The knowledge and information generated through the safety analysis and modeling can then be used for the online real-time monitoring and prediction components.
As shown above, in order to estimate the current states of the NAS, the monitoring or estimation algorithms take in as inputs the known system inputs and measurements obtained from the NAS and output state estimates as probability distributions. The estimation algorithms typically have two steps:
Prediction step, in which the probability distribution for the state in the next time step is computed starting from the state estimate at the current time step.
Correction step, in which Bayes Theorem is used to update the predictions of the next time step made during the prediction step above based on observations of the system state.
Several standard filters can be used to perform estimation based on whether the system is linear or nonlinear, whether the distributions are assumed to be Gaussian or not, and so on. Examples of these filters are Kalman filter, Extended Kalman filter, Unscented Kalman filter, Particle filter, etc.
Once the estimate of the system state is obtained, an estimate of the safety, in the form of safety metrics, can be computed, along with predictions for probability of future threat encounters and for time to threat encounters.