Localization is a crucial requirement for mobile underwater systems. Real-time position information is needed for control and navigation of underwater vehicles, in early warning systems and for certain routing protocols. Past research has shown that the localization accuracy of networked underwater systems can be significantly improved using inter-vehicle collaboration. More specifically the Maximum Likelihood (ML) position estimates of a mobile collective can be computed from measurements of relative positions and motion, albeit in a non-real-time fashion. In this work we extend this solution to compute the position estimates of a network in real-time and in a distributed fashion. We first describe a centralized approach to identify key factors that fundamentally limit the performance of a real-time solution. Using the centralized approach as a benchmark, we arrive at a real-time distributed solution that additionally computes the location of vehicles using information obtained locally by them. We address practical considerations in the implementation of our algorithm and propose solutions to mitigate computational errors. With this proposed implementation, we provide insight on how to appropriately plan a deployment of nodes when collaborative tracking is to be utilized. Lastly, we shed light on situations where implementing collaborative tracking can hinder the localization performance of the network so that these can be avoided.