This paper studies performance metrics that are of use in the evaluation of conflict detection and resolution in air traffic management. The metrics studied are conflict probability and incrossing probability, both of which are closely related to the safety criteria used by the civil aviation community. The main contribution of this paper is to develop mathematical characterisations for these metrics, and to show typical differences in their behaviour through numerical evaluations of these metrics for some simple examples. 1

Title of document: A multi-aircraft model for conflict detection and resolution algorithm evaluation Authors of document: W. Glover and J. Lygeros Deliverable number: D1.3

Abstract. We address the problem of optimal coordinated motions of multiple agents moving in the same planar region. The agents ’ motions must satisfy a separation constraint throughout the encounter to be conflict-free. The objective is to determine the conflict-free maneuvers (motions) with the least combined energy, while taking into account the fact that agents may have different priorities. A formal classification of conflict-free maneuvers into homotopy types is introduced by using their braid representation. Various local and global optimality conditions are derived through variational analysis in the presence of the separation constraint. In the case of two agents, these optimality conditions allow us to construct the optimal maneuvers geometrically. For the general multi-agent case, a convex optimization algorithm is proposed to compute within each homotopy type a solution to the optimization problem restricted to the class of multi-legged maneuvers. Since the number of types grows explosively with the number of agents, a stochastic algorithm is suggested as the “type chooser”, thus leading to a randomized optimization algorithm.

Abstract. This paper focuses on hybrid systems whose discrete state transitions depend on both deterministic and stochastic events. For such systems, after introducing a suitable hybrid model called Discrete Hybrid Stochastic Automaton (DHSA), different finite-time optimal control approaches are examined: (1) Stochastic Hybrid Optimal Control (SHOC), which “optimistically ” determines the trajectory providing the best trade off between the tracking performance and the probability that stochastic events realize as expected, under specified chance constraints; (2) Robust Hybrid Optimal Control (RHOC) which, in addition, less optimistically, ensures that the system remains within a specified safety region for all possible realizations of stochastic events. Sufficient conditions for the asymptotic convergence of the state vector are given for receding-horizon implementations of the above schemes. The proposed approaches are exemplified on a simple benchmark problem in production system management. 1

The safety of the flights, and in particular separation assurance, is one of the main tasks of Air Traffic Control. Conflict resolution refers to the process used by air traffic controllers to prevent loss of separation. Conflict resolution involves issuing instructions to aircraft to avoid loss of safe separation between them and, at the same time, direct them to their destinations. Conflict resolution requires decision making in the face of the considerable levels of uncertainty inherent in the motion of aircraft. We present a framework for conflict resolution which allows one to take into account such levels of uncertainty through the use of a stochastic simulator. The conflict resolution task is posed as the problem of optimizing an expected value criterion. Optimization of the expected value resolution criterion is carried out through an iterative procedure based on Monte Carlo Markov Chain. Simulation examples inspired by current air traffic control practice in terminal maneuvering areas and approach sectors illustrate the proposed conflict resolution strategy. 1

Abstract—This paper proposes a SIMD solution to air traffic control (ATC) using an enhanced SIMD machine model called an Associative Processor (AP). This differs from previous ATC systems that are designed for MIMD computers and have a great deal of difficulty meeting the predictability requirements for ATC, which are critical for meeting the strict certification standards required for safety critical software components. The proposed SIMD solution will support accurate and meaningful predictions of worst case execution times and will guarantee all deadlines are met. Also, the software will be much simpler and smaller in size than the current corresponding ATC software. An important consequence of these features is that the V&V (Validation and Verification) process will be considerably simpler than for current ATC software. Additionally, the associative processor is enhanced SIMD hardware and is considerably cheaper and simpler than the MIMD hardware currently used to support ATC. The ClearSpeed CSX600 accelerator is used to emulate the AP model. A preliminary implementation of the proposed method has been developed and experimental results comparing MIMD and CSX600 approaches are presented. The performance of CSX600 has better scalability, efficiency, and predictability than that of MIMD.

Abstract—In this paper, the problem of automated aircraft conflict prediction is studied for two-aircraft midair encounters. A model is introduced to predict the aircraft positions along some look-ahead time horizon, during which each aircraft is trying to follow a prescribed flight plan despite the presence of additive wind perturbations to its velocity. A spatial correlation structure is assumed for the wind perturbations such that the closer the two aircraft, the stronger the correlation between the perturbations to their velocities. Using this model, a method is introduced to evaluate the criticality of the encounter situation by estimating the probability of conflict, namely, the probability that the two aircraft come closer than a minimum allowed distance at some time instant during the look-ahead time horizon. The proposed method is based on the introduction of a Markov chain approximation of the stochastic processes modeling the aircraft motions. Several generalizations of the proposed approach are also discussed. Index Terms—Air traffic control, conflict prediction, stochastic approximation, stochastic fields, stochastic modeling, wind correlation. I.

Abstract — Rapid development of mobile devices makes it possible that billions of mobile and personal devices will soon be used in every daily routine work. This emerging environment presents a number of challenging problems in several research areas including databases. The need for managing and querying continuously moving objects is among the new demands of this development. Although global positioning systems (GPS) are widely used nowadays, it is still a fact that the position information obtained is not accurate at every time instant. Thus, in most cases trajectory information is in fact “expected” trajectory with uncertainty. An interesting problem is indexing and querying trajectories with uncertain information. In this paper we introduce a data model for moving object trajectories with uncertainty and develop a new index structure (TPRU-tree) for uncertain trajectories based on TPR-tree. We discuss query evaluation using TPRU-tree and present an empirical study. I.

In this paper we propose a testing based method for safety/reachability analysis of stochastic hybrid systems. Testing based methods are characterized by analysis based on the execution traces of the system or the simulation thereof. Testing based method is very appealing because of the simplicity of its execution, the possibility of having a partial verification, and its highly parallel structure. The key idea in this paper is the construction of a robust neighborhood consisting of states that have the same probabilistic safety/reachability properties. We construct the robust neighborhood using the level sets of a stochastic bisimulation function. We also show how to construct stochastic bisimulation functions for systems whose continuous dynamics is stable and linear. As a case example, we consider the problem of conflict detection of aircraft flight, and show that we can infer some robust probabilistic safety property by using the algorithm that we present in this paper.

Abstract—Alerting systems and related decision-making automation are widely used to enhance the safety and capability of controlled processes across many applications. Traditional alerting systems use physical metrics such as temperature, distance between vehicles, or time-to-impact as bases for making alerting decisions. Threshold values on these metrics are typically derived using an iterative process to ensure the achievement of desired performance goals, defined by higher-level metrics such as false alarm, safety, or success probabilities. We generalize this problem and develop two state spaces, one representing physical metrics and one representing performance metrics. A traditional alerting system operates completely within the physical space, using decision thresholds that have been developed offline during the design process by examining how the physical threshold translates across to the performance state space. The physical metrics thus act as an indirect means to control the performance of the system. We propose an alternate approach that enables the system to operate online in the performance space. Alerting decisions are based directly on the computed values of metrics such as false alarm probability rather than on surrogate physical metrics. These two design approaches are then contrasted in case studies of recently-developed alerting systems. Index Terms—Alarm systems, algorithms, decision support systems, threshold logic. I.