cultivations, despite continuous supply by a feed, the substrate concentration can
drop to zero as the cell takes it up very fast. In such cultivations, linearization in the
time and measurement update can lead to significant inaccuracies in the process,
while the EKF assumes a certain probability for substrate concentrations below zero,
even though this is physically impossible [54]. Therefore in recent years, application
of other non-linear extensions of the Kalman filter is used. For example, Fernandes
et al. [54] have implemented an UKF algorithm in order to estimate glucose and
glutamine from biomass, lactate and ammonia measurement during fed-batch cultivation of hybridoma cells. The predictions were compared to the ones obtained with
an EKF; they have reported the UKF achieves better level of accuracy. Krämer and
King [57] have implemented a UKF in fed-batch cultivation of S. cerevisiae for
noise filtering from predicted biomass values with NIR spectrometer. In another
study, the same authors [54] have implemented an EKF for the same process. The
authors have reported accurate predicted values in both studies; however there is no
comparison between the two methods. Other types of the non-linear Kalman filtering
method have also been reported in literature. Zhao et al. [53] have implemented a
CKF for incorporating delayed measurements of biomass, substrate, and product
concentration in fed-batch cultivation for penicillin production. Bavdekar et al. [47]
have implemented an EnKF for overcoming delayed measurements of biomass,
substrate and ethanol concentration in fed-batch cultivation of S. cerevisiae.
Addressing the same delay problem Klockow et al. [43] complemented a ring buffer
by an EKF and got satisfied results.
In order to indicate which Kalman filter extension describes the process better,
numerical simulation runs are required. According to this perspective, a closer look
to the presented articles indicates that most studies (31 articles) had relied on
practical applications and simulation studies have been reported only 12 times.
3.2 Microorganism
Regarding the type of microorganism, the articles show that the majority of the
research has focused on applying the Kalman filter or its extensions for state or
parameter estimation during the cultivation of S. cerevisiae (19 articles) and E. coli
(7 articles). The importance of these microorganisms for the biopharmaceutical
industry is widely recognized, as E. coli and S. cerevisiae are the most important
host microorganism used to produce recombinant proteins [58]. In addition,
S. cerevisiae is also widely used for the production of the backers yeast as well as
wine and beer. Only a few articles demonstrate state estimation in the cultivation
process of other microorganisms. For instance, some authors have implemented state
estimation methods for prediction of substrate and product concentration during
cultivations of Candida utilis [30], Penicillium chrysogenum [46, 53] and
Kluyveromyces marxianus [34].
The Kalman Filter for the Supervision of Cultivation Processes
107
drop to zero as the cell takes it up very fast. In such cultivations, linearization in the
time and measurement update can lead to significant inaccuracies in the process,
while the EKF assumes a certain probability for substrate concentrations below zero,
even though this is physically impossible [54]. Therefore in recent years, application
of other non-linear extensions of the Kalman filter is used. For example, Fernandes
et al. [54] have implemented an UKF algorithm in order to estimate glucose and
glutamine from biomass, lactate and ammonia measurement during fed-batch cultivation of hybridoma cells. The predictions were compared to the ones obtained with
an EKF; they have reported the UKF achieves better level of accuracy. Krämer and
King [57] have implemented a UKF in fed-batch cultivation of S. cerevisiae for
noise filtering from predicted biomass values with NIR spectrometer. In another
study, the same authors [54] have implemented an EKF for the same process. The
authors have reported accurate predicted values in both studies; however there is no
comparison between the two methods. Other types of the non-linear Kalman filtering
method have also been reported in literature. Zhao et al. [53] have implemented a
CKF for incorporating delayed measurements of biomass, substrate, and product
concentration in fed-batch cultivation for penicillin production. Bavdekar et al. [47]
have implemented an EnKF for overcoming delayed measurements of biomass,
substrate and ethanol concentration in fed-batch cultivation of S. cerevisiae.
Addressing the same delay problem Klockow et al. [43] complemented a ring buffer
by an EKF and got satisfied results.
In order to indicate which Kalman filter extension describes the process better,
numerical simulation runs are required. According to this perspective, a closer look
to the presented articles indicates that most studies (31 articles) had relied on
practical applications and simulation studies have been reported only 12 times.
3.2 Microorganism
Regarding the type of microorganism, the articles show that the majority of the
research has focused on applying the Kalman filter or its extensions for state or
parameter estimation during the cultivation of S. cerevisiae (19 articles) and E. coli
(7 articles). The importance of these microorganisms for the biopharmaceutical
industry is widely recognized, as E. coli and S. cerevisiae are the most important
host microorganism used to produce recombinant proteins [58]. In addition,
S. cerevisiae is also widely used for the production of the backers yeast as well as
wine and beer. Only a few articles demonstrate state estimation in the cultivation
process of other microorganisms. For instance, some authors have implemented state
estimation methods for prediction of substrate and product concentration during
cultivations of Candida utilis [30], Penicillium chrysogenum [46, 53] and
Kluyveromyces marxianus [34].
The Kalman Filter for the Supervision of Cultivation Processes
107