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Estimation of covariance parameters for GNSS/leveling geoid data by Leave-One-Out validation

Jarmołowski W.

Technical Sciences / University of Warmia and Mazury in Olsztyn

2013

nr 16(4)

291--307

The article describes the estimation of covariance parameters in Least Squares Collocation (LSC) by Leave-One-Out (LOO) validation, which is often considered as a kind of cross validation (CV). Two examples of GNSS/leveling (GNSS/lev) geoid data, characterized by different area extent and resolution are applied in the numerical test. A special attention is focused on the noise, which is not correlated in this case. The noise variance is set to be homogeneous for all points. Two parameters in three covariance models are analyzed via LOO, together with a priori noise standard deviation, which is a third parameter. The LOO validation finds individual parameters for different applied functions i.e. different correlation lengths and a priori noise standard deviations. Diverse standard deviations of a priori noise found for individual datasets illustrate a relevance of applying LOO in LSC. Two examples of data representing different spatial resolutions require individual noise covariance matrices to obtain optimal LSC results in terms of RMS in LOO validation. The computation of appropriate a priori noise variance is however difficult via typical covariance function fitting, especially in the case of sparse GNSS/leveling geoid data. Therefore LOO validation may be helpful in describing how the a priori noise parameter may affect LSC result and a posteriori error.