  This paper proposes a method to probabilistically quantify the moments (mean
and variance) of excavated material during excavation by aggregating the prior
moments of the grade blocks around the given bucket dig location. By modelling
the moments as random probability density functions (pdf) at sampled locations,
a formulation of the sums of Gaussian based uncertainty estimation is presented
that jointly estimates the location pdfs, as well as the prior values for
uncertainty coming from ore body knowledge (obk) sub block models. The moments
calculated at each random location is a single Gaussian and they are the
components of Gaussian mixture distribution. The overall uncertainty of the
excavated material at the given bucket location is represented by the Gaussian
Mixture Model (GMM) and therefore moment matching method is proposed to
estimate the moments of the reduced GMM. The method was tested in a region at a
Pilbara iron ore deposit situated in the Brockman Iron Formation of the
Hamersley Province, Western Australia, and suggests a frame work to quantify
the uncertainty in the excavated material that hasn't been studied anywhere in
the literature yet.
