Abstract
The extended Kalman filter has been shown to be a precise method for nonlinear state estimation and is the facto standard in navigation systems. However, if the initial estimated state is far from the true one, the filter may diverge, mainly due to an inconsistent linearization. Moreover, interval filters guarantee a robust and reliable, yet unprecise and discontinuous localization. This paper proposes to choose a point estimated by an interval method, as a linearization point of the extended Kalman filter. We will show that this combination allows us to get a higher level of integrity of the extended Kalman filter.
Highlights
The dynamic of a mobile robot is generally described by the following discrete time nonlinear state equation (x k +1 = f k ( x k, u k, n k ) (1) yk= gk + νk where k ∈ N is the time, xk ∈ Rn is the state vector, uk is the input vector, nk is the state noise, νk is the measurement noise, and yk is the measured output vector
The interval filter [15,16] (IF) we propose to consider here is based on interval analysis
Since the extended Kalman filter (EKF) can diverge if the linearization point is far from the real state, we propose a new observer called Interval Extended Kalman Filter (IEKF) (Interval EKF)
Summary
The dynamic of a mobile robot is generally described by the following discrete time nonlinear state equation The main reason why an EKF may converge toward a fake state is that the linearization point that is chosen can be far from the true state [1] This linearization point, taken from the Kalman filter itself, can be totally inconsistent and would have been rejected by the interval filter. The idea we want to develop here is to select a linearization point inside the feasible set generated by an interval filter. This consistent point could still be far from the true one, but we understand that this choice reduces the possibility of bad behavior of the observer.
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