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Parameter and state estimation in nonlinear stochastic continuous‐time dynamic models with unknown disturbance intensity
Author(s) -
Varziri M. S.,
McAuley K. B.,
McLellan P. J.
Publication year - 2008
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.20100
Subject(s) - kalman filter , stochastic differential equation , nonlinear system , noise (video) , control theory (sociology) , disturbance (geology) , linearization , a priori and a posteriori , mathematics , estimation theory , computer science , statistics , physics , control (management) , artificial intelligence , paleontology , philosophy , epistemology , quantum mechanics , image (mathematics) , biology
Approximate Maximum Likelihood Estimation (AMLE) is an algorithm for estimating the states and parameters of models described by stochastic differential equations (SDEs). In previous work (Varziri et al., Ind. Eng. Chem. Res., 47 (2), 380‐393, (2008); Varziri et al., Comp. Chem. Eng., in press), AMLE was developed for SDE systems in which process‐disturbance intensities and measurement‐noise variances were assumed to be known. In the current article, a new formulation of the AMLE objective function is proposed for the case in which measurement‐noise variance is available but the process‐disturbance intensity is not known a priori. The revised formulation provides estimates of the model parameters and disturbance intensities, as demonstrated using a nonlinear CSTR simulation study. Parameter confidence intervals are computed using theoretical linearization‐based expressions. The proposed method compares favourably with a Kalman‐filter‐based maximum likelihood method. The resulting parameter estimates and information about model mismatch will be useful to chemical engineers who use fundamental models for process monitoring and control.