Finite-range sensing and communication are factors in the connectivity of a dynamic mobile-robot network. State estimation becomes a difficult problem when communication connections allowing information exchange between all robots are not guaranteed. This paper presents a decentralized state-estimation algorithm guaranteed to work in dynamic robot networks without connectivity requirements. We prove that a robot only needs to consider its own knowledge of network topology in order to produce an estimate equivalent to the centralized state estimate whenever possible while ensuring that the same can be performed by all other robots in the network. We prove certain properties of our technique and then it is validated through simulations. We present a comprehensive set of results, indicating the performance benefit in different network connectivity settings, as well as the scalability of our approach.