Set-membership localization with probabilistic errors

Interval methods have been shown to be efficient, robust and reliable to solve difficult set-membership localization problems. However, they are unsuitable in a probabilistic context, where the approximation of an unbounded probability density function by a set cannot be accepted. This paper proposes a new probabilistic approach which makes possible to use classical set-membership localization methods which are robust with respect to outliers. The approach is illustrated on two simulated examples.

► A probabilistic approach can easily be combined with set-membership estimation.
► In this study, a robust interval estimation is compared with an extended Kalman filter.
► Interval analysis can be used to solve efficiently nonlinear estimation with outliers.
► Robustness with respect to outliers can be obtained by relaxing some data.