Independent Component Extraction from the Incomplete Coordinate Time Series of Regional GNSS Networks

Independent component analysis (ICA) is one of the most effective approaches in extracting independent signals from a global navigation satellite system (GNSS) regional station network. However, ICA requires the involved time series to be complete, thereby the missing data of incomplete time series should be interpolated beforehand. In this contribution, a modified ICA is proposed, by which the missing data are first recovered based on the reversible property between the original time series and decomposed principal components, then the complete time series are further processed with FastICA. To evaluate the performance of the modified ICA for extracting independent components, 24 regional GNSS network stations located in North China from 2011 to 2019 were selected. After the trend, annual and semiannual terms were removed from the GNSS time series, the first two independent components captured 17.42, 18.44 and 17.38% of the total energy for the North, East and Up coordinate components, more than those derived by the iterative ICA that accounted for 16.21%, 17.72% and 16.93%, respectively. Therefore, modified ICA can extract more independent signals than iterative ICA. Subsequently, selecting the 7 stations with less missing data from the network, we repeatedly process the time series after randomly deleting parts of the data and compute the root mean square error (RMSE) from the differences of reconstructed signals before and after deleting data. All RMSEs of modified ICA are smaller than those of iterative ICA, indicating that modified ICA can extract more exact signals than iterative ICA.

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Signal Extraction from GNSS Position Time Series Using Weighted Wavelet Analysis

Remote Sensing ◽

10.3390/rs12060992 ◽

2020 ◽

Vol 12 (6) ◽

pp. 992 ◽

Cited By ~ 1

Author(s):

Kunpu Ji ◽

Yunzhong Shen ◽

Fengwei Wang

Keyword(s):

Time Series ◽

Wavelet Analysis ◽

Satellite System ◽

Signal Extraction ◽

Average Error ◽

North East ◽

Observation Network ◽

Position Time Series ◽

Global Navigation Satellite ◽

Gnss Position Time Series

The daily position time series derived by Global Navigation Satellite System (GNSS) contain nonlinear signals which are suitably extracted by using wavelet analysis. Considering formal errors are also provided in daily GNSS solutions, a weighted wavelet analysis is proposed in this contribution where the weight factors are constructed via the formal errors. The proposed approach is applied to process the position time series of 27 permanent stations from the Crustal Movement Observation Network of China (CMONOC), compared to traditional wavelet analysis. The results show that the proposed approach can extract more exact signals than traditional wavelet analysis, with the average error reductions are 13.24%, 13.53% and 9.35% in north, east and up coordinate components, respectively. The results from 500 simulations indicate that the signals extracted by proposed approach are closer to true signals than the traditional wavelet analysis.

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Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series

Remote Sensing ◽

10.3390/rs13173478 ◽

2021 ◽

Vol 13 (17) ◽

pp. 3478

Author(s):

Sorin Nistor ◽

Norbert-Szabolcs Suba ◽

Ahmed El-Mowafy ◽

Michal Apollo ◽

Zinovy Malkin ◽

...

Keyword(s):

Time Series ◽

Satellite System ◽

Phase Lag ◽

Time Frequency ◽

Richter Scale ◽

Different Types ◽

Before And After ◽

Position Time Series ◽

Global Navigation Satellite ◽

Seasonal Signal

The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study is to explore the implication of different types of geophysical events on the seasonal signal in three stages—in the time span that contains the geophysical events, before and after the geophysical event, but also the stationarity phenomena, which is analysed on approximately 200 reference stations from the EPN network since 1995. The novelty of the article is demonstrated by correlating three different types of geophysical events, such as earthquakes with a magnitude greater than 6° on the Richter scale, landslides, and volcanic activity, and analysing the variation in amplitude of the seasonal signal. The geophysical events situated within a radius of 30 km from the epicentre showed a higher seasonal value than when the timespan did not contain a geophysical event. The presence of flicker and random walk noise was computed using overlapping Hadamard variance (OHVAR) and the non-stationary behaviour of the time series of the CORS coordinates in the time frequency analysis was done using continuous wavelet transform (CWT).

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Analyzing GNSS Measurements to Detect and Predict Bridge Movements Using the Kalman Filter (KF) and Neural Network (NN) Techniques

Geomatics ◽

10.3390/geomatics1010006 ◽

2021 ◽

Vol 1 (1) ◽

pp. 65-80

Author(s):

Ehsan Forootan ◽

Saeed Farzaneh ◽

Kowsar Naderi ◽

Jens Peter Cederholm

Keyword(s):

Neural Network ◽

Kalman Filter ◽

Satellite System ◽

Dynamic Component ◽

North East ◽

The North ◽

Dynamic Components ◽

Least Squares Harmonic Estimation ◽

Gnss Measurements ◽

Global Navigation Satellite

In this study, we present a data processing framework to apply measurements of the Global Navigation Satellite System (GNSS) technique for analyzing and predicting the movements of civil structures such as bridges. The proposed approach reduces the noise level of GNSS measurements using the Kalman Filter (KF) approach and enables the estimation of static, semi-static, and dynamic components of the bridge’s movements using a series of analyses such as the temporal filtering and the Least Squares Harmonic Estimation (LS-HE). The numerical results indicate that by using a RTK-GNSS system the semi-static component is extracted with a Standard Deviation (STD) of 0.032, 0.048, and 0.06 m in the North, East, and Up (NEU) directions, while that of the dynamic component is 0.004, 0.003, and 0.01 m, respectively. Comparing the dominant frequencies of the bridge movements from LS-HE with those of the permanent stations provides information about the bridge’s stability. To predict its deflection, the Neural Network (NN) technique is tested to simulate the time-varying components, which are then compared with the safety limits, known by its design, to assess the structural health under usual load.

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The Noise Properties and Velocities from a Time-Series of Estonian Permanent GNSS Stations

Geosciences ◽

10.3390/geosciences9050233 ◽

2019 ◽

Vol 9 (5) ◽

pp. 233

Author(s):

Tarmo Kall ◽

Tõnis Oja ◽

Karin Kollo ◽

Aive Liibusk

Keyword(s):

Time Series ◽

Flicker Noise ◽

Satellite System ◽

Noise Model ◽

Land Uplift ◽

Isostatic Adjustment ◽

The North ◽

East Component ◽

Conservative Values ◽

Global Navigation Satellite

The aim of this study was to estimate the noise properties, velocities, and their uncertainties from a time-series of selected (~9 years long) Estonian continuously operating Global Navigation Satellite System (GNSS) stations. Two software packages based on different processing methods, Gipsy–Oasis and Bernese, were used for daily coordinate calculations. Different methods and software (Tsview, Hector, and MIDAS) were used for coordinate time-series analysis. Outliers were removed using three different strategies. Six different stochastic noise models were used for trend estimation altogether with the analysis of the noise properties of the residual time-series with Hector. Obtained velocities were compared with different land uplift and glacial isostatic adjustment models (e.g., ICE-6G (VM5a), NKG2016LU, etc.). All compared solutions showed similar fit to the compared models. It was confirmed that the best fit to the time-series residuals were with the flicker noise plus white noise model (for the North and East component) and generalized Gauss–Markov model (for Up). Velocities from MIDAS, Tsview, and Hector solutions within the same time-series (Gipsy–Oasis or Bernese) agreed well but velocity uncertainties differed up to four times. The smallest uncertainties were obtained from Tsview; the MIDAS solution produced the most conservative values. Although the East and Up component velocities between Gipsy and Bernese solutions agreed well, the North component velocities were systematically shifted.

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An Innovative Approach to Accuracy of Co-Seismic Surface Displacement Detection Using Satellite GNSS Technology

Applied Sciences ◽

10.3390/app11062800 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2800

Author(s):

Hana Staňková ◽

Jakub Kostelecký ◽

Miroslav Novosad

Keyword(s):

Time Series ◽

Surface Displacement ◽

Satellite System ◽

Dual Approach ◽

Seismic Displacement ◽

Accuracy Of Measurements ◽

Before And After ◽

Using Data ◽

Global Navigation Satellite ◽

Seismic Models

This paper discusses a new method for determining co-seismic displacement using the Global Navigation Satellite System (GNSS) for the precise detection of positional changes at permanent stations after an earthquake. Positioning by the Precise Point Positioning (PPP) method is undertaken using data from the GNSS satellites and one designated station. A time series is processed by an anharmonic analysis before and after an earthquake and these one-day solutions increase the accuracy of measurements. The co-seismic static displacement can be precisely detected from the analysed time series before and after the earthquake, which can be used for the verification of seismic models. Reliability of the estimation of the size of the co-seismic offset is given by the mean square error (RMSE) of the shift. In this study, RMSE was determined by two approaches, initially from variances within PPP processing, and secondly when no positional change from the GNSS before or after the earthquake was assumed. The variance of the data in the time series gives a more realistic estimate of RMSE. This dual approach can affect seismological interpretation due to the need for the interpreting geophysicists to determine which case of co-seismic displacement is more probable for any given locality. The second approach has been shown to provide a more realistic co-seismic displacement accuracy in this study.

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Investigation of GIM-TEC disturbances before M ≥ 6.0 inland earthquakes during 2003–2017

Scientific Reports ◽

10.1038/s41598-020-74995-w ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Fuying Zhu ◽

Yingchun Jiang

Keyword(s):

Rapid Development ◽

Science Research ◽

Satellite System ◽

Statistical Investigation ◽

Electron Content ◽

Total Electron ◽

Spatial And Temporal Distributions ◽

Before And After ◽

Global Ionosphere Map ◽

Global Navigation Satellite

Abstract With the rapid development of the Global Navigation Satellite System (GNSS) and its wide applications to atmospheric science research, the global ionosphere map (GIM) total electron content (TEC) data are extensively used as a potential tool to detect ionospheric disturbances related to seismic activity and they are frequently used to statistically study the relation between the ionosphere and earthquakes (EQs). Indeed, due to the distribution of ground based GPS receivers is very sparse or absent in large areas of ocean, the GIM-TEC data over oceans are results of interpolation between stations and extrapolation in both space and time, and therefore, they are not suitable for studying the marine EQs. In this paper, based on the GIM-TEC data, a statistical investigation of ionospheric TEC variations of 15 days before and after the 276 M ≥ 6.0 inland EQs is undertaken. After eliminating the interference of geomagnetic activities, the spatial and temporal distributions of the ionospheric TEC disturbances before and after the EQs are investigated and compared. There are no particularly distinct features in the time distribution of the ionospheric TEC disturbances before the inland EQs. However, there are some differences in the spatial distribution, and the biggest difference is precisely in the epicenter area. On the other hand, the occurrence rates of ionospheric TEC disturbances within 5 days before the EQs are overall higher than those after EQs, in addition both of them slightly increase with the earthquake magnitude. These results suggest that the anomalous variations of the GIM-TEC before the EQs might be related to the seismic activities.

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Performance Assessment of GNSS-R Polarimetric Observations for Sea Level Monitoring

10.5194/egusphere-egu21-12709 ◽

2021 ◽

Author(s):

Mahmoud Rajabi ◽

Mstafa Hoseini ◽

Hossein Nahavandchi ◽

Maximilian Semmling ◽

Markus Ramatschi ◽

...

Keyword(s):

Time Series ◽

Circular Polarization ◽

Sea Level ◽

Tide Gauge ◽

Satellite System ◽

Sea Surface ◽

Analysis Tool ◽

Lower Accuracy ◽

Coastal Sea ◽

Global Navigation Satellite

Determination and monitoring of the mean sea level especially in the coastal areas are essential, environmentally, and as a vertical datum. Ground-based Global Navigation Satellite System Reflectometry (GNSS-R) is an innovative way which is becoming a reliable alternative for coastal sea-level altimetry. Comparing to traditional tide gauges, GNSS-R can offer different parameters of sea surface, one of which is the sea level. The measurements derived from this technique can cover wider areas of the sea surface in contrast to point-wise observations of a tide gauge. &#160;We use long-term ground-based GNSS-R observations to estimate sea level. The dataset includes one-year data from January to December 2016. The data was collected by a coastal GNSS-R experiment at the Onsala space observatory in Sweden. The experiment utilizes three antennas with different polarization designs and orientations. The setup has one up-looking, and two sea-looking antennas at about 3 meters above the sea surface level. The up-looking antenna is Right-Handed Circular Polarization (RHCP). The sea-looking antennas with RHCP and Left-Handed Circular Polarization (LHCP) are used for capturing sea reflected Global Positioning System (GPS) signals. A dedicated reflectometry receiver (GORS type) provides In-phase and Quadrature (I/Q) correlation sums for each antenna based on the captured interferometric signal. The generated time series of I/Q samples from different satellites are analyzed using the Least Squares Harmonic Estimation (LSHE) method. This method is a multivariate analysis tool which can flexibly retrieve the frequencies of a time series regardless of possible gaps or unevenly spaced sampling. The interferometric frequency, which is related to the reflection geometry and sea level, is obtained by LSHE with a temporal resolution of 15&#160;minutes. The sea level is calculated based on this frequency in six modes from the three antennas in GPS L1 and L2 signals.Our investigation shows that the sea-looking antennas perform better compared to the up-looking antenna. The highest accuracy is achieved using the sea-looking LHCP antenna and GPS L1 signal. The annual Root Mean Square Error (RMSE) of 15-min GNSS-R water level time series compared to tide gauge observations is 3.7 (L1) and 5.2 (L2) cm for sea-looking LHCP, 5.8 (L1) and 9.1 (L2) cm for sea-looking RHCP, 6.2 (L1) and 8.5 (L2) cm for up-looking RHCP. It is worth noting that the GPS IIR block satellites show lower accuracy due to the lack of L2C code. Therefore, the L2 observations from this block are eliminated.

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Updating of digital topographic maps in the new national spatial coordinate system: case Fergana valley in Uzbekistan

Proceedings of the ICA ◽

10.5194/ica-proc-4-31-2021 ◽

2021 ◽

Vol 4 ◽

pp. 1-5

Author(s):

Dilbarkhon Fazilova ◽

Hasan Magdiev

Keyword(s):

Coordinate System ◽

Spatial Data ◽

Information Technologies ◽

Satellite System ◽

Topographic Maps ◽

The North ◽

New Information ◽

Global Navigation Satellite ◽

Geodetic Coordinate System ◽

Geocentric Coordinate System

Abstract. The classical geodetic coordinate system (CS42) in Uzbekistan uses the Krasovsky ellipsoid. The implementation of new information technologies, such as the Global Navigation Satellite System, became the basis for the development of a new national open geocentric coordinate system. This paper describes the development of a distortion grid for transforming horizontal spatial data from the local geodetic datum CS42 to a geocentric datum WGS84 for 1:100000 scale maps of the Fergana Valley in Uzbekistan. A first version of the distortion grid file has been created for transforming between CS42 and WGS84 for the whole territory of the country. The significant influence of the longitudinal drift of the region has been confirmed. The grid was used to transform topographic maps at a scale of 1:100000 for the Fergana Valley. Changing the map datum has shifted the grid of coordinate systems by 70 m in the East and 7 m in the North.

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Extracting Common Mode Errors of Regional GNSS Position Time Series in the Presence of Missing Data by Variational Bayesian Principal Component Analysis

Sensors ◽

10.3390/s20082298 ◽

2020 ◽

Vol 20 (8) ◽

pp. 2298 ◽

Cited By ~ 2

Author(s):

Wudong Li ◽

Weiping Jiang ◽

Zhao Li ◽

Hua Chen ◽

Qusen Chen ◽

...

Keyword(s):

Principal Component Analysis ◽

Time Series ◽

Missing Data ◽

Principal Component ◽

Component Analysis ◽

Common Mode ◽

Variational Bayesian ◽

North East ◽

Position Time Series ◽

Gnss Position Time Series

Removal of the common mode error (CME) is very important for the investigation of global navigation satellite systems’ (GNSS) error and the estimation of an accurate GNSS velocity field for geodynamic applications. The commonly used spatiotemporal filtering methods normally process the evenly spaced time series without missing data. In this article, we present the variational Bayesian principal component analysis (VBPCA) to estimate and extract CME from the incomplete GNSS position time series. The VBPCA method can naturally handle missing data in the Bayesian framework and utilizes the variational expectation-maximization iterative algorithm to search each principal subspace. Moreover, it could automatically select the optimal number of principal components for data reconstruction and avoid the overfitting problem. To evaluate the performance of the VBPCA algorithm for extracting CME, 44 continuous GNSS stations located in Southern California were selected. Compared to previous approaches, VBPCA could achieve better performance with lower CME relative errors when more missing data exists. Since the first principal component (PC) extracted by VBPCA is remarkably larger than the other components, and its corresponding spatial response presents nearly uniform distribution, we only use the first PC and its eigenvector to reconstruct the CME for each station. After filtering out CME, the interstation correlation coefficients are significantly reduced from 0.43, 0.46, and 0.38 to 0.11, 0.10, and 0.08, for the north, east, and up (NEU) components, respectively. The root mean square (RMS) values of the residual time series and the colored noise amplitudes for the NEU components are also greatly suppressed, with average reductions of 27.11%, 28.15%, and 23.28% for the former, and 49.90%, 54.56%, and 49.75% for the latter. Moreover, the velocity estimates are more reliable and precise after removing CME, with average uncertainty reductions of 51.95%, 57.31%, and 49.92% for the NEU components, respectively. All these results indicate that the VBPCA method is an alternative and efficient way to extract CME from regional GNSS position time series in the presence of missing data. Further work is still required to consider the effect of formal errors on the CME extraction during the VBPCA implementation.

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GNSS Multipath Detection Using Continuous Time-Series C/N0

Sensors ◽

10.3390/s20144059 ◽

2020 ◽

Vol 20 (14) ◽

pp. 4059

Author(s):

Nobuaki Kubo ◽

Kaito Kobayashi ◽

Rei Furukawa

Keyword(s):

Time Series ◽

Continuous Time ◽

Urban Areas ◽

Satellite System ◽

Line Of Sight ◽

Static Tests ◽

Gnss Receivers ◽

Multipath Detection ◽

Global Navigation Satellite ◽

Multipath Errors

The reduction of multipath errors is a significant challenge in the Global Navigation Satellite System (GNSS), especially when receiving non-line-of-sight (NLOS) signals. However, selecting line-of-sight (LOS) satellites correctly is still a difficult task in dense urban areas, even with the latest GNSS receivers. This study demonstrates a new method of utilization of C/N0 of the GNSS to detect NLOS signals. The elevation-dependent threshold of the C/N0 setting may be effective in mitigating multipath errors. However, the C/N0 fluctuation affected by NLOS signals is quite large. If the C/N0 is over the threshold, the satellite is used for positioning even if it is still affected by the NLOS signal, which causes the positioning error to jump easily. To overcome this issue, we focused on the value of continuous time-series C/N0 for a certain period. If the C/N0 of the satellite was less than the determined threshold, the satellite was not used for positioning for a certain period, even if the C/N0 recovered over the threshold. Three static tests were conducted at challenging locations near high-rise buildings in Tokyo. The results proved that our method could substantially mitigate multipath errors in differential GNSS by appropriately removing the NLOS signals. Therefore, the performance of real-time kinematic GNSS was significantly improved.

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