Multiple Target Tracking with The Probability Hypothesis Density Filter

The random-set framework for multiple target tracking offers a distinct alternative to the traditional approach to multiple target tracking by treating the collections of individual targets and observations as finite-sets. The multi-target state is predicted and updated recursively based on the set-valued observation. The complexity of computing the multi-target recursion grows exponentially with the number of targets and so a method for approximating the optimal filter using a recursion for the first-order moment of the multi-target posterior, known as the Probability Hypothesis Density (PHD) filter, was developed. This thesis addresses some of the essential issues required for the PHD filter to be of practical value in multiple target tracking applications. Two implementations of the PHD filter are studied in detail; the Particle PHD filter, which is a Sequential Monte Carlo technique based on particle filtering, and the Gaussian Mixture PHD filter, which provides a closed form solution to the PHD filter. A detailed study of the convergence properties is conducted which gives theoretical justification for the use of the algorithms. Novel methods to determine the trajectories of the targets for each of the algorithms are developed which enable the PHD filter to be used for true multiple target tracking. These methods are implemented on forward-looking sonar data and demonstrate that the multiple target tracking methods developed for the PHD filter can be used for real applications. Acknowledgements A big thanks to Judith Bell for her excellent supervision throughout the course of my PhD, her consistent support and guidance has been invaluable. Thanks to QinetiQ for supporting this work, and, in particular, Douglas Carmichael and Samantha Dugelay for their interest in this work. At Heriot-Watt, thanks to Yvan Petillot and Ioseba Tena Ruiz for their expertise on tracking and sonar and for developing the tracking algorithm with Kalman filters on sonar data. Also at Heriot-Watt, thanks to Yves de Saint-Pern for providing his code, Chris Haworth for the tracking work on millimetre wave images, Chris Capus for helping me recover this thesis from my dead laptop, and to the excellent support staff in the department. Thanks to Ba-Ngu Vo for an interesting couple of months in Melbourne and for developing the algorithms on which this thesis is based. Also in Melbourne, thanks to Kusha Panta for his contribution to the Fusion paper. In Cambridge, thanks to Sumeetpal Singh for helping with the complicated mathematics and his high level of rigour. Thanks to Ronald Mahler for developing this interesting area in mathematics and engineering and for inviting me to Florida to present some of this work. The anonymous reviewers, some of whom have refereed a number of the articles in this thesis, have contributed substantially to improving this work and deserve a special thanks. Thanks to Špela for inspiring me to do something good. Finally, the biggest thanks go to my parents for always supporting me, without whom this work would not have been possible.