Issues in sampling and estimating continuous-time models with stochastic disturbances , Report no. LiTH-ISY-R-2988

The standard continuous time state space model with stochastic disturbances contains the mathematical abstraction of continuous time white noise. To work with well de ned, 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 identi cation. 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 identi cation 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.