  Multicellular systems play a key role in bioprocess and biomedical
engineering. Cell ensembles encountered in these setups show phenotypic
variability like size and biochemical composition. As this variability may
result in undesired effects in bioreactors, close monitoring of the cell
population heterogeneity is important for maximum production output, and
accurate control. However, direct measurements are mostly restricted to a few
cellular properties. This motivates the application of model-based online
estimation techniques for the reconstruction of non-measurable cellular
properties. Population balance modeling allows for a natural description of
cell-to-cell variability. In this contribution, we present an estimation
approach that, in contrast to existing ones, does not rely on a
finite-dimensional approximation through grid based discretization of the
underlying population balance model. Instead, our so-called characteristics
based density estimator employs sample approximations. With two and
three-dimensional benchmark examples we demonstrate that our approach is
superior to the grid based designs in terms of accuracy and computational
demand.
