Planar geodetic covariance functions

Meier, Siegfried

doi:10.1029/rg019i004p00673

Cited by 30 publications

(7 citation statements)

References 42 publications

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“…The Mátern parameters can be estimated from the data via Maximum Likelihood Estimation (Handcock and Wallis 1994), or fixed aprori (Stein 1999) which was implicitly done by Howind et al (1999), El-Rabbany (1994) when using an exponential function to model carrier phase correlations of GPS observations. Indeed, particular cases corresponding to a smoothness of 1 = 2 ; 1; 1 are known in geodesy as the exponential covariance function, the first order Markov or the Gaussian model respectively (Whittle 1954; Grafarend and Awange 2012; Meier 1981). Other parametrizations of the Mátern covariance function presented in Eq.…”

Section: Temporal Correlationsmentioning

confidence: 99%

On modelling GPS phase correlations: a parametric model

Kermarrec

Schön

2017

Acta Geod Geophys

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Least-squares estimates are unbiased with minimal variance if the correct stochastic model is used. However, due to computational burden, diagonal variance covariance matrices (VCM) are often preferred where only the elevation dependency of the variance of GPS observations is described. This simplification that neglects correlations between measurements leads to a less efficient least-squares solution. In this contribution, an improved stochastic model based on a simple parametric function to model correlations between GPS phase observations is presented. Built on an adapted and flexible Mátern function accounting for spatiotemporal variabilities, its parameters are fixed thanks to maximum likelihood estimation. Consecutively, fully populated VCM can be computed that both model the correlations of one satellite with itself as well as the correlations between one satellite and other ones. The whitening of the observations thanks to such matrices is particularly effective, allowing a more homogeneous Fourier amplitude spectrum with respect to the one obtained by using diagonal VCM. Wrong Mátern parameters-as for instance too long correlation or too low smoothness-are shown to skew the least-squares solution impacting principally results of test statistics such as the apriori cofactor matrix of the estimates or the aposteriori variance factor. The effects at the estimates level are minimal as long as the correlation structure is not strongly wrongly estimated. Thus, taking correlations into account in least-squares adjustment for positioning leads to a more realistic precision and better distributed test statistics such as the overall model test and should not be neglected. Our simple proposal shows an improvement in that direction with respect to often empirical used model.

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Section: Temporal Correlationsmentioning

confidence: 99%

On modelling GPS phase correlations: a parametric model

Kermarrec

Schön

2017

Acta Geod Geophys

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“…Various models used for comparison with our model. The explanation for the terms in the table can be found for models 3 to 10 in Meier (1981) and for model 2 in Forsberg (1987 used in the form of a covariance function. The autocovariance function of the free air anomaly is calculated from the high-resolution gravity field obtained from high-density satellite altimeter data.…”

Section: Covari a N C E M O D E Lmentioning

confidence: 99%

Self-affine gravity covariance model for the Bay of Bengal

Bansal

Dimri

2005

Geophysical Journal International

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S U M M A R YAn anisotropic covariance model embedded with self-affine characteristics of gravity and bathymetry anomalies is proposed. High-resolution free air gravity data obtained from the high-density satellite altimetry data have been used to study the self-affinity of the gravity measurements. The digital terrain model-5 (DTM-5) is used for the bathymetry data. The Hurst coefficients (H) are calculated using 2-D power spectral density of the free air gravity and bathymetry data from 140 blocks of 1 • × 1 • . The Hurst coefficients (H) are also determined for free air gravity data along 24 orthogonal profiles using rescaled range (R/S) analysis. Further, the estimated H values are used in order to find the appropriate gravity and bathymetry covariance model for the area. The average value of H is more for 2-D free air gravity data as compared with the bathymetry data. The H values from the 1-D free air gravity profiles are found to be 0.75 and 0.77 along the N-S and E-W directions, respectively. The Von Karman covariance model with different correlation lengths is found to be suitable for 2-D and 1-D free air gravity and 2-D bathymetry data.

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“…These two classes, which have been proved to be the members of Φ 3 (Shkarofsky 1968) and of Φ ∞ classes (Gneiting et al (1999)), can be applied to many geodetic problems, e.g. Grafarend (1979), Meier (1981), Wimmer (1982), .…”

Section: Tatarski's Class Of Homogeneous and Isotropic Correlation Fumentioning

confidence: 99%

Space gravity spectroscopy: the benefits of Taylor-Karman structured criterion matrices

2003

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Abstract. As soon as a space gravity spectroscopy was successfully performed, for instance by means of semicontinuous ephemeris of LEO - GPS tracked satellites, the problem of data validation appeared. It is for this purpose that a stochastic model for the homogeneous and isotropic analysis of measurements, obtained as “directly" measured values in LEO satellite missions (CHAMP, GRACE, GOCE), is studied. An isotropic analysis is represented by the homogeneous distribution of measured values and the statistical properties of the model are calculated. In particular, a correlation structure function is defined by the third order tensor (Taylor-Karman tensor) for the ensemble average of a set of incremental differences in measured components. Specifically, Taylor-Karman correlation tensor is calculated with the assumption that the analyzed random function is of a “potential type". The special class of homogeneous and isotropic correlation functions is introduced. Finally, a successful application of the concept is presented in the case study CHAMP and a comparison between modeled and estimated correlations is performed.Key words. data validation, 3D correlation tensor, homogeneous and isotropic correlation functions, Taylor-Karman structure, CHAMP

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Planar geodetic covariance functions

Cited by 30 publications

References 42 publications

On modelling GPS phase correlations: a parametric model

On modelling GPS phase correlations: a parametric model

Self-affine gravity covariance model for the Bay of Bengal

Space gravity spectroscopy: the benefits of Taylor-Karman structured criterion matrices

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