Optimally Bounded Interval Kalman Filter

Abstract

This paper is concerned with the optimization of the upper bounds of the interval covariance matrices appearing in the Interval Kalman filter [1]. This filter is applied to discrete time linear systems subject to mixed uncertainties (combining bounded and stochastic uncertainties), in terms of observations and noises (mainly sensors limitations). It uses interval analysis in order to provide the optimal bound of the state estimation error covariance. Based on that, an optimal state estimation enclosing the set of all possible solutions w.r.t admissible uncertainties is performed. In this article, theorems and lemmas proving the optimality of the proposed solution are provided. Simulations on an example show the efficiency of the developed interval estimation.