Multitarget tracking is the process of jointly determining the number of targets present and their states from noisy sets of measurements. The difficulty of the multitarget tracking problem is that the number of targets present can change as targets appear and disappear while the sets of measurements may contain false alarms and measurements of true targets may be missed. The theory of random finite sets was proposed as a systematic, Bayesian approach to solving the multitarget tracking problem. The conceptual solution is given by Bayes filtering for the probability distribution of the set of target states, conditioned on the sets of measurements received, known as the multitarget Bayes filter. A first-moment approximation to this filter, the probability hypothesis density (PHD) filter, provides a more computationally practical, but theoretically sound, solution. The central thesis of this work is that the random finite set framework is theoretically sound, compatible with the Bayesian methodology and amenable to immediate implementation in a wide range of contexts. In advancing this thesis, new links between the PHD filter and existing Bayesian approaches for manoeuvre handling and incorporation of target amplitude information are presented. A new multitarget metric which permits incorporation of target confidence information is derived and new algorithms are developed which facilitate sequential Monte Carlo implementations of the PHD filter. Several applications of the PHD filter are presented, with a focus on applications for tracking in sonar data. Good results are presented for implementations on real active and passive sonar data. The PHD filter is also deployed in order to extract bacterial trajectories from microscopic visual data in order to aid ongoing work in understanding bacterial chemotaxis. A performance comparison between the PHD filter and conventional multitarget tracking methods using simulated data is also presented, showing favourable results for the PHD filter.

This dissertation concerns with the formulation of an improved multi-target multi-Bernoulli (MeMBer) filter and the use of the joint multi-target (JoM) estimator in an effective and efficient manner for a specific implementation of MeMBer filters. After reviewing random finite set (RFS) formalism for multi-target tracking problems and the related Bayes estimators the major contributions of this dissertation are explained in detail. The second chapter of this dissertation is dedicated to the analysis of the relationship between the multi-Bernoulli RFS distribution and the MeMBer corrector. This analysis leads to the formulation of an unbiased MeMBer filter without making any limiting assumption. Hence, as opposed to the popular cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter, the proposed MeMBer filter can be employed under the cases when sensor detection probability is moderate to low. Furthermore, a statistical refinement process is introduced to improve the stability of the estimated cardinality of targets obtained from the proposed MeMBer filter. The results from simulations demonstrate the effectiveness of the improved MeMBer filter. In Chapters III and IV, the Bayesian optimal estimators proposed for the RFS based multi-target tracking filters are examined in detail. First, an optimal solution to the unknown constant in the definition of the JoM estimator is determined by solving a multi-objective optimization problem. Thus, the JoM estimator can be implemented for tracking of a Bernoulli target using the optimal joint target detection and tracking (JoTT) filter. The results from simulations confirm assertions about its performance obtained by theoretical analysis in the literature. Finally, in the third chapter of this dissertation, the proposed JoM estimator is reformulated for RFS multi-Bernoulli distributions. Hence, an effective and efficient implementation of the JoM estimator is proposed for the Gaussian mixture implementations of the MeMBer filters. Simulation results demonstrate the robustness of the proposed JoM estimator under low-observable conditions. / Thesis / Doctor of Philosophy (PhD)

Social networking sites such as Twitter, Facebook and Flickr play an important role in disseminating breaking news about natural disasters, terrorist attacks and other events. They serve as sources of first-hand information to deliver instantaneous news to the masses, since millions of users visit these sites to post and read news items regularly. Hence, by exploring e fficient mathematical techniques like Dempster-Shafer theory and Modi ed Dempster's rule of combination, we can process large amounts of data from these sites to extract useful information in a timely manner. In surveillance related applications, the objective of processing voluminous social network data is to predict events like revolutions and terrorist attacks before they unfold. By fusing the soft and often unreliable data from these sites with hard and more reliable data from sensors like radar and the Automatic Identi cation System (AIS), we can improve our event prediction capability. In this paper, we present a class of algorithms to fuse hard sensor data with soft social network data (tweets) in an e ffective manner. Preliminary results using are also presented. / Thesis / Master of Applied Science (MASc)