We present a mobile robot localization method for known 2D environments, which is an evidence accumulation method where the complexity is reduced by means of a multi-resolution scheme. The method is called multi-resolution evidence accumulation (MUREA). The added values of the work include: the capability of the system to accept both raw sensor data as well as independently generated localization estimates; the capability of the system to be both a global or local localization system, depending on the availability of a global estimate; and the capability of the system to give out an accurate estimate when required (e.g. before its regular completion), which could be called any-time localization. We elaborate and evaluate a strategy for travelling the search-space, which expands the pose current estimate alternating between subspaces. Real experiments, based on omnidirectional sensing in an indoor environment, are presented.