RS Overview


Background

Multiplatform-multisensor-multitarget systems are multi-object systems:  multiple platforms carrying multiple sensors, observing multiple targets using multiple measurements.  A rigorous mathematical theory of multi-object systems—point process theory—has been available for a half-century.  However, the instant that a point process is applied to practical multitarget tracking, it reduces to a random finite set (RFS).  In fact, non-RFS point processes are a phenomenologically erroneous foundation for practical multitarget tracking.  In addition point processes are (unlike random sets) not theoretically general enough to provide a provably Bayes-optimal unification of "hard + soft" fusion. 

For a systematic examination of "point processes" vs. RFS's in a multitarget tracking context, see the paper "On point processes in multitarget tracking," listed below.

An RFS is easily visualized as a random point pattern.  An everyday example:  the stars in a nighttime sky, which randomly appear and disappear and whose positions shift randomly. 

The RS approach provides systematic techniques for statistically modeling information fusion systems and for deriving practical and effective information fusion algorithms based on principled statistical approximations.  One
result is a family of algorithms, scalable to the combinatorial complexity of particular applications:

  • Bernoulli filters:  The Bayes-optimal solution to tracking at most one target in arbitrary clutter and detection profiles.
  • Probability hypothesis density (PHD) filters:   The simplest, fastest, and least accurate RS filter can nevertheless detect and track multiple targets in heavy clutter while avoiding the computational logjams of measurement-to-track association.
  • Cardinalized PHD (CPHD) filters:   A generalization of the PHD filter with better tracking performance but greater (but still low-degree polynomial) computational complexity.
  • Multi-Bernoulli (MB) filters:  Generalizations of the Bernoulli filter to multiple targets.  These filters also avoid measurement-to-track association and often have better performance than CPHD filters.
  • Generalized labeled multi-Bernoulli (GLMB or "Vo-Vo") filter:   A generalized multi-Bernoulli filter in which track labels are explicitly taken into account.  It is the first, and thus far only, provably Bayes-optimal and implementable multitarget detection and tracking filter.  Efficient computational implementations have been devised that can run real-time on a cellphone.

Many of these RS algorithms have been shown to significantly outperform conventional algorithms in various applications.

Short Survey Paper

        1.  R. Mahler, "A brief survey of recent advances in random-set Fusion," Proc. 2015 International Conf. on Control,
             Automation and Information Sciences (ICCAIS2015), Changshu, China, Oct. 29-31, 2015 (available on ieeexplore).

Point Processes vs. RFS's

        1.  R. Mahler, “On point processes in multitarget tracking" (available at http://arxiv.org/abs/1603.02373).

Tutorials

  1. R. Mahler, “`Statistics 101' for multisensor, multitarget data fusion,” IEEE AESS Mag. Tutorials, 19(1): 53-64, 2004.
  2. R. Mahler, "Random Set Theory for Target Tracking and Identification," Chapter 16 of D.L. Hall and J. Llinas (eds.), Handbook of Multisensor Data Fusion: Theory and Practice, Second Edition, CRC Press, Boca Raton FL, 2008.
  3. B. Ristic, B.-T. Vo, B.-N. Vo, and A. Farina, "A tutorial on Bernoulli filters," IEEE Trans. Sign. Proc., 61(13): 3406 - 3430, 2012
  4. R. Mahler, “'Statistics 102' for multisensor-multitarget tracking," IEEE J. Selected Topics in Sign. Proc., 7(3): 376-389, 2013
  5. B.-N. Vo, B.-T. Vo, and D. Clark, “Bayesian multiple target filtering using random finite sets," Chapter 3 in M. Mallick, V. Krishnamurthy, and B.-N. Vo (eds.), Integrated Tracking, Classification, and Sensor Management, Wiley, 2013.
Books
  1. R. Mahler, Advances in Statistical Multisource-Multitarget Information Fusion, Artech House, 2014
  2. R. Mahler, Statistical Multisource-Multitarget Information Fusion, Artech House, 2007
  3. B. Ristic, Particle Filters for Random Set Models, Springer, New York, 2013.
  4. J. Mullane, B.-N. Vo, M. Adams and B.-T. Vo, Random Finite Sets in Robotic Map Building and SLAM, Springer, 2011
Websites
  1. RFS Filtering:  http://randomsets.ee.unimelb.edu.au/index.html;
  2. RFS SLAM (Prof. M. Adams):  http://www.cec.uchile.cl/~martin/Martin_research_18_8_11.html;
  3. RFS algorithms (Prof. B.-T. Vo):   http://ba-tuong-vo-au.com;  http://ba-tuong-vo-au.com/codes/html;