New computation aspects for the Interval Kalman Filtering

In this paper, we consider Filtering of discrete time linear models with bounded uncertainties on parameters and measurement noise modeled by gaussian distribution. This work is based on a previous work Chen et al. [1997] in which the classical Kalman Filtering technique (Kalman [1960]) has been extended to interval linear models with known classical statistical assumptions. As the expressions for deriving the Kalman flter involve matrix inversion, one must find a way to implement or avoid this tricky algebraic operation within an interval framework. Our contribution consists in proposing an alternative approach to solve the interval matrix inversion problem without loss of solution while controlling the inherent pessimism of interval calculus. Several techniques are proposed to limit highly overestimation eects propagating within the interval Kalman flter recursive structure. In particular the gain of the flter is obtained by a calculus based on the set inversion algorithm SIVIA. A dedicated example is developed to compare diérent approaches.