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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]

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]

As the deployment of large Low Earth Orbiters (LEO) communication constellations, navigation from the LEO satellites becomes an emerging opportunity to enhance the existing satellite navigation systems. The LEO navigation augmentation (LEO-NA) systems require a centimeter to decimeter accuracy broadcast ephemeris to support high accuracy positioning applications. Thus, how to design the broadcast ephemeris becomes the key issue for the LEO-NA systems. In this paper, the temporal variation characteristics of the LEO orbit elements were analyzed via a spectrum analysis. A non-singular element set for orbit fitting was introduced to overcome the potential singularity problem of the LEO orbits. Based on the orbit characteristics, a few new parameters were introduced into the classical 16 parameter ephemeris set to improve the LEO orbit fitting accuracy. In order to identify the optimal parameter set, different parameter sets were tested and compared and the 21 parameters data set was recommended to make an optimal balance between the orbit accuracy and the bandwidth requirements. Considering the real-time broadcast ephemeris generation procedure, the performance of the LEO ephemeris based on the predicted orbit is also investigated. The performance of the proposed ephemeris set was evaluated with four in-orbit LEO satellites and the results indicate the proposed 21 parameter schemes improve the fitting accuracy by 87.4% subject to the 16 parameters scheme. The accuracy for the predicted LEO ephemeris is strongly dependent on the orbit altitude. For these LEO satellites operating higher than 500 km, 10 cm signal-in-space ranging error (SISRE) is achievable for over 20 min prediction. [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]

Summary: This study investigates the multipath error modeling and mitigation for triple‐frequency global navigation satellite system (GNSS) signals inside South Korea. Multifrequency global positioning system (GPS), globalnaya navigatsionnaya sputnikovaya sistema (GLONASS), and Galileo data are collected in an environment where the receiver must track these three constellations in both low and high multipath scenarios. First, an advanced power spectrum analysis technique known as Welch method is performed using experimental data, and its benefits and drawbacks are described. In the second attempt, the spectrogram method is utilized to perform multipath feature time–frequency analysis. Although the abnormal frequency peak presented by the spectrogram is stable, the spectrogram does not support the precise recognition of the multipath error peak occurrence. Hence, in the third attempt, continuous wavelet transforms (CWT) are applied to highlight this type of peak resolution. The CWT function successfully indicated the maximum and minimum peak resolutions and exhibited a clear wavelet energy spread. In the final stage, experimental data are reconstructed by inverse CWT (ICWT), and comparative results in terms of root mean square before and after the ICWT are estimated. After implementing the inverse wavelet method in high and low multipath error of experimental data, overall average percentages of multipath mitigation reduction compared to actual multipath error are estimated to be 95.74% and 98.79%, respectively. This study demonstrates the high efficiency of the wavelet method as well as the effectiveness as a multipath error reduction approach. These improvements can be considered as significant in achieving high‐precision positioning accuracy. [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]

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]