Search

• Automatic selection of embedding dimension in Singular spectrum analysis is achieved. • Singular spectrum analysis yields the most stable and accurate sea level heights among the methods. • Singular spectrum analysis provides a better concentration of spectral power in the periodogram. In order to obtain reliable GNSS-R derived sea level heights (SLHs), it is crucial to extract accurate reflected signals from signal-to-noise ratio (SNR) data. In this study, Quadratic Fitting, Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), and Singular Spectrum Analysis (SSA) are adopted for extracting the reflected signals from SNR data, which are then analyzed with Lomb Scargle Periodogram (LSP) assisted with tidal harmonic analysis for GNSS-R SLHs. Three continuous GNSS stations including Onsala in Sweden, Friday Harbor in the United States, and Brest in France with tidal ranges of approximately 1 m, 3 m, and 7 m, respectively, were used in the study. The derived SLHs were evaluated against the nearby or co-located tide gauge records. The results reveal that the three proposed algorithms effectively cope with the multi-peaks spectrum problems when using the conventional Quadratic Fitting without a priori reflected height constraint, and SSA can provide the solutions with fewer outliers among the proposed methods with the RMSEs of 6.7 cm, 13.4 cm and 39.6 cm at Onsala, Friday Harbor, and Brest stations, respectively. Without implementing tidal harmonic analysis, SSA is the method capable of acquiring reliable SLHs among the stations, as evidenced by comparing with co-located gauge records, particularly at the Brest station. In summary, SSA not only distinguishes signals across different frequencies, but also orders the signal components according to their eigenvalues, demonstrating the potential to extract the reflected signals from SNR and enhance the stability and accuracy of GNSS-R applications. [ABSTRACT FROM AUTHOR]

Real-time estimates of the Earth orientation parameters (EOP) are currently unavailable for users owing to the delay caused by complex data processing and heavy computation procedures. Accurate short-term predictions of the EOP are therefore essential for several real-time applications such as navigation and tracking of interplanetary spacecrafts and precise orbit determination of Earth satellites, whilst medium- and long-term predictions are required for Global Navigation Satellite System (GNSS) autonomous satellite navigation, climate forecasting as well as for astrogeodynamic studies. Universal time (UT1 – UTC) or its first time derivative, length of day (ΔLOD), representing the changes of the Earth's rotation rate, are the most challenging to predict among the EOP. Various methods and techniques have been used to improve ΔLOD predictions since the present prediction accuracy is yet unsatisfactory even up a few days into the future. This study employs a popular time-series analysis method, called singular spectrum analysis (SSA), in combination with the neural network (NN) technique for medium- and long-term prediction of ΔLOD up to 2 years in the future. The SSA is first applied to extracting the predominant periodic components including annual and semiannual oscillations and irregular short-period signals in ΔLOD data. These extracted predominant periodic components are then extrapolated by the proposed SSA-based data filling strategy. Next, the residuals (the difference between these predominant components and the data themselves) are modeled and predicted by the NN technique. The predicted ΔLOD value is sum of the extrapolation of the predominant periodic components and the prediction of the residuals. The results show that the accuracy of the 180-day ahead predictions is worse than that by the combination of least squares (LS) extrapolation and a stochastic method including autoregressive and NN technology in terms of the mean absolute prediction error. However, the proposed SSA extrapolation in combination with NN modeling can achieve a noticeably better accuracy for the medium- and long-term predictions out 180 days than the combined LS + stochastic technology. The improvement in the prediction accuracy for lead time of 1 year and 2 years can reach up to 53% and 56%, respectively. The combined SSA extrapolation and NN modeling is thus very promising for medium- and long-term prediction of ΔLOD. [ABSTRACT FROM AUTHOR]

In recent years, the Global Navigation Satellite System (GNSS) has witnessed rapid development. However, during the sandstorm season, the precipitable water vapor (PWVGNSS) determined from the GNSS data produces large fluctuations due to the influence of particulate matter, which can indirectly reflect the change in particulate matter concentration. To study the variations of PWVGNSS during the sandstorm season, daily data of PWVGNSS, particulate matter (PM10), and precipitation in Wuhai from 2017 to 2021 were used in this study. The principal components of PWV residual (PWVRPC) were obtained by using the least-squares linear fitting, singular spectrum analysis, and least-squares spectral analysis on PWVGNSS. The principal components of PM10 (PM10PC) were obtained by using least squares linear fitting and singular spectrum analysis for PM10. This study performed a correlation analysis of PWVRPC with PM10PC and precipitation data. The results showed a strong correlation between PWVRPC and PM10PC, with a correlation coefficient greater than 0.6. However, it was found that the correlation between PWVRPC and precipitation was not significant. This indicates that during the sandstorm season, PM10 affects PWV determined from GNSS data. [ABSTRACT FROM AUTHOR]

In Global Navigation Satellite System Reflectometry (GNSS-R), SNR spectrum analysis is widely used for surface altimetry inversion because of its low cost and easy operation. However, this method is somewhat limited in environmental situations with large tidal variations in sea level. In this paper, we implemented a machine learning approach to retrieve sea level height using three feature parameters of frequency, amplitude, and phase extracted by GNSS-R as inputs for the support vector regression (SVR) model, achieving better robustness in environments with large tidal variations. In this experiment, two stations, SC02 and BRST, were selected for research comparison, in which the sea surface fluctuation at the SC02 station was smaller at around 3 m while the sea surface fluctuation at the BRST station was larger at around 7 m. Global Navigation Satellite System (GNSS) observations were selected for 6 months for use to perform the assessment. The SC02 station improved 25.64% and 24.05% in the accuracy of RMSE (14.5 cm) and MAE (12.0 cm), respectively, using the SVR model compared to the conventional method (CM). In the environment with large sea level tidal fluctuations, the BRST station improved accuracy by 17.32% and 15.81% using the SVR model compared to the CM for RMSE (25.3 cm) and MAE (21.3 cm), respectively. It is shown that the SVR model is robust for sea level height retrieval with large tidal variations and that these three feature parameters, including frequency, amplitude, and phase extracted by GNSS-R, are crucial for optimizing sea surface height retrieval. [ABSTRACT FROM AUTHOR]

The singular spectrum analysis (SSA) is a powerful tool to de-noise the geodetic time series and extract geophysical signals of interest. However, when missing data exists in geodetic time series, the ordinary SSA cannot be directly used to process them. Moreover, the heterogeneous properties of the geodetic time series are usually not considered in ordinary SSA, though their formal errors are provided beforehand. In this contribution, we develop an extended singular spectrum analysis (ESSA) to directly process the incomplete and heterogeneous geodetic time series. To validate the proposed approach, we select the 27 vertical position time series of GNSS permanent stations located in the Chinese mainland for analysis, and the results are compared with that of the improved SSA (ISSA, Shen et al. in Nonlinear Process Geophys 22(4):371–376, 2015) which is an effective approach for analyzing the time series with missing data. The results show that (i) our ESSA method performs faster than ISSA, with mean reductions in computation time by 40.14% for 27 stations; moreover, the time consumption of ISSA is more sensitive to the window size and the length of observations than that of ESSA; (ii) the ESSA method can extract more signals than ISSA in terms of fitting errors and root-mean-square ratios of extracted signals over residuals, specifically for the consideration of formal errors. The power spectrum analysis shows that the power of annual oscillation extracted by ESSA is stronger than that by ISSA; (iii) the repeated simulations based on the real data further demonstrate that the signals extracted by ESSA are closer to the true signals than ISSA, and the accuracy improvement is portal to the percentage of data missing. [ABSTRACT FROM AUTHOR]

Global navigation satellite system reflectometry(GNSS-R)has shown great potential in surface and marine environment parameters monitoring, with the advantages of extensive data sources, low cost, high spatial and temporal resolution, and has become an important approach for sea surface height(SSH)inversion. The existing research mainly focuses on the short-term GPS sea surface inversion within 3-6 months, which is difficult to reflect the seasonal variation and interannual characteristics of SSH. Meanwhile, only the influence of vertical velocity is considered in the dynamic sea surface correction, and the vertical acceleration of sea surface fluctuation is ignored, resulting in the poor estimation accuracy of low and high tide levels. For the above issues, a shore-based tracking station BRST in France was taken as an example, and the reflected signals of 3 consecutive years from BDS/GPS/GLONASS/Galileo system were used to estimate SSH. Based on Lomb-Scargle spectrum analysis and second-order dynamic tide level correction model, a robust regression strategy was adopted. The estimation results were compared with tide gauge records to analyze the trend of sea level change. The results show that the inversion results of GNSS-R technology are in good agreement with tide gauge records, and the inversion accuracy has a tendency to improve year by year, with a root mean square error(RMSE)of 7.57 cm and a correlation coefficient of 0.935 for the three-year daily average; the seasonal variation of SSH is obvious, the average SSH is high in autumn and winter, and low in summer, and the seasonal variation of SSH is opposite to that of temperature; the differences of amplitude for nine tidal constituents including M2, S2, K1, O1, N2, K2, P1, Q1 and M4, range from 0.06 cm to 6.76 cm with the mean absolute error(MAE)of 1.60 cm, and the differences of phase range from 0.03° to 6.96° with the MAE of 2.45°. It is further verified that the reliability of GNSS-R technology in monitoring SSH change in the frequency domain. [ABSTRACT FROM AUTHOR]

Objectives: There are obvious seasonal variations in the GPS height time series, which affect the improvement of precision and can be corrected by both mathematical modelling and geophysical mechanisms. Compared to least square fitting, singular spectrum analysis (SSA) can extract random seasonal signals effectively through signal reconstruction, which is unaffected by the assumed sinusoidal waves. According to the elastic loading theory, the gravity recovery and climate experiment (GRACE) can be used to calculate the vertical surface displacement caused by changes in terrestrial water storage. Methods: This paper mainly studies the feasibility of correcting the seasonal variations in GPS heights using SSA and GRACE inversion results. The height time series of 27 GPS stations in Australia with a time span of from 5 to 10 years were chosen and combined with GRACE simultaneous inversions. Results: Because the spatial resolutions of GRACE are coarse and the loading displacement is much more sensitive to near‑field mass changes than far‑field ones, the amplitudes of GRACE ‑inferred hydrological loading deformations are significantly smaller than GPS. The weighted root mean square (WRMS) are reduced at 22 stations after GRACE ‑inferred displacement corrections, and the correlation coefficients between deformations estimated by GPS and GRACE range from 0.12 to 0.78 with a mean value of 0.43, indicating that GPS and GRACE results have good consistency and correlation. SSA is used to extract the annual signals of vertical displacements derived from GPS and GRACE, and contribution rates of singular spectral variance of annual signals are 21.60% and 34.48%, respectively, expressing that annual signals are the main components of GRACE inferred results. Geographical climatic conditions have a significant impact on the consistency of annual signals derived from GPS and GRACE. Compared with the arid areas in central and western Australia, the amplitude and phase of annual signals derived from GPS and GRACE are more consistent in the northern region with seasonal rainfall. Furthermore, cross wavelet transform (XWT) finds that the vertical displacement series derived from GPS and GRACE of each station have a significant resonance period of one year. The circular average phase angles of GPS/GRACE at the period closet to 1 cycle per year (cpy) outside the cone of influence range from − 74.03° to 67.23° . The mean XWT ‑ based semblances range from 0.28 to 0.99 with an average value of 0.79, showing that there is a significant positive correlation between the annual variations derived from GPS and GRACE. Conclusions: Overall, GRACE‑inferred deformations can explain the annual variations of GPS‑derived displacements, particularly in areas with high hydrological loading. It is possible to correct the annual signals of GPS heights by GRACE inversions, but the effect is not as good as the SSA‑filtered annual signals. [ABSTRACT FROM AUTHOR]

Continuous monitoring of ionospheric behavior and subsequent development or improvement of models for the prediction of its parameters with consistent accuracy remains an ongoing challenge. In this sense, an integrated approach by combining the signal extraction technique Singular Spectrum Analysis (SSA) with Autoregressive Moving Average (ARMA) is presented in this work to predict the ionospheric Total Electron Content (TEC) values that are responsible for causing ionospheric delays in the trans-ionospheric signal propagation associated with satellite-based communication, navigation, and timing applications. In general, SSA is a nonparametric spectral estimation procedure that decomposes the signals into interpretable and physically significant components. The observed TEC from two Global Positioning System (GPS) stations across the low latitude Saudi Arabian region are considered during the year 2017 that falls in the descending phase of solar cycle-24. The performance of the proposed hybrid model is evaluated by comparing with the sole estimation from the ARMA model and the observed GPS–TEC dataset for two different geomagnetic conditions: a) the regular geomagnetically quiet period of 15 to 29 December, 2017 (Ap < 24 and Dst > − 30 nT) and b) the geomagnetic storm period from 7 to 9 September, 2017 (Dst min = − 142 nT). The corresponding average Precision, Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) of the proposed SSA–ARMA model predictions are 1.79 TECU, 1.23 TECU, and 13.02%. In contrast, the respective values in the exclusive ARMA model are 2.01 TECU, 1.37 TECU, 14.42% at Oman station. The corresponding values for Magna station are 0.92 TECU, 0.61 TECU, and 10.76% (SSA–ARMA) and 1.01 TECU, 0.75 TECU, and 11.33% (ARMA). The results show an improved computational efficiency with minor improvement in the TEC predictions with the proposed SSA–ARMA method compared to the sole employment of the ARMA model by disregarding the extraneous components. [ABSTRACT FROM AUTHOR]

• This study proposes a novel sidereal filtering algorithm for accurate extraction of GPS multipath errors that can obtain precision displacements in a harsh environment. • The algorithm incorporates dynamic time warping (DTW) for separating gross errors and gross error-like multipath (GEM) from the data, enabling effective multipath modeling. • MSSA is utilized to extract the multipath errors considering the correlation between different components of the measurement matrix. • The proposed weighted fusion (WF) algorithm addresses the effects of missing data on multipath extraction, providing a reliable and comprehensive multipath correction model. Multipath is a significant obstacle to achieving high-precision deformation monitoring using the Global Positioning System (GPS) technique. Sidereal filtering (SF) can mitigate GPS multipath effects based on the multipath models derived from historical measurements, but its practical application in complex scenarios is still challenging due to unavoidable gross errors and missing data problems. In this paper, an improved SF algorithm is proposed that accurately extracts multipath immune to the effects of gross errors and missing values in historical measurements, aiming to obtain accurate displacements in a harsh environment. Specifically, a gross error detection method is first developed based on the dynamic time warping (DTW) algorithm to filter gross errors. Then, we adopt the multichannel singular spectrum analysis (MSSA) algorithm to extract initial multipath errors. Finally, we propose a weighted fusion (WF) algorithm to eliminate the impact of missing values and obtain the final multipath sequences. Extensive experiments with datasets collected from a real-world landslide, including both stable and sliding stations, demonstrate the effectiveness of our proposed method. Results show that compared with the traditional SF method, our proposed method can effectively mitigate the effects of gross errors and missing values on multipath modeling, with the multipath filtering accuracy improving by approximately 12% and 21% for stable and sliding scenarios, respectively. [ABSTRACT FROM AUTHOR]

In order to effectively extract useful information from time series of the global naviga- tion satellite system(GNSS) sites, and improve the modeling accuracy of coordinate time series, this paper proposes a nonlinear motion modeling method combining wavelet decomposition and singular spectrum analysis. Experiments were carried out using global positioning system(GPS) vertical coordinate time series of 11 stations around the world from 1999 to 2018. Methods: Firstly, the coordinate time series is decom-posed into different scales by wavelet decomposition.And then the singular spectrum analysis(SSA) is per- formed on the high-frequency part and the low -frequency part of each layer. Finally, combine the fitting value that is the fitting coordinate time series, and the fitting effect of the new method was evaluated. Results: The results show that, compared with the simple singular spectrum analysis method, the new method can extract useful information such as trend and period more accurately from the limited scale of the time series with noise. And reduce the partial period items in the singular spectrum analysis method to some extent, for example, the seasonal period item and the monthly period item are regarded as the probability of noise rejec- tion, and the modeling accuracy is improved by 26%. Conclusions: The purpose is to propose a nonlinear motion modeling method based on wavelet decomposition and singular spectrum analysis, so as to improve the modeling accuracy of coordinate time series. [ABSTRACT FROM AUTHOR]

Ionospheric modeling across the Indian low latitudes continues to be a challenging task because of the day-to-day variability pertaining to the underlying complex equatorial and low latitude electrodynamics. In this paper, we aimed at developing an ionospheric Total Electron Content (TEC) model based on Singular Spectrum Analysis (SSA) using the Global Positioning System (GPS)-TEC observations (from 2009 to 2019) at Bengaluru (Geographic: 13.02° N, 77.57° E; Dip Angle: 13.77° N), a low latitude station in India. SSA has the most significant advantage of extracting information from the noisy time-series data with the first-four SSA modes in the decomposition, almost converging to total variance of about 99%. The proposed SSA-TEC model has been assessed by comparing it with the GPS-TEC observations as well as the outcomes from the latest version of the International Reference Ionosphere model (IRI-2016) and International GNSS Services Global Ionosphere Maps (IGS-GIM). The results demonstrate excellent outcomes with the Root Mean Square Error (RMSE) values between observed and model estimations laying at 1.58 TECU (SSA), 7.04 TECU (IRI-2016), and 8.89 TECU (GIM) with the respective correlation coefficients 0.99, 0.91, and 0.94. The model outcomes are in good agreement with the GPS-TEC observations, presenting relatively better estimates of TEC than the IRI-2016 and GIM during the geomagnetically quiet and disturbed daytime and nighttime conditions under different seasons and solar activity. Moreover, the proposed SSA-TEC model replicates the significant changes and time distribution characteristics of the ionosphere over the low latitude location, foreseeing the scopes for its regional implementation with a wide range of operations. • Ionospheric TEC model is proposed based on Singular Spectrum Analysis (SSA). • Model outcomes is assessed by comparing with the GPS-TEC, IRI and GIM estimations. • Excellent model outcomes are achieved with low RMSE and high correlations. • A decent agreement with GPS-TEC is seen even during geomagnetic storm conditions. • The outcomes suggest a regional model implementation for near-realtime operations. [ABSTRACT FROM AUTHOR]

Global navigation satellite system reflectometry (GNSS-R) is a new remote sensing technique, which can be used to measure a wide range of geophysical parameters. GNSS-R makes use of the simultaneous reception of the direct transmission and the coherent surface reflections of the GNSS signal with either a single antenna or multiple separate antennas. This paper presents a new snow depth estimation method using a combination of pseudorange and carrier phase of GNSS dual-frequency signals. The proposed method is geometry-free and is not affected by ionospheric delays. The formulas of the amplitude attenuation factor of reflected signals, multipath-induced carrier-phase error, and pesudorange error for ground-based GNSS receivers are used to describe the combined signals. Using theoretical formulas instead of in situ measurement data, analytical linear models are established in advance to describe the relationship between snow depth and main frequency of combined signal time series. When the main frequency of the combined measurements is obtained by spectrum analysis, the model is used to determine snow depth. Two experimental data sets recorded in two different environments were used to test the proposed method. The results demonstrate that there exists good agreement between the proposed method and the ground-truth measurements. [ABSTRACT FROM AUTHOR]

Abstract Hydrological loading effects are one of the principal sources of the seasonal oscillations in GPS position time series, and they should be taken into account for improving GPS system accuracy. In this study, the daily vertical position time series of 23 GPS stations derived from the Crustal Movement Observation Network of China (CMONOC) are used to investigate the hydrological loading contributors of seasonal oscillations in GPS observations. The hydrological loading deformations at each GPS station are estimated by the Global Land Surface Discharge Model (LSDM). The result of period analysis suggests that the hydrological loading primarily results in the annual oscillation in GPS observations. Therefore, Multichannel Singular Spectrum Analysis (MSSA) is utilized to derive the annual signal from GPS observations and LSDM-derived deformations simultaneously for each GPS station. Compared with Singular Spectrum Analysis (SSA), the percentage of the variance of the annual signal estimated by MSSA and SSA differs by 6% on average, indicating that MSSA can effectively separate annual signal from other signals and clear noise. Meanwhile, Cross Wavelet Transform (XWT) is performed to measure the correlation and phase relationship between GPS observations and LSDM-derived deformations in the time-frequency space. The result demonstrates that the hydrological loading can only explain the annual oscillation in GPS observations at 5 stations (namely LHAS, LUZH, KMIN, QION, and XIAG) well. For the most GPS stations, other factors (e.g., other geophysical factors, hydrological modeling errors, and systematic errors) and hydrological loading jointly contribute to the annual oscillation in GPS observations. After hydrological loading correction, the Root Mean Square (RMS) values of GPS observations are reduced at 15 stations, especially for the GPS stations located in regions with significant water storage variations (up to 2.46 mm at KMIN). Moreover, the percentage of the variance of the annual signal estimated by MSSA correlates well with the RMS reduction, implying that the RMS reduction may be related to the annual signal derived from hydrological loading deformations. [ABSTRACT FROM AUTHOR]

The Pseudo Random Noise (PRN) codes is an important part of the GNSS system based on Codes Division Multiple Access (CDMA), and it is the key to channel separation and satellite distinction. The GNSS system excellent performance characteristics of multiple access and spread spectrum are realized by the PRN codes. According to the officially released Interface Control Documents (ICDs), the Beidou global navigation satellite system (BDS-3) B1C and GPS L1C have chosen the Weil codes as PRN codes whose generation is based on the number theoretic method. The Weil codes has the advantages of flexible codes length, good performance and large candidate set, therefore, this paper mainly studies 63 pairs of data/pilot channel PRN codes for BDS-3 B1C and GPS L1C. On the basis of introducing BDS-3 B1C and GPS L1C PRN codes, mainly for the Weil codes generation principle, codes evaluation criteria and intra-system and inter-system odd/even auto-correlation and cross-correlation characteristics are simulated in detail. The experimental results show that the upper limit value, lower limit value, the mean and standard deviation of the odd auto-correlation and cross-correlation of the PRN codes of the BDS-3 B1C signal were better than those of the GPS L1C PRN codes. The performance of odd and even cross-correlation are almost similar between BDS-3 B1C and GPS L1C signal inter-systems, which are slightly worse than the intra-system, and the upper limit value of the inter-system is lower than 2.94 dB in the GPS L1C intra-system. [ABSTRACT FROM AUTHOR]

By analyzing the newly released in situ data in medium earth orbit (MEO) of global positioning system satellites, we studied the spatiotemporal distribution and statistical characteristics of electrons over one solar cycle. The Weibull distribution of daily-averaged flux cumulative occurrence probability is proven. For >2-MeV electron flux, the determination coefficient of Weibull fitting is 99.92%. In the magnetic storm of late July 2004, the radial diffusion of electrons to low L-shell position was obvious. The center of 0.04-MeV electrons moved inward from $L = 6$ to $L = 4.3$ in the main phase and moved outward slowly in the recovery phase. In 0–4 MeV range, the in situ electron flux data are consistent with the AE9 mean and MEO-v2 model. The percentile of the AE9 model is also validated. The differential spectra are fitted based on exponential function at different percentiles. We also develop a rapid analysis method of internal charging in a changing electron environment. Using this method, we find that the electric field of internal charging fluctuates a lot because of the time-varying electron environment in MEO. The charging processes of different dielectrics (time constant ranges from 1 day to 100 days) in one solar cycle are also simulated. The longer the time constant, the bigger is the maximum charging electric field. But the worst case flux needed for discharging hazard evaluation is smaller. The daily-averaged worst case flux for charging assessment is not applicable. [ABSTRACT FROM AUTHOR]

Wave buoys are important devices to monitor and analyze wave data for ocean and coastal engineering. A GNSS wave buoy is briefly introduced in the paper, which has high resolution to measure the buoy motion by vertical, north-south and west-east displacements and independent velocities in above three directions. Based on the displacements and velocities, statistical results, frequency spectra and directional spectra are analyzed, and results based on the displacements are compared with that from Waverider with a distance less than 6m deployed in the special sea water with the GNSS buoy. Wave profiles comparison show that GNSS buoy presented slightly large significant wave height and mean wave height due to its high sampling frequency, and resulted in smaller mean wave period than that from Waverider. Statisticaly, between the analyzing result of the GNSS and wave rider, the maximum error of wave height is about 5.5%; and the maximum difference of wave period is about 0.5s, when sampling frequency is similar. The energy spectra were basically consistent from these two devices. The peaks of directional spectra were similar but the spreading angle was smaller from GNSS. Results mean the GNSS device presents almost similar wave information to that from Waverider. • Time history of displacement of a GNSS wave buoy and a Waverider with distance about 6m is comparable. • Displacements and velocities are contributed to form directional wave spectrum for GNSS measuring data. • Statistically the mean wave height coincident; by GNSS H 1/10 and H 1/3 slightly higher, mean wave period less about 15%–20%. • From spectrum analysis, H s is about 2%–4% higher and T ave is about 15% less by GNSS; peak frequency is very close. • The difference of wave direction by two buoys at f P is within 16°; S P is less about 25–52° and is 25% higher by GNSS. [ABSTRACT FROM AUTHOR]

This paper presents a general framework for the analysis of dyadic cooperation of finite-state machines (FSMs) performing code acquisition, as applied to navigation and communication spread-spectrum systems. Our aim is to show how code acquisition performance can be improved by relying on the unidirectional or bidirectional exchange of timing information between two FSMs. We develop an analytical framework based on the flow-graph approach to derive closed forms for the mean and variance of the acquisition time of various cooperating structures. An approximate form of the cumulative distribution function (CDF) is also provided. This framework is suitable for multiple applications, including peer-to-peer navigation, hierarchical codes, assisted global navigation satellite systems (GNSS), multiple navigation signals, and others. As a study case, we provide quantitative results for a dual-band Galileo receiver, which demonstrate the superiority of dyadic cooperation approaches in acquiring synchronization in both the E1 and E5 bands. [ABSTRACT FROM PUBLISHER]

The seasonal signal and long-term trend in the height time series of 10 IGS sites in China are investigated in this paper. The offset detection and outlier removal as well as the removal of common mode error are performed on the raw GPS time-series data developed by the Scripps Orbit and Permanent Array Center (SOPAC). The seasonal-trend decomposition procedure based on LOESS (STL) is utilized to extract precise seasonal signals, followed by an estimation of the long-term trend with the application of maximum likelihood estimation (MLE) to the seasonally adjusted time series. The Up-components of all sites are featured by obvious seasonal variations, with significant phase and amplitude modulation on some sites. After Kendall's tau test, a significant trend (99% confidence interval) for all sites is achieved. Furthermore, the trends at sites TCMS and TNML have significant changes at epochs 2009.5384 and 2009.1493 (95% confidence interval), respectively, using the Breaks For Additive Seasonal and Trend test. Finally, the velocities and their uncertainties for all sites are estimated using MLE with the white noise plus flicker noise model. And the results are analyzed and compared with those announced by SOPAC. The results obtained in this paper have a higher precision than the SOPAC results. [ABSTRACT FROM AUTHOR]

The Indian Mesosphere–Stratosphere–Troposphere (MST) radar, located at Gadanki, Andhra Pradesh, serves the purpose of providing data regarding atmospheric movements. In order to obtain information on the wind parameters, the signals collected from the radar are to be analyzed, which mainly involves the estimation of power spectrum. Parametric and nonparametric methods for spectrum estimation were applied on the complex radar data and were found to fail in accurately estimating the Doppler spectrum, particularly in the height range of 14–17 km. This made way for the introduction of a new category of spectrum estimation methods called semiparametric. This paper aims at spectral analysis of MST radar signals using a sparse spectrum estimation algorithm termed as SemiParametric/sparse Iterative Covariance-based Estimation (SPICE). This algorithm was found to successfully estimate the spectrum for simulated data even in the scenario of low SNR. For the MST radar data, the zonal $U$, meridional $V$, and wind velocity $W$ components have been estimated from the Doppler spectrum. For the purpose of validation, the obtained wind speed has been compared with the Global Positioning System radiosonde data, along with the wind speed acquired using the previously attempted methods of spectrum estimation. [ABSTRACT FROM AUTHOR]

In this study we describe a previously unreported error in the vertical-displacement time series made with GPS-based Datawell DWR-G4 wave buoys and introduce a simple method to correct the resulting wave spectra. The artefact in the time series is found to resemble a sawtooth wave, which produces an erroneous trend following an f -2 power law in frequency space. The correction method quantifies the amount of erroneous trend below a certain maximum frequency and removes the spurious energy from all frequencies assuming the above-mentioned f -2 power law. The presented correction method is validated against an experimental field test, and its impact on the measured significant wave height is quantified. The method's sensitivity to the choice of the maximum frequency is also briefly discussed. [ABSTRACT FROM AUTHOR]

Due to the spectrum congestion of current navigation signals in L-band, C-band has been taken into consideration as a candidate frequency band for global navigation satellite system (GNSS). As is known, modulation scheme is the core part of signal structure, and how to design a modulation waveform that could make full use of narrow bandwidth 20 MHz and satisfy the constraint condition of frequency compatibility in C-band is the main research content of this paper. In view of transmission characteristics and constraint condition of compatibility in C-band, multi-h continuous phase modulation (CPM) is proposed as a candidate modulation scheme. Then the classical channel capacity estimation and a comprehensive evaluation criterion for GNSS modulation signals are employed to assess the proposed scheme in the aspects of the capacity over additive white Gaussian noise (AWGN), tracking accuracy, multipath mitigation, antijamming, and so on. Simulation results reveal that, through optimizing the number and size of modulation indexes, the flexible scheme could offer better performance in terms of code tracking, multipath mitigation, and antijamming compared with other candidates such as MSK and GMSK while maintaining high band efficiency and moderate implementation complexity of receiver. Moreover, this paper also provides a reference for next generation modulation signals in C-band. [ABSTRACT FROM AUTHOR]

The multipath error is considered to be the most limiting factor for high precision positioning applications. The sidereal filtering (SF) method can be used to mitigate the multipath error in the observation domain, and it has been successfully applied in the multipath mitigation in global positioning systems (GPS) and regional BeiDou navigation satellite systems (BDS2). However, there are few reports on the SF method in other systems. The performance of the SF method relies on the explicit orbit repeat periods of satellites in diverse systems or even different types of constellations. It is therefore inconvenient to utilize the SF method for multi-GNSS multipath error mitigation. Alternatively, a space domain multipath error reduction method, which establishes the multi-point hemispherical grid model (MHGM) using the residuals of the double-differenced carrier phase observations in the ambiguity-fixed period, has been modified. It is an integrated model for multi-GNSS, without considering the diversity of different systems and constellations. To compare the performance of MHGM and SF from a multi-GNSS point of view, the determination method of orbit repeat periods via the broadcast ephemerides is summarized, and the SF method is extended to the global BeiDou navigation satellite system (BDS3) and Galileo navigation satellite system. Further test results show that the performance of MHGM and SF are comparable from the perspective of root mean squares (RMS) and the power spectrum analysis of double-differenced residuals, as well as the static positioning results. This implies that the space domain MHGM can obtain similar correction effects as the SF method in the observation domain, but the former is more flexible for modeling with various systems' data. In addition, the established MHGM using the data of multi orbit periods demonstrates a better performance compared with that of only one orbit period, and an average improvement of 13.1% in the RMS of the double-differenced residuals can be achieved. [ABSTRACT FROM AUTHOR]

Environmental loading, in particular from continental water storage changes, induces geodetic station displacements up to several centimeters for the vertical components. We investigate surface deformation due to loading processes in South America using a set of 247 permanent GPS (Global Positioning System) stations for the 2003–2016 period and compare them to loading estimates from global circulation models. Unfortunately, some of the hydrological components, and in particular surface waters, may be missing in hydrological models. This is especially an issue in South America where almost half of the seasonal water storage variations are due to surface water changes, e.g., rivers and floodplains. We derive river storage variations by rerouting runoffs of global hydrology models, allowing a better agreement with the mass variations observed from GRACE (Gravity Recovery and Climate Experiment) mission. We extract coherent seasonal GPS displacements using Multichannel Singular Spectrum Analysis (M-SSA) and show that modeling the river storage induced loading effects significantly improve the agreement between observed vertical and horizontal displacements and loading models. Such an agreement has been markedly achieved in the Amazon basin. Whilst the initial models only explained half of the amplitude of GPS, the new ones compensate for these gaps and remain consistent with GRACE. [ABSTRACT FROM AUTHOR]

The Mw7.9 Alaska earthquake at 09:31:40 UTC on 23 January 2018 occurred as the result of strike slip faulting within the shallow lithosphere of the Pacific plate. Global positioning system (GPS) data were used to calculate the slant total electron contents above the epicenter. The singular spectrum analysis (SSA) method was used to extract detailed ionospheric disturbance information, and to monitor the co-seismic ionospheric disturbances (CIDs) of the Alaska earthquake. The results show that the near-field CIDs were detected 8–12 min after the main shock, and the typical compression-rarefaction wave (N-shaped wave) appeared. The ionospheric disturbances propagate to the southwest at a horizontal velocity of 2.61 km/s within 500 km from the epicenter. The maximum amplitude of CIDs appears about 0.16 TECU (1TECU = 1016 el m−2) near the epicenter, and gradually decreases with the location of sub-ionospheric points (SIPs) far away from the epicenter. The attenuation rate of amplitude slows down as the distance between the SIPs and the epicenter increases. The direction of the CIDs caused by strike-slip faults may be affected by the horizontal direction of fault slip. The propagation characteristics of the ionospheric disturbance in the Alaska earthquake may be related to the complex conditions of focal mechanisms and fault location. [ABSTRACT FROM AUTHOR]

Despite being a systematic error source in global navigation satellite system (GNSS) positioning and navigation, tropospheric delay is a key parameter in GNSS meteorology. Therefore, deriving a zenith tropospheric delay (ZTD) value as accurately as possible from an empirical model without using auxiliary data is a prerequisite for the high-precision application of GNSS positioning and navigation. To reach the goal above, this paper proposes an improved model to estimate the ZTD based on the Global Pressure and Temperature 2 wet (GPT2w) model, which is called the improved GPT2w (IGPT2w) model. The GPT2w-derived ZTD is first calculated as the initial value of the IGPT2w model, and the time series of ZTD residual can thus be obtained between the GNSS- and GPT2w-derived ZTDs over GNSS stations. Analysis of the long time series variation of ZTD residuals using the multichannel singular spectrum analysis method reveals evident periodic signals. The Lomb–Scargle method is then used to determine the specific values of these periodic signals, and different periods are identified at various GNSS stations. Therefore, a ZTD residual model that considers annual, semi-annual, and seasonal periods is established. The IGPT2w model, in which the ZTD value is obtained by combining the estimated ZTD residual and the GPT2w-derived ZTD, can be acquired. A total of 188 GNSS stations in China throughout 2015 to 2017 are selected to validate the IGPT2w model. In the model, the GNSS-derived ZTD is obtained using the GAMIT/GLOBK software, and the accuracy is validated using radiosonde data with root mean square and bias of 1.9 and 0.1 cm, respectively, at 33 collocated stations in China. Statistical results reveal that the accuracy of the IGPT2w-derived ZTD is improved by 13.7% compared with that of the GPT2w-derived ZTD when the GNSS-derived ZTD is regarded as the reference. Such result indicates that the proposed IGPT2w model outperforms the GPT2w model in China. [ABSTRACT FROM AUTHOR]

The present paper investigates GPS, GLONASS, and Beidou observables from the Multi-GNSS Experiment (MGEX) network of stations in the East Asia region. Precise Point Positioning (PPP) estimates, Dilution of Precision (DOP), Slant Total Electron Content (STEC), and Zenith Total Delay (ZTD), along with their prediction from the Singular Spectrum Analysis (SSA), were studied to analyze and understand their effectiveness on the overall positioning accuracy over the region. The analysis confirms that the PPP accuracy does not solely depend on the DOP values, but is also affected by seasonal changes or partial corrections of the ionospheric and tropospheric delays. The accuracy is improved by approximately 70% for the GPS (G), GPS+GLONASS (GR), and GPS+GLONASS+Beidou (GRC) constellations after applying the SSA method. The GNSS-derived STEC and ZTD values were also predicted with the SSA methods to evaluate the trustworthiness of the approach for mitigation of atmospheric errors. The results show that the STEC and ZTD seem to be in perfect agreement with the SSA model. The technique could be applicable for improved navigational measurements augmenting other available constellations such as the Galileo, IRNSS, and QZSS, as well as satellite-based augmentation systems across the globe. [ABSTRACT FROM AUTHOR]