1. A system for facilitating warning of collision between a primary principal and one or more non-primary principals, comprising: a triggering mechanism configured to determine whether a trigger condition is met based on a state of the primary principal, wherein the state of a principal is represented by a geometric object which indicates a location of the principal at a given time interval; and a preliminary assessment mechanism, wherein when the trigger condition is met, the preliminary assessment mechanism is configured to: generate one or more collision scenarios associated with the trigger condition, wherein a collision scenario indicates a possible collision at a future state of the primary principal; assess a preliminary probability of collision in a collision scenario, which involves determining that geometric objects for the primary principal and a non-primary principal intersect at a future state of the primary principal; and based on the preliminary probability of collision in the collision scenario, activate a specialized assessment mechanism to assess a refined probability of collision in the collision scenario.