On the design of a guaranteed Extended Kalman filter using set inversion techniques

This paper studies the problem of a design of an Extended Kalman filter (EKF) for a nonlinear dynamic system under bounded measurement noise. The goal is to design a guaranteed EKF-to provide validated values of tuning parameters of the EKF-that gives a specified estimation performance which is defined via the mean and the variance of the estimation error for the given range of initial estimation errors and for the given range of measurement noise. The problem is formulated as a problem of inverting the set of desired estimation performance measures into a set of design parameters while taking into account the nonlinear dynamics and bounded measurement noise. We use the continuous formulation of the EKF and the set inversion via interval analysis that uses a bounding of solutions of the underlying system of differential equations via Taylor-model arithmetics. The approach is demonstrated on a case study taken from open literature.