Machine learning and meteorological data for spatio-temporal prediction of tropospheric parameters

The study of climate change is an important field of research. Monitoring of atmospheric variability especially the tropospheric precipitable water vapor (PWV) is a powerful way to investigate climate change. Global navigation satellite systems (GNSS) provide a good tool for studying atmospheric parameters as GNSS signals along its path from the satellites to the ground based receivers suffer a significant delay due to the refractivity of earth’s atmosphere. GNSS signals are not only delayed but also refracted in the neutral atmosphere. The zenith wet delays (ZWD) caused by the troposphere can be estimated during the geodetic processing of GNSS signals. Since the ZWD is tightly correlated to the PWV, GNSS observations can be used to study the changes of PWV. In this study GNSS data from the Egyptian permanent GNSS network (EPGN), International GNSS Service (IGS), EUREF Permanent Network (EPN) and Scripps Orbit and Permanent Array Center (SOPAC), for the years 2013 and 2014, were used. These GNSS stations provided a good geometrical coverage over the respective region. All GNSS data were processed using Bernese V 5.2 software. The needed product from GNSS data processing is the tropospheric zenith total delay (ZTD) over each GNSS site. The ZTD is divided based on physical parameters into zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD). The ZWD is the basic observable used to calculate PWV. The values of the PWV were calculated and its variation over the study area was investigated. The quality of calculated PWV values from GNSS data evaluated against traditional Radiosonde (RS) measurements. The results of GNSS PWV showed good agreement with RS PWV when the PWV values were low, but this agreement became worse at high PWV values as the differences between the two techniques increased. The correlation coefficient between RS PWV and GNSS PWV varied from 0.31 to 0.84. Standard deviation of the differences between RS PWV and GNSS PWV ranged from 2.369 to 5.973 mm. The PWV estimated from GNSS observations had annual cycle, and its cycle in 2013 was different from that in 2014. The PWV differences between the 2 years clarified that the water vapor content over the east Mediterranean in most of 2014 days was higher than that in 2013. Furthermore, PWV variations were noted on both temporal and spatial scales. The highest temporal variation value was 25.41 mm whereas the maximum value of the spatial variation was 19.67 mm. The present study illustrated the importance of using geodetic networks to provide atmospheric information.

The Global Navigation Satellite System (GNSS) has the capacity for remote sensing of water vapor content in the atmosphere. Post-processing of GNSS data can provide Integrated Water Vapor (IWV) with accuracies comparable to measurements of traditional sensors, i.e. water vapor radiometers. While GNSS meteorology benefits from thousands of permanent GNSS stations operating worldwide the spatial resolution of GNSS-derived IWV is limited to tens of kilometers. Further densification of GNSS networks is achievable with low-cost GNSS receivers. We investigated the feasibility of low-cost multi-GNSS receivers for monitoring IWV. The post-processing and the real-time solution are validated against 1) the results from a geodetic-grade GNSS receiver, 2) co-located water vapor radiometer, and 3) numerical weather model (NWM). Despite the high variability of the IWV during the validation period, the standard deviation of IWV differences with respect to the water vapor radiometer was 1.0 kg/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 1.5 kg/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in post-processing and real-time, respectively. The city-scale variability of water vapor content in the atmosphere was monitored by a network of 16 low-cost GNSS receivers deployed in the city of Wroclaw, Poland. During rapidly changing weather conditions the disagreement between the low-cost GNSS-derived IWV field and the NWM reached up to 5.4 kg/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and inter-station IWV differences exceeded 5 kg/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . It has been demonstrated that low-cost GNSS receivers are reliable tools for precise determination of IWV, also in real-time. This study is the first to measure the water vapor content with a spatial resolution of single kilometers and to present a significantly diversified city-scale IWV field.

Sports watches come equipped with Global Navigation Satellite System (GNSS) receivers capable of tracking GPS, GLONASS, and Galileo, and thus, can be considered low-cost GNSS receivers. In our research, we conducted three distinct experiments to evaluate the accuracy of 1) positioning, 2) distance determination, and 3) height determination based on sports watches using different GNSS combinations: GPS, GPS + GLONASS, and GPS + Galileo. For positioning, a professional GNSS receiver served as the reference. To determine height, we used a laser rangefinder. The assessment of distance measurement utilized a full-size athletics track. A noteworthy outcome of this study is that the increased cost of sports watches does not consistently correlate with higher GNSS positioning accuracy. The most accurate 2D results are achieved by the Polar M430 for the GPS case with the mean positioning error of 1.74 m, and the Garmin Fenix 6 PRO for GPS + GLONASS case with the mean error of 1.43 m.

Electromagnetic waves propagating through the Earth’s ionosphere are subjected to changes in group and phase velocities, refraction, dispersion, and diffraction. For systems relying on the usage of radio signals affected by the ionosphere, it is of crucial importance to account for these effects. As far as ionospheric monitoring is concerned, high-grade multi-frequency and multi-constellation Global Navigation Satellite System (GNSS) receivers are commonly used. The existing ground-based GNSS receiver networks can provide information on a global scale. Nevertheless, geographic regions still exist where ionospheric monitoring facilities are limited. To improve our knowledge about ionosphere in areas where the existing networks coverage is sparse, an increase in the receivers’ density would be desirable. The cost of the devices has indeed constituted a major obstacle, however, with the significant advance of software-defined radio, the situation is changing through the availability of low-cost solutions. The present work will discuss the performance of the available off-the-shelf low-cost dual-frequency GNSS receivers, testing them in the controlled environment and comparing the derived data with scientific-grade instruments. The accuracy of the collected ionospheric data, such as uncalibrated and calibrated total electron content (TEC) will be analyzed.

The wet delay is one of the most difficult sources of error to quantify in global navigation satellite systems (GNSS) due to its spatial and temporal variability. However, its estimation is vital in some applications, such as in Precise Point Positioning (PPP), network real-time kinematic and weather forecast. Such estimation is usually carried out for its projected component along the zenith, defined as the zenith wet delay (ZWD). Prediction of the ZWD is important if there is a break in its estimation, and in providing initial values for future processing. In this paper, prediction modeling for the ZWD is investigated. An autocorrelation study was first performed on ZWD data over three different days at the international GNSS service station ONSALA to provide an insight into the temporal correlations among ZWDs. The choice of this station was based on the availability of reliable ZWD data measured by water vapor radiometers, which provide a reference for assessment of the accuracy of predicted values. Results have shown that successive ZWD estimates are significantly correlated for up to 1.7 hours. Different trend and smoothing prediction models were then investigated. Since prediction of ZWD requires continuous data sequence, interpolation methods of possible missing ZWD values are discussed. The use of linear interpolation or a cubic Hermite polynomial was found to be sufficient for interpolation of ZWD. Test results of prediction models show that the single-exponential smoothing model was the best performer where ZWD estimates were forecasted with a root mean square error of less than 1 cm for up to two hours.

In the recent years, the threat of radio frequency interference (RFI) to Global Navigation Satellite Systems (GNSS) receivers has been increasing due to an escalating number of RFI related GNSS issues, and enhanced complexity of jammers and spoofers. This poses significant integrity threats to various systems that depend on GNSS measurements for navigation and guidance. One of the most versatile methods to detect such instances of spoofing is the use of Automatic Gain Control (AGC) measurements provided by GNSS receivers. AGC is indicative of the change in thermal noise levels observed by the frontend of the receiver, thus it can be used to detect presence of RFI. If AGC is coupled with the carrier to noise ratio density (??/????) values of visible GNSS satellites, it is possible to gain insight into which specific constellations or satellites may have been spoofed. Although AGC has been available in some commercial GNSS receivers and customized frontends for some time, the introduction of raw GNSS measurements in Android 7 has recently allowed it to be accessible in some smartphones as well. This study looks at AGC measurements from multiple smartphone models which have different GNSS chipsets, assesses their behavior under RFI, points out the current limitations, and proposes future improvements that would assist in its usage as a GNSS RFI indicator. Furthermore, the paper discusses the future of AGC measurements that would assist in broadening their applications to all GNSS receivers.

This study evaluates the suitability of compact, lowcost Global Navigation Satellite System (GNSS) receiver module in estimating the effects of tropospheric delay on accuracy of GNSS position solution at GNSS laboratory, the University of Burdwan, West Bengal, India with geographical coordinate of 23.2545°N, 87.8467°E, −11.402 m, using compact, low-cost uBlox F9P GNSS module and high cost Leica GR 50 geodetic receiver in March 2023. GNSS observation data were logged by the two receivers for 24 hours at 1Hz dual-frequency and converted into Rinex observation files in GPS-only, GLONASS-only, and GPS+GLONASS hybrid modes. The converted Rinex observation data were uploaded to the Natural Resources of Canada (NRCan) online service to obtain the user fixed values of latitude, longitude and attitude, and the wet and dry tropospheric delay files via email. The converted Rinex observation files were post-processed using GNSS positioning analysis tool that estimate the GNSS positioning accuracy parameters namely Distance Root Mean Square (2DRMS), Circle of Error Probable (CEP), Spherical Error Probable (SEP), and Mean Radian Spherical Error (MRSE) from the users defined known fixed values of latitude, longitude and altitude. The total delay obtained from the two GNSS receivers were compared with their positioning accuracy parameters. The results showed better position solution on observation days with the least total zenith delay in all the constellations considered. The Leica GR 50 shows an average total zenith delay of 2.476 m in GPS mode, 2.486 m in GLONASS mode and 2.4680 m in GPS+GLONASS hybrid mode while the uBlox F9P shows 2.477 m in GPS mode, 2.494 m in GLONASS mode and 2.4684 m in GPS+GLONASS hybrid mode of operation. The GPS+GLONASS hybrid mode of operation reduces the total zenith delay and enhanced the position solution. Hence, there is no distinct difference between the two GNSS receivers, suggesting that compact, low-cost, GNSS receiver modules can be used for tropospheric study.

With the ever-increasing number of small satellites launched into space, on-board orbit determination is becoming more and more important. Precise satellite positions are needed for constellation maintenance, formation flying, communication optimization, collision avoidance and Earth observation. In addition, accurate time information is required for the functioning of the instruments on board. Low-cost off-the-shelf Global Navigation Satellite System (GNSS) receivers and antennas, adapted to the small size and weight of the satellite, allow precise on-board orbit determination and time synchronization for even the smallest satellites.We analysed more than one year of on-board navigation solutions (NAVSOL) from 8 Astrocast CubeSats, which are equipped with our multi-GNSS single-frequency payload. Based on the residuals from a dynamic orbit fitting, we found that the quality of the NAVSOL from the Astrocast satellites varies strongly both over time and between satellites, with an RMS ranging from a few meters to several tens of meters.In this study, we focus on three main effects that influence the quality of the NAVSOL from the Astrocast satellites: (1) The orbit-fit residuals show a positive radial offset in the range of about 6 m to 15 m, which is caused by ionospheric refraction. Our data show that GNSS signals at negative elevations are very strongly affected by the ionospheric refraction and thus account for the major part of the radial offset. (2) Discrepancies between the NAVSOL positions and velocities, and simulations with a GNSS signal generator show a once-per-revolution periodicity in the out-of-plane component, with amplitudes of 2 m and 5 cm/s in position and velocity, respectively. This effect is probably due to an inappropriate dynamic model used in the real-time navigation algorithm of the GNSS receiver. (3) Depending on the location of the GNSS antenna on board the satellite, the noise level varies by a multiple. This is assumed to be due to the antenna orientations, interference of the GNSS signals with electromagnetic waves coming from the satellite platform, signal attenuation during the transmission from the antenna to the receiver and differences in the soldering or tuning of the individual GNSS antennas.These findings help us refine hardware configurations and firmware settings in preparation for future Astrocast satellites or other nanosatellite missions. By eliminating or minimizing the mentioned effects, we expect to consistently achieve an accuracy on the level of a few meters for the real-time navigation solution of commercial off-the-shelf single-frequency GNSS receivers in space.

Global Navigation Satellite Systems (GNSS) rely on one-way signal travel time measurements from satellites to receivers. To ensure accurate ranging, GNSS must estimate and compensate for clock offsets on at least one end of the transmitter-receiver system. Consequently, clock offsets are highly correlated with GNSS-derived parameters such as station coordinates, tropospheric delay estimates, satellite radial orbit parameters, and apparent geocenter coordinates. Improper handling of clock offsets can lead to their absorption into these parameters, degrading geodetic product accuracy. Traditionally, clocks have been handled within individual techniques without being specially addressed. However, some research efforts and experimental trials have explored using VLBI to synchronize clocks for GNSS and refining clock models to reduce correlations with other estimated parameters in GNSS, thereby improving overall precision.With recent advancements, high-precision optical clocks and fiber-optic time transfer technologies provide new possibilities for enhancing clock synchronization in GNSS. Optical fiber offers a stable, interference-free medium for time and frequency transfer, eliminating atmospheric effects such as ionospheric and tropospheric delays that impact GNSS-based synchronization. Moreover, fiber-optic time transfer is inherently two-way, removing the need for external clock offset estimation. Thus, fiber-optic clock synchronization represents the most precise timing technique currently available. Establishing a common clock by connecting multiple GNSS receivers via optical fiber could significantly reduce the number of estimated clock parameters in GNSS solutions, leading to improved geodetic measurement precision and a more accurate geodetic reference frame.Despite its potential, the approach of implementing a common clock with optical fiber for GNSS receivers remains largely untested. Although optical fiber links have been successfully used in clock synchronization, their integration into GNSS receiver clocking is still in an experimental stage. Notable existing efforts include: (1) the Geodetic Observatory Wettzell, where multiple receivers are connected to a single clock via optical fiber, representing a local baseline setup, and (2) the GFZ experiment, where a receiver is linked to the ultra-stable clock of PTB, representing a regional baseline approach.This study characterizes existing fiber-optic connections among GNSS receivers to identify practical challenges and evaluate their impact on GNSS parameter estimation. We process data from receivers sharing a common clock using Bernese GNSS Software. Initially, PPP will be performed to compare GNSS-derived clock parameters across receivers sharing a common clock, verifying the effectiveness of fiber-optic clock synchronization. Following this validation, we will leverage GNSS-derived clock parameters to evaluate inter-receiver clock differences measured via optical fiber. Subsequently, we will implement a strategy in which only one receiver&amp;#8217;s clock parameters are estimated, using fiber-measured clock differences as a priori constraints for other receivers in the PPP solution. This approach reduces the number of estimated clock parameters and serves as a preliminary test of the feasibility of a GNSS common clock framework.Future developments will focus on refining our analysis framework to enable simultaneous estimation of GNSS receivers operating under a common clock. This research contributes to the broader goal of integrating ultra-stable clocks into global GNSS networks, ultimately enhancing the stability of geodetic reference frames and improving GNSS-derived geodetic products.

Unscented Kalman filter for a low-cost GNSS/IMU-based mobile mapping application under demanding conditions

The aging and multimorbid population and health personnel shortages pose a substantial burden on primary health care. While predictive machine learning (ML) algorithms have the potential to address these challenges, concerns include transparency and insufficient reporting of model validation and effectiveness of the implementation in the clinical workflow. To systematically identify predictive ML algorithms implemented in primary care from peer-reviewed literature and US Food and Drug Administration (FDA) and Conformité Européene (CE) registration databases and to ascertain the public availability of evidence, including peer-reviewed literature, gray literature, and technical reports across the artificial intelligence (AI) life cycle. PubMed, Embase, Web of Science, Cochrane Library, Emcare, Academic Search Premier, IEEE Xplore, ACM Digital Library, MathSciNet, AAAI.org (Association for the Advancement of Artificial Intelligence), arXiv, Epistemonikos, PsycINFO, and Google Scholar were searched for studies published between January 2000 and July 2023, with search terms that were related to AI, primary care, and implementation. The search extended to CE-marked or FDA-approved predictive ML algorithms obtained from relevant registration databases. Three reviewers gathered subsequent evidence involving strategies such as product searches, exploration of references, manufacturer website visits, and direct inquiries to authors and product owners. The extent to which the evidence for each predictive ML algorithm aligned with the Dutch AI predictive algorithm (AIPA) guideline requirements was assessed per AI life cycle phase, producing evidence availability scores. The systematic search identified 43 predictive ML algorithms, of which 25 were commercially available and CE-marked or FDA-approved. The predictive ML algorithms spanned multiple clinical domains, but most (27 [63%]) focused on cardiovascular diseases and diabetes. Most (35 [81%]) were published within the past 5 years. The availability of evidence varied across different phases of the predictive ML algorithm life cycle, with evidence being reported the least for phase 1 (preparation) and phase 5 (impact assessment) (19% and 30%, respectively). Twelve (28%) predictive ML algorithms achieved approximately half of their maximum individual evidence availability score. Overall, predictive ML algorithms from peer-reviewed literature showed higher evidence availability compared with those from FDA-approved or CE-marked databases (45% vs 29%). The findings indicate an urgent need to improve the availability of evidence regarding the predictive ML algorithms' quality criteria. Adopting the Dutch AIPA guideline could facilitate transparent and consistent reporting of the quality criteria that could foster trust among end users and facilitating large-scale implementation.

With the continuing spread of distributed measurement and control systems (e.g. Cyber-Physical Systems, Industry 4.0) there is an increased need to implement synchronized sampling and actuation over the components of a distributed system. To achieve this goal, the clocks of the system must be synchronized, including the ones doing sampling and actuation. In most cases local synchronization alone is not enough; It is also needed to keep in sync with a global reference time in order, for example, to be able to implement timestamps based on global time and simultaneous sampling across system components that are spatially distributed (operate on different sites). This global reference time mostly means one which is provided by a GNSS (Global Navigation Satellite System) service, such as GPS. In these systems, it is the master clock which is responsible for attaining (e.g. via a GNSS receiver) and keeping the global reference time. It can then pass it on in the local communication network, usually using IEEE 1588 (Precision Time Protocol). It follows, that thus, the characteristics of such systems are heavily limited by the precision, accuracy and reliability of the used GNSS receiver. Our paper thus is about the examination of potentially promising GNSS receivers for which we developed a custom measurement system. This includes the design of a test PCB, the writing of a PC data collecting program, the formulation of MATLAB scripts which process the collected data, and the validation of the data collecting system via GNSS receivers simulated by TI evaluation boards. We also conducted measurements with the system on the Quectel L86 GNSS receiver, the results of which are presented in the paper.

Signal fading is the main disturbing phenomenon for Global Navigation Satellite System (GNSS) receivers in urban environment, which induces frequent loss of carrier lock in GNSS phase tracking loops. By taking advantage of the prevalent configuration of multi-frequency reception in emerging GNSS receivers, this paper proposes a Frequency Diversity combined GNSS carrier Tracking Loop (FDTL) for robust and centimeter-level positioning under harsh propagation conditions. Specifically, a bank of correlators is used to estimate the signal parameters of interest with a Maximum Likelihood Estimation (MLE) discriminator to avoid the need for a separate acquisition which normally requires the most processing time in GNSS receivers. The Doppler relationship between multifrequency signals offers an inherent constraint which is used to improve accuracy of MLE measurements. In the loop tuning process, a frequency diversity combined Adaptive Kalman Filter (AKF) is implemented for system dynamic propagation and measurement update. The primary advantages of the proposed FDTL algorithm include: 1) significantly improved carrier tracking robustness compared with traditional Phase Lock Loops (PLLs); 2) enhanced sensitivity obtained from the diversity combination. The effectiveness of the algorithm is demonstrated by simulated and real GNSS fading signals.

Despite the significant advances in signal processing methods used nowadays, Global Navigation Satellite Systems (GNSS) receivers still experience substantial challenges, such as signal jamming, which remains a crucial source of degradation of the receiver performance. The presence of jamming signal influences the acquisition and tracking modules inside the receiver leading to loss-of-lock of the GNSS satellite signals. Consequently, GNSS receivers cannot provide reliable position, velocity and time services. The aim of this paper is to comprehensively explore the effects of linear chirp jamming on commercial receivers under high-dynamic scenarios. Moreover, the paper investigates the advantages of using combined GPS/GLONASS receivers under jamming conditions in comparison to using GPS-only receivers. In this paper, a SPIRENT GSS6700 Multi-GNSS Simulator controlled by Spirent SimGEN™ software is used to provide realistic controlled simulation scenarios. The linear chirp jamming signals are created using an Agilent interference signal generator (ISG) unit. Both commercial NovAtel ProPak-G2 Plus and NovAtel OEMV receivers are used to conduct these tests. The results show different behaviors of the various receivers in response to the applied jamming signals. The Carrier-to-Noise (C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ), the Dilution of Precision (DOP), and the navigation solution accuracy are used as measures to assess the performance of the receivers under study. Results show that the NovAtel OEMV receiver outperforms the NovAtel ProPak-G2 Plus receiver. Moreover, it is revealed that multi-constellation receivers achieved higher resistance for signal jamming effects than GPS only receivers.

Observations performed with ground-based space geodetic and remote sensing techniques are sensitive to the amount of water vapour in the neutral atmosphere. Corresponding parameters that describe the signal delay in the troposphere can be derived for example from the analysis of data collected from geodetic Very Long Baseline Interferometry (VLBI), Global Navigation Satellite System (GNSS), as well as microwave radiometers. The latter instruments are often referred to as water vapour radiometers (WVR). The Onsala Space Observatory (OSO) operates a number of such instruments for VLBI, GNSS and WVR measurements, all co-located within about 600 m. Among these are the Onsala twin telescopes (OTT), two modern 13.2~m diameter radio telescopes performing observations in the VLBI Global Observing System (VGOS) of the International VLBI Service for Geodesy and Astrometry (IVS). The OTT are the first operational VGOS twin telescopes worldwide and are contributing with observations to the IVS since 2019. OSO also operates eight permanently installed GNSS stations, of which two are official stations in the International GNSS Service (IGS) network. Furthermore, OSO operates ground-based microwave radiometers, which are used for atmospheric research and perform continuous observations of the water vapour content in the neutral atmosphere. Data analysis of all three techniques, VLBI, GNSS and WVR, allows to derive information on the temporal and spatial variations of water vapour in the neutral atmosphere. Using co-located instrumentation within a few hundred metres distance thus offers a perfect opportunity for comparisons and assessments of the results. We focus on data recorded at OSO during 2022 and compare the parameters describing the signal delay in the neutral atmosphere, i.e. the so-called equivalent zenith total delays and the linear horizontal delay gradients. The temporal resolution of the derived parameters is 15 min or less. Out of more than 40 VGOS experiments in 2022, each of a duration of 24 h, we have WVR data covering at least half of the session in all except one. &amp;#160;We have examples where the equivalent zenith wet delay only varies by 2--3 cm over an experiment during rather stable atmospheres. &amp;#160;When the atmosphere is more variable the zenith wet delay can vary by more than 10 cm over 24 h.