Multiple target tracking (MTT) is the process of localizing targets in an environment using sensors that perceive the environment. MTT has many applications such as wildlife monitoring, air traffic monitoring, and surveillance. These applications motivate further research in the different challenging aspects of MTT. One of these challenges that we will focus on in this dissertation is constructing a high fidelity target model. A common approach to target modeling is to use linear models or other simplified models that do not properly describe the target's pose (position and orientation), motion, and uncertainty. These simplified models are typically used because they are easy to implement and computationally efficient. A more accurate approach that improves tracking performance is to define the target model using a geometric representation of the target's natural configuration manifold. In essence, this geometric approach seeks to define a target model that can express every pose and motion of the target while preserving geometric properties such as distances and angles. We restrict our discussion of MTT to objects that move in physical space and can be modeled as a rigid body. This restriction allows us to construct generic geometric target models defined on Lie groups. Since not every Lie group has additional structure that permits vector space arithmetic like Euclidean space, many components of MTT such as data association, track initialization, track propagation and updating, track association and fusing, etc, must be adapted to work with Lie groups. The main contribution of this dissertation is the presentation of a novel MTT algorithm that implements the different MTT components to work with target models defined on Lie groups. We call this new algorithm, Geometric Multiple Target Tracking (G-MTT). This dissertation also serves as a guide on how other MTT algorithms can be modified to work with geometric target models. As part of the presentation there are various experimental results that strengthen the argument that a geometric approach to target modeling improves tracking performance.

Detection of multiple-lane markings (lane-line) on road surfaces is an essential aspect of autonomous vehicles. Although several approaches have been proposed to detect lanes, detecting multiple lane-lines consistently, particularly across a stream of frames and under varying lighting conditions is still a challenging problem. Since the road's markings are designed to be smooth and parallel, lane-line sampled features tend to be spatially and temporally correlated inside and between frames. In this thesis, we develop novel methods to model these spatial and temporal dependencies in the form of the target tracking problem. In fact, instead of resorting to the conventional method of processing each frame to detect lanes only in the space domain, we treat the overall problem as a Multiple Extended Target Tracking (METT) problem. In the first step, we modelled lane-lines as multiple "independent" extended targets and developed a spline mathematical model for the shape of the targets. We showed that expanding the estimations across the time domain could improve the result of estimation. We identify a set of control points for each spline, which will track over time. To overcome the clutter problem, we developed an integrated probabilistic data association fi lter (IPDAF) as our basis, and formulated a METT algorithm to track multiple splines corresponding to each lane-line.In the second part of our work, we investigated the coupling between multiple extended targets. We considered the non-parametric case and modeled target dependency using the Multi-Output Gaussian Process. We showed that considering dependency between extended targets could improve shape estimation results. We exploit the dependency between extended targets by proposing a novel recursive approach called the Multi-Output Spatio-Temporal Gaussian Process Kalman Filter (MO-STGP-KF). We used MO-STGP-KF to estimate and track multiple dependent lane markings that are possibly degraded or obscured by traffic. Our method tested for tracking multiple lane-lines but can be employed to track multiple dependent rigid-shape targets by using the measurement model in the radial space In the third section, we developed a Spatio-Temporal Joint Probabilistic Data Association Filter (ST-JPDAF). In multiple extended target tracking problems with clutter, sometimes extended targets share measurements: for example, in lane-line detection, when two-lane markings pass or merge together. In single-point target tracking, this problem can be solved using the famous Joint Probabilistic Data Association (JPDA) filter. In the single-point case, even when measurements are dependent, we can stack them in the coupled form of JPDA. In this last chapter, we expanded JPDA for tracking multiple dependent extended targets using an approach called ST-JPDAF. We managed dependency of measurements in space (inside a frame) and time (between frames) using different kernel functions, which can be learned using the trained data. This extension can be used to track the shape and dynamic of dependent extended targets within clutter when targets share measurements. The performance of the proposed methods in all three chapters are quanti ed on real data scenarios and their results are compared against well-known model-based, semi-supervised, and fully-supervised methods. The proposed methods offer very promising results. / Thesis / Doctor of Philosophy (PhD)

Most publications discussing missile interception systems assume a zero computer response time. This thesis studies the impact of computer response time on single-missile single-target and multiple- missile multiple-target systems. Simulation results for the final miss distance as the computer response time increases are presented. A simple online cooperative adjustment model for multiple-missile multiple-target system is created for the purpose of studying the computer delay effect.

Multiple target tracking (MTT) is the process of identifying the number of targets present in a surveillance region and the state estimates, or track, of each target. MTT remains a challenging problem due to the NP-hard data association step, where unlabeled measurements are identified as either a measurement of an existing target, a new target, or a spurious measurement called clutter. Existing techniques suffer from at least one of the following drawbacks: divergence in clutter, underlying assumptions on the number of targets, high computational complexity, time-consuming implementation, poor performance at low detection rates, and/or poor track continuity. Our goal is to develop an efficient MTT algorithm that is simple yet effective and that maintains track continuity enabling persistent tracking of an unknown number of targets. A related field to tracking is regression analysis, where the parameters of static signals are estimated from a batch or a sequence of data. The random sample consensus (RANSAC) algorithm was developed to mitigate the effects of spurious measurements, and has since found wide application within the computer vision community due to its robustness and efficiency. The main concept of RANSAC is to form numerous simple hypotheses from a batch of data and identify the hypothesis with the most supporting measurements. Unfortunately, RANSAC is not designed to track multiple targets using sequential measurements.To this end, we have developed the recursive-RANSAC (R-RANSAC) algorithm, which tracks multiple signals in clutter without requiring prior knowledge of the number of existing signals. The basic premise of the R-RANSAC algorithm is to store a set of RANSAC hypotheses between time steps. New measurements are used to either update existing hypotheses or generate new hypotheses using RANSAC. Storing multiple hypotheses enables R-RANSAC to track multiple targets. Good tracks are identified when a sufficient number of measurements support a hypothesis track. The complexity of R-RANSAC is shown to be squared in the number of measurements and stored tracks, and under moderate assumptions R-RANSAC converges in mean to the true states. We apply R-RANSAC to a variety of simulation, camera, and radar tracking examples.

This thesis focuses on visual multiple-target tracking (MTT) from a UAV. Typical state-of-the-art multiple-target trackers rely on an object detector as the primary detection source. However, object detectors usually require a GPU to process images in real-time, which may not be feasible to carry on-board a UAV. Additionally, they often do not produce consistent detections for small objects typical of UAV imagery.In our method, we instead detect motion to identify objects of interest in the scene. We detect motion at corners in the image using optical flow. We also track points long-term to continue tracking stopped objects. Since our motion detection algorithm generates multiple detections at each time-step, we use a hybrid probabilistic data association filter combined with a single iteration of expectation maximization to improve tracking accuracy.We also present a motion detection algorithm that accounts for parallax in non-planar UAV imagery. We use the essential matrix to distinguish between true object motion and apparent object motion due to parallax. Instead of calculating the essential matrix directly, which can be time-consuming, we design a new algorithm that optimizes the rotation and translation between frames. This new algorithm requires only 4 ms instead of 47 ms per frame of the video sequence.We demonstrate the performance of these algorithms on video data. These algorithms are shown to improve tracking accuracy, reliability, and speed. All these contributions are capable of running in real-time without a GPU.

<p>Multiple target tracking (MTT) is a major area that occurs in a variety of real world systems. The problem involves the detection and estimation of an unknown number of targets within a scenario space given a sequence of noisy, incomplete measurements. The classic approach to MTT performs data association between individual measurements, however, this step is a computationally complex problem. Recently, a series of algorithms based on Random Finite Set (RFS) theory, that do not require data association, have been introduced. This thesis addresses some of the main deficiencies involved with RFS methods and derives key extensions to improve them for use in real world systems.\\</p> <p>The first contribution is the Weight Partitioned PHD filter. It separates the Probability Hypothesis Density (PHD) surface into partitions that represent the individual state estimates both spatially and proportionally. The partitions are labeled and propagated over several time steps to form continuous track estimates. Multiple variants of the filter are presented. Next, the Multitarget Multi-Bernoulli (MeMBer) filter is extended to allow the tracking of manoeuvring targets. A model state variable is incorporated into the filter framework to estimate the probability of each motion model. The standard implementations are derived. Finally, a new linear variant of the Intensity filter (iFilter) is presented. A Gaussian Mixture approximation provides more computationally efficient implementation of the iFilter.</p> <p>Each of the new algorithms are validated on simulated data using standard multitarget tracking metrics. In each case, the methods improve on several aspects of multitarget tracking in the real world.</p> / Doctor of Engineering (DEng)

For unmanned aircraft systems to gain full access to the National Airspace System (NAS), they must have the capability to detect and avoid other aircraft. This research focuses on the development of a detect-and-avoid (DAA) system for small unmanned aircraft systems. To safely avoid another aircraft, an unmanned aircraft must detect the intruder aircraft with ample time and distance. Two analytical methods for finding the minimum detection range needed are described. The first method, time-based geometric velocity vectors (TGVV), includes the bank-angle dynamics of the ownship while the second, geometric velocity vectors (GVV), assumes an instantaneous bank-angle maneuver. The solution using the first method must be found numerically, while the second has a closed-form analytical solution. These methods are compared to two existing methods. Results show the time-based geometric velocity vectors approach is precise, and the geometric velocity vectors approach is a good approximation under many conditions. The DAA problem requires the use of a robust target detection and tracking algorithm for tracking multiple maneuvering aircraft in the presence of noisy, cluttered, and missed measurements. Additionally these algorithms needs to be able to detect overtaking intruders, which has been resolved by using multiple radar sensors around the aircraft. To achieve these goals the formulation of a nonlinear extension to R-RANSAC has been performed, known as extended recursive-RANSAC (ER-RANSAC). The primary modifications needed for this ER-RANSAC implementation include the use of an EKF, nonlinear inlier functions, and the Gauss-Newton method for model hypothesis and generation. A fully functional DAA system includes target detection and tracking, collision detection, and collision avoidance. In this research we demonstrate the integration of each of the DAA-system subcomponents into fully functional simulation and hardware implementations using a ground-based radar setup. This integration resulted in various modifications of the radar DSP, collision detection, and collision avoidance algorithms, to improve the performance of the fully integrated DAA system. Using these subcomponents we present flight results of a complete ground-based radar DAA system, using actual radar hardware.

This thesis represents Bayesian joint audio-visual tracking for the 3D locations of multiple people and a current speaker in a real conference environment. To achieve this objective, it focuses on several different research interests, such as acoustic-feature detection, visual-feature detection, a non-linear Bayesian framework, data association, and sensor fusion. As acoustic-feature detection, time-delay-of-arrival~(TDOA) estimation is used for multiple source detection. Localization performance using TDOAs is also analyzed according to different configurations of microphones. As a visual-feature detection, Viola-Jones face detection is used to initialize the locations of unknown multiple objects. Then, a corner feature, based on the results from the Viola-Jones face detection, is used for motion detection for robust objects. Simple point-to-line correspondences between multiple cameras using fundamental matrices are used to determine which features are more robust. As a method for data association and sensor fusion, Monte-Carlo JPDAF and a data association with IPPF~(DA-IPPF) are implemented in the framework of particle filtering. Three different tracking scenarios of acoustic source tracking, visual source tracking, and joint acoustic-visual source tracking are represented using the proposed algorithms. Finally the real-time implementation of this joint acoustic-visual tracking system using a PC, four cameras, and six microphones is addressed with two parts of system implementation and real-time processing.

Radiotherapy is a common and useful method for treating prostate cancer, often using gold fiducial markers in the prostate as guidance. However, when there is a high risk of lymph node involvement, the independent motion of volumes causes complications in patient positioning since there is a choice between position against the gold fiducial markers or the bone anatomy. This leads to expansion of margins for either the prostate or the pelvic lymph nodes. In this thesis two different treatment strategies were performed and compared against given treatment plans. The purpose was to evaluate the standard treatment and to be able to recommend a new clinical approach for treatment of high-risk prostate cancer. Nine high-risk prostate cancer patients with their given treatment plans were used as a baseline. The patients underwent a planning CT and five CBCTs during the treatment. Two new treatment plan setups were done, a robust treatment and a sequential treatment with three and nine different plans respectively. The baseline and the robust treatment used gold fiducial markers as reference, with a prescribed dose of 2.20 Gy over 35 fractions with a VMAT. The sequential treatment used both gold fiducial markers and bone anatomy as reference, done by 35 fractions with a prescribed dose of 0.6 Gy with a single arc and 1.6 Gy with a dual arc respectively. A total of thirteen different treatment plan setups for each patient were simulated 100 times each, resulting in 11700 simulated treatments in total. The resulting simulated treatments were evaluated by the percentage passing nine different clinical goals, as well as dose and percentage volume averages for these goals. The results from the simulated robust treatments showed a decrease in percentage passing and D98 for the prostate and an increase in percentage passing and D98 for the lymph nodes and vesicles compared to the baseline. An increase in percentage passing and D98 was seen in the sequential treatment strategy for both targets compared to the baseline. The rectum had a larger percentage passing the clinical goals and a lower V69, V74 and V59 for both the robust and sequential treatment strategies. The D2 for the external were lower in the robust treatment strategy but higher in the sequential treatment strategy, while the D2 to the femoral heads were lower for both compared to the baseline treatment strategy. In conclusion, an improved dose coverage was seen in the sequential strategy with good sparing of risk organs. The robust treatment strategy showed promising results for sparing risk organs, but with a less robust dose coverage of the prostate.