Parameter estimation in stochastic grey-box models

An e2cient and 3exible parameter estimation scheme for grey-box models in the sense of discretely, partially observed Itô stochastic di6erential equations with measurement noise is presented along with a corresponding software implementation. The estimation scheme is based on the extended Kalman 9lter 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 signi9cant di6usion and in terms of reproducibility. In particular, the new tool provides more accurate and more consistent estimates of the parameters of the di6usion term. ? 2003 Elsevier Ltd. All rights reserved.