One aspect of the molecular distance geometry problem (MDGP) described in this PDF, can be written as follows:
"Given observations of noisy distances between atoms in a molecule, estimate the values of the true distances."
More formally: Given the datasets $\mathcal{D}_1,\mathcal{D}_2,\dots,\mathcal{D}_n$ of noisy distances for the atoms defined by the points $\mathcal{S} = \{x_1,x_2,\dots,x_n\}$, estimate the $n \times n$ symmetric distance matrix $\mathbf{A} = (d_{ij})$, where $d_{ij} = \lvert\lvert x_i - x_j\rvert\rvert$ and $x_i \in \mathbb{R}^K$ for $i,j \in \{1,2,...,n\}$.
Are there references that explore different noise models for the distances between atoms and references that attempt to estimate these distances?