SET INVERSION VIA INTERVAL-ANALYSIS FOR NONLINEAR BOUNDED-ERROR ESTIMATION

In the context of bounded-error estimation, one is interested in chara cterizing 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 proble m can be considered as solved when the model output is linear in the p arameters, the situation is far less advanced in the general nonlinear case. In this paper, the problem of nonlinear bounded-error estimatio n 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 prov ed and the algorithm is applied to two test cases. The results obtaine d are compared with those provided by signomial analysis.