An analysis of the Bayesian track labelling problem

E.H. Aoki, Y. Boers, Lennart Svensson, Pranab K. Mandal, Arunabha Bagchi

Research output: Book/ReportReport

Abstract

In multi-target tracking (MTT), the problem of assigning labels to tracks (track labelling) is vastly covered in literature, but its exact mathematical formulation, in terms of Bayesian statistics, has not been yet looked at in detail. Doing so, however, may help us to understand how Bayes-optimal track labelling should be performed or numerically approximated. Moreover, it can help us to better understand and tackle some practical difficulties associated with the MTT problem, in particular the so-called ``mixed labelling'' phenomenon that has been observed in MTT algorithms. In this memorandum, we rigorously formulate the optimal track labelling problem using Finite Set Statistics (FISST), and look in detail at the mixed labeling phenomenon. As practical contributions of the memorandum, we derive a new track extraction formulation with some nice properties and a statistic associated with track labelling with clear physical meaning. Additionally, we show how to calculate this statistic for two well-known MTT algorithms.
LanguageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages8
StatePublished - Mar 2012

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.1980
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Keywords

  • Particle filter
  • Track labelling
  • EWI-21663
  • Finite Set Statistics
  • Target tracking
  • IR-79947
  • METIS-296044

Cite this

Aoki, E. H., Boers, Y., Svensson, L., Mandal, P. K., & Bagchi, A. (2012). An analysis of the Bayesian track labelling problem. (Memorandum / Department of Applied Mathematics; No. 1980). Enschede: University of Twente, Department of Applied Mathematics.
Aoki, E.H. ; Boers, Y. ; Svensson, Lennart ; Mandal, Pranab K. ; Bagchi, Arunabha. / An analysis of the Bayesian track labelling problem. Enschede : University of Twente, Department of Applied Mathematics, 2012. 8 p. (Memorandum / Department of Applied Mathematics; 1980).
@book{6f325f756b5342cf9447de61eeedeb87,
title = "An analysis of the Bayesian track labelling problem",
abstract = "In multi-target tracking (MTT), the problem of assigning labels to tracks (track labelling) is vastly covered in literature, but its exact mathematical formulation, in terms of Bayesian statistics, has not been yet looked at in detail. Doing so, however, may help us to understand how Bayes-optimal track labelling should be performed or numerically approximated. Moreover, it can help us to better understand and tackle some practical difficulties associated with the MTT problem, in particular the so-called ``mixed labelling'' phenomenon that has been observed in MTT algorithms. In this memorandum, we rigorously formulate the optimal track labelling problem using Finite Set Statistics (FISST), and look in detail at the mixed labeling phenomenon. As practical contributions of the memorandum, we derive a new track extraction formulation with some nice properties and a statistic associated with track labelling with clear physical meaning. Additionally, we show how to calculate this statistic for two well-known MTT algorithms.",
keywords = "Particle filter, Track labelling, EWI-21663, Finite Set Statistics, Target tracking, IR-79947, METIS-296044",
author = "E.H. Aoki and Y. Boers and Lennart Svensson and Mandal, {Pranab K.} and Arunabha Bagchi",
year = "2012",
month = "3",
language = "Undefined",
series = "Memorandum / Department of Applied Mathematics",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1980",

}

Aoki, EH, Boers, Y, Svensson, L, Mandal, PK & Bagchi, A 2012, An analysis of the Bayesian track labelling problem. Memorandum / Department of Applied Mathematics, no. 1980, University of Twente, Department of Applied Mathematics, Enschede.

An analysis of the Bayesian track labelling problem. / Aoki, E.H.; Boers, Y.; Svensson, Lennart; Mandal, Pranab K.; Bagchi, Arunabha.

Enschede : University of Twente, Department of Applied Mathematics, 2012. 8 p. (Memorandum / Department of Applied Mathematics; No. 1980).

Research output: Book/ReportReport

TY - BOOK

T1 - An analysis of the Bayesian track labelling problem

AU - Aoki,E.H.

AU - Boers,Y.

AU - Svensson,Lennart

AU - Mandal,Pranab K.

AU - Bagchi,Arunabha

PY - 2012/3

Y1 - 2012/3

N2 - In multi-target tracking (MTT), the problem of assigning labels to tracks (track labelling) is vastly covered in literature, but its exact mathematical formulation, in terms of Bayesian statistics, has not been yet looked at in detail. Doing so, however, may help us to understand how Bayes-optimal track labelling should be performed or numerically approximated. Moreover, it can help us to better understand and tackle some practical difficulties associated with the MTT problem, in particular the so-called ``mixed labelling'' phenomenon that has been observed in MTT algorithms. In this memorandum, we rigorously formulate the optimal track labelling problem using Finite Set Statistics (FISST), and look in detail at the mixed labeling phenomenon. As practical contributions of the memorandum, we derive a new track extraction formulation with some nice properties and a statistic associated with track labelling with clear physical meaning. Additionally, we show how to calculate this statistic for two well-known MTT algorithms.

AB - In multi-target tracking (MTT), the problem of assigning labels to tracks (track labelling) is vastly covered in literature, but its exact mathematical formulation, in terms of Bayesian statistics, has not been yet looked at in detail. Doing so, however, may help us to understand how Bayes-optimal track labelling should be performed or numerically approximated. Moreover, it can help us to better understand and tackle some practical difficulties associated with the MTT problem, in particular the so-called ``mixed labelling'' phenomenon that has been observed in MTT algorithms. In this memorandum, we rigorously formulate the optimal track labelling problem using Finite Set Statistics (FISST), and look in detail at the mixed labeling phenomenon. As practical contributions of the memorandum, we derive a new track extraction formulation with some nice properties and a statistic associated with track labelling with clear physical meaning. Additionally, we show how to calculate this statistic for two well-known MTT algorithms.

KW - Particle filter

KW - Track labelling

KW - EWI-21663

KW - Finite Set Statistics

KW - Target tracking

KW - IR-79947

KW - METIS-296044

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - An analysis of the Bayesian track labelling problem

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Aoki EH, Boers Y, Svensson L, Mandal PK, Bagchi A. An analysis of the Bayesian track labelling problem. Enschede: University of Twente, Department of Applied Mathematics, 2012. 8 p. (Memorandum / Department of Applied Mathematics; 1980).