Kalman-Bucy filters

The Kalman filter is a model-driven estimator used to improve reliability of estimated data and noise filtering. The Kalman filters are useful and powerful estimators when a process is linear and a model is available. Subsequent improvements to the model brought about the development of the so-called extended Kalman filter, which attempt to estimate system behavior based on nonlinear models and prior knowledge of the mean and covariance associated with the measurement error. Some types of Kalman filters include unscented Kalman filter, the ensemble Kalman filter, and the cubature Kalman filter.

·       Arndt, M., Hitzmann, B., 2004. Kalman filter based glucose control at small set points during fed-batch cultivation of Saccharomyces cerevisiae. Biotechnol Prog 20, 377–383. https://doi.org/10.1021/bp034156p

·        Arndt, M., Kleist, S., Miksch, G., Friehs, K., Flaschel, E., Trierweiler, J., Hitzmann, B., 2005. A feedforward–feedback substrate controller based on a Kalman filter for a fed-batch cultivation of Escherichia coli producing phytase. Computers & Chemical Engineering 29, 1113–1120. https://doi.org/10.1016/j.compchemeng.2004.11.011

·       Daboussy, M., Titica, M., Boillereaux, L., 2014. Parameter identification and state estimation of a microalgae dynamical model in sulphur deprived conditions: global sensitivity analysis, optimization criterion, extended Kalman filter. Can. J. Chem. Eng. 92, 1378–1395. https://doi.org/10.1002/cjce.22007

·       Dewasme, L., Goffaux, G., Hantson, A.-L., Wouwer, A.V., 2013. Experimental validation of an extended Kalman filter estimating acetate concentration in E. coli cultures. Journal of Process Control, IFAC World Congress Special Issue 23, 148–157. https://doi.org/10.1016/j.jprocont.2012.09.004

·        García-Mañas, F., Guzmán, J.L., Berenguel, M., Acién, F.G., 2019. Biomass estimation of an industrial raceway photobioreactor using an extended Kalman filter and a dynamic model for microalgae production. Algal Research 37, 103–114.

·        Hitzmann, B., Broxtermann, O., Cha, Y.-L., Sobieh, O., Stärk, E., Scheper, T., 2000. The control of glucose concentration during yeast fed-batch cultivation using a fast measurement complemented by an extended Kalman filter. Bioprocess Engineering 23, 337–341. https://doi.org/10.1007/s004499900190

·        Klockow, C., Hüll, D., Hitzmann, B., 2008. Model based substrate set point control of yeast cultivation processes based on FIA measurements. Analytica Chimica Acta 623, 30–37. https://doi.org/10.1016/j.aca.2008.06.011

·        Krämer, D., King, R., 2019. A hybrid approach for bioprocess state estimation using NIR spectroscopy and a sigma-point Kalman filter. Journal of Process Control 82, 91–104. https://doi.org/10.1016/j.jprocont.2017.11.008

·       Krämer, D., King, R., 2016. On-line monitoring of substrates and biomass using near-infrared spectroscopy and model-based state estimation for enzyme production by S. cerevisiae. IFAC-PapersOnLine, 11th IFAC Symposium on Dynamics and Control of Process Systems Including Biosystems DYCOPS-CAB 2016 49, 609–614. https://doi.org/10.1016/j.ifacol.2016.07.235

·       Paquet-Durand, O., Zettel, V., Yousefi-Darani, A., Hitzmann, B., 2020. The supervision of dough fermentation using image analysis complemented by a continuous discrete extended Kalman filter. Processes 8, 1669. https://doi.org/10.3390/pr8121669

·       Tebbani, S., Lopes, F., Celis, G.B., 2015. Nonlinear control of continuous cultures of Porphyridium purpureum in a photobioreactor. Chem. Eng. Sci. 123, 207–219. https://doi.org/10.1016/j.ces.2014.11.016

·       Tuveri, A., Pérez-García, F., Lira-Parada, P.A., Imsland, L., Bar, N., 2021. Sensor fusion based on extended and unscented Kalman filter for bioprocess monitoring. Journal of Process Control 106, 195–207. https://doi.org/10.1016/j.jprocont.2021.09.005

·        Yoo, S.J., Jeong, D.H., Kim, J.H., Lee, J.M., 2016. Optimization of microalgal photobioreactor system using model predictive control with experimental validation. Bioprocess. Biosyst. Eng. 39, 1235–1246. https://doi.org/10.1007/s00449-016-1602-0

·        Yousefi-Darani, Abdolrahimahim, Paquet-Durand, O., Hinrichs, J., Hitzmann, B., 2021. Parameter and state estimation of backers yeast cultivation with a gas sensor array and unscented Kalman filter. Engineering in Life Sciences 21, 170–180. https://doi.org/10.1002/elsc.202000058

·        Yousefi-Darani, Abdolrahim, Paquet-Durand, O., Hitzmann, B., 2021. The Kalman filter for the supervision of cultivation processes. Adv Biochem Eng Biotechnol 177, 95–125. https://doi.org/10.1007/10_2020_145

Specialist for Kalman-Bucy filters

Professor Dr. Bernd Hitzmann

FG Prozessanalytik und Getreidetechnologie
Institut für Lebensmittelwissenschaft und Biotechnologie
Universität Hohenheim
Garbenstr. 23
70599 Stuttgart, Germany
Tel.: + 49 711-459-23286
Fax: +49 711-459-23259
Email: Bernd.Hitzmann@uni-hohenheim.de