Avoiding collisions is a crucial problem in most transportation systems, as well as in many other applications. The task of a collision avoidance system is to track potential collision risk objects and determine any action to avoid or mitigate a collision. This thesis presents a theory for monitoring and decision making in collision prevention systems. The main focus is how to make decisions based on uncertain estimates and the presence of multiple obstacles. A general framework is proposed to deal with nonlinear dynamic systems and arbitrary noise distributions in collision avoidance decisions. Some novel decision functions are also suggested. In addition, performance assessments are presented using simulated and experimental data. Most of the examples in this thesis are automotive applications. A driving application for the work presented in this thesis is an automotive emergency braking system. This system is called a collision brake attenuation system (CMbB). Its aim is to mitigate the consequences of an accident by applying the brakes once the collision becomes inevitable. It is estimated that a CMbB system that provides a maximum collision speed reduction of 15 km / h and a reduction of the average speed of 7.5 km / h reduces all injuries, classified as moderate and fatal, for subsequent collisions in 16%. Since the rear-end collision corresponds to approximately 30% of all accidents, it corresponds to a 5% reduction for all accidents. The evaluation includes simulation results, as well as two demonstration vehicles, with different sensor configurations and different decision logic, which perform autonomous emergency braking.