Kalman-based approaches for online estimation of bioreactor dynamics from fluorescent reporter measurements

We address online estimation of microbial growth dynamics in bioreactors from measurements of a fluorescent reporter protein synthesized along with microbial growth. We consider an extended version of standard growth models that accounts for the dynamics of reporter synthesis. We develop state estimation from sampled, noisy measurements in the cases of known and unknown growth rate functions. Leveraging conservation laws and regularized estimation techniques, we reduce these nonlinear estimation problems to linear time-varying ones, and solve them via Kalman filtering. We establish convergence results in absence of noise and show performance on noisy data in simulation.