Probabilistic uncertainty bounding in output error models with unmodelled dynamics

In prediction error identification probabilistic model uncertainty bounds are generally derived from the statistical properties of the parameter estimator. The probabilistic bounds are then based on an (asymptotic) normal distribution of the parameter estimator, accompanied by a covariance matrix, which generally has to be estimated from data too. When the primal interest of the identification is in quantifying the parameter uncertainty on the basis of one single experiment, alternative methods exist that do no require the specification of the full pdf of the parameter estimator. The objective then is to have simpler computations and less dependency on (asymptotic) assumptions. While in earlier publications the situation of ARX models has been studied, here we consider the situation of nonlinearly parametrized (output error) models. It is shown that for this class relatively simple probabilistic uncertainty bounds can be constructed, that are applicable also to the situation where there is unmodelled dynamics (S notin M)