The probability hypothesis density (PHD), popularized by Ronald Mahler, presents a novel and theoretically-rigorous approach to multitarget, multisensor tracking. Based on random set theory, the PHD is the first moment of a point process of a random track set, and it can be propagated by Bayesian prediction and observation equations to form a multitarget, multisensor tracking filter. The advantage of the PHD filter lies in its ability to estimate automatically the expected number of targets present, to fuse easily different kinds of data observations, and to locate targets without performing any explicit report-to-track association. We apply a particle-filter implementation of the PHD filter to realistic multitarget, multisensor tracking using passive coherent location (PCL) systems that exploit illuminators of opportunity such as FM radio stations. The objective of this dissertation is to enhance the usefulness of the PHD particle filter for multitarget, multisensor tracking, in general, and within the context of PCL, in particular. This involves a number of thrusts, including: 1) devising intelligent proposal densities for particle placement, 2) devising a peak-extraction algorithm for extracting information from the PHD, 3) incorporating realistic probabilities of detection and signal-to-noise ratios (including multipath effects) to model realistic PCL scenarios, 4) using range, Doppler, and direction of arrival (DOA) observations to test the target detection and data fusion capabilities of the PHD filter, and 5) clarifying the concepts behind FISST and the PHD to make them more accessible to the practicing engineer. A goal of this dissertation is to serve as a tutorial for anyone interested in becoming familiar with the probability hypothesis density and associated PHD particle filter. It is hoped that, after reading this thesis, the reader will have gained a clearer understanding of the PHD and the functionality and effectiveness of the PHD particle filter.

<div>Multi-target tracking (MTT) is the problem to simultaneously estimate the number of targets and their states or trajectories. Numerous techniques have been developed for over 50 years, with a multitude of applications in many fields of study; however, there are two most widely used approaches to MTT: i) data association-based traditional algorithms; and ii) finite set statistics (FISST)-based data association free Bayesian multi-target filtering algorithms. Most data association-based traditional filters mainly use a statistical or simple model of the feature without explicitly considering the correlation between the target behavior</div><div>and feature characteristics. The inaccurate model of the feature can lead to divergence of the estimation error or the loss of a target in heavily cluttered and/or low signal-to-noise ratio environments. Furthermore, the FISST-based data association free Bayesian multi-target filters can lose estimates of targets frequently in harsh environments mainly</div><div>attributed to insufficient consideration of uncertainties not only measurement origin but also target's maneuvers.</div><div>To address these problems, three main approaches are proposed in this research work: i) new feature models (e.g., target dimensions) dependent on the target behavior</div><div>(i.e., distance between the sensor and the target, and aspect-angle between the longitudinal axis of the target and the axis of sensor line of sight); ii) new Gaussian mixture probability hypothesis density (GM-PHD) filter which explicitly considers the uncertainty in the measurement origin; and iii) new GM-PHD filter and tracker with jump Markov system models. The effectiveness of the analytical findings is demonstrated and validated with illustrative target tracking examples and real data collected from the surveillance radar.</div>