Issues in sampling and estimating continuous-time models with stochastic disturbances

: The standard continuous time state space model with stochastic disturbances the mathematical abstraction of continuous time white noise. To work with well defined, discrete time observations, it is necessary to sample the model with care. The basic issues are well known, and have been discussed in the literature. However, the consequences have not quite penetrated the practise of estimation and identification. One example is that the standard model of an observation being a snapshot of the current state plus noise independent of the state cannot be reconciled with this picture. Another is that estimation and identification of time continuous models require a more careful treatment of the sampling formulas. We discuss and illustrate these issues in the current contribution. An application of particular practical importance is the estimation of models based on irregularly sampled observations.

• Type: Journal
• Year: 2010
• Where: AUTOMATICA
• Authors: Lennart Ljung, Adrian Wills
• Keywords: AUTOMATICA 2010, Continuous Time, Standard Continuous Time, State Space Model