A Bayesian Approach to Aircraft Encounter Modeling ∗ Mykel J. Kochenderfer † , Leo P. Espindle ‡ , James K. Kuchar § , and J. Daniel Griffith ¶ Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, MA 02420 Aircraft encounter models can be used in a variety of analyses, including collision avoid- ance system safety assessment, sensor design trade studies, and visual acquisition analysis. This paper presents an approach to airspace encounter model construction based on Markov models estimated from radar data. We use Bayesian networks to represent the distribution over initial states and dynamic Bayesian networks to represent transition probabilities. We apply Bayesian statistical techniques to identify the relationships between the variables in the model to best leverage a large volume of raw aircraft track data obtained from more than 130 radars across the United States. I. Introduction One of the main challenges to integrating unmanned aircraft into the National Airspace System is the development of systems that sense and avoid local air traffic. If designed properly, these collision avoidance systems could provide an additional layer of protection that maintains the current exceptional level of aviation safety. However, due to their safety-critical nature, rigorous assessment is required before sufficient confidence can exist to certify collision avoidance systems for operational use. Evaluations typically include flight tests, operational impact studies, and simulation of millions of traffic encounters with the goal of exploring the robustness of the collision avoidance system. Key to these simulations are so-called encounter models that describe the statistical makeup of the encounters in a way that represents what actually occurs in the airspace. One system that has been rigorously tested in this manner is the Traffic alert and Collision Avoidance System (TCAS). As part of the TCAS certification process in the 1980s and 1990s, several organizations tested the system across millions of simulated close encounters and evaluated the risk of a near mid-air collision (NMAC, defined as separation less than 500 ft horizontally and 100 ft vertically). 1–4 This analysis ultimately led to the certification and U.S. mandate for TCAS equipage on large transport aircraft. More recently, Eurocontrol and ICAO performed similar sets of simulation studies to support European and worldwide TCAS mandates. 5, 6 The design of a collision avoidance system represents a careful balance between preventing collision and not maneuvering unnecessarily. This balance is strongly affected by the types of encounter situations to which the system is exposed. It is therefore important that simulated encounters are representative of those that occur in the airspace. Hence, tremendous effort has been made by various institutions since the early 1980s to develop encounter models. 1, 3, 7–10 The primary contribution of this paper is to introduce a new approach to encounter modeling that is based on a Bayesian statistical framework. The advantage of such a theoretical framework is that it allows us to optimally leverage available radar data to produce a model that is representative of reality. There are two fundamental types of close traffic encounters. In the first, both aircraft involved are cooperative (i.e., have a transponder) and at least one is in contact with air traffic control. It is then likely that at least one aircraft will receive some notification about the traffic conflict and begin to take * This work is sponsored by the Air Force under Air Force Contract #FA8721-05-C-0002. Opinions, interpretations, conclu- sions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government. † Technical Staff, Surveillance Systems, 244 Wood Street. ‡ Assistant Staff, Surveillance Systems, 244 Wood Street. § Assistant Group Leader, Surveillance Systems, 244 Wood Street. Senior Member AIAA. ¶ Associate Staff, Surveillance Systems, 244 Wood Street. 1 of 21 American Institute of Aeronautics and Astronautics AIAA Guidance, Navigation and Control Conference and Exhibit 18 - 21 August 2008, Honolulu, Hawaii AIAA 2008-6629 Copyright © 2008 by MIT Lincoln Laboratory. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.