Nonlinear system identification in presence of nuisance parameters

This paper deals with the general problem of the estimation of physical parameters in the presence of nuisance parameters for which an explicit characterisation of the uncertainty is available. Within a Bayesian context, the maximum a posteriori estimation is used. The asymptotic confidence ellipsoid is then determined. The projection of the latter onto the parameter axes is used to obtain the confidence interval. The method is illustrated on an example with actual data from a measurement device in the context of thermo-physical parameters identification.