UKACC Paper Final Version.pdf (740.53 kB)
Download file

Estimation of time to point of closest approach for collision avoidance and separation systems

Download (740.53 kB)
conference contribution
posted on 15.10.2014, 10:23 by James Dunthorne, Wen-Hua ChenWen-Hua Chen, Sarah DunnettSarah Dunnett
This paper proposes a method for estimating the amount of time until the point of closest approach (TPCA) between two aircraft. A range of simple methods which use derivatives to estimate the time to collision are analysed. These methods are only accurate when the angle subtended between the direction of the relative velocity vector, and the bearing of the intruder aircraft is small. An extended method is developed which calculates the exact TPCA from relative distance and bearing measurements. Representative levels of Gaussian white noise are introduced to the core equation variables for both the derivative and extended methods. It is found that as we increase the value of θ, the extended method's accuracy increases beyond that of the derivative method. A fusion algorithm is developed to switch between methods and is shown to perform well for a range of conflicts. When the relative velocity between the two aircraft is small, the signal to noise ratio on the relative velocity variable reduces causing large errors to the TPCA estimation. It is therefore concluded that at a certain relative velocity threshold, Vk (dependant on sensor and filter performance) both the derivative and extended TPCA estimation methods would become undesirable as risk estimators. It is suggested that in these situations distance could be better to use since it can be measured directly.



  • Aeronautical, Automotive, Chemical and Materials Engineering


  • Aeronautical and Automotive Engineering

Published in

2014 UKACC International Conference on Control


646 - 651


DUNTHORNE, J., CHEN, W-H. and DUNNETT, S., 2014. Estimation of time to point of closest approach for collision avoidance and separation systems. IN: 2014 UKACC International Conference on Control, Loughborough, UK, 9-11 July 2014, pp. 646 - 651.




AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at:

Publication date



This is a conference paper [© 2014 IEEE]. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.




Loughborough, UK

Usage metrics