Real Time Monitoring and Prediction of National Airspace System Safety

# Prediction of Safety

Given the state estimates and a probability distribution of future inputs to the NAS, one can then predict the evolution of the NAS - the future state - and the occurrence of threat encounters.

To predict the future safety of the NAS, the prediction algorithms use models to simulate the system forward in time to some specified prediction horizon (for example, 20 minutes). Then as the state is simulated, at a desired frequency, the future safety metrics are computed from these states and then it is determined if the predicted safety metrics violate any safety threshold. If violated, the time and probability of such threat encounters are computed.

One algorithm for prediction is based on sampling all the uncertain variables in a system using, for example, Monte Carlo sampling or Latin hypercube sampling. These samples or realizations of the state of the NAS are simulated forward in time. As shown below, prediction requires some knowledge of future system inputs, such as flight plans and weather forecasts. Since these future inputs are highly uncertain, the entire probability distribution -- not just point estimates -- of airspace safety metrics is computed in a systematic and rigorous manner without significant assumptions regarding the distribution type and/or parameters.

### Prediction of future states.

At any given time, several threats need to be tracked and predicted. Therefore, it is important to account for probability-based information from multiple safety-related incidents. Principles of conditional probability and total probability, as shown below, can be used to compute these integrated probability metrics. Note that the probability of a threat and the integrated probability of all threats can be calculated for all future time instants based on information available at the present time instant. As time keeps evolving, these probabilities also keep evolving.

### Probability Tree: Likelihood of unsafe events.