Sequential Monte Carlo Methods in Multiple Target Tracking

Researchers: Simo Särkkä, Toni Tamminen, Aki Vehtari and Jouko Lampinen

The goal of the project was to develop Bayesian Sequential Monte Carlo (particle filter) based algorithms for multiple target tracking in multi-sensor environment. The idea of multiple target tracking is to optimally fuse information from sensor measurements and modeled target dynamics to form best possible estimates of states of multiple targets (e.g., positions and velocities) and their uncertainties. The models and methods used in this project were based on Bayesian filtering theory.

The main topic of the project was data association, which makes multiple target tracking much harder task than single target tracking and it also rules out the usage of basic Kalman and Extended Kalman filters. In multiple target tracking, the algorithm has to estimate which of the targets produced the measurements, before it is able to use the measurements in actual tracking. In this project we developed new Rao-Blackwellized Monte Carlo data association algorithm [1], which efficiently solves the joint data association and tracking problem.

The secondary topic of the project was the modeling of unknown and varying number of targets. This problem was solved by modeling the target appearances and disappearances as birth-death stochastic process. The Rao-Blackwellized particle filter was extended to cope with this extended model [2].

The third topic of project was modeling of negative information. In a target tracking system physical sensors report measurements only when they receive some kind of signal, which can be further processed into a measurement. In the single-sensor case all we can do is to use these signal-induced measurements. However, when there are multiple sensors measuring from the same origin (e.g. the radar of a target), and some sensors can detect this signal and some cannot, our information is increased by knowing the fact that some sensors could not detect the target. This is called negative information. Example scenarios where this information can be utilized are presented in [3].

The Matlab source codes, which implement the methods were also published under GPL license as RMBCDA Toolbox [4].

Figure 1 shows an example of classical bearings only multiple target tracking problem, which frequently arises in context of passive sensor tracking. The particles in the figures are used for visualizing the distribution, such that the particles are a random sample drawn from the posterior distribution estimate. The actual posterior distribution estimate is a mixture of Gaussians, which is hard to visualize directly. The prior distribution is on purpose selected such that all the four crossings of measurements from the two sensors contain some probability mass, and the distributions of targets are two-modal as can be seen in Figure 1. This phenomenon is often called as ghost phenomenon in tracking literature.

References

• [1] Simo Särkkä, Aki Vehtari, and Jouko Lampinen (2004). Rao-Blackwellized Monte Carlo data association for multiple target tracking. In FUSION 2004: The 7th International Conference on Information Fusion, Stockholm, June 2004. (PDF).
• [2] Simo Särkkä, Aki Vehtari, and Jouko Lampinen (2007). Rao-Blackwellized Particle Filter for Multiple Target Tracking. Information Fusion Journal, Volume 8, Issue 1, Pages 2-15. http://dx.doi.org/10.1016/j.inffus.2005.09.009. (Preprint as PDF)
• [3] Simo Särkkä, Toni Tamminen, Aki Vehtari, and Jouko Lampinen (2004). Probabilistic methods in multiple target tracking - Review and bibliography. Published as technical report B36, ISBN 951-22-6938-4, Helsinki University of Technology. Laboratory of Computational Engineering, 2004. (PDF)
• [4] RBMCDA Toolbox for Matlab. http://www.lce.hut.fi/research/mm/rbmcda/