Guaranteed nonlinear parameter estimation from bounded-error data via interval analysis

This paper deals with parameter estimation in the bounded-error context. A new approach, based on interval analysis, is proposed to compute guaranteed estimates of suitable characteristics of the set of all values of the parameter vector such that the error between the experimental data and the model outputs belongs to some predefined feasible set. This approach is especially suited to models whose output is nonlinear in their parameters, a situation where most available methods fail to provide any guarantee as to the global validity of the results obtained. After a brief presentation of interval analysis, an algorithm is proposed, which makes it possible to obtain guaranteed estimates of characteristics of such as its volume or the smallest axis-aligned box that contains it. Properties of this algorithm are established, and illustrated on a simple example.