Variance–covariance analysis of two high-resolution regional least-squares quasi-geoid models

This paper investigates the full variance–covariance (VC) matrix of two high-resolution regional quasi-geoid models, utilizing a spherical radial basis function parameterization. Model parameters were estimated using weighted least-squares techniques and variance component estimation (VCE) for data weighting. The first model, known as the ...

How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model?

The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared...

A methodology for least-squares local quasi-geoid modelling using a noisy satellite-only gravity field model

The paper is about a methodology to combine a noisy satellite-only global gravity field model (GGM) with other noisy datasets to estimate a local quasi-geoid model using weighted least-squares techniques. In this way, we attempt to improve the quality of the estimated quasi-geoid model and to complement it with a full noise covariance matrix...

The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise

We propose a methodology for the combination of a gravimetric (quasi-) geoid with GNSS-levelling data in the presence of noise with correlations and/or spatially varying noise variances. It comprises two steps: first, a gravimetric (quasi-) geoid is computed using the available gravity data, which, in a second step, is improved using ellipsoidal...

The choice of the spherical radial basis functions in local gravity field modeling

The choice of the optimal spherical radial basis function (SRBF) in local gravity field modelling from terrestrial gravity data is investigated. Various types of SRBFs are considered: the point-mass kernel, radial multipoles, Poisson wavelets, and the Poisson kernel. The analytical expressions for the Poisson kernel, the point-mass kernel and...

A data-driven approach to local gravity field modelling using spherical radial basis functions

We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing potential using least-squares techniques. The latter is represented as a linear...

On the non-uniqueness of local quasi-geoids computed from terrestrial gravity anomalies

We consider the problem of local (quasi-)geoid modelling from terrestrial gravity anomalies. Whereas this problem is uniquely solvable (up to spherical harmonic degree one) if gravity anomalies are globally available, the problem is non-unique if gravity anomalies are only available within a local area, which is the typical situation in local...