IEEE Robotics & Automation Magazine - June 2014 - 82
density function. The Bayesian filter has a very simple
structure, as illustrated in (1).
2) Bayesian state estimation for single extended objects.
Using parametric extension models such as ellipses or
rectangles, the extension parameters can be augmented to
the state vector, and the problem is recast to 1 and above.
3) Bayesian state estimation for multiple-point object tracking
[Figure 3(b)]. This gives a combinatorial explosion in complexity due to the association of detections to objects and
clutter as outliers. For that reason, suboptimal track handling algorithms have been developed to again recast the
problem to 1 and above.
4) Bayesian estimation of the phd for multiple extended
objects. The phd filter is a mathematically beautiful
approach, originally developed for multiple-point object
estimation, and later generalized to extended objects. The
filter in (5) has the same simple structure as in (1).
The phd is a representation of object existence probability. It should not be confused with the state's density
function, although it has the same function form, and the
same numerical representations with particles or GMs have
been proposed in literature.
Figure 4 shows an example where ellipse models are fitted to each object. An additional benefit of having extended
objects is that occlusion can be modeled in a direct and natural way. Ultimately, such filters should be able to give very
accurate situational awareness, including both stationary
and moving objects and their extensions in a scenario such
as in Figure 1.
References
[1] Y. Bar-Shalom, p. K. Willett, and X. Tian, Tracking and Data Fusion, A
Handbook of Algorithms. Bradford, West Yorkshire: YBS, 2011.
[2] h. durrant-Whyte and T. Bailey, "Simultaneous localization and mapping
(SlAM): part I," IEEE Robot. Automat. Mag., vol. 13, no. 2, pp. 99-110, June 2006.
[3] R. Mahler, Statistical Multisource-Multitarget Information Fusion.
Norwood, MA: Artech house, 2007.
[4] R. Mahler, "Multitarget Bayes filtering via first-order multitarget
moments," IEEE Trans. Aerosp. Electron. Syst., vol. 39, no. 4, pp. 1152-1178,
Oct. 2003.
[5] R. Mahler, "phd filters for nonstandard targets, I: Extended targets," in
Proc. Int. Conf. Information Fusion, Seattle, WA, July 2009, pp. 915-921.
[6] A. Swain and d. Clark, "Extended object filtering using spatial independent cluster processes," in Proc. Int. Conf. Information Fusion, Edinburgh,
U.K., July 2010, pp. 1-8.
[7] J. Mullane, B.-N. Vo, M. Adams, and B.-T. Vo, "A random-finite-set approach
to Bayesian SlAM," IEEE Trans. Robot., vol. 27, no. 2, pp. 268-282, Apr. 2011.
[8] C. S. lee, d. Clark, and J. Salvi, "SlAM with dynamic targets via singlecluster phd filtering," IEEE J. Select Topics Signal Processing (Special Issue on
Multi-Target Tracking), vol. 7, no. 3, pp. 543-552, 2013.
[9] J. Neira and J. d. Tardos, "data association in stochastic mapping using the
joint compatibility test," IEEE Trans. Robot., vol. 17, no. 6, pp. 890-897, dec. 2001.
82
*
IEEE ROBOTICS & AUTOMATION MAGAZINE
*
June 2014
[10] K. Granström, C. lundquist, and U. Orguner, "Extended target tracking
using a Gaussian mixture phd filter," IEEE Trans. Aerosp. Electron. Syst., vol.
48, no. 4, pp. 3268-3286, Oct. 2012.
[11] K. Granström and U. Orguner, "A phd filter for tracking multiple
extended targets using random matrices," IEEE Trans. Signal Processing, vol.
60, no. 11, pp. 5657-5671, Nov. 2012.
[12] K. Gilholm and d. Salmond, "Spatial distribution model for tracking
extended objects," IEE Proc. Radar, Sonar Navig., vol. 152, no. 5, pp. 364-371,
Oct. 2005.
[13] J. W. Koch, "Bayesian approach to extended object and cluster tracking
using random matrices," IEEE Trans. Aerosp. Electron. Syst., vol. 44, no. 3, pp.
1042-1059, July 2008.
[14] M. Baum and U. d. hanebeck, "Shape tracking of extended objects and
group targets with star-convex RhMs," in Proc. Int. Conf. Information Fusion,
Chicago, Il, July 2011, pp. 338-345.
[15] C. lundquist, K. GranstrÖm, and U. Orguner, "Estimating the shape of
targets with a phd filter," in Proc. Int. Conf. Information Fusion, Chicago, Il,
July 2011, pp. 49-56.
[16] B.-N. Vo and W.-K. Ma, "The Gaussian mixture probability hypothesis
density filter," IEEE Trans. Signal Processing, vol. 54, no. 11, pp. 4091-4104,
Nov. 2006.
[17] K. GranstrÖm, C. lundquist, and U. Orguner, "Tracking rectangular and
elliptical extended targets using laser measurements," in Proc. Int. Conf.
Information Fusion, Chicago, Il, July 2011, pp. 592-599.
[18] B.-T. Vo, B.-N. Vo, and A. Cantoni, "Analytic implementations of the cardinalized probability hypothesis density filter," IEEE Trans. Signal Processing,
vol. 55, no. 7, pp. 3553-3567, July 2007.
[19] C. lundquist, K. GranstrÖm, and U. Orguner, "An extended target Cphd
filter and a gamma Gaussian inverse Wishart implementation," IEEE J. Sel.
Topics Signal Processing (Special Issue on Multi-Target Tracking), vol. 7, no. 3,
pp. 472-483, June 2013.
[20] X.-R. li and V. Jilkov, "Survey of maneuvering target tracking: part I.
dynamic models," IEEE Trans. Aerosp. Electron. Syst., vol. 39, no. 4, pp. 1333-
1364, Oct. 2003.
Karl Granström, department of Electrical Engineering,
division of Automatic Control, linköping University,
Sweden. E-mail: karl@isy.liu.se.
Christian Lundquist, department of Electrical Engineering,
division of Automatic Control, linköping University,
Sweden. E-mail: lundquist@isy.liu.se.
Fredrik Gustafsson, department of Electrical Engineering,
division of Automatic Control, linköping University,
Sweden. E-mail: fredrik@isy.liu.se.
Umut Orguner, department of Electrical and Electronics
Engineering, Middle East Technical University, Ankara,
Turkey. E-mail: umut@eee.metu.edu.tr.
Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - June 2014
IEEE Robotics & Automation Magazine - June 2014 - Cover1
IEEE Robotics & Automation Magazine - June 2014 - Cover2
IEEE Robotics & Automation Magazine - June 2014 - 1
IEEE Robotics & Automation Magazine - June 2014 - 2
IEEE Robotics & Automation Magazine - June 2014 - 3
IEEE Robotics & Automation Magazine - June 2014 - 4
IEEE Robotics & Automation Magazine - June 2014 - 5
IEEE Robotics & Automation Magazine - June 2014 - 6
IEEE Robotics & Automation Magazine - June 2014 - 7
IEEE Robotics & Automation Magazine - June 2014 - 8
IEEE Robotics & Automation Magazine - June 2014 - 9
IEEE Robotics & Automation Magazine - June 2014 - 10
IEEE Robotics & Automation Magazine - June 2014 - 11
IEEE Robotics & Automation Magazine - June 2014 - 12
IEEE Robotics & Automation Magazine - June 2014 - 13
IEEE Robotics & Automation Magazine - June 2014 - 14
IEEE Robotics & Automation Magazine - June 2014 - 15
IEEE Robotics & Automation Magazine - June 2014 - 16
IEEE Robotics & Automation Magazine - June 2014 - 17
IEEE Robotics & Automation Magazine - June 2014 - 18
IEEE Robotics & Automation Magazine - June 2014 - 19
IEEE Robotics & Automation Magazine - June 2014 - 20
IEEE Robotics & Automation Magazine - June 2014 - 21
IEEE Robotics & Automation Magazine - June 2014 - 22
IEEE Robotics & Automation Magazine - June 2014 - 23
IEEE Robotics & Automation Magazine - June 2014 - 24
IEEE Robotics & Automation Magazine - June 2014 - 25
IEEE Robotics & Automation Magazine - June 2014 - 26
IEEE Robotics & Automation Magazine - June 2014 - 27
IEEE Robotics & Automation Magazine - June 2014 - 28
IEEE Robotics & Automation Magazine - June 2014 - 29
IEEE Robotics & Automation Magazine - June 2014 - 30
IEEE Robotics & Automation Magazine - June 2014 - 31
IEEE Robotics & Automation Magazine - June 2014 - 32
IEEE Robotics & Automation Magazine - June 2014 - 33
IEEE Robotics & Automation Magazine - June 2014 - 34
IEEE Robotics & Automation Magazine - June 2014 - 35
IEEE Robotics & Automation Magazine - June 2014 - 36
IEEE Robotics & Automation Magazine - June 2014 - 37
IEEE Robotics & Automation Magazine - June 2014 - 38
IEEE Robotics & Automation Magazine - June 2014 - 39
IEEE Robotics & Automation Magazine - June 2014 - 40
IEEE Robotics & Automation Magazine - June 2014 - 41
IEEE Robotics & Automation Magazine - June 2014 - 42
IEEE Robotics & Automation Magazine - June 2014 - 43
IEEE Robotics & Automation Magazine - June 2014 - 44
IEEE Robotics & Automation Magazine - June 2014 - 45
IEEE Robotics & Automation Magazine - June 2014 - 46
IEEE Robotics & Automation Magazine - June 2014 - 47
IEEE Robotics & Automation Magazine - June 2014 - 48
IEEE Robotics & Automation Magazine - June 2014 - 49
IEEE Robotics & Automation Magazine - June 2014 - 50
IEEE Robotics & Automation Magazine - June 2014 - 51
IEEE Robotics & Automation Magazine - June 2014 - 52
IEEE Robotics & Automation Magazine - June 2014 - 53
IEEE Robotics & Automation Magazine - June 2014 - 54
IEEE Robotics & Automation Magazine - June 2014 - 55
IEEE Robotics & Automation Magazine - June 2014 - 56
IEEE Robotics & Automation Magazine - June 2014 - 57
IEEE Robotics & Automation Magazine - June 2014 - 58
IEEE Robotics & Automation Magazine - June 2014 - 59
IEEE Robotics & Automation Magazine - June 2014 - 60
IEEE Robotics & Automation Magazine - June 2014 - 61
IEEE Robotics & Automation Magazine - June 2014 - 62
IEEE Robotics & Automation Magazine - June 2014 - 63
IEEE Robotics & Automation Magazine - June 2014 - 64
IEEE Robotics & Automation Magazine - June 2014 - 65
IEEE Robotics & Automation Magazine - June 2014 - 66
IEEE Robotics & Automation Magazine - June 2014 - 67
IEEE Robotics & Automation Magazine - June 2014 - 68
IEEE Robotics & Automation Magazine - June 2014 - 69
IEEE Robotics & Automation Magazine - June 2014 - 70
IEEE Robotics & Automation Magazine - June 2014 - 71
IEEE Robotics & Automation Magazine - June 2014 - 72
IEEE Robotics & Automation Magazine - June 2014 - 73
IEEE Robotics & Automation Magazine - June 2014 - 74
IEEE Robotics & Automation Magazine - June 2014 - 75
IEEE Robotics & Automation Magazine - June 2014 - 76
IEEE Robotics & Automation Magazine - June 2014 - 77
IEEE Robotics & Automation Magazine - June 2014 - 78
IEEE Robotics & Automation Magazine - June 2014 - 79
IEEE Robotics & Automation Magazine - June 2014 - 80
IEEE Robotics & Automation Magazine - June 2014 - 81
IEEE Robotics & Automation Magazine - June 2014 - 82
IEEE Robotics & Automation Magazine - June 2014 - 83
IEEE Robotics & Automation Magazine - June 2014 - 84
IEEE Robotics & Automation Magazine - June 2014 - 85
IEEE Robotics & Automation Magazine - June 2014 - 86
IEEE Robotics & Automation Magazine - June 2014 - 87
IEEE Robotics & Automation Magazine - June 2014 - 88
IEEE Robotics & Automation Magazine - June 2014 - 89
IEEE Robotics & Automation Magazine - June 2014 - 90
IEEE Robotics & Automation Magazine - June 2014 - 91
IEEE Robotics & Automation Magazine - June 2014 - 92
IEEE Robotics & Automation Magazine - June 2014 - 93
IEEE Robotics & Automation Magazine - June 2014 - 94
IEEE Robotics & Automation Magazine - June 2014 - 95
IEEE Robotics & Automation Magazine - June 2014 - 96
IEEE Robotics & Automation Magazine - June 2014 - 97
IEEE Robotics & Automation Magazine - June 2014 - 98
IEEE Robotics & Automation Magazine - June 2014 - 99
IEEE Robotics & Automation Magazine - June 2014 - 100
IEEE Robotics & Automation Magazine - June 2014 - 101
IEEE Robotics & Automation Magazine - June 2014 - 102
IEEE Robotics & Automation Magazine - June 2014 - 103
IEEE Robotics & Automation Magazine - June 2014 - 104
IEEE Robotics & Automation Magazine - June 2014 - Cover3
IEEE Robotics & Automation Magazine - June 2014 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2023
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2022
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2021
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2020
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2019
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2018
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2017
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2016
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2015
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2014
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2013
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2012
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_june2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_march2011
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_december2010
https://www.nxtbook.com/nxtbooks/ieee/roboticsautomation_september2010
https://www.nxtbookmedia.com