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• 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]

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]

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]

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 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]