An Initial Examination for Verifying Separation Algorithms by Simulation

An open question in algorithms for aircraft is what can be validated by simulation where the simulation shows that the probability of undesirable events is below some given level at some confidence level. The problem is including enough realism to be convincing while retaining enough efficiency to run the large number of trials needed for high confidence. The paper first proposes a goal based on the number of flights per year in several regions. The paper examines the probabilistic interpretation of this goal and computes the number of trials needed to establish it at an equivalent confidence level. Since any simulation is likely to consider the algorithms for only one type of event and there are several types of events, the paper examines under what conditions this separate consideration is valid. This paper is an initial effort, and as such, it considers separation maneuvers, which are elementary but include numerous aspects of aircraft behavior. The scenario includes decisions under uncertainty since the position of each aircraft is only known to the other by broadcasting where GPS believes each aircraft to be (ADS-B). Each aircraft operates under feedback control with perturbations. It is shown that a scenario three or four orders of magnitude more complex is feasible. The question of what can be validated by simulation remains open, but there is reason to be optimistic.