LPT-2009-20 [BibTeX]
Nina Paula Salau, Jorge O. Trierweiler, Argimiro R. Secchi, Wolfgang Marquardt:
A new process noise covariance matrix tuning algorithm for Kalman based state estimators
In: ADCHEM 2009 (International Symposium on Advanced Control of Chemical Processes), Istanbul, Turkey, 12-15.07.2009
Abstract:
A suitable design of state estimators requires a representative model for capturing the plant
behavior and knowledge about the noise statistics, which are generally not known in practical
applications. While the measurement noise covariance can be directly derived from the measurement
device reproducibility, the choice of the process noise covariance is much less straightforward. Further,
processes such as continuous process with grade transitions and batch or semi-batch process are
characterized by time-varying structural uncertainties which are, in many cases, partially and indirectly
reflected in the uncertainty of the model parameters. It has been shown that the robust performance of
state estimators significantly enhances with a time-varying and non-diagonal process noise covariance
matrix, which explicitly takes parameter uncertainty into account. For this case, the parameter uncertainty
is quantified through the parameter covariance matrix. This paper presents a direct and a sensitivity
method for the parameter covariance matrix computation. In the direct method, the parameter covariance
matrix is found during the parameter estimation step of the SELEST algorithm, while in the sensitivity
method, the parameter covariance matrix is obtained through a time-varying sensitivity matrix. The
results have shown the efficacy of these methods in improving the performance of an extended Kalman
filter (EKF) for a semi-batch reactor process.
Keywords:
state estimator design, noise statistics, parameter estimation, sensitivity analyses
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