Interval Analysis for Guaranteed Nonlinear Parameter and State Estimation

Parameter and state estimation problems are encountered when modeling processes that involve uncertain quantities to be estimated from measurements. In this paper, it is assumed that all uncertain quantities (state perturbation, measurement noise, parameter vector. . .) are bounded and belong to known sets. Many tools are available for characterizing the set of all values of the parameter or state vector that are consistent with this hypothesis. Most of these methods apply when the model output is linear in the parameters or initial state. The set to be characterized is then usually enclosed in simple geometric shapes such as polytopes, parallelotopes or ellipsoids (see, e.g., [16] and the references therein). When the model under study is nonlinear, the situation is much more complicated, as the set to be characterized may be nonconvex and may even consist of several disconnected components1. As we shall see, interval analysis provides tools for enclosing such sets in unions of nonoverlapping interval vectors, the precision of the approximation being tuned by the user. The aim of this paper is to summarize some recent results on guaranteed parameter and state estimation in this nonlinear bounded-error context.