  Dynamic operation of biological processes, such as anaerobic digestion (AD),
requires reliable process monitoring to guarantee stable operating conditions
at all times. Unscented Kalman filters (UKF) are an established tool for
nonlinear state estimation, and there exist numerous variants of UKF
implementations, treating state constraints, improvements of numerical
performance and different noise cases. So far, however, a unified comparison of
proposed methods emphasizing the algorithmic details is lacking. The present
study thus examines multiple unconstrained and constrained UKF variants,
addresses aspects crucial for direct implementation and applies them to a
simplified AD model. The constrained UKF considering additive noise delivered
the most accurate state estimations. The long run time of the underlying
optimization could be vastly reduced through pre-calculated gradients and
Hessian of the associated cost function, as well as by reformulation of the
cost function as a quadratic program. However, unconstrained UKF variants
showed lower run times at competitive estimation accuracy. This study provides
useful advice to practitioners working with nonlinear Kalman filters by paying
close attention to algorithmic details and modifications crucial for successful
implementation.
