The effect of coloured noise on the uncertainties of rates estimated from geodetic time series

By Simon D. P. Williams. 2003

446 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Geophysics

View Paper: https://www.semanticscholar.org/paper/4415375d360c763f05a6583287aff4d209010e34

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Citations in the corpus

Geophysics From Terrestrial Time‐Variable Gravity Measurements (2017, background): “Neglecting these signatures leads to underestimating the uncertainties on the computed gravity rates of change (Agnew, 1992; Van Camp et al., 2005; Williams, 2003).”
Correlated errors in GPS position time series: Implications for velocity estimates (2011, methodology): “[41] Therefore to properly account for the colored noise dependency on data time period, the known data covariance matrix used in noise analyses [e.g., Langbein and Johnson, 1997; Zhang et al., 1997; Mao et al., 1999; Langbein, 2004; Williams, 2003b; Williams et al., 2004; Amiri‐Simkooei et al., 2”
Uncertainty of absolute gravity measurements (2005, methodology): “Accounting for the type of noise is very important when estimating the related uncertainties but does not influence the slope estimate significantly [Williams, 2003].”
Least-squares variance component estimation: theory and GPS applications (2007, methodology): “The power spectra, Py, of many geophysical phenomena, including the noise in GPS position time series, are well approximated as a power-law process (Mandelbrot, 1983; Agnew, 1992; Mao et al., 1999; Williams, 2003a; Williams et al., 2004).”
Fast error analysis of continuous GNSS observations with missing data (2013, methodology): “Mao et al. (1999), Williams (2003) and Langbein (2010) assume that the power-law noise starts to develop at the same time when one starts the measurements.”
Error analysis of continuous GPS position time series (2004, background): “Finally, different sites are subject to varying amounts of disruption leading to the addition of noise due to offsets [Williams, 2003b].”
Detecting offsets in GPS time series: First results from the detection of offsets in GPS experiment (2013, unknown): “Some studies have also been dedicated to the importance of offsets in GPS studies [ Williams , 2003a] and their detection [ Khodabandeh et al. , 2012; Williams , 2003a; Borghi et al. , 2012; Vitti , 2012].”
A continuous GPS coordinate time series analysis strategy for high-accuracy vertical land movements (2008, methodology): “Jκ, the covariance matrix of the power-law noise is computed by means of fractional differencing (Hosking, 1981; Williams, 2003a) such that Jκ = TT T (5) whereT is a transformation matrix obtained from T = ∆T−κ/4 ψ0 0 0 . . . 0 ψ1 ψ0 0 . . . 0 ψ2 ψ1 ψ0 . . . 0 ... ... ...…”
Noise in multivariate GPS position time-series (2009, methodology): “The flicker noise variances estimated in this paper are roughly one-half the size of those quoted in these papers (see Williams 2003a).”
Network-based estimation of time-dependent noise in GPS position time series (2015, background): “This could be a cause for concern since the presence of lowfrequency noise in the data (e.g., random walk) can significantly affect velocity uncertainty (Williams 2003a; Langbein 2012).”
Estimation of velocity uncertainties from GPS time series: Examples from the analysis of the South African TrigNet network (2011, result): “This relationship between m and n is also in agreement with Williams [2003a]. Unlike the position, the velocity information still improves with observation length for n > − 3.”
Convergence rate across the Nepal Himalaya and interseismic coupling on the Main Himalayan Thrust: Implications for seismic hazard (2011, background): “Also the daily estimates are temporally correlated and it is therefore incorrect to assume a purely white noise model [Zhang et al., 1997; Langbein and Johnson, 1997; Williams, 2003].”
Spatiotemporal filtering of regional GNSS network’s position time series with missing data using principle component analysis (2013, background): “…quadratic unbiased 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…”