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A probabilistic approach to aircraft conflict detection

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TLDR
An algorithm for decentralized conflict detection and resolution that generalizes potential fields methods for path planning to a probabilistic dynamic environment is proposed and validated using Monte Carlo simulations.
Abstract
Conflict detection and resolution schemes operating at the mid-range and short-range level of the air traffic management process are discussed. Probabilistic models for predicting the aircraft position in the near-term and mid-term future are developed. Based on the mid-term prediction model, the maximum instantaneous probability of conflict is proposed as a criticality measure for two aircraft encounters. Randomized algorithms are introduced to efficiently estimate this measure of criticality and provide quantitative bounds on the level of approximation introduced. For short-term detection, approximate closed-form analytical expressions for the probability of conflict are obtained, using the short-term prediction model. Based on these expressions, an algorithm for decentralized conflict detection and resolution that generalizes potential fields methods for path planning to a probabilistic dynamic environment is proposed. The algorithms are validated using Monte Carlo simulations.

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Optimal Strategies for Free-Flight Air Traffic Conflict Resolution

TL;DR: This paper presents the development of a conflict resolution algorithm based on the quasilinearization method to enable the practical implementation of the free flight concept and uses nonlinear point-mass aircraft models, and incorporates realistic operational constraints on individual aircraft.
References
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Book

Probability: Theory and Examples

TL;DR: In this paper, a comprehensive introduction to probability theory covering laws of large numbers, central limit theorem, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion is presented.
Journal ArticleDOI

Stochastic differential equations : an introduction with applications

TL;DR: Some Mathematical Preliminaries as mentioned in this paper include the Ito Integrals, Ito Formula and the Martingale Representation Theorem, and Stochastic Differential Equations.
Book ChapterDOI

Stochastic Differential Equations

TL;DR: In this paper, the authors return to the possible solutions X t (ω) of the stochastic differential equation where W t is 1-dimensional "white noise" and where X t satisfies the integral equation in differential form.
Journal ArticleDOI

A review of conflict detection and resolution modeling methods

TL;DR: A survey of 68 CDR modeling methods, several of which are currently in use or under operational evaluation, and a framework that articulates the basic functions of CDR is used to categorize the models.

Conflict resolution for air traffic management : a study in mutiagent hybrid systems

C. Tomlin
TL;DR: In this article, the authors present a method to synthesize provably safe conflict resolution manoeuvres for free flight, in which aircraft choose their own optimal routes, altitudes, and velocities.
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