A MATLAB-based Kriged Kalman Filter software for interpolating missing data in GNSS coordinate time series

Liu, Ning; Dai, Wujiao; Santerre, Rock; Kuang, Cuilin

doi:10.1007/s10291-017-0689-3

Cited by 59 publications

(25 citation statements)

References 21 publications

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“…A Kalman filter-based method was recently proposed by Liu et al (2018) to estimate and account for the spatial correlations of GNSS time series in order to improve their interpolation. However, this study did not evaluate the impact of modeling spatial correlations on the estimation of station velocities.…”

Section: Introductionmentioning

confidence: 99%

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Accounting for spatiotemporal correlations of GNSS coordinate time series to estimate station velocities

Benoist

Collilieux

Rebischung

et al. 2020

Journal of Geodynamics

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It is well known that GNSS permanent station coordinate time series exhibit time-correlated noise. Spatial correlations between coordinate time series of nearby stations are also long-established and generally handled by means of spatial filtering techniques. Accounting for both the temporal and spatial correlations of the noise via a spatiotemporal covariance model is however not yet a common practice. We demonstrate in this paper the interest of using such a spatiotemporal covariance model of the stochastic variations in GNSS time series in order to estimate long-term station coordinates and especially velocities. We provide a methodology to rigorously assess the covariances between horizontal coordinate variations and use it to derive a simple exponential spatiotemporal covariance model for the stochastic variations in the IGS repro2 station coordinate time series. We then use this model to estimate station velocities for two selected datasets of 10 time series in Europe and 11 time series in the USA. We show that coordinate prediction as well as velocity determination from short time series are improved when using this spatiotemporal model, as compared with the case where spatiotemporal correlations are ignored.

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Section: Introductionmentioning

confidence: 99%

“…However, this study did not evaluate the impact of modeling spatial correlations on the estimation of station velocities. In the present study, we introduce a methodology, similar to that of Liu et al (2018), although developed independently, and focus on the impact of modeling spatial correlations on the estimation of station velocities.…”

Section: Introductionmentioning

confidence: 99%

Accounting for spatiotemporal correlations of GNSS coordinate time series to estimate station velocities

Benoist

Collilieux

Rebischung

et al. 2020

Journal of Geodynamics

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“…Finally, a total of 262 GPS sites around the world were chosen in the case study, and the distribution of the sites are shown in Figure 2 . After this, a kriged kalman filter technique was used to interpolate the missing data of the 262 vertical GPS time series [ 44 ]. We did not complete additional processing in the correction of other potential seasonal signals, including the draconic year effect and bedrock thermal expansion, although we think the mass loadings are the main contribution to the seasonal variation in vertical GPS coordinate time series.…”

Section: Case Studymentioning

confidence: 99%

Modeling Seasonal Variations in Vertical GPS Coordinate Time Series Using Independent Component Analysis and Varying Coefficient Regression

Liu

Xing

Tan

et al. 2020

Sensors

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Common seasonal variations in Global Positioning System (GPS) coordinate time series always exist, and the modeling and correction of the seasonal signals are helpful for many geodetic studies using GPS observations. A spatiotemporal model was proposed to model the common seasonal variations in vertical GPS coordinate time series, based on independent component analysis and varying coefficient regression method. In the model, independent component analysis (ICA) is used to separate the common seasonal signals in the vertical GPS coordinate time series. Considering that the periodic signals in GPS coordinate time series change with time, a varying coefficient regression method is used to fit the separated independent components. The spatiotemporal model was then used to fit the vertical GPS coordinate time series of 262 global International GPS Service for Geodynamics (IGS) GPS sites. The results show that compared with least squares regression, the varying coefficient method can achieve a more reliable fitting result for the seasonal variation of the separated independent components. The proposed method can accurately model the common seasonal variations in the vertical GPS coordinate time series, with an average root mean square (RMS) reduction of 41.6% after the model correction.

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“…Here, we shall use the real GPS deformation data to demonstrate the effectiveness of the proposed MSTME model for missing data and compare with the KKF model used in Liu et al [27] and the STME model.…”

Section: Real Experiments For Gps Deformation Datamentioning

confidence: 99%

“…As mentioned earlier, the KKF model considers spatiotemporal correlation of stations and has high interpolation accuracy for sparse stations. However, the KKF model used in Liu et al [27] relies too much on the initial values of the parameters and needs to adjust the initial parameters repeatedly to obtain the best accuracy, which limits the usefulness and reliability of the model.…”

Section: Introductionmentioning

confidence: 99%

A Modified Spatiotemporal Mixed-Effects Model for Interpolating Missing Values in Spatiotemporal Observation Data Series

Shi

Dai

Santerre

et al. 2020

Mathematical Problems in Engineering

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Missing values in data series is a common problem in many research and applications. Most of existing interpolation methods are based on spatial or temporal interpolation, without considering the spatiotemporal correlation of observation data, resulting in poor interpolation effect. In this paper, a Modified Spatiotemporal Mixed-Effects (MSTME) model for interpolation of spatiotemporal data series is proposed. Experiments with simulated data and real SCIGN data are performed to assess the validity of the proposed model in comparison with Kriged Kalman Filter (KKF) model and Spatiotemporal Mixed-Effects (STME) model. The average improvements of simulated data and SCIGN data for observed stations are around 46% and 19% over the KKF model and 62% and 21% over the STME model, and those for unobserved stations are around 23% and 34% over the KKF model and 41% and 16% over the STME model, respectively, indicating that the proposed MSTME model can achieve better accuracy for interpolating missing values.

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A MATLAB-based Kriged Kalman Filter software for interpolating missing data in GNSS coordinate time series

Cited by 59 publications

References 21 publications

Accounting for spatiotemporal correlations of GNSS coordinate time series to estimate station velocities

Accounting for spatiotemporal correlations of GNSS coordinate time series to estimate station velocities

Modeling Seasonal Variations in Vertical GPS Coordinate Time Series Using Independent Component Analysis and Varying Coefficient Regression

A Modified Spatiotemporal Mixed-Effects Model for Interpolating Missing Values in Spatiotemporal Observation Data Series

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