Global Navigation Satellite System Time Research Articles

Deep Learning CNN-GRU Method for GNSS Deformation Monitoring Prediction

Hydraulic structures are the key national infrastructures, whose safety and stability are crucial for socio-economic development. Global Navigation Satellite System (GNSS) technology, as a high-precision deformation monitoring method, is of great significance for the safety and stability of hydraulic structures. However, the GNSS time series exhibits characteristics such as high nonlinearity, spatiotemporal correlation, and noise interference, making it difficult to model for prediction. The Neural Networks (CNN) model has strong feature extraction capabilities and translation invariance. However, it remains sensitive to changes in the scale and position of the target and requires large amounts of data. The Gated Recurrent Units (GRU) model could improve the training effectiveness by introducing gate mechanisms, but its ability to model long-term dependencies is limited. This study proposes a combined model, using CNN to extract spatial features and GRU to capture temporal information, to achieve an accurate prediction. The experiment shows that the proposed CNN-GRU model has a better performance, with an improvement of approximately 45%, demonstrating higher accuracy and reliability in predictions for GNSS deformation monitoring. This provides a new feasible solution for the safety monitoring and early warning of hydraulic structures.

Selection of noise models for GNSS coordinate time series based on model averaging algorithm

In the field of global navigation satellite system (GNSS) time series noise analysis, appropriately modeling the noise components plays an important role in determining the velocity of GNSS sites and quantifying the uncertainty associated with the velocity estimation. Over the years, researchers have focused on only one optimal noise model, while other noise models that show similar performance to the optimal model have been ignored. We investigated whether these ignored noise models can be made use of to describe the noise in the GNSS time series after applying a model averaging algorithm. The experimental data were derived from 28 International GNSS Service (IGS) sites in the California region of the United States and 110 IGS sites worldwide. The results showed that for the GNSS time series of 28 IGS sites in the California, 79%, 68%, and 75% of the site components can be applied the model averaging algorithm in the east/north/up (E/N/U) directions, respectively. Based on it, the east direction showed the best performance, with 50% of the site components obtaining more conservative velocity uncertainty after applying the model averaging algorithm compared to the optimal noise model. For GNSS time series of 110 IGS stations worldwide, the model averaging algorithm demonstrates excellent performance in all the E/N/U directions. In the E/N/U directions, 86%, 94%, and 57% of the site components can apply the model averaging algorithm. Building upon this, 77%, 65%, and 62% of the site components achieve more conservative velocity uncertainty in the E/N/U directions compared to the optimal noise model. To fully validate the feasibility of the model averaging algorithm, we also tested GNSS time series of varying lengths and different thresholds of the model averaging algorithm. In summary, the model averaging algorithm performs exceptionally well in the noise analysis of GNSS time series. It helps prevent overly optimistic estimation results.

Extraction of periodic signals in Global Navigation Satellite System (GNSS) vertical coordinate time series using the adaptive ensemble empirical modal decomposition method

Abstract. Empirical modal decomposition (EMD) is an efficient tool for extracting a signal from stationary or non-stationary time series and is enhanced in stability and robustness by ensemble empirical mode decomposition (EEMD). Adaptive EEMD further improves computational efficiency through adaptability in the white noise amplitude and set average number. However, its effectiveness in the periodic signal extraction in Global Navigation Satellite System (GNSS) coordinate time series regarding the inevitable missing data and offset issues has not been comprehensively validated. In order to thoroughly investigate their impacts, we simulated 5 years of daily time series data with different missing data percentages or a different number of offsets and conducted them 300 times for each simulation. The results show that high accuracy could reach the overall random missing rate below 15 % and avoid consecutive misses exceeding 30 d. Meanwhile, offsets should be corrected in advance regardless of their magnitudes. The analysis of the vertical components of 13 stations within the Australian Global Sea Level Observing System (GLOSS) monitoring network demonstrates the advantage of adaptive EEMD in revealing the time-varying characteristics of periodic signals. From the perspectives of correlation coefficients (CCs), root mean square error (RMSE), power spectral density indices (κ) and signal-to-noise ratio (SNR), the means for adaptive EEMD are 0.36, 0.81, −0.18 and 0.48, respectively, while for least squares (LS), they are 0.27, 0.86, −0.50 and 0.23. Meanwhile, a significance test of the residuals further substantiates the effectiveness in periodic signal extraction, which shows that there is no annual signal remaining. Also, the longer the series, the higher the accuracy of the reasonable extracted periodic signal concluded via the significance test. Moreover, driving factors are more effectively facilitated by the time-varying periodic characteristics compared with the constant periodic signal derived by LS. Overall, the application of adaptive EEMD could achieve high accuracy in analyzing GNSS time series, but it should be based on properly dealing with missing data and offsets.

Comparison of Low-Cost GNSS Receivers for Time Transfer using Zero-Length Baseline

Abstract A comparison between low-cost single-frequency and dual-frequency Global Navigation Satellite System (GNSS) receiver timing modules is presented, focusing on their suitability for time transfer applications. The study uses a zero-length baseline measurement approach to assess their performance and highlights the advantages of dual-frequency receivers. The clock comparison residuals between these low-cost devices and a reference receiver are analyzed. In particular, it is shown that the use of averages longer than 200s can effectively mitigate the quantization error inherent in pulse per second outputs of the timing modules. The results showcase sub-nanosecond time deviation instabilities between the reference receiver and the dual-frequency timing module. In contrast, the single-frequency module exhibits time deviations of 3.3ns at a one-day averaging interval. This research provides insights into the selection and utilization of GNSS timing modules for time transfer applications, where such modules can serve as attractive, cost-effective alternatives for applications requiring moderate accuracy.

Real-time clock estimation using system time offset maintenance aiming at multi-GNSS time interoperability

Time interoperability is one of the important aspects of Global Navigation Satellite System (GNSS) compatibility and interoperability, which will greatly benefit the accuracy and availability of the positioning, navigation and timing (PNT) solution. In this paper, we proposed a real-time satellite clock estimation method using system time offset (STO) maintenance to help users realize GNSS time interoperability. First, receiver inter-system bias (ISB) was investigated and modeled for STO maintenance. Then, we presented clock estimation assessment results, which demonstrate that the new method can make the satellite clock product maintain a stable STO. Finally, precise point positioning (PPP) was used for further validation. The results show that in the condition of a 45° cutoff elevation angle, fixing the ISB can significantly reduce the convergence time, increase the availability by 21.5%, and improve the average positioning accuracy in horizontal and vertical by 37.7% and 44.4%, respectively.

Evaluation of receiver calibration based on clock-steering for time–frequency transfer

Calibrating the global navigation satellite system (GNSS) time–frequency transfer system is crucial for accurate GNSS time–frequency transfer. The most commonly used relative calibration method relies on the common-clock to eliminate clock differences. However, it cannot eliminate the changes in clock signal reference point delay (REFDLY). The changes in REFDLY during calibration could not be ignored, especially for ordinary users in an unstable environment. To address this issue, we use the GNSS real-time single-difference time synchronization calibration based on clock-steering, which can detect the change in REFDLY. According to this method, the clock differences and REFDLY are eliminated simultaneously. We installed two GNSS antennas on the roof of the Xinghu Building of Wuhan University and designed a clock synchronization terminal to evaluate the performance of this method. The data were collected on Day of Year 152–156, 167–171, 222–226, 231–235, 244, 258, 260, and 262 in 2022. In accordance with the calibration results, the standard deviation better than 100 ps, and the stability reaches 10−15@10000s . Also, the time variance better than 60 ps, and the uncertainty uCAL better than 0.5 ns. Compared to the common-clock calibration, one of the most significant benefits is the elimination of REFDLY, which leads to decreased uncertainty and better stability over both the short-term and long-term.

Localized uplift, widespread subsidence, and implications for sea level rise in the NewYork City metropolitan area.

Regional relative sea level rise is exacerbating flooding hazards in the coastal zone. In addition to changes in the ocean, vertical land motion (VLM) is a driver of spatial variation in sea level change that can either diminish or enhance flood risk. Here, we apply state-of-the-art interferometric synthetic aperture radar and global navigation satellite system time series analysis to estimate velocities and corresponding uncertainties at 30-m resolution in the NewYork City metropolitan area, revealing VLM with unprecedented detail. We find broad subsidence of 1.6 mm/year, consistent with glacial isostatic adjustment to the melting of the former ice sheets, and previously undocumented hot spots of both subsidence and uplift that can be physically explained in some locations. Our results inform ongoing efforts to adapt to sea level rise and reveal points of VLM that motivate both future scientific investigations into surface geology and assessments of engineering projects.

Global Navigation Satellite Systems disciplined oscillator synchronisation of multistatic radar

AbstractA fundamental challenge in the practical implementation of multistatic radar systems (MSRS) is the requirement for precise time and frequency synchronisation between the spatially separated radar nodes. The authors evaluate the performance of different classes of commercially available Global Navigation Satellite Systems (GNSS) timing receivers, Local Oscillators (LO) and GNSS Disciplined Oscillators (GNSSDOs) to determine the limitations of using one‐way GNSS Time and Frequency Transfer (TFT) in this application. From evaluating the performance of three pairs of GNSSDOs, it is concluded that one‐way GNSS TFT will likely be suitable only for the synchronisation of fully spatially coherent MSRS with carrier frequencies up to 100 MHz and waveform bandwidths up to 20 MHz. Whereas, in the case of short‐term spatially coherent MSRS, synchronisation of systems with carrier frequencies up to a few GHz and waveform bandwidths of over 100 MHz will likely be possible. The performance of the different classes of GNSSDOs during GNSS denial (holdover) are evaluated, where it is concluded that frequency offsets between LOs at the point of GNSS denial will often significantly contribute, or even dominate, the holdover performance. Analysis of two practical multistatic radar measurements verifies the function of using the GNSSDOs for wireless synchronisation of the ARESTOR MSRS.

Precise GNSS Time Synchronization With Experimental Validation in Vehicular Networks

Time synchronization utilizing the Global Navigation Satellite System (GNSS) is being increasingly investigated for vehicular networks. Due to GNSS signal blockages, the availability and accuracy of GNSS timing solutions in various road settings is a recognized challenge. With the recent improvement of Multi-GNSS technology and the increased capacity of consumer-grade receivers, the application of GNSS in vehicular environments has brightened up. This paper systematically analyzes the required time synchronization of vehicular networks and presents a GNSS-based time synchronization solution. It also experimentally demonstrates the availability and capabilities of GNSS time synchronization using commercial-grade GNSS receivers and off-the-shelf communication devices. Our experiments show that the timing accuracy of an individual vehicular node can be as good as ±2 microseconds, resulting in synchronization accuracy of sub-10 microseconds among nodes. A momentary complete outage of the GNSS time solution due to signal blockage on the road adds clock error, leading to synchronization inaccuracy of up to sub-20 microseconds. This level of inaccuracy still meets the desired requirement for most applications in vehicular communication.

Joint Bayesian Modeling of Velocity Break Points, Noise Characteristics, and Their Uncertainties in GNSS Time Series: Far‐Field Velocity Anomalies Concurrent With Magmatic Activity in Iceland

AbstractEstimating the timing of velocity changes (break points) in Global Navigation Satellite System (GNSS) coordinate time series is required for understanding various Earth processes and how they may couple with each other. We jointly estimate break points, noise parameters and their uncertainties in GNSS time series using Bayesian interference. Synthetic data experiments demonstrate that time‐correlated noise can cause spurious estimates of break points for small velocity change and suggest the lower limits of velocity change for reliable estimates. A case study at the Krafla volcanic system shows increased rift‐perpendicular movementof 7.6–9.8 mm/yr, preceding by 23–77 days the 2014 Bárðarbunga rifting episode that occurred ∼120 km to the south (maximum likelihood estimates). These far‐field velocity anomalies occur in the same period as enhanced near‐field seismicity and deformation before the dike intrusion at Bárðarbunga, possibly indicating the coupling between the two volcanic systems through a deep partial melt zone.

Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

Singular spectrum analysis is widely used in geodetic time series analysis. However, when extracting time-varying periodic signals from a large number of Global Navigation Satellite System (GNSS) time series, the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient. To improve the efficiency and accuracy of singular spectrum analysis, this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix. The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series, and the extraction efficiency of a single time series is six times that of singular spectrum analysis. The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.

A Multi-Global Navigation Satellite System (GNSS) Time Transfer Method with Federated Kalman Filter (FKF)

Relative to single Global Navigation Satellite System (GNSS) measurements, i.e., the measurements from a single GNSS system, a single GNSS code, and a single GNSS receiver, multi-GNSS measurements for time transfer could improve reliability and provide better short-term stability. Previous studies applied equal weighting to different GNSS systems or different GNSS time transfer receivers, which, to some extent, revealed the improvement in the additional short-term stability from the combination of two or more kinds of GNSS measurements. In this study, the effects of the different weight allocation for multi-measurements of GNSS time transfer were analyzed, and a federated Kalman filter was designed and applied to fuse multi-GNSS measurements combined with the standard-deviation-allocated weight. Tests with real data showed that the proposed approach can reduce the noise level to well below about 250 ps for short averaging times.

The Separate Clock Drift Matched Filter to Detect Time Synchronization Attacks Toward Global Navigation Satellite Systems

This article is concerned with the security problem of industrial networks. Smart grids, telecommunications, and many other wide-area networks heavily depend on the time synchronization service of the Global Navigation Satellite System (GNSS). This service is exposed to the Time Synchronization Attack (TSA) which can spoof GNSS timing results and bring serious consequences. Therefore, to improve the time security of networks, a novel TSA detection method named the Separate Clock Drift Matched Filter (SCD-MF) is introduced. It aims at concealed TSA signals that won't bring conspicuous abnormalities in positioning or timing solutions. This method works by monitoring the synchronicity of signal pseudorange measurements, which are expected to be synchronously changed by concealed TSA signals. This article also presents real-world experiment results. TSA detection experiments are done on a self-developed testbed that contains a real-time TSA spoofer. Compared with two benchmark methods, the SCD-MF shows better detection abilities in different conditions. Moreover, the detection performance of the SCD-MF method is analyzed both theoretically and experimentally.

Function Model Based on Nonlinear Transient Rheology of Rocks: An Analysis of Decadal GNSS Time Series After the 2011 Tohoku‐oki Earthquake

AbstractThe postseismic Global Navigation Satellite System (GNSS) time series after the 2011 Tohoku‐oki earthquake is often empirically explained by one or more logarithmic and exponential decay functions. However, a function model with these decay functions struggles to illuminate various deformation mechanisms. Here, we propose a new function model incorporating laboratory‐derived constitutive laws (power‐law flow and velocity‐strengthening friction) utilized in mechanical postseismic models of the last decade. We demonstrated that our function model accurately predicts the decade‐long time series of inland GNSS stations, including coastal areas where significant postseismic uplift continues now. Moreover, it decomposes them into displacements due to viscoelastic relaxation and afterslip, similar to results produced by previous stress‐dependent postseismic models of the 2011 Tohoku‐oki earthquake. This physics‐based function model is an effective tool to ease the process of forecasting long‐term GNSS time series by dividing them into two dominant mechanisms at the plate interface and the surrounding viscoelastic mantle.

Accuracy Enhancement and Feature Extraction for GNSS Daily Time Series Using Adaptive CEEMD-Multi-PCA-Based Filter

Global navigation satellite system (GNSS) positions include various useful signals and some unmodeled errors. In order to enhance the accuracy and extract the features of the GNSS daily time sequence, an improved method of complete ensemble empirical mode decomposition (CEEMD) and multi-PCA (MPCA) based on correlation coefficients and block spatial filtering was proposed. The results showed that the mean standard deviations of the raw residual time sequence were 1.09, 1.20 and 4.79 mm, while those of the newly proposed method were 0.15, 0.20 and 2.86 mm in north, east and up directions, respectively. The proposed method outperforms wavelet decomposition (WD)-PCA and empirical mode decomposition (EMD)-PCA in effectively eliminating low- and high-frequency noise, and is suitable for denoising nonlinear and nonstationary GNSS position sequences. Furthermore, feature extraction of the denoised GNSS daily time series was based on CEEMD, which is superior to WD and EMD. Results of noise analysis suggested that the noise components in the original and denoised GNSS time sequence are complex. The advantages of the proposed method are the following: (i) it fully exploits the merits of CEEMD and WD, where CEEMD is first used to obtain the limited intrinsic modal functions (IMFs) and then to extract seasonal and trend features; (ii) it has good adaptive processing ability via WD for noise-dominant IMFs; and (iii) it fully considers the correlation between the different components of each station and the non-uniform behavior of common mode error on a spatial scale.

Wavelet-like denoising of GNSS data through machine learning. Application to the time series of the Campi Flegrei volcanic area (Southern Italy)

The great potential of the Global Navigation Satellite System (GNSS) in monitoring ground deformation is widely recognized. As with other geophysical data, GNSS time series can be significantly noisy, hiding elusive ground deformation signals. Several denoising techniques have been proposed to improve the signal-to-noise ratio over the years. One of the most effective denoising techniques has been proved to be multi-resolution decomposition through the discrete wavelet transform. However, wavelet analysis requires long data sets to be effective, as well as long computation times, that hinder its use as a real or near real-time monitoring tool. We propose training by a Convolutional Neural Network (CNN) to perform the equivalent of wavelet analysis to overcome these limitations. Once trained, the CNN model provides answers within seconds, making it feasible as a real-time data analysis tool. Our Machine Learning algorithm is tested on daily GNSS time series collected in the Campi Flegrei caldera (Southern Italy), which is a highly volcanic risk area. Without significant gaps, the retrieved RMSE and R2 values vary in the ranges 0.65–0.98 and 0.06–0.52 cm, respectively. These results are encouraging, as they hint at the possibility of applying this methodology in more effective real-time monitoring solutions for active volcanoes.

A method and its validation for measuring the absolute time-delay of the read-out system of a space electrostatic accelerometer.

High-precision accelerometers play an important role in satellite gravity field missions to measure the non-conservative forces acting on the satellites. To map the Earth's gravity field, the accelerometer data must be time-tagged using the on-board global navigation satellite system time reference. For example, in the Gravity Recovery and Climate Experiment mission, the time-tag error of the accelerometers must be within 0.1ms with respect to the satellite clock. To realize this requirement, the time delay between the actual measurement time and the nominal time of the accelerometer should be considered and corrected. This paper presents the techniques for measuring the absolute time delay of an electrostatic accelerometer on the ground, where this delay is mainly introduced by the low-noise scientific data read-out system, which is based on a Σ-Δ (sigma-delta) analog-to-digital converter (ADC). First, the time-delay sources of the system are theoretically analyzed. Then, a time-delay measurement method is proposed, and its principle and system error are presented. Finally, a prototype is built to demonstrate and investigate the feasibility of the method. Experimental results show that the absolute time delay of the read-out system is 150.80 ± 0.04ms. This important value is the basis for the final time-tag error correction of the scientific accelerometer data. Meanwhile, the time-delay measurement method described in this paper is also useful for other data acquisition systems.

A Temporal and Spatial Denoising Method for Intelligent Settlement Sensing System

Global Navigation Satellite System (GNSS) has the ability to provide timely structural settlement information and been widely installed on the critical infrastructures. However, the inevitable noise negatively affects the accurate assessment, measurement and evaluation of the status. Although some methods have been developed in previous studies, fully mining the temporal and spatial correlations is still necessary to further analyze. Therefore, we propose a new denoising method based on truncated high-order singular value decomposition to reduce the noise in multivariate GNSS signals. Using synthetic signals and real-world GNSS signals, the proposed method is evaluated by comparison with some benchmark models. The results show that the proposed method can effectively reduce both white noise (WN) and flicker noise (FN). Moreover, experiments on the signal-noise ratio (SNR) from 1 to 10 demonstrate that the proposed method can achieve stable performances for GNSS time series denoising. The organization of GNSS signals as the high-dimensional tensor has been proved to be an effective analytical tool to mine the complicated spatial and temporal correlations.

A VMD-PE-SG denoising method based on K–L divergence for satellite atomic clock

The time scale of the global navigation satellite system (GNSS) is the core element for its position, navigation and timing services. A highly stable atomic clock is essential to ensure the reliability of the GNSS time scale. This study proposed a novel hybrid denoising model combining variational mode decomposition (VMD), K–L divergence, permutation entropy (PE), and Savitzky–Golay (SG) filter for satellite atomic clocks. Firstly, the key parameter of VMD is solved efficiently by taking the minimum sum of K–L divergence of decomposed modes as the constraint condition, and the optimised parameters are applied to the decomposition process. On this basis, the PE algorithm is used to determine the modes decomposed by VMD into signal-dominant and noise-dominant components by searching for the mutation of PE value at two adjacent points. Finally, the noise-dominant components are denoised by the SG filter and then reconstructed with the signal-dominant components to form the denoised signal. The analysis of the simulated signal shows that the method can effectively remove noise from the simulated signal, and the resulting denoised signal is similar to the pure signal. Compared with commonly used ensemble empirical mode decomposition and wavelet denoising methods, the signal-noise ratio of the proposed method is improved by 21.2% and 28.9%, and the root mean square error is improved by 24.1% and 29.8%, respectively. The results of experimental data testify that the K–L VMD-PE-SG-based denoising method can significantly reduce the dominant noise within one day, thus effectively improving the short to medium-term frequency stability. Compared with the original signal, the stability of the smoothing time within 76 800 s is generally improved, and the degree of improvement depends on the type of atomic clock and the smoothing time.

Geodetic evidence of land subsidence in Cirebon, Indonesia

The subsidence phenomena occur in numerous cities in Indonesia (Jakarta, Bandung, and Semarang) and have been observed over the last few decades using geodetic techniques such as interferometric synthetic aperture radar (InSAR) and the Global Navigation Satellite System (GNSS). Three variables are considered the leading causes of substantial subsidence in those cities: urban development, excessive groundwater removal, and geological context. Considering these considerations, we assess surface displacement in the surrounding area of Cirebon, Indonesia, which has similar background circumstances. We used 43 Sentinel-1A images covering from 2014 to 2021 and processed them using the small baseline subset (SBAS) method obtaining 78 interferograms for time series analysis. A weighted correction from two weather models was used to correct tropospheric errors. The results from the InSAR time series were compared with the continuous GNSS time series (2010–2021) processed using GAMIT/GLOBK GNSS processing softwares. Cirebon experienced a slow land subsidence rate with an average magnitude of -2.6 mm/yr. Furthermore, we underline that more significant subsidence rates were found in several locations. Conic-shaped subsidence with a diameter of around 1 km was observed in a highly inhabited area, with a maximum rate of up to -17 mm/yr near the cone’s center. We also found more prominent land subsidence along the coastline with magnitudes up to -25 mm/yr. Surface lowering with a magnitude of up to -32 mm/yr also affects power plant regions close to Cirebon city. Meanwhile, the fastest subsidence rate was observed over the salt evaporation field area of about -50 mm/yr. We attribute the natural and anthropogenic factors to causing the subsidence in this area.