Location awareness is a fundamental requirement for many applications of sensor networks. This paper proposes an original technique for self-localization in mobile ad-hoc networks. This method is adapted to the limited computational and memory resources of mobile nodes. The localization problem is solved in an interval analysis framework. The propagation of the estimation errors is based on an interval formulation of a state space model, where observations consist of anchor-based connectivities. The problem is then formulated as a constraint satisfaction problem where a simple Waltz algorithm is applied in order to contract the solution. This technique yields a guaranteed and robust online estimation of the mobile node positions. Observation errors as well as anchor node imperfections are taken into consideration in a simple and computational-consistent way. Multihop anchor-based and backpropagated localizations are also made possible in our method. Simulation results on mobile node trajectories corroborate the efficiency of the proposed technique and show that it outperforms the particle filtering methods.