Distributional Kalman Filter for Reseource Model Updating

Working with geometallurgical variables presents different challenges in mathematical geosciences, particularly, scale problems (van den Boogaart and Tolosana-Delgado, 2018). Geometallurgical data with distributional scale requires theoretical and practical developments. Methods for statistical interpolation and simulation of distributional data in space have been recently proposed by (Menafoglio et al., 2014, 2016). However, no method is available to sequentially incorporate new information into spatial models. One of the most promising implementations of such sequential information update in resource modelling estimation industry are data assimilation techniques (Wambeke and Benndorf, 2017; Benndorf, 2015).
These techniques are becoming popular due to the ability of dealing with large amount of data that new sensor-based technologies nowadays provide. Among the measurement modes that these sensors can obtain, there are also distributional scale data such as, grain size or particle size distributions. This information is of crucial importance in order to relate upstream deposit information with downstream processing processes. Data assimilation of distributional variables still presents several challenges. For instance, an adaptation of the classical formulation of Kalman filtering needs to be extended to the general Bayes Hilbert Space.
In this work, we apply the general theory of Bayes Hilbert spaces to develop a Kalman Filter method allowing for sequential data assimilation of distributional variables with infinite support.
Two different sets of information with different variability are tested. These are particle size and grain size distribution. After validation, a sensitivity analysis is performed to investigate the effects of different parameters. Practical implementation aspects are also discussed to allow for an effective application within an operating mine.