Guaranteed recursive nonlinear state estimation using interval analysis

TL;DR: In this article, a new state estimator based on interval analysis and the notion of set inversion is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the noise bounds and a set containing the initial value of the states.

Abstract: The problem considered is state estimation in the presence of unknown state and measurement noise, each noise component being assumed to belong to some known interval. In such a bounded-error context, most available results are for linear models, and the purpose of the present paper is to deal with the nonlinear case. Based on interval analysis and the notion of set inversion, a new state estimator is presented, which evaluates a set estimate guaranteed to contain all values of the state that are consistent with the available observations, given the noise bounds and a set containing the initial value of the state. To the best of our knowledge, it is the first time that such a guaranteed estimator is made available. The precision of the set estimate can be improved, at the cost of more computation. The theoretical properties of the estimator are studied, and computer implementation has received special attention. A simple illustrative example is treated.