Estimation of specific growth rate from cell density measurements

For modelling purposes it is of great importance to derive the specific growth rate as a function of time from biomass measurements. Traditional methods such as exponential or polynomial fitting do not give satisfactory results nor do these methods take the noise characteristics of the biomass measurements into account. Standard recursive techniques, such as Kalman filtering, use only the data up to the time under consideration and are dependent of a good initial estimation. This paper describes a technique based on combining subsequent backward and forward extended Kalman filtering to give a smoothing estimator for the specific growth rate. The estimator does not need an initial value and is shown to have a single tuning parameter. The applicability of the estimator is demonstrated on batch and fed-batch cultivations of two organisms: Bordetella pertussis and Neisseria meningitidis.