Set inversion via interval analysis for nonlinear bounded-error estimation

AlWlmet--ln the context of bounded-error estimation, one is interested in characterizing the set of all the values of the parameters to be estimated that are consistent with the data in the sense that the errors between the data and model outputs fall within prior bounds. While the problem can be considered as solved when the model output is linear in the parameters, the situation is far less advanced in the general nonlinear case. In this paper, the problem of nonlinear bounded-error estimation is viewed as one of set inversion. An original algorithm is proposed, based upon interval analysis, that makes it possible to characterize the feasible set for the parameters by enclosing it between internal and external unions of boxes. The convergence of the algorithm is proved and the algorithm is applied to two test cases. The results obtained are compared with those provided by signomial analysis.