We propose a novel distributed algorithm to estimate the 3D trajectories of multiple cooperative robots from relative pose measurements. Our approach leverages recent results which show that the maximum likelihood trajectory is well approximated by a sequence of two quadratic subproblems. The main contribution of the present work is to show that these subproblems can be solved in a distributed manner, using the distributed Jacobi (DJ) algorithm. Our approach has several advantages. It requires minimal information exchange, which is beneficial in presence of communication and privacy constraints. It has an anytime flavor: after few iterations the trajectory estimates are already accurate, and they asymptotically convergence to the centralized estimate. The DJ approach scales well to large teams, and it has a straightforward implementation. We test the approach in extensive simulations and field tests, confirming its practicality and showing its advantages over related techniques.