GPS Time Research Articles

A multi-layer perceptron neural network to mitigate the interference of time synchronization attacks in stationary GPS receivers

Accurate timing is one of the key features of the Global Positioning System (GPS), which is employed in many critical infrastructures. Any imprecise time measurement in GPS-based structures, such as smart power grids, economic activities, and communication towers, can lead to disastrous results. The vulnerability of the stationary GPS receivers to the time synchronization attacks (TSAs) jeopardizes the GPS timing precision and trust level. In the past few years, studies suggested the adoption of estimators to follow the authentic trend of the clock offset information under attack conditions. However, the estimators would lose track of the authentic signal without proper knowledge of the signal characteristics. Therefore, a multi-layer perceptron neural network (MLP NN) is proposed to follow the trend of the data. The main difference between the proposed method and typical estimators is the reliance of the network on the training information consisting of signal features. The proposed MLP NN performance has been evaluated through two real-world datasets and two well-known types of TSA. The root mean square error results exhibit an improvement of at least six times compared to other conventional and state-of-art methods.

Analysis and implementation of virtual impedance for fixed‐frequency control strategy in microgrid

Classic droop control ensures the synchronization of distributed generation (DG) units inside a microgrid without requiring any deployment of communication links, however it causes unwanted frequency fluctuations and degrades system dynamics. Angle droop control and V − I control have been developed as two major global positioning system (GPS)-based control methods, both of which realize a fixed-frequency operation of the microgrid through synchronizing DG units with GPS timing technology and brings improvement to the dynamic response of the overall system. This paper reveals the similarities and the correlations between these two methods that they can both be regarded as different forms of virtual impedance control. A novel adaptive virtual impedance control method is proposed accordingly to generalize GPS-based control strategies into a unified control frame. An impedance and inner controller design approach considering both stability constraints and power quality requirements based on the small-signal model of GPS-based microgrids is presented for practical implementation. An adaptive transient resistance concept is adopted to enhance the system stability during large disturbances and grid faults. Case studies are presented to validate the system performance and fault ride-through abilities of the proposed control scheme.

Combination of the Levenberg–Marquardt and differential evolution algorithms for the fitting of postseismic GPS time series

Postseismic global positioning system (GPS) time series are of fundamental importance for investigating the physical mechanisms of postseismic deformations, as well as the construction and maintenance of terrestrial reference frames. Particularly, methods for constructing accurate fitting models for such time series are critical. Based on the physical features of postseismic deformation models, we propose a new algorithm that combines the strengths of the Levenberg–Marquardt (LM) and differential evolution (DE) algorithms, that is, the LM + DE algorithm. In this algorithm, the parameters are initialised by the constrained DE algorithm; the final parameters of the postseismic model are then solved by the LM algorithm. To validate the proposed method, DE, LM, and LM + DE were compared using synthetic and observational data from the 2011 Tohoku Earthquake. For all tests based on synthetic data, the LM + DE algorithm consistently converged to the global solution and the residual is small, regardless of how the independent parameter was varied. In the 2011 Tohoku earthquake, the parameters calculated by the LM + DE algorithm matched consistently for the global solution with a 100% passing rate after constraints were provided for the ratios of the initial relaxation time parameters. In contrast, the LM and DE algorithms individually achieved passing rates of only 22% and 1%, respectively. These results demonstrate that the proposed LM + DE algorithm effectively solves the initial estimate problem in the fitting of nonlinear postseismic models, and also ensures that the fits are mathematically optimal and consistent with physical reality.

Digital phenotyping of student mental health during COVID-19: an observational study of 100 college students

Objective: This study assessed the feasibility of capturing smartphone based digital phenotyping data in college students during the COVID-19 pandemic with the goal of understanding how digital biomarkers of behavior correlate with mental health. Participants: Participants were 100 students enrolled in 4-year universities. Methods: Each participant attended a virtual visit to complete a series of gold-standard mental health assessments, and then used a mobile app for 28 days to complete mood assessments and allow for passive collection of GPS, accelerometer, phone call, and screen time data. Students completed another virtual visit at the end of the study to collect a second round of mental health assessments. Results: In-app daily mood assessments were strongly correlated with their corresponding gold standard clinical assessment. Sleep variance among students was correlated to depression scores (ρ = .28) and stress scores (ρ = .27). Conclusions: Digital Phenotyping among college students is feasible on both an individual and a sample level. Studies with larger sample sizes are necessary to understand population trends, but there are practical applications of the data today.

Low-Power GPS-Disciplined Oscillator Module for Distributed Wireless Sensor Nodes

Many sensor systems, such as distributed wireless sensor arrays, require high-accuracy timing while maintaining low power consumption. Although the capabilities of chip-scale atomic clocks have advanced significantly, their cost continues to be prohibitive for many applications. GPS signals are commonly used to discipline local oscillators in order to inherit the long-term stability of GPS timing; however, commercially available GPS-disciplined oscillators typically use temperature-controlled oscillators and take an extended period of time to reach their stated accuracy, resulting in a large power consumption, usually over a watt. This has subsequently limited their adoption in low-power applications. Modern temperature-compensated crystal oscillators now have stabilities that enable the possibility of duty cycling a GPS receiver and intermittently correcting the oscillator for drift. Based on this principle, a design for a GPS-disciplined oscillator is presented that achieves an accuracy of 5 μs rms in its operational environment, while consuming only 45 mW of average power. The circuit is implemented in a system called geoPebble, which uses a large grid of wireless sensors to perform glacial reflectometry.

Chameleonic Noise in GPS Position Time Series

AbstractIt has been a standard practice for about 2 decades to compute global positioning system (GPS)‐based station velocity uncertainties using the apparent noise statistics of the non‐linear position residuals rather than assume white noise (WN) behavior. The latter choice would yield unrealistic velocity uncertainties. The most common noise types used are power‐law, usually close to flicker noise (FN), over most frequencies mixed with WN at the shortest periods. The complicating impact of offsets in the position time series, mostly caused by equipment changes or tectonic events, has not been fully appreciated. These are far less benign than recently suggested. In addition to contributing a pseudo‐random walk noise (RW) component to the velocity errors, estimating offset parameters changes the apparent noise color toward whiter. Spectral power is effectively drained by offsets at periods longer than roughly the mean span between them. This consequently favors a Gauss‐Markov process as the apparently preferred noise model and, importantly, obscures the presence of RW and long‐period Earth deformation in the series. Both effects can lead to potentially under‐estimated velocity uncertainties. The full value of decadal‐long GPS time series for geodynamical applications is thereby greatly eroded by recurring offsets, especially when they occur quasi‐regularly. In addition, contrary to common assumption, the noise color is generally not fixed with time, but clearly becomes whiter in more recent data. The origin of the colored noise and its whitening over time remain elusive.

Improving long-baseline rapid GPS time transfers by a modified common-view method

We propose a new data analysis process that is referred to as the upsampled common-view (UCV) method, which evolved via the interpolation techniques of portable clock trips and digital signal processing. By interpolating the locally measured global positioning system (GPS) P3 code time offsets to obtain global visible common-view (CV)-like results, we increase the number of data points at each epoch; these points are not restricted to the epoch in which the observations occur. The time transfer results between two laboratories are obtained from a weighted average among all the visible GPS satellites. Daily files of GPS observation data were used in the study. We demonstrate the results of three long-baseline links among the Telecommunication Laboratories (TL) in Asia, the Physikalisch-Technische Bundesanstalt (PTB) in Europe and the United States Naval Observatory (USNO) in North America. The rapid UCV results provide time stability at the level of 100 ps at averaging times around 1 d, which is comparable to the P3 all-in-view (AV) results. Comparing the UCV results with precise point positioning (PPP), the root mean square (RMS) of the double differences for the TL-PTB, TL-USNO and USNO-PTB links are 0.29 ns, 0.38 ns and 0.34 ns, respectively, during a period of 40 d. The low RMS values show that the smooth UCV results are close to the PPP results.

Performance Analysis in Olympic Sailors of the Formula Kite Class Using GPS.

Formula Kite is an Olympic sport that mainly differs from other kitesurfing modalities for the use of a hydrofoil. It is considered an extreme sport due to the great technical ability required. Regarding performance, the variables that determine performance in a real competition situation have not been studied, and even less so with Olympic sailors. Therefore, the objective of this study was to determine the technical and tactical variables that differentiate elite sailors. The sample consisted of 42 Olympic sailors of the Formula Kite class, who were evaluated in three World Cups. Using a GPS device, the speed, distance traveled, maneuvers, and time spent on the courses of upwind, downwind, and beam reach were recorded. The highest-level sailors presented a higher speed in upwind/downwind/beam reach and a shorter time in upwind and beam reach. Performance seems to be more strongly influenced by technical variables, such as speed, than by tactical variables.

GPS time series inversion of the healing process of the middle segment of the Longmenshan fault after the 2008 Wenchuan earthquake

GPS time series inversion of the healing process of the middle segment of the Longmenshan fault after the 2008 Wenchuan earthquake

Feature Extraction Algorithm Using a Correlation Coefficient Combined With the VMD and Its Application to the GPS and GRACE

To improve the reliability of the Global Positioning System (GPS) and Gravity Recovery and Climate Experiment (GRACE) feature extraction, this paper uses a correlation coefficient combined with the traditional variational mode decomposition (VMD), proposing a new correlation variational mode decomposition (CVMD). In contrast to previous studies, the CVMD denoises the sequences before feature extraction and it is the first time that be used in the GPS and GRACE. First, the correlation between the intrinsic mode function (IMF) and the original sequence is obtained to denoise the original sequence. Moreover, the algorithm reuses the VMD to obtain the IMF components with different frequencies. Then the Lomb Scargle (L-S) spectral analysis and energy density are used to obtain the trend-, seasonal, and residual items. Second, the features of the GPS and GRACE time series are extracted based on the CVMD and multidimensional ensemble empirical mode decomposition (MEEMD) to verify the availability of the CVMD. The results indicate that the CVMD is more superior to the MEEMD in feature extraction. Third, the CVMD is used to extract the trend- and seasonal terms of GPS and GRACE in the North China Plain (NCP). The conclusions are as follows: (1) the seasonal items of GRACE are used to correct the GPS sequences, and the average reduction of the weighted root mean square (WRMS) of each GPS station is 0.69, which demonstrates a strong consistency between the seasonal terms of the GPS sequence and GRACE sequence; (2) during 2003-2015, the mean slope of vertical displacements is 0.20 ± 0.07 mm / yr, and the uplift rate increases substantially (1.66 ± 0.62 mm / yr) after 2013. Then, the temporal and spatial relationship between rainfall and crustal load-deformation in the NCP is analyzed, and it is found that the crustal load-deformation is primarily related to rainfall, while human activities play a leading role in the southwestern regions where agricultural irrigation is relatively strong.

Atmospheric pressure loading in GPS positions: dependency on GPS processing methods and effect on assessment of seasonal deformation in the contiguous USA and Alaska

The Global Positioning System (GPS) has revolutionized the ability to monitor Earth-system processes, including Earth’s water cycle. Several analysis centers process GPS data to estimate ground-antenna positions at daily temporal resolution. Differences in processing strategies can lead to inconsistencies in coordinate-position estimates and therefore influence the analysis of crustal displacement associated with variations in atmospheric and hydrologic mass loading. Here, we compare five GPS data products produced by three processing centers: the Nevada Geodetic Laboratory, Jet Propulsion Laboratory, and UNAVCO Consortium. We find that 5 to 30% of the scatter in residual GPS time series (commonly considered noise) can be explained by atmospheric loading in the contiguous USA and Alaska, but that the percentages vary widely by data product. Positions derived using high-resolution troposphere models (e.g., ECMWF) exhibit significantly lower scatter after correcting for atmospheric loading than positions estimated using constant or slowly varying troposphere models (e.g., GPT2w). The data products also exhibit differences in seasonal deformation (commonly attributed, in large part, to fluctuations in hydrologic mass loading): median vector differences in estimated seasonal amplitude range from 0.4–1.0 mm in the vertical component and 0.1–0.3 mm in the horizontal components, or about 10–40% of the mean amplitudes of seasonal oscillation. Newer products exhibit lower total scatter and stronger correlations than older products. Network-coherent differences in estimates of seasonal deformation reveal reference-frame inconsistencies between data products. We also cross-check two independent models of atmospheric pressure loading: ESMGFZ and LoadDef.

Degradation of Kinematic PPP of GNSS Stations in Central Europe Caused by Medium-Scale Traveling Ionospheric Disturbances During the St. Patrick’s Day 2015 Geomagnetic Storm

In solar cycle 24, the strongest geomagnetic storm took place on 17 March 2015, when the geomagnetic activity index was as high as −223 nT. To verify the impact that the storm had on the Global Navigation Satellite System (GNSS)’s positioning accuracy and precision, we used 30-s observations from 15 reference stations located in Central Europe. For each of them, we applied kinematic precise point positioning (PPP) using gLAB software for the day of the storm and, for comparison, for a selected quiet day (13 March 2015). Based on the conducted analyses, we found out that the position root mean square (RMS) values on the day of the geomagnetic storm were significantly high and amounted to several dozen centimeters. The average RMS for the altitude coordinates was 0.58 m between 12:00 and 24:00 (GPS time), and 0.37 and 0.26 m for directions North and East, respectively. The compromised accuracy level was caused by a sudden decrease in the number of satellites used for calculations. This was due to a high number of cycle slips (CSs) detected during this period. The occurrence of these effects was strictly correlated with the appearance of traveling ionospheric disturbances (TIDs). This was proven by analyzing changes in the total electron content (TEC) estimated for each station–satellite pair.

Lateral Control of an Autonomous and Connected Following Vehicle With Limited Preview Information

Lateral control of an autonomous and connected vehicle (ACV), especially in emergency situations, is important from the safety viewpoint. In these situations, the trajectory to be followed by an ACV must either be planned in real-time (e.g., for a possible evasion maneuver if the obstacle to be avoided is detected) or be communicated from its preceding vehicle. Typically, the trajectory information is available to the following ACV in the form of GPS time samples. From the viewpoint of lateral control, the lateral velocity information is not readily available and the feedback structure must reflect this reality. In this paper, we develop a methodology to synthesize a lateral control algorithm for a following ACV in a two-vehicle platoon in two steps: 1) From the limited preview information of the trajectory to be tracked via samples of GPS way points, we estimate the radius of curvature of the trajectory using “least-square” estimation and 2) develop a fixed-structure feedback control scheme for following the predecessor by synthesizing the set of stabilizing gains corresponding to lateral position error, heading error and heading rate error. Numerical simulation and experimental results corroborate the effectiveness of the proposed schemes.

Using Teleseismic P-Wave Arrivals to Calibrate the Clock Drift of Autonomous Underwater Hydrophones

ABSTRACT Networks of autonomous underwater hydrophones (AUHs) are successfully employed for monitoring the low-level seismicity of mid-oceanic ridges by detecting hydroacoustic phases known as T waves. For a precise localization of a seismic event from T-wave arrival times, all AUHs must be synchronized. To this effect, at the beginning of the experiment, all instrument clocks are set to GPS time, which serves as a common reference. However, during the experiment, the instrument clock often deviates from GPS time, and, because the amount of deviation differs from one instrument to another, the synchronization of the AUHs deteriorates, as the experiment progresses in time. Just after the instrument recovery, the time difference (called “skew”) between the instrument and the GPS clocks is measured. Assuming that the skew varies linearly with time, the correction of a time series for the clock drift is a straightforward procedure. When the final skew cannot be determined, correcting for the clock drift is not possible, and any event localization becomes problematic. In this article, we demonstrate that the clock-drift rate (assumed to be time-independent) can be successfully estimated from arrival times of teleseismic P waves, commonly recorded by AUHs. Using a ray-tracing code, and accounting for the uncertainties in event hypocenter locations, origin times, and the Earth seismic-velocity model, confidence intervals of the estimated drift rates are deduced. The validity of the approach is tested on data from two AUHs with known clock drifts. Our results show that a reliable estimation is possible for skews as small as 4 s per two years (corresponding to a drift rate of about 5.5 ms·day−1). This method can also be applied to correct data of other recording instruments subject to internal-clock drift, such as ocean-bottom seismometers, when the skew is unknown.

Triggered crustal earthquake swarm across subduction segment boundary after the 2016 Pedernales, Ecuador megathrust earthquake

Megathrust ruptures and the ensuing postseismic deformation cause stress changes that may induce seismicity on upper plate crustal faults far from the coseismic rupture area. In this study, we analyze seismic swarms that occurred in the north Ecuador area of Esmeraldas, beginning two months after the 2016 Mw 7.8 Pedernales, Ecuador megathrust earthquake. The Esmeraldas region is 70 km from the Pedernales rupture area in a separate segment of the subduction zone. We characterize the Esmeraldas sequence, relocating the events using manual arrival time picks and a local a-priori 3D velocity model. The earthquake locations from the Esmeraldas sequence outline an upper plate fault or shear zone. The sequence contains one major swarm and several smaller swarms. Moment tensor solutions of several events include normal and strike-slip motion and non-double-couple components. During the main swarm, earthquake hypocenters increase in distance from the first event over time, at a rate of a few hundred meters per day, consistent with fluid diffusion. Events with similar waveforms occur within the sequence, and a transient is seen in time series of nearby GPS stations concurrent with the seismicity. The events with similar waveforms and the transient in GPS time series suggest that slow aseismic slip took place along a crustal normal fault during the sequence. Coulomb stress calculations show a positive Coulomb stress change in the Esmeraldas region, consistent with seismicity being triggered by the Pedernales mainshock and large aftershocks. The characteristics of the seismicity indicate that postseismic deformation involving fluid flow and slow slip activated upper plate faults in the Esmeraldas area. These findings suggest the need for further investigation into the seismic hazard potential of shallow upper plate faults and the potential for megathrust earthquakes to trigger slow-slip and shallow seismicity across separate segments of subduction zones.

Tectonic and non-tectonic crustal deformation in Kumaun Garhwal Himalaya

A detailed characterization of the crustal deformation in the Himalaya is important to understand the tectonic and non-tectonic deformation processes responsible for the strain build-up and transients in deformation. In the present work, we have characterised the present day tectonic and non-tectonic deformations in the Kumaun Garhwal Himalaya estimated from the continuous GPS measurements. We observed strong seasonal variations in the horizontal and vertical displacement components (i.e. North, East and Vertical). The transient surface deformation estimated from global hydrological models is found to explain ~40–60% of the observed seasonal variations at sites. Plate convergence rate, and variation of slip deficit on the Main Himalayan Thrust (MHT) are calculated using site velocity estimated after removal of seasonal variations from the GPS time series. We report an excessive compression with an average principal shortening rate of −0.09 μ strain/yr in the north-northeast direction. The derived plate convergence rate is 18 ± 1 mm/yr and the width of locked frontal part of MHT is 100 ± 15 km. The quiescence of major to great earthquakes in the region since at least past 200 years and high rate of strain build up make this region vulnerable for a potentially devastating earthquake of Mw ≥ 8 in near future.

Online detection of offsets in GPS time series

This paper deals with the online offset detection in GPS time series recorded in volcanic areas. The interest for this problem lies in the fact that an offset can indicate the opening of eruptive fissures. A Change Point Detection algorithm is applied to carry out, in an online framework, the offset detection. Experimental results show that the algorithm is able to recognize the offset generated by the Mount Etna eruption, occurred on December 24, 2018, with a delay of about 4 samples, corresponding to 40 min, compared to the best offline detection. Furthermore, analysis of the trade-off between success and false alarms is carried out and discussed.

Effect of antenna snow intrusion on vertical GPS position time series in Antarctica

Vertical surface displacements from continuous Global Positioning System (GPS) stations often show strong seasonal signals, which in some cases may be associated with surface mass loading, including hydrological, and non-tidal oceanic and atmospheric loading. In Antarctica, many GPS stations show vertical motions in phase with seasonal snow accumulation changes, but these variations cannot be fully explained with snow load variations between seasons. Instead we show, for many sites in Antarctica, that a significant component of the annual cycle in vertical GPS coordinates time series may be related to snow/ice inside antennas causing as an artefact apparent seasonal variation, with amplitudes of up to 4 mm. We present a method based on the Empirical Mode Decomposition (EMD) algorithm to remove this artefact signal. The corrected GPS time series show an improvement in the agreement with displacements predicted by elastic modelling using GRACE-derived surface mass loads.

Impacts of Local Effects and Surface Loads on the Common Mode Error Filtering in Continuous GPS Measurements in the Northwest of Yunnan Province, China.

While seasonal hydrological mass loading, derived from Gravity Recovery and Climate Experiment (GRACE) measurements, shows coherent spatial patterns and is an important source for the common mode error (CME) in continuous global positioning system (cGPS) measurements in Yunnan, it is a challenge to quantify local effects and detailed changes in daily GPS measurements by using GRACE data due to its low time and spatial resolutions. In this study, we computed and compared two groups of CMEs for nine cGPS sites in the northwest Yunnan province; rCMEs were computed with the residual cGPS time series having high inter-station correlations, while oCMEs were computed with all the GPS time series. The rCMEs-filtered time series had smaller variances and larger root mean square (RMS) reductions than those that were oCMEs-filtered, and when the stations local effects were not removed, spurious transient-like signals occurred. Compared with hydrological mass loading (HYDL), its combination with non-tidal atmosphere pressure and ocean mass reached a better agreement with the CME in the vertical component, with the Nash–Sutcliffe efficiency (NSE) increasing from 0.28 to 0.55 and the RMS reduction increasing from 15.19% to 33.4%, respectively. Our results suggest that it is necessary to evaluate the inter-station correlation and remove the possible noisy stations before conducting CME filtering, and that one should carefully choose surface loading models to correct the raw cGPS time series if CME filtering is not conducted.

High-rate GPS positioning for tracing anthropogenic seismic activity: The 29 January 2019 mining tremor in Legnica- Głogów Copper District, Poland

High-rate GNSS observations are usually studied in relation to earthquake analysis and structural monitoring. Most of the previous research on short-term dynamic deformations has been limited to natural earthquakes with magnitudes exceeding 5 and amplitudes equal to several dozen centimetres. High-frequency position monitoring via GNSS stations is particularly important in mining areas due to the need to monitor mining damages. On 29 January 2019 (12:53:44 UTC), an M3.7 event occurred in the area of Legnica-Głogów Copper District.This study presents GPS-derived displacement analysis in relation to seismological data. Station position time series were determined by double differencing and Precise Point Positioning. The peak ground displacement was 2–14 mm. The correlation coefficients between GPS and seismological displacement time series reached 0.92. A statistical evaluation of GPS displacement time series was carried out to detect an event using only GPS observations.