Covariance Function

The covariance function is one of the most fundamental mathematical tools used in Least Squares Collocation (LSC) that defines the spatial and statistical relationship of a physical process which his sampled on the Earth’s surface. It quantifies how a geodetic signal (e.g., gravity anomaly) at one location relates to the same or a different signal (geoid heights) at another based on their distance, allowing the model to analyze phenomena like the Earth’s gravity field or crustal deformation as stochastic processes rather than simple fixed parameters. The covariance function allows the prediction of unknown signals (such as geoid undulations) from different input data (such as gravity anomalies, deflections of the vertical, etc.) using cross-covariance relationships that reflect their shared statistical properties and physical characteristics.