Localizing tiny sensor nodes in large wireless sensor networks is extremely complex, due to the node's strict resource limitations regarding memory size, processor performance and overall battery capacity. Moreover, in case of mobile nodes the developing process for localization methods is even more challenging. This paper presents an efficient approach for localization in mobile sensor networks, which is based on an extension of the already known "Distributed Least Squares (DLS)"-algorithm. The extension consist of a mobile phase, where sensor nodes update their initial position by QR-factorization. We show in extensive simulations that the mobile DLS-algorithm leaves only minimal computations at the resource constrained sensor nodes.