Abbreviations
A
State transition matrix
B
Process input transition matrix
C
Measurement model
CKF
Cubature Kalman filter
EKF
Extended Kalman filter
EnKF Ensemble Kalman filter
F
Jacoby matrix of f()
f()
Non-linear function describing the process change
FIA
Flow injection analysis
H
Jacoby matrix of measurement model
h()
Measurement model
KF
Kalman filter
P
Estimation error covariance matrix
p
Model parameter vector for estimation
Q
Process noise covariance matrix
R
Measurement noise covariance matrix
t
Time
UKF
Unscented Kalman filter
v
Measurement noise vector
w
Process noise vector
x
State variables vector
x(t)
State variable at continuous time k
x [k]
State variable at discrete time k
x f,[k]
Filtered state variable at discrete time k
z
Measurement vector
1 Introduction
Bioprocesses are described as biological systems that are non-linear, complex and
unsteady; thus development of precise control systems in order to achieve robust
product quality and productivity can be challenging. The control of these processes
can be significantly improved by online process monitoring followed by corrective
actions. In this context, bioprocess digital twins are helpful tools.
Digital twins are virtual representations of the production process which enable
pre-emptive process control by using online data to predict the process outcome in
advance. They convert the physical process to a smart process and thus achieve the
ultimate goal of the digital transformation. This enables unprecedented possibilities
for timely and automated intervention to provide critical decision support during
process development [1].
The Kalman Filter for the Supervision of Cultivation Processes
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