Initial localization by set inversion

In this paper, initial localization problems are solved by using set-membership estimation. The method can be used with any robot and any kind of sensor(s), provided that a computable model of the environment/sensor interaction is available. With a pedagogical aim in mind, it is detailed in the case of the localization of a vehicle from range measurements in a polygonal environment. Salient properties of the method are as follows. First, it does not need any explicit management of matching hypotheses. Second, it is able to deal with ambiguous situations where several radically different vehicle configurations are consistent with the measurements. Third, it can be made robust to outliers. Fourth, it can deal with nonlinear observation models without any approximation. Fifth, the result is guaranteed in the sense that no configuration consistent with the data and the hypotheses can be missed.