One embodiment of the present invention provides a system that facilitates assessment of collision between a primary principal and a non-primary principal for early warning. During operation, the system receives information which indicates a state of the primary principal and a state of the non-primary principal. The system divides future time into a number of time intervals, and estimates a number of possible future states of the primary and non-primary principals, wherein each future state corresponds to a time interval. The system further represents the possible future states of the primary or non-primary principal as one or more geometric objects in a space of which at least one dimension indicates the time. In addition, the system determines a probability of collision between the primary and non-primary principals based on the geometric objects.