The ability to predict, and thus react to, oncoming collisions among a set of mobile agents is a fundamental requirement for safe autonomous movement, both human and robotic. This paper addresses systems that use range measurements between mobile agents for the purpose of collision prediction, which involves prediction of the agents' future paths to know if they will collide at any time. One straightforward system would use known-location static anchors to estimate agent coordinates over time, and use the track to predict collision. Fundamentally, no fixed coordinate system is required for collision prediction, so using only the pairwise range between two agents can be used to predict collision. We present lower bound analysis which shows the limitations of this pairwise method. As an alternative anchor-free method, we propose the friend-based autonomous collision prediction and tracking (FACT) method that uses all measured ranges between nearby (unknown location mobile) agents, in a distributed algorithm, to estimate their relative locations and velocities and predict future collisions between agents. Using analysis and simulation, we show the potential for FACT to achieve equal or better collision detection performance compared to other methods, while avoiding the need for anchors. We then build a network of $N$ ultra wideband (UWB) devices and an efficient multi-node protocol which allows all ${\cal O}(N^2)$ pairwise ranges to be measured in $N$ slots. We run experiments with up to six independent robot agents moving and colliding in a 2D plane and up to four anchor nodes to compare the performance of the collision prediction methods. We show that the FACT method can perform better than either other method but without the need for a fixed infrastructure of anchor nodes.