish a worldwide unified vertical reference frame based on a conventional (quasi)geoid model. Such a frame would be accessible through GNSS measurements, i.e., physical heights would be derived by the method of GNSS-leveling. The question arises, whether existing geodetic leveling data are abolished completely for the realization of vertical reference frames, are used for validation purposes only, or whether existing or future geodetic leveling data can still be of use for the realization of vertical reference frames. The question is mainly driven by the high quality of leveled potential differences over short distances. In the following we investigate two approaches for the combination of geopotential numbers from GNSS-leveling and potential differences from geodetic leveling. In the first approach, both data sets are combined in a common network adjustment leading to potential values at the benchmarks of the leveling network. In the second approach, potential differences from geodetic leveling are used as observable for regional gravity field modeling. This leads to a grid of geoid heights based on classical observables like gravity anomalies and now also on leveled potential differences. Based on synthetic data and a realistic stochastic model, we show that incorporating leveled potential differences improves the quality of a continent-wide network of GNSS-heights (approach 1) by about 40% and that formal and empirical errors of a regional geoid model (approach 2) are reduced by about 20% at leveling benchmarks. While these numbers strongly depend on the chosen stochastic model, the results show the benefit of using leveled potential differences for the realization of a modern geoid-based reference frame. Independent of the specific numbers of the improvement, an additional benefit is the consistency (within the error bounds of each observation type) of leveling data with vertical coordinates from GNSS and a conventional geoid model. Even though we focus on geodetic leveling, the methods proposed are independent of the specific technique used to observe potential (or equivalently height) differences and can thus be applied also to other techniques like chronometric or hydrodynamic leveling.

The Largest Geodetic Coseismic Assessment of the 2020 Mw = 6.4 Petrinja Earthquake

On 28 December 2020, the area of the city of Petrinja was hit by two strong earthquakes of magnitudes 5.0 and 4.7 on the Richter scale, and the following day, 29 December 2020, the same area was hit by an even stronger earthquake of magnitude 6.2. It was one of the two strongest instrumentally recorded earthquakes that hit the territory of the Republic of Croatia in the last hundred years, and the strongest earthquake in the Banovina area after the great earthquake in 1909. Increased seismic activity in this area is caused by two vertical strike–slip faults, Pokupski and Petrinjski. This article aims to determine the displacements of the Earth’s crust caused by seismic activity in this area using GNSS measurements and InSAR techniques and comparing their results. Our study showed that horizontal coseismic displacements of 20 cm and more were limited to a radius of 20 km from the epicenter, with a maximum displacement of around half a meter. Considering the original plate tectonic movements of the region and the time elapsed since the previous earthquake of similar magnitude, the geodynamic movements of the Dinarides area are in substantial part sudden displacements associated with earthquakes.

The accuracy of vehicle position and heading angle improvement based on dual-antenna GNSS/INS/Barometer integration using extended Kalman filter

Abstract In the field of autonomous driving progresses, obtaining the precise position and attitude of vehicles through measurement technology is vital. An integrated GNSS/INS/Barometer (Global Navigation Satellite System/Inertial Navigation System/Barometer) fusion method is proposed to improve vehicle positioning and heading angle accuracy. An extended Kalman filter (EKF) based on horizontal dilution of precision (HDOP) is designed to fuse the INS error and the GNSS measurement. Furthermore, GNSS dual antennas are utilized to increase a state variable in EKF based on HDOP in addition to position and velocity. The kinematic constraint of zero velocity in the lateral and vertical directions of vehicle movement is used to measure the mounting angle to reduce error. The position and heading angle accuracy of the proposed method are 0.483 m and 1.358°, which represent reductions of 37.03% and 43.86% compared to the conventional EKF method, respectively. The experimental results demonstrate that the proposed method can measure accurate position and heading angle in both open and occluded environments.

Enhancing Positioning in GNSS Denied Environments Based on an Extended Kalman Filter Using Past GNSS Measurements and IMU

Enhancing Positioning in GNSS Denied Environments Based on an Extended Kalman Filter Using Past GNSS Measurements and IMU

A method for detecting faults in integrated navigation system based on improved SPRT adaptive filtering

GNSS measurement noise faults can easily cause a drop or even divergence in the filter accuracy of integrated navigation system. Therefore, real-time fault detection and processing are necessary. With the aim of the defects of residual Chi-square test and sequential probability ratio test (SPRT) in detecting measurement noise faults, an adaptive filtering algorithm based on improved SPRT detection is proposed. On the one hand, the influence of the current time innovation on the statistics is strengthened by the method of fading weighting. On the other hand, the measurement update equation of the adaptive filter is constructed by calculating the weight factor of the statistics in real-time, which improves the accuracy and robustness of the state estimation. Simulation experiments show that the proposed algorithm is more sensitive and non-missing compared to the residual Chi-square test in the case of large value abrupt faults in the measurement noise. The proposed algorithm reduces the fault detection delay time by about 65.5% compared to SPRT in the case of slow change faults in measurement noise. In the case of slow change faults with small values, the proposed algorithm reduces the missing detection rate by 40% compared to the residual Chi-square test. In addition, the proposed algorithm is compared with the robust Kalman filter based on the residual Chi-square and Sage-Husa adaptive filtering. The results show that the proposed algorithm has higher navigation accuracy when the system has slow change faults.

Precise Positioning of Primary System of Geodetic Points by GNSS Technology in Railway Operating Conditions

This article deals with the analysis of the accuracy of the geodetic real-time GNSS measurement procedure used in railway operating conditions in the Czech Republic. The purpose was to determine to what extent the operating conditions affect the accuracy of the measurement result and whether an accuracy of standard deviation σx,y = 5 mm in the horizontal plane could be achieved. The use of geodetic GNSS equipment with an IMU unit was also tested. The accuracy obtained in operational conditions is compared with the accuracy obtained on a calibration base using the same measurement procedure. The consistency between the accuracy of the primary system (satellite-based) and the secondary system (terrestrially measured by the traverse method) is also discussed. The analysis includes the issue of residual inhomogeneities of the uniform transformation key when converted to the Czech national coordinate system S-JTSK. It is shown that a homogeneous accuracy in coordinate standard deviation better than σx,y = 5 mm can be achieved. The results indicate that the accuracy under operational conditions is two–three times worse than the accuracy achieved by the same procedure under ideal conditions on a calibration base. This is due to the non-ideal observing conditions, i.e., horizon occlusion by overlays, surrounding vegetation and multipath effects. It has been shown that the effect of multipath can be reduced by repeating short observations 3–4 h apart. Older GNSS instruments using an IMU unit in combination with an electronic compass (eCompass) are at risk of a systematic bias of up to several tens of millimeters, which can be detected by rotating the antenna by 180°. The current uniform transformation key used in the Czech Republic for the conversion of GNSS coordinates into the national system has residual geometric inhomogeneities (p = 0.90 to 10 mm/km, sporadically up to 20 mm/km), which metrologically deteriorate the results of the calculation of the terrestrially measured secondary system inserted into the GNSS measured primary system. Achieving homogeneous accuracy in coordinate standard deviation in a horizontal plane better than σx,y = 5 mm has been demonstrated in non-ideal railway operating conditions with increased risk of multipath. The innovative aspect of the approach used is that it simplifies and thus increases the efficiency of the measurement with respect to the availability of GPS, GLONASS, Galileo and BeiDou satellites, as well as reducing the effect of multipath on the noise by repeating the measurement procedure.

Моніторинг сезонних вертикальних зміщень греблі Дніпровської ГЕС

The relationship Methods. A program developed for this purpose processed a time series of GNSS measurements, which allows for determining vertical seasonal displacements and their dependence on seasonal changes in ambient air temperature. Results. A review of scientific works on the temperature field impact on the deformation of hydraulic structures is presented. Based on the studies performed, it was found that in the absence of sharp drops in the water level in the upper reservoir, seasonal changes in ambient temperature have a significant impact on the vertical displacements of dams (in the example of the Dnipro HPP). The magnitude of extreme displacements and the epochs of their manifestation will depend on the dam design and technical parameters. Based on the processed data, a linear relationship was established between the average ambient temperature and the vertical displacements of GNSS control points located at the Dnipro HPP dam, which makes it possible to predict the value of vertical displacements of control points based on the measured temperature value. Accordingly, monitoring these displacements and their changes over time is one of the criteria for assessing the overall condition of the dam. We noticed that during the study period, the extremely positive average rate of the vertical displacements of the control points was in the first half of 2018, +1.03 mm per month, and the extremely negative average rate of 0.83 mm/month was in the second half of 2019. It explained the correlation between the vertical displacement rate of the control point and the depth of the reservoir near it. Scientific novelty and practical significance. The regularities of the relationship between temperature changes and GNSS point displacements revealed in the study can be useful for further research on the processing and analysis of monitoring data for hydraulic structures.

Modelling and estimating trajectory points from RTK-GNSS based on an integrated modelling approach

The sparse Gaussian process regression (GPR) has been used to model trajectory data from Real time kinematics-global navigation satellite system (RTK-GNSS). However, upon scrutinizing the model residuals; the sparse GPR model poorly fits the data and exhibits presence of correlated noise. This work attempts to address these issues by proposing an integrated modeling approach called GPR-LR-ARIMA where the sparse GPR was integrated with the linear regression with autoregressive integrated moving average errors (LR-ARIMA) to further enhance the description of the trajectory data. In this integrated approach, the predicted trajectory points from the GPR were further described by the LR-ARIMA. Simulation of the GPR-LR-ARIMA on three sets of trajectory data indicated better model fit, revealed in the normally distributed model residuals and symmetrically distributed scatter plots. Correlated noise was also successfully eliminated by the model. The GPR-LR-ARIMA outperformed both the GPR and LRARIMA by its ability to improve mean-absolute-error in 2-dimension positioning by up to 86%. The GPR-LR-ARIMA contributes to enhancement of positioning accuracy of dynamic GNSS measurements in localization and navigation system with good model fit.