Kriging data with measurement error: A review and a generalized approach

Abstract

Filtered kriging with parametric error (FKPE) is a mathematically sound method that generalizes and addresses the oversimplifications of previous kriging algorithms designed to filter error. The proposed approach is developed for handling grade-dependent (heteroscedastic), non-stationary, and spatially correlated sampling errors. The covariance between each pair of measurements or nodes is estimated from their model of errors and the spatial continuity of the underlying process. This research is driven by the fact that sampling and analytical errors are inherent in the samples used in the mining industry. In recent decades, data from quality control programs monitoring these errors have become widely available. FKPE handles more types of errors than other kriging algorithms to filter error and, for any number of subsets, it avoids jointly modelling the models of co-regionalization required by co-kriging methods. The precision gains of FKPE over other methods depend on how well the error model is fit to the data. Therefore, a detailed analysis of the error model and how to estimate its components is discussed. In a five-data toy example with high independent and grade-dependent error, kriging methods with oversimplified error models overweighted a high-grade datum by 50% compared to FKPE estimates. The performance of FKPE and other methods is illustrated by two synthetic examples.