This paper describes a cooperative method for relative localization of mobile robot teams; that is, it describes a method whereby every robot in the team can estimate the pose of every other robot, relative to itself. This robot does not require the use of GPS, landmarks, or maps of any kind; instead, robots make direct measurement of the relative pose of nearby robots, and broadcast this information to the team as a whole. Each robot processes this information independently to generate ego-centric estimate for the pose of other robots. Our method uses Bayesian formalism with a particle filter implementation, and is, as a consequence, very robust. It is also completely distributed, yet requires relatively little communication between robots. This paper describes the basic ego-centric formalism, sketches the implementation, and presents experimental results obtained using a team of four mobile robots.