New Covariance Models for Local Applications of Collocation

The least-squares collocation method, used to predict or filter a signal, is based on the estimation of the empirical covariance function and the fitting of the empirical values with a proper model function. Generally, with the standard methods on the sphere, we reach a good fitting only up to the first zero of the empirical function. In this work we have investigated how much the collocation filtering is affected by a poor fitting of the empirical covariance.Numerical tests have been done both on 1D observed and simulated data to quantify the combined impact on filtering of non stationarity and covariance fitting.Furthermore, a new model function on the sphere has been developed which is able to fit in an optimal way the empirical values.Simulations have been also carried out on the sphere to test the effectiveness of the collocation filtering using the new covariance model.