A new covariance model for inertial gravimetry and gradiometry

Forsberg, R.

doi:10.1029/jb092ib02p01305

Cited by 90 publications

(64 citation statements)

References 6 publications

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“…Different spherical or planar covariance models are often investigated in geoid or gravity fi eld modeling (Arabelos and Tscherning, 2003;Forsberg, 1987), however quite simple one is selected here. It has two parameters and is easy in the investigation of the problem.…”

Section: Introductionmentioning

confidence: 99%

A priori noise and regularization in least squares collocation of gravity anomalies

Jarmołowski¹

2013

Geodesy and Cartography

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Abstract:The paper describes the estimation of covariance parameters in least squares collocation (LSC) by the cross-validation (CV) technique called leave-one-out (LOO). Two parameters of Gauss-Markov third order model (GM3) are estimated together with a priori noise standard deviation, which contributes signifi cantly to the covariance matrix composed of the signal and noise. Numerical tests are performed using large set of Bouguer gravity anomalies located in the central part of the U.S. Around 103 000 gravity stations are available in the selected area. This dataset, together with regular grids generated from EGM2008 geopotential model, give an opportunity to work with various spatial resolutions of the data and heterogeneous variances of the signal and noise. This plays a crucial role in the numerical investigations, because the spatial resolution of the gravity data determines the number of gravity details that we may observe and model. This establishes a relation between the spatial resolution of the data and the resolution of the gravity fi eld model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.

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Section: Introductionmentioning

confidence: 99%

A priori noise and regularization in least squares collocation of gravity anomalies

Jarmołowski¹

2013

Geodesy and Cartography

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“…Development and applications of LSC techniques in geodesy and related fields have been studied by several authors (e.g. Krarup 1969;Moritz 1973;Tscherning 1976;Kearsley 1977;Moritz 1980;Knudsen 1987;Forsberg 1987;Schaffrin 1989).…”

Section: Planar Fitting and Offsets Methodsmentioning

confidence: 99%

Recovery of orthometric heights from ellipsoidal heights using offsets method over Japan

Odera

2015

Earth Planet Sp

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One of the most important applications of a geoid model is a recovery of orthometric heights from ellipsoidal heights (normally obtained from GNSS). The application of the geoid model for recovering orthometric heights from ellipsoidal heights is normally achieved by fitting the geoid model to a local vertical datum. The fitting procedure is usually accomplished by least squares collocation (LSC), using planar or spherical covariance functions. This procedure warps the gravimetric geoid model onto the local vertical datum, hence the local geoid model derived by this procedure, though convenient for local applications, it is not an equipotential surface. We propose offsets method for practical orthometric height recovery from a geoid model. The proposed procedure is more realistic because it does not constrain the local geoid to be coincident to the local vertical datum. We compare the performance of plannar fitting and offsets methods over Japan using a cross-validation procedure. Results show that offsets method performs better than the normally used planar fitting in the recovery of orthometric heights from ellipsoidal heights using a geoid model. The standard deviations of the differences between established and converted orthometric heights at randomly selected GPS/levelling test points over Japan are ±4 and ±3 cm for planar fitting and offsets methods, respectively. The offsets method is therefore more appropriate for converting ellipsoidal heights to orthometric heights than the planar fitting in the area of study.

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“…They can be estimated assuming a certain model of the covariance function. In this case, a logarithmic function was used (Forsberg, 1987). The logarithmic model consists of three parameters, i.e.…”

Section: Summary Of the Collocation Methods For Geoid Calculationmentioning

confidence: 99%

“…In this routine, the gravity covariance model between gravity anomalies at two altitudes is of form (Forsberg, 1987) …”

Section: Calculation Of a Residual Geoid Using The Collocation Methodsmentioning

confidence: 99%

A new geoid for Brunei Darussalam by the collocation method

Łyszkowicz¹,

Biryło²,

Bęcek³

2014

Geodesy and Cartography

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Computation of a new gravimetric geoid in Brunei was carried out using terrestrial, airborne and altimetric gravity data and the EGM08 geopotential model by the collocation method. The computations were carried out by the "remove-restore" technique. In order to have better insight in the quality of input data the estimation of accuracy of the gravity data and geoid undulations from GPS/levelling data was carried out using EGM08 geopotential model. It shows a poor quality of GPS/levelling data. Result of the computation is the gravimetric geoid for the territory of Brunei computed by collocation method with an accuracy estimated below of ±0.3 m.

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A new covariance model for inertial gravimetry and gradiometry

Cited by 90 publications

References 6 publications

A priori noise and regularization in least squares collocation of gravity anomalies

A priori noise and regularization in least squares collocation of gravity anomalies

Recovery of orthometric heights from ellipsoidal heights using offsets method over Japan

A new geoid for Brunei Darussalam by the collocation method

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