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Parameter estimation in stochastic grey-box models. (English) Zbl 1048.93088
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:
93E10Estimation and detection in stochastic control
93A30Mathematical modelling of systems
60H10Stochastic ordinary differential equations