Application of artificial neural networks to weighted interval Kalman filtering

The interval Kalman filter is a variant of the traditional Kalman filter for systems with bounded parametric uncertainty. For such systems, modelled in terms of intervals, the interval Kalman filter provides estimates of the system state also in the form of intervals, guaranteed to contain the Kalman filter estimates of all point-valued systems contained in the interval model. However, for practical purposes, a single, point-valued estimate of the system state is often required. This point value can be seen as a weighted average of the interval bounds provided by the interval Kalman filter. This article proposes a methodology based on the application of artificial neural networks by which an adequate weight can be computed at each time step, whereby the weighted average of the interval bounds approximates the optimal estimate or estimate which would be obtained using a Kalman filter if no parametric uncertainty was present in the system model, even when this is not the case. The practical applicability and robustness of the method are demonstrated through its application to the navigation of an uninhabited surface vehicle.