Generalized Philosophy of Alerting with Applications for Parallel Approach Collision Prevention

16 system. In the limit, a worst case model of an aircraft trusted to follow a normal approach might consist of a single trajectory (making it equivalent to a single-trajectory model), even though large deviations from the approach path are dynamically possible. Thus, a worst case model might more descriptively be termed an unweighted trajectory set model. In general the longer the attempted time projection, the more complex the description of the worst case set becomes for a given maximum error, and the more difficult it is to simulate the set in an alerting algorithm. Therefore an issue usually exists in choosing when to cut off trajectories in a worst case prediction model. Even if a particular worst case model can be simulated arbitrarily far into the future, the model may tend to have diminishing value for increasing prediction time due to the increasingly large set of possible system states (i.e. it can become difficult to rule out or guarantee future occurrence of a given event). If a probability function is defined over a worst case trajectory set (that is, each element is assigned a probability and the probabilities sum to 1), where the set is considered an event space, then the whole is termed a probabilistic trajectory model (Fig. 4c). This additional information allows computation of the probability of a particular event (e.g. hazard) occurring within the limited time of the model, whereas when using a worst case model only a statement of whether or not an event is possible can be made. Different verification requirements apply to probabilistic versus worst case models. Whereas use of a worst case model requires belief that trajectory error lies within acceptable error bounds for an element of the trajectory set, use of a probabilistic model requires belief that computed probabilities are within acceptable error bounds. Alerting system performance is often quantified in terms of the rates of hazard and false alarm events. These are defined below. In addition, a third event type, the “perceived incorrect alert” is suggested.