Model Error Modeling and Stochastic Embedding

To estimate a model of useful complexity for control design, at the same time as having a good insight into its reliability is a central issue in system identification, in particular for identification for control. Basically one can think of a (simpler) design model and a (more complex and exible) error model. These concepts are discussed in terms of model error modeling and stochastic embedding in a framework that allows the error model to vary over time. It is then of interest to estimate a probabilistic description of this error model. This can be accomplished by estimating parameters that describe the pdf of the errors. In this contribution explicit expressions for the likelihood function for these parameters are derived by marginalization over the error model, in case this is a linear regression.