Use of a Kalman filter to reconstruct particle size distributions from FBRM measurements

The reconstruction of particle size distributions from chord length distributions is well known to be a tricky task. The usual approach is to first set up a model that describes the relation between a given particle size distribution and the resulting chord length distribution and then try to invert this model. The difficulty is that the inversion turns out to be an ill-posed problem. The idea of this work is to use not only information about the measurement procedure, but also about the crystallisation process. Process knowledge and measurement knowledge are combined by a Kalman filter with a constrained update step. By this approach, a direct inversion of the measurement equation is no longer necessary.

► Focus beam reflectance measurement (FBRM) measures particle distributions on-line.
► FBRM generates chord length distributions (CLDs) instead of size distributions (PSDs).
► Reconstructing PSDs from CLDs by direct inversion is an ill-posed problem.
► In this work, a Kalman filter is used to overcome the ill-posedness.
► In addition to the PSDs the particle growth rate is estimated.