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Abstract

Partial ambiguity resolution (PAR) has been widely adopted in real-time kinematic (RTK) and precise point positioning with augmentation from continuously operating reference station (PPP-RTK). However, current PAR methods, either in the position domain or the ambiguity domain, suffer from high false alarm and miss detection, particularly in challenging environments with poor satellite geometry and observations contaminated by non-line-of-sight (NLOS) effects, gross errors, biases, and high observation noise. To address these issues, a PAR method based on machine learning is proposed to significantly improve the correct fix rate and positioning accuracy of PAR in challenging environments. This method combines two support vector machine (SVM) classifiers to effectively identify and exclude ambiguities those are contaminated by bias sources from PAR without relying on satellite geometry. The proposed method is validated with three vehicle-based field tests covering open sky, suburban, and dense urban environments, and the results show significant improvements in terms of correct fix rate and positioning accuracy over the traditional PAR method that only utilizes ambiguity covariances. The fix rates achieved with the proposed method are 93.9%, 81.9%, and 93.1% with the three respective field tests, with no wrong fixes, compared to 72.8%, 20.9%, and 16.0% correct fix rates using the traditional method. The positioning error root mean square (RMS) is 0.020 m, 0.035 m, and 0.056 m in the east, north, and up directions for the first field test, 0.027 m, 0.080 m, and 0.126 m for the second field test, and 0.035 m, 0.042 m, and 0.071 m for the third field test. In contrast, only decimeter- to meter-level accuracy was obtainable with these datasets using the traditional method due to the high wrong fix rate. The proposed method provides a correct and fast time-to-first-fix (TTFF) of 3–5 s, even in challenging environments. Overall, the proposed method offers significant improvements in positioning accuracy and ambiguity fix rate with high reliability, making it a promising solution for PAR in challenging environments.

Nature Geoscience, Published online: 16 January 2025; doi:10.1038/s41561-025-01643-1

Author Correction: Recent uplift of Chomolungma enhanced by river drainage piracy

Abstract

Tidal interactions play a key role in the dynamics and evolution of icy worlds. The intense tectonic activity of Europa and the eruption activity on Enceladus are clear examples of the manifestation of tidal deformation and associated dissipation. While tidal heating has long been recognized as a major driver in the activity of these icy worlds, the mechanism controlling how tidal forces deform the different internal layers and produce heat by tidal friction still remains poorly constrained. As tidal forcing varies with orbital characteristics (distance to the central planet, eccentricity, obliquity), the contribution of tidal heating to the internal heat budget can strongly change over geological timescales. In some circumstances, the tidally-produced heat can result in internal melting and surface activity taking various forms. Even in the absence of significant heat production, tidal deformation can be used to probe the interior structure, the tidal response of icy moons being strongly sensitive to their hydrosphere structure. In the present paper, we review the methods to compute tidal deformation and dissipation in the different layers composing icy worlds. After summarizing the main principle of tidal deformation and the different rheological models used to model visco-elastic tidal response, we describe the dissipation processes expected in rock-dominated cores, subsurface oceans and icy shells and highlight the potential effects of tidal heating in terms of thermal evolution and activity. We finally anticipate how data collected by future missions to Jupiter’s and Saturn’s moons could be used to constrain their tidal response and the consequences for past and present activities.

Abstract

This study addresses the frequent convergence issues of satellite clocks within regional network, with a particular focus on the multifrequency advantages using data from 25 uniformly distributed reference stations across China. Experimental results demonstrate that incorporating the third frequency significantly enhances the accuracy of BDS-3 clock solutions, reducing the root mean square (RMS) by 44.5%. Additionally, employing a 2-min smoothing interval, multifrequency inclusion increases the wide-lane (WL) fixing rate by 30.4% at low elevation angles, which in turn leads to a marked improvement in narrow-lane (NL) ambiguity resolution. By leveraging phase-wide-lane observations, the stable wide-lane phase bias enables the continuous generation of inter-frequency clock bias (IFCB), ensuring reliable cyclic sequence construction even when satellites exit the observed region. The effectiveness of regional observable specific bias (OSB) on ambiguity resolution at the user level is highlighted, and over 95% of GPS, BDS-3, and Galileo NL fractional biases below 0.15 cycles could be achieved. Furthermore, the single-epoch convergence rates of multi-constellation precise point positioning (PPP) reach horizontal 91.9% and vertical 84.5% for multifrequency, a substantial improvement over the dual-frequency, which does not exceed 25%.

Nature Geoscience, Published online: 15 January 2025; doi:10.1038/s41561-025-01641-3

Author Correction: An ongoing satellite–ring cycle of Mars and the origins of Phobos and Deimos

Nature Geoscience, Published online: 15 January 2025; doi:10.1038/s41561-024-01626-8

Photochemical modelling suggests that H2 outgassing from crustal hydration could have supported transient warming episodes on early Mars in a CO2-rich atmosphere with abrupt transitions to cold climate states in a CO-rich atmosphere.

Nature Geoscience, Published online: 14 January 2025; doi:10.1038/s41561-024-01624-w

Near-daily sampling of volcanic ash during a three-month eruption reveals shifts in mantle-derived liquid magma (melt) composition, highlighting its potential as a monitoring and forecasting tool. These shifts align with the amplitude of volcanic tremor, a persistent seismic signal, suggesting a link between magma viscosity, shallow bubble escape dynamics, and tremor changes.

Abstract

In this paper, we propose a novel algorithm for fast frequency and phase synchronization of high-stability oscillators synchronized with 1 PPS signal from satellite navigation systems. The algorithm uses a model of a control object in the space of state variables and controls the frequency of an oscillator operating in a phase-locked loop. A new element is the introduction to the theoretical analysis and the design process, the time of entering synchronization. Currently, the literature lacks theoretical analysis and design methodology that considers the impact of the synchronization time on the choice of the steering algorithm and its parameters. All the data needed to determine the numerical values of the model were found experimentally for three different classes of control objects. Short synchronization times, a detailed description of the design methodology, and the use of values measured in the real system distinguish the proposed algorithm from the solutions described in the literature. The effect of optimization was achieved thanks to the algorithm’s two-stage operation. In the first stage, the algorithm aims to minimize the phase error quickly. The best solution for this stage is Sliding Mode Control (SMC). In the second stage, the algorithm strives to maximize the control quality, understood as minimizing the values of Maximum Time Interval Error (MTIE) and Time Deviation (TDEV). The Model Predictive Control (MPC) and Linear-Quadratic Regulator (LQR) optimal control algorithms were used at this stage. The paper also investigated the influence of the tuning parameters of these algorithms (weights as a function of cost) on the long-term behavior of the control system.

Nature Geoscience, Published online: 13 January 2025; doi:10.1038/s41561-024-01627-7

Space exploration has expanded the realm of geoscience to the outermost Solar System. A new generation of missions shines the way.

The micromechanics of friction has been investigated from the viewpoint of the healing of real contacts. In this study, the underlying processes of friction are discussed from the viewpoint of the contact junc...

Constraining the effective rheology of major faults contributes to improving our understanding of the physics of plate boundary deformation. Geodetic observations over the earthquake cycle are often used to e...

On February 8, 2022, approximately 40 of the 49 Starlink satellites were reported to have lost altitude, leading to atmospheric re-entry. SpaceX reported that the orbital decay on Starlink satellites was consi...

Nature Geoscience, Published online: 10 January 2025; doi:10.1038/s41561-024-01623-x

The SiO2 contents of erupted volcanic melts are correlated with persistent seismic signals that accompany eruptions—volcanic tremor—and may represent an eruption monitoring tool, according to a study of volcanic ash glasses from Cumbre Vieja volcano.

Abstract

In order to further improve the convergence rate and positioning accuracy of multi-frequency multi-system precise point positioning (PPP), an open-sourced software for fractional cycle bias (FCB) estimation (M_FCB) was produced based on MATLAB 2016a for GPS, BDS-2, Galileo, and BDS-3 satellite users. Based on raw frequency float ambiguity, the software can estimate ultra-wide-lane, wide-lane, narrow-lane combined FCB and raw frequency FCB. To validate the usability of the M_FCB software, 180 and 24 globally uniformly distributed multi-GNSS experiment stations were used to perform FCB estimation and triple-frequency uncombined PPP ambiguity resolution performance evaluation. The results show that the M_FCB software can generate stable and reliable FCB products. Particularly, Galileo satellites presented the best FCB stability. In addition, taking GPS/Galileo/BDS-2/BDS-3 fusion positioning as an example, the kinematic PPP after ambiguity resolution was significantly improved in terms of three-dimensional coordinate accuracy and positioning stability. Relative to the float solution, the average root mean square of the fixed-solution coordinate residuals in the east, north and vertical directions decreased by 30.3%, 12.5% and 16.0%, respectively.

Nature Geoscience, Published online: 09 January 2025; doi:10.1038/s41561-024-01618-8

This study examines the influence of agricultural irrigation on heat stress and contrasts it against local impacts of urbanization in North American cities using regional climate model simulations. The results indicate that irrigation decreases air temperature and increases relative humidity, with daytime urban moist heat stress reduced according to most indices.

Nature Geoscience, Published online: 09 January 2025; doi:10.1038/s41561-024-01613-z

Convection-permitting regional climate simulations suggest that irrigation reduces daytime urban heat stress in North America.

Abstract

In this paper, we studied the impact of solar activity, especially proton density, He++/H+ ratio and temperature of solar wind, on the geomagnetic field and thereby on earth’s climate. The verified data of these indices are collected from the official websites: wdc.kugi.kyoto-u.ac.jp and www.srl.caltech.edu/ace. Using the data values, both the indices are analyzed and studied to explore the link between solar activity and geomagnetic field. The magnetic field is irregular with negative and positive peaks and at the same time it shows the uniformity with the irregularities of solar wind plasma parameters. It has been observed that solar wind plasma has a significant influence on the intensity of magnetic field of earth and this correlation can be used for weather forecasts and climatic studies in the future.

Abstract

This study investigates the vertical electron content (VTEC) variations and depletions using two years of Global Positioning System (GPS), Total Electron Content (TEC) data from 2012 and 2013. The data, gathered at altitudes between 5° and 15° and longitudes between 34° and 48°, was specifically focused on quiet days and analyzed from nine GPS stations. Employing a spherical model and standard kriging interpolation techniques, the research explored hourly, diurnal, and seasonal fluctuations of VTEC over the two-year period. The spherical model demonstrated high efficacy in estimating data with short lag distances, effectively capturing hourly and daily VTEC fluctuations. Diurnal VTEC variations showed a consistent pattern: increasing from dawn, peaking at 1200 UT, and declining to a minimum after 1800 UT. The peak in diurnal variation was most pronounced at Debark, with similar patterns observed at other stations, reflecting consistent ionospheric behaviors due to geomagnetic conjugcy. A strong correlation was observed between the alignment of the solar terminator and magnetic meridian during equinox seasons and VTEC variation and depletion, with the most significant effects during equinoctial seasons. The study identified a distinct north-south gradient in VTEC within the region, with levels exceeding 65 TECU in the north and around 40 TECU in the south, depending on ionospheric conditions. Nighttime VTEC levels typically decreased to approximately 5 TECU. The spatial distribution analysis of TEC revealed a pronounced maximum concentration in the northeastern sector, contrasting with a minimal concentration in the southwestern sector. This research provides valuable insights into the spatial and temporal behaviors of VTEC, enhancing our understanding of ionospheric dynamics within the specified region.

Abstract

Fractal analysis of VLF electric field data obtained by using vertical antenna located at Chaumuhan, Mathura station (Lat., 27.5° N, Long., 72.68° E) has been carried out using Higuchi method for investigating the impact of moderate shallow earthquakes (M = 4.9–5.6, depth 4.44–16.7 Km) that occurred during February 1, 2016 to October 31, 2016 (excluding April 2016) on the fractal dimension of VLF data. The results of the analysis show that daily values of fractal dimension vary much above and below the monthly mean during the period of observations, 1–30 days before and 1–30 days after the onset of the quakes considered in the present study. The ranges of reductions and enhancements in fractal dimension from the monthly mean are 0.05–0.33 and 0.054–0.43 respectively while the percentage ranges of reductions and enhancements in its daily variation are 3.0–23.21 and 2.81–19.88% respectively. The observed variations in fractal dimension have also been studied in the light of other expected sources like, magnetic storms, lightning activity, local building noises, and instrumental errors which may affect the fractal dimension of the VLF data. It is noticed that the observed variations of fractal dimensions do not correspond to these spurious sources considered. Further, model describing the genesis of VLF emissions in preparatory zones of the impending seismic events and their mechanism of transmission to the observing station have also been discussed.

Abstract

Satellite navigation systems are used for positioning purposes, however to calculate an accurate position, it is crucial to take into account all possible sources of error. The Ionosphere is the primary cause of the positional error. There is a lot of research into first-order ionospheric error estimation and removal. Due to the growing demand for positioning precision across a wide range of applications, significant research has been done over the last two decades to ascertain the impact of second-order ionospheric error (SOIE). However, very less research has been identified that examines the relationship between SOIE and the receiver’s geographic location and total electron content (TEC). Achieving the desired millimeter/centimeter level positional accuracy in these regions requires the study of a realistic diurnal and seasonal variability of SOIE because the behavior of ionospheric TEC in equatorial and low-latitude regions (Indian region in this case) is highly dynamic. Additionally, NavIC (Navigation with Indian Constellation), an Indian satellite navigation system, uses carrier frequencies, namely L5 and new frequency S1, as opposed to GPS L1 and L2, which presents a fresh chance to investigate the effects of SOIE on these frequencies. This research may serve as a benchmark for systems like NavIC that are using L5 and new S-band frequencies for satellite signal transmission, space weather monitoring, and ionosphere abnormalities research. To comprehend various elements of its seasonal properties, this research estimates and analyses SOIE. Data from the SOIE were examined for 12 months, from May 2018 to February 2019, to analyze the diurnal and seasonal fluctuation. It has been noted that seasonal and diurnal fluctuations have a substantial impact on the SOIE. In comparison to the winter months, the SOIE levels are higher in the summer and equinoctial months. Although the SOIE peak levels are similar during the equinoctial and summer months, a higher midnight value and a slowly declining rate have been noted. At L5 frequency, there is a significant seasonal fluctuation in SOIE (–1.1 to –2.84 cm), whereas at S1 shows just a little seasonal variation (–0.1 to –0.3 cm) throughout the year. Additionally, geostationary orbit (GEO) satellites are discovered to be more suitable for the analysis of SOIE than satellites in geosynchronous orbit (GSO), and they might also be employed for ionospheric studies.