Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Inference and estimation in probabilistic time series models
- I Monte Carlo
- II Deterministic approximations
- III Switching models
- IV Multi-object models
- 11 Approximate likelihood estimation of static parameters in multi-target models
- 12 Sequential inference for dynamically evolving groups of objects
- 13 Non-commutative harmonic analysis in multi-object tracking
- V Nonparametric models
- VI Agent-based models
- Index
- Plate section
- References
12 - Sequential inference for dynamically evolving groups of objects
from IV - Multi-object models
Published online by Cambridge University Press: 07 September 2011
Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Inference and estimation in probabilistic time series models
- I Monte Carlo
- II Deterministic approximations
- III Switching models
- IV Multi-object models
- 11 Approximate likelihood estimation of static parameters in multi-target models
- 12 Sequential inference for dynamically evolving groups of objects
- 13 Non-commutative harmonic analysis in multi-object tracking
- V Nonparametric models
- VI Agent-based models
- Index
- Plate section
- References
Summary
Introduction
In nature there are many examples of group behaviour arising from the action of individuals without any apparent central coordinator, such as the highly coordinated movements of flocks of birds or schools of fish. These are among the most fascinating phenomena to be found in nature; where the groups seem to turn and manoeuvre as a single unit, changing direction almost instantaneously. Similarly, in man-made activities, there are many cases of group-like behaviour, such as a group of aircraft flying in formation.
There are two principal reasons why it is very helpful to model the behaviour of groups explicitly, as opposed to treating all objects independently as in most multiple target tracking approaches. The first is that the joint tracking of (a priori) dependent objects within a group will lead to greater detection and tracking ability in hostile environments with high noise and low detection probabilities. For example, in the radar target tracking application, if several targets are in a group formation, then some information on the positions and speeds of those targets with missing measurements (due to poor detection probability) can be inferred given those targets that are detected. Similarly, if a newly detected target appears close to an existing group, the target can be initialised using the group velocity.
- Type
- Chapter
- Information
- Bayesian Time Series Models , pp. 245 - 276Publisher: Cambridge University PressPrint publication year: 2011
References
[1] , and . Particle Markov chain Monte Carlo methods. Journal of Royal Statistical Society Series B, 72:1–33, 2010.Google Scholar
[2] , , and . Dynamic conditional independence models and Markov chain Monte Carlo methods. Journal of the American Statistical Association, 440:1403–1412, 1997.Google Scholar
[4] , and . Latent Dirichlet allocation. Journal of Machine Learning Research, 3:993–1022, March 2003.Google Scholar
[5] . Combinatorics: Topics, Techniques, Algorithms. Cambridge University Press, 1994.Google Scholar
[6] , and . An overview of existing methods and recent advances in sequential Monte Carlo. Proceedings of the IEEE, 95:899–924, May 2007.Google Scholar
[8] and . Fixed-lag smoothing using sequential importance sampling. In , , and , editors, Bayesian Statistics VI, pages 743–752. 1998.Google Scholar
[9] and . Meshfree adjoint methods for nonlinear filtering. In Proceedings of the IEEE Aerospace Conference, page 16, 2006.Google Scholar
[10] , and . On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10:197–208, 2000.Google Scholar
[12] and . Multi target acoustic source tracking using track before detect. In Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, pages 102–105, 2007.Google Scholar
[13] , and . Pairs trading: performance of a relative average arbitrage rule. NBER Working Paper 7032, 1999. http://www.nber.org/papers/w7032.Google Scholar
[14] . Markov chain Monte Carlo maximum likelihood. In , editor, Computing Science and Statistics: The 23rd symposium on the interface, pages 156–163, 1991.Google Scholar
[15] and . Following a moving target: Monte Carlo inference for dynamic Bayesian models. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 63:127–146, 2001.Google Scholar
[17] . On the relationship between Markov chain Monte Carlo methods for model uncertainty. Journal of Computational and Graphical Statistics, 10(2):230–248, 2001.Google Scholar
[18] and . Models and algorithms for tracking using trans-dimensional sequential Monte Carlo. In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, volume 3, pages 976–979, 2004.Google Scholar
[19] , , and . Models and algorithms for tracking of manoeuvring objects using variable rate particle filters. Proceedings of the IEEE, 95(5):925–952, 2007.Google Scholar
[20] and . Bayesian sequential inference for nonlinear multivariate diffusions. Statistics and Computing, pages 323–338, 2006.Google Scholar
[21] , and . Bayesian target tracking after group pattern distortion. In , editor, Signal and Data Processing of Small Targets, volume 3163, pages 238–248. SPIE, 1997.Google Scholar
[22] , and . Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In IEEE Proceedings of Radar and Signal Processing, volume 140, pages 107–113, 1993.Google Scholar
[23] , , and . An introduction to variational methods for graphical models. In , editor, Learning in Graphical Models, pages 183–233. MIT Press, 1999.Google Scholar
[24] , and . MCMC-based particle filtering for tracking a variable number of interacting targets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27:1805–1819, 2005.Google Scholar
[25] , and . Sequential imputation and Bayesian missing data problems. Journal of the Americian Statistical Association, 89:278–288, March 1994.Google Scholar
[26] , , and . Particle filtering for multitarget detection and tracking. IEEE Transactions on Aerospace and Electronic Systems, 41:1396–1414, 2005.Google Scholar
[27] and . Combined parameter and state estimation in simulation-based filtering. In , , and , editors, Sequential Monte Carlo in Practice, pages 197–217. Springer-Verlag, 2001.Google Scholar
[29] . Stochastic Differential Equations: An Introduction with Applications (Sixth Edition). Springer-Verlag, 2003.Google Scholar
[30] , and . Models and algorithms for detection and tracking of coordinated groups. In Proceedings of the IEEE Aerospace Conference, 2008.Google Scholar
[31] , and . Detection and tracking of coordinated groups. IEEE Transactions on Aerospace and Electronic Systems, 47(1):472–502, 2011.Google Scholar
[32] and . Filtering via simulation: Auxiliary Particle Filter. Journal of the American Statistical Association, 94:590–599, 1999.Google Scholar
[33] , and . Practical filtering with sequential parameter learning. Journal of the Royal Statistical Society, pages 413–428, 2008.Google Scholar
[34] , and . Beyond the Kalman Filter – Particle Filters for Tracking Applications. Artech House, 2004.Google Scholar
[36] . Recursive Bayesian inference on stochastic differential equations. PhD Thesis, Helsinki University of Technology, 2006.
[37] , , and . Tracking of coordinated groups using marginalised MCMC-based Particle Algorithm. In Proceedings of the IEEE Aerospace Conference, 2009.Google Scholar
[38] and . Time-varying topic models using dependent Dirichlet processes. The University of Chicago Technical Report UTML-TR-2005-003, March 2005.Google Scholar
[40] . Dealing with label switching in mixture models. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 62:795–809, 2000.Google Scholar
[41] . Markov chains for exploring posterior distributions. Annals of Statistics, 22:1701–1786, 1994.Google Scholar
[42] , and . Dynamic mixture models for multiple time series. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 2909–2914, 2007.Google Scholar