Estimation of Spatial Distribution Considering Indirect Data Using Gaussian Process Regression

Since soil properties are generally measured at limited locations, it is preferable to use all available measured data including indirect data effectively to estimate the spatial distribution in a rational manner. A more accurate estimation can be achieved by considering the indirect measurement data that are highly correlated with the soil property in interest. In this study, we use GPR with multiple random fields. The random and trend components are estimated using the Whittle-Matérn autocorrelation function. The accuracy of estimation is compared between the cases with and without consideration of indirect data for the random component. Even if the direct data is not observed around the target point, a detailed spatial distribution is obtained by considering the surrounding indirect data when they have strong correlation.