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Zbl 1048.93088
Kristensen, Niels Rode; Madsen, Henrik; Jørgensen, Sten Bay
Parameter estimation in stochastic grey-box models. (English)
[J] Automatica 40, No. 2, 225-237 (2004). ISSN 0005-1098

Summary: An efficient and flexible parameter estimation scheme for grey-box models in the sense of discretely, partially observed Itô stochastic differential equations with measurement noise is presented along with a corresponding software implementation. The estimation scheme is based on the extended Kalman filter and features maximum likelihood as well as maximum a posteriori estimation on multiple independent data sets, including irregularly sampled data sets and data sets with occasional outliers and missing observations. The software implementation is compared to an existing software tool and proves to have better performance both in terms of quality of estimates for nonlinear systems with significant diffusion and in terms of reproducibility. In particular, the new tool provides more accurate and more consistent estimates of the parameters of the diffusion term.

MSC 2000:: *93E10 Estimation and detection in stochastic control
93A30 Mathematical modelling of systems
60H10 Stochastic ordinary differential equations

Keywords: Grey-box models; Parameter estimation; Stochastic differential equations; Maximum likelihood estimation; Extended Kalman filter; Estimation with missing observations; Robust estimation; Estimation accuracy; Software tools

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Zentralblatt MATH Berlin [Germany]