A short course in Random Finite Sets for multiple object filtering

Prof. Ba-Ngu Vo

The University of Melbourne

International Centre for Mathematical Sciences

Edinburgh

Tuesday 10^th November 2009

www.icms.org.uk

Topics covered:

1 Bayesian filtering and its applications

2 Random finite set formulation of Bayesian multi-object filtering

3 Metrics for multi-object estimation error.

4 The Probability Hypothesis Density filter

5 The Cardinalized Probability Hypothesis Density filter

6 The Multi-target Multi-Bernoulli filter

7 Open research problems.

Multi-object filtering has been an intensive research area since the early 1970s, driven primarily by aerospace applications such as radar, sonar, guidance, navigation, and air traffic control. Recent surveys reported a plethora of techniques and applications. The last decade has witnessed exciting developments in multi-object filtering theory and practice. Mahler’s Finite set statistics (FISST) provides a general systematic foundation for multi-object filtering based on the theory of random finite sets (RFS). The theory of RFS, or point processes, is a rigorous mathematical discipline for dealing with random spatial patterns that has long been used by statisticians in many diverse applications including agriculture, geology, seismology, and epidemiology. The RFS framework has led to the development of novel and efficient multi-object filters, which attracted substantial interest.

This series of lectures outlines recent application of RFS theory in multi-object filtering. These include elements of RFS theory, the optimal Bayes multi-object filter, the Probability Hypothesis density (PHD) filter, the Cardinalised PHD filter, the Multi-target Multi-Bernoulli filter and implementations. The last lecture discusses open problems that are of interest to statisticians, such as the application of Markov Chain Monte Carlo, optimal estimators, performance bounds, entropy.

References

• The Gaussian mixture Probability Hypothesis Density filter,

B. Vo, and W. K. Ma,

IEEE Trans. Signal Proc., Vol 54, No 11 pp. 4091-4104

• Sequential Monte Carlo methods for multitarget filtering with random finite sets

Vo, B.-N.; Singh, S.; Doucet, A.;

Aerospace and Electronic Systems, IEEE Transactions on Volume 41, Issue 4, Oct. 2005 Page(s):1224 - 1245

• Multi-target Bayes filtering via first-order multi-target moments,

R. Mahler

IEEE Trans. Aerospace and Electronic Systems, vol. 39, no. 4, pp. 1152-1178, 2003.

• Random Set Filtering Techniques for Multi-Object State Estimation and Multi-Target Tracking

http://randomsets.eps.hw.ac.uk/