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 significantly 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 field model. This relation is inspected in the article and compared to the regularization problem occurring frequently in data modeling.

Calculation of the effect of topography on the observed gravity becomes particularly important when modelling high-precision geoid. It requires a digital terrain model of appropriate resolution and accuracy. Various global, regional and local digital terrain models of different accuracy and resolution are recently available. Evaluation of the DTM used is required for verification and validation of its quality as well as for estimating accuracy of geoid model derived with considering the effect of topographic masses. Two DTMs: the SRTM3 of 3" x 3" resolution and the national DTM for Poland of l" x l" or l" x 2" resolution - called DTED2 - were evaluated with use of high-resolution local DTMs developed using digital photogrammetry of 25 m x 25 m as well as the regional model in Tatra mountains of 10 m x 10 m. Then the heights of almost 1000 GPS/levelling stations of Polish geodetic control were compared with the heights from the DTED2 model. The heights of over a million of gravity stations from gravity database, that were the basis of previous geoid modelling in Poland, were also compared with the heights from the DTED2 model. The effect of uncertainty of a DTM on estimation of mean gravity anomalies was discussed. In particular, the effect of replacing heights from gravity database with the heights from the DTED2 model in the process of calculating mean gravity anomalies, on the accuracy of geoid modelling was investigated. The use of the DTED2 model is at present recommended for determination of precise geoid model in Poland.