Sequential Monte Carlo Methods

Filtering is the problem of sequentially estimating the states (parameters or hidden variables) of a system as a set of observations become available on-line. To solve it, one begins by modeling the evolution of the system and the noise in the measurements. The resulting models typically exhibit complex nonlinearities and non-Gaussian distributions, thus precluding analytical solution.

A popular solution strategy for the general filtering problem is to use sequential Monte Carlo methods, also known as Particle Filters (Doucet: 1998, Doucet, de Freitas and Gordon: 2000, Gordon, Salmond and Smith: 1993). These methods allow for a complete representation of the posterior distribution of the states, so that any statistical estimates can be easily computed. They can therefore, deal with any nonlinearities or distributions.

Particle Filter Group.
Sequential Monte Carlo Methods Homepage.

Stochastic Reachability Analysis with application to Aircraft Conflict Detection

The primary concern of all advanced air traffic management systems (ATMSs) is to guarantee safety of air travel. Safety is typically quantified in terms of numbers of conflicts, i.e., situations where two aircraft come closer than a certain distance from one another. The safety distance is encoded by means of a minimum allowed horizontal separation and a minimum vertical separation. Currently, for en-route airspace the minimum horizontal separation is 5 nautical miles (nmi), while close to airports it is reduced to 3 nmi. The minimum vertical separation is 1000 feet (ft).

To prevent conflicts, ATMS resorts to a two stage process. In the first stage conflict detection is performed: the positions of the aircraft in the future are predicted based on their current positions and flight plans, and they are compared so as to detect potential situations of conflict. Once a potential conflict has been detected, the trajectories of the aircraft involved in the conflict are re-planned in the conflict resolution stage.

HYBRIDGE Web-site.
Center-TRACON Automation System.