An Alternative Paradigm for Probabilistic Uncertainty Bounding in Prediction Error Identification

In prediction error identification model uncertainty bounds are generally derived from the statistical properties of the parameter estimator. These statistical properties reflect the variability in the estimated model under repetition of experiments with different realizations of the measured signals. However when the primal interest of the identification is in quantifying the uncertainty in an estimated parameter on the basis of one single experiment, this is not necessarily the best and only approach. In the alternative paradigm that is presented here, not the covariance of the estimator will be used for bounding the model uncertainty, but an a posteriori bound on the error in the estimated parameter will be constructed that is structurally dependent on the particular data sequence. This will allow simpler computations for probabilistic model uncertainty bounds also applicable to the situation of approximate modelling (S ∉ M) and to model structures that are nonlinear in the parameters, such as Output Error (OE) models.