Mode identification using stochastic hybrid models with applications to conflict detection and resolution

Most models of aircraft trajectories are non-linear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multi-aircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizon-thereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finite-state Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the non-deterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers.We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs