Time delay estimation (TDE) is a growing area of mathematical research, finding applications in a wide range of fields including medical imaging and sensor fusion. Numerous TDE algorithms have been constructed, often in response to particular real-world problems. A sensor fusion problem for localising a mobile robot has previously arisen for which Zaman created an appropriate TDE algorithm and made conjectures from the data the algorithm produced. The algorithm is novel in that it can synchronise data streams to guaranteed bounds from discrete sensor readings alone. A new algorithm was needed for the mobile robot problem because the sensors were commercial off-the-shelf (COTS) products manufactured to different specifications. They took readings at different frequencies and their clocks were independent. The increasing dissemination of COTS products is likely to lead to further applications for Zaman's algorithm. In this paper we have given the algorithm a rigorous grounding, proving that it converges to estimates of sub-sample accuracy. We have also numerically investigated convergence rates and shown how results from a real-world robot experiment resemble corresponding simulations. (C) 2012 Elsevier Inc. All rights reserved.