Error analysis of continuous GPS position time series

By Simon D. P. Williams, Yehuda Bock, Peng Fang, Paul Jamason, R. Nikolaidis, Linette Prawirodirdjo, M. Miller, Daniel J. Johnson. 2004

698 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Geophysics, Oceanography

View Paper: https://www.semanticscholar.org/paper/661c6d34ffefff3d2a02828f7bcb84d76c45d1fd

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Citations in the corpus

Constraining Models of Postglacial Rebound Using Space Geodesy (2008, positive): “The velocity sigmas we infer are roughly comparable to those Williams et al. (2004) estimate using maximum likelihood estimation (see Notes of Table 1).”
Network-based estimation of time-dependent noise in GPS position time series (2015, methodology): “Removing common-mode error decreases flicker noise in time series (Williams et al. 2004; Langbein 2012).”
Spatiotemporal filtering of regional GNSS network’s position time series with missing data using principle component analysis (2013, background): “…estimation (Shen and Li 2011), the maximum likelihood estimation (Zhang et al. 1997; Langbein and Johnson 1997; Mao et al. 1999; Williams 2003; Williams et al. 2004; Langbein 2004; Williams and Willis 2006) or the least squares variance component estimation (Amiri-Simkooei et al. 2007;…”
On the nature of GPS draconitic year periodic pattern in multivariate position time series (2013, background): “Random walk noise, which is mainly related to monument instability, was shown not to be present in the global GPS solutions [Williams et al., 2004].”
Least-squares variance component estimation (2008, background): “Examples are Zhang et al. (1997); Mao et al. (1999); Williams et al. (2004), and Amiri-Simkooei et al. (2007), who studied the noise characteristics (e.g., white noise, random walk and flicker noise) in daily GPS coordinate time-series of permanent networks.”
Fast error analysis of continuous GNSS observations with missing data (2013, methodology): “Our choice of noise model will be the standard power-law plus white noise model which exist in many GNSS observations (Williams et al. 2004): C = σ 2 ( sin2(φ)I + cos2(φ)E(α) ) (32) where σ is the innovation noise and I is the unit matrix, which is the covariance matrix for white noise, and E is…”
Long GPS coordinate time series: Multipath and geometry effects (2009, background): “This finding is of interest given the observed presence of flicker noise with unknown origin in real GPS time series [e.g., Langbein , 2008; Williams et al. , 2004].”
On the precision and accuracy of IGS orbits (2009, background): “9 by the dashed diagonal line), commonly seen in the spectra of GPS station time series (e.g., Williams et al. 2004), but the lower frequencies are poorly resolved.”
Correlated errors in GPS position time series: Implications for velocity estimates (2011, methodology): “ment instability, was not clearly found in our results, in agreement to other global GPS solutions [Williams et al., 2004].”
Least-squares variance component estimation: theory and GPS applications (2007, methodology): “Global time series of site positions are supposed to have more noise than those from a regional solution (Williams et al., 2004).”
Uncertainty of absolute gravity measurements (2005, background): “[4] The power law process has been observed in geodetic time series such as continuously recording strain meters [Agnew, 1992], GPS [Zhang et al., 1997; Mao et al., 1999; Williams et al., 2004] and sea level changes [Harrison, 2002].”
Detecting time-varying seasonal signal in GPS position time series with different noise levels (2017, methodology): “Supported and confirmed by previously published papers (Williams et al. 2004; Klos et al. 2014), this range of noise level was used to create a set of synthetic series.”
A continuous GPS coordinate time series analysis strategy for high-accuracy vertical land movements (2008, methodology): “…effect of time-correlated (coloured) noise (e.g. Langbein & Johnson, 1997; Zhang et al., 1997; Mao et al., 1999; Williams, 2003a; Langbein, 2004; Williams et al., 2004), the reduction of spatially correlated variations (e.g. Wdowinski et al., 1997; Nikolaidis, 2002; Johansson et al., 2002),…”
Noise in multivariate GPS position time-series (2009, methodology): “Williams et al. (2004) simulated pairs of time-series with white and flicker noise to investigate the significance of spatial correlations.”