Formal verification of lateral and temporal safety buffers for state-based conflict detection

This article presents an analytical definition of lateral and temporal safety buffers to be used in state-based conflict detection algorithms. A lateral buffer is a distance to be added to the minimum lateral separation to accommodate for uncertainty in the surveillance information. A temporal buffer is a time to be added to the lookahead conflict detection time to accommodate for dropped surveillance messages due to signal attenuation. These safety buffers are defined using precise mathematical statements and the main theorems give numerical upper bounds on the probability of a missed alert. A particular case is considered where absolute bounds on the errors in position and velocity information are known. In this case, under well-defined assumptions provided in this article, safety buffers are given that guarantee mathematically that the probability of a missed alert is zero. The results are presented as theorems, which were formally proven using a mechanical theorem prover.

[1]  César Muñoz,et al.  Conflict Detection and Resolution for 1,2,...N Aircraft , 2007 .

[2]  Robert A. Vivona,et al.  Airborne Tactical Intent-Based Conflict Resolution Capability , 2009 .

[3]  John Lygeros,et al.  A probabilistic approach to aircraft conflict detection , 2000, IEEE Trans. Intell. Transp. Syst..

[4]  R. Y. Gazit,et al.  The effect of GPS-based surveillance on aircraft separation standards , 1996, Proceedings of Position, Location and Navigation Symposium - PLANS '96.

[5]  M. S. Eby,et al.  A self-organizational approach for resolving air traffic conflicts , 1995 .

[6]  James K. Kuchar,et al.  A review of conflict detection and resolution modeling methods , 2000, IEEE Trans. Intell. Transp. Syst..

[7]  Robert A. Vivona,et al.  An Integrated Flight-Deck Decision-Support Tool in an Autonomous Flight Simulation , 2004 .

[8]  Jean-Baptiste Jeannin,et al.  Formal Verification of Safety Buffers for Sate-Based Conflict Detection and Resolution , 2010 .

[9]  Yiyuan J. Zhao.  A SYSTEMATIC PROCEDURE FOR DETERMINING SEPARATION MINIMA , 2008 .

[10]  Munoz Cesar,et al.  Tactical conflict detection and resolution in a 3-d airspace , 2001 .

[11]  K. Bilimoria.  A Geometric Optimization Approach to Aircraft Conflict Resolution , 2000 .

[12]  Natarajan Shankar,et al.  PVS: A Prototype Verification System , 1992, CADE.

[13]  Ricky W. Butler,et al.  Formal Verification of a Conflict Resolution and Recovery Algorithm , 2013 .

[14]  Kellen Petersen August.  Real Analysis , 2009 .

[15]  J. Rosenthal.  A First Look at Rigorous Probability Theory , 2000 .

[16]  L. M. B. C. Campos,et al.  ON THE THREE-DIMENSIONAL COLLISION PROBABILITIES RELEVANT TO ATM , .

[17]  César A. Muñoz,et al.  Formal Verification of an Optimal Air Traffic Conflict Resolution and Recovery Algorithm , 2007, WoLLIC.

[18]  Maria C. Consiglio,et al.  Estimation of Separation Buffers for Wind-Prediction Error in an Airborne Separation Assistance System , 2009 .

[19]  Mark H. Davis.  Markov Models and Optimization , 1995 .

[20]  Heinz Erzberger,et al.  Conflict Probability Estimation for Free Flight , 1997 .

[21]  William W Chung,et al.  A 1090 Extended Squitter Automatic Dependent Surveillance - Broadcast (ADS-B) Reception Model for Air- Traffic-Management Simulations , 2006 .

[22]  Jacco M. Hoekstra,et al.  Overview of NLR Free Flight Project 1997 -1999 , 2000 .