Tracking systems are already encountered in everyday life in numerous applications, but many algorithms from the existing literature rely on assumptions that do not always hold in realistic scenarios, or can only be applied in niche circumstances. Therefor this thesis is motivated to develop new approaches that relax assumptions and restrictions, improve tracking performance, and are applicable in a broad range of scenarios. In the area of terrain-aided tracking this an algorithm is proposed to track targets using a Gaussian mixture measurement distribution to better represent multimodal distributions that can arise due to terrain conditions. This allowed effective use in a wider range of terrain conditions than existing approaches, which assume a unimodal Gaussian measurement distribution. Next, the problem of estimating and compensating for sensor biases is considered in the context of terrain-aided tracking. Existing approaches to bias estimation cannot be easily reconciled with the nonlinear converted measurement model applied in terrain-aided tracking. To address this, a novel efficient bias estimation algorithm is proposed that can be applied to a wide range of measurement models and operational scenarios, allowing for effective bias estimation and measurement compensation to be performed in situations that cannot be handled by existing algorithms. Finally, to address scenarios where converted measurement tracking is not possible or desired, the problem of sensor motion compensation when tracking in pixel coordinates is considered. Existing approaches compensate for sensor motion by transforming state estimates between frames, but are only able to achieve partial transformation of the state estimate and its covariance matrix. This thesis proposes a novel algorithm used to transform the full state estimate and its covariance matrix, improving tracking performance when tracking with a low frame rate and when tracking targets moving with a nearly coordinated turn motion model. Each of the proposed algorithms are evaluated in several simulated scenarios and compared against existing approaches and baselines to demonstrate their efficacy. / Thesis / Doctor of Philosophy (PhD)

Mean shift is an effective iterative algorithm widely used in image analysis tasks like tracking, image segmentation, smoothing, filtering, edge detection and etc. It iteratively estimates the modes of the probability function of a set of sample data points based in a region. Mean shift was invented in 1975, but it was not widely used until the work by Cheng in 1995. After that, it becomes popular in computer vision. However the convergence, a key character of any iterative algorithm, has been rigorously proved only very recently, but with strong assumptions. In this thesis, the method of mean shift is introduced systematically first and then the convergence is established under more relaxed assumptions. Finally, generalization of the mean shift method is also given for the estimation of probability density function using generalized multivariate smoothing functions to meet the need for more real life applications.

This thesis applies the methods of previous work in aerial magnetic field mapping and use in state estimation to the Virginia Tech Swing Space motion capture indoor facility. State estimation with magnetic field data acquired from a quadrotor is comparatively performed with Gaussian process regression, a multiplicative extended Kalman filter, and a particle filter to estimate the position and attitude of an uncrewed aircraft system (UAS) at any point in the motion capture testing environment. Motion capture truth data is used in the analysis. The first experimental method utilized in this thesis is Gaussian process regression. This machine learning tool allows us to create three-dimensional magnetic field maps of the indoor test space by collecting magnetic field vector data with a small UAS. Here, the maps illustrate the 3D magnetic field strengths and directions in the Virginia Tech Swing Space motion capture lab. Also, the magnetic field spatial variation of the test space is analyzed, yielding higher magnetic field gradient at lower heights above the ground. Next, the multiplicative extended Kalman filter is used with our Gaussian process regression magnetic field maps to estimate the attitude of the quadrotor. The results indicate an increase in attitude estimation accuracy when magnetic field mapping is utilized compared to when it is not. Here, results show that the addition of aerial magnetic field mapping leads to enhanced attitude estimation. Finally, the particle filter is utilized with support from our magnetic field maps to estimate the position of a small quadrotor UAS. The magnetic field maps allow us to obtain UAS position vectors by tracking UAS movement through magnetic field data. The particle filter gives three-dimensional position estimates to within 0.2 meters for five out of our eight test flights. The root mean square error is within 0.1 meters for each test flight. The effects of magnetic field spatial variation are also analyzed. The accuracy of position estimation is higher for two out the four flights in the maximum magnetic gradient area, while the accuracy is similar in both minimum and maximum gradient regions for the remaining two flights. There is evidence to support an increase in accuracy for high magnetic variation areas, but further work is needed to confirm utility for practical applications. / Master of Science / This thesis investigates airborne magnetic field mapping for the Virginia Tech Swing Space motion capture indoor facility. Position and attitude estimation with magnetic field data acquired from a small uncrewed aircraft system (UAS) is comparatively performed with multiple estimation methods. Motion capture truth data is used in analyses. The first data processing method is called Gaussian process regression. This machine learning tool allows us to create magnetic field maps of the indoor test space by averaging or regressing field estimates over collected UAS data. The maps illustrate the magnetic field strengths and directions over a three dimensional volume in the Virginia Tech Swing Space motion capture lab. Next, a multiplicative extended Kalman filter is used with our Gaussian process regression magnetic field maps to estimate UAS attitude. Results show improvement in attitude estimation accuracy when magnetic field mapping is utilized compared to when it is not. Finally, a particle filter method is utilized with our magnetic field maps to estimate UAS position. The particle filter estimates three-dimensional UAS position estimates to within 0.2 meters for five out of our eight test flights. The effects of magnetic field spatial variation are also analyzed, indicating the need for future work before magnetic field based position estimation can be practically applied.

Forecasting tools play an important role in public response to epidemics. Despite this, limited work has been done in comparing best-in-class techniques across the broad spectrum of time series forecasting methodologies. Forecasting frameworks were developed that utilised three methods designed to work with nonlinear dynamics: Iterated Filtering (IF) 2, Hamiltonian MCMC (HMC), and S-mapping. These were compared in several forecasting scenarios including a seasonal epidemic and a spatiotemporal epidemic. IF2 combined with parametric bootstrapping produced superior predictions in all scenarios. S-mapping combined with Dewdrop Regression produced forecasts slightly less-accurate than IF2 and HMC, but demonstrated vastly reduced running times. Hence, S-mapping with or without Dewdrop Regression should be used to glean initial insight into future epidemic behaviour, while IF2 and parametric bootstrapping should be used to refine forecast estimates in time. / Thesis / Master of Science (MSc)

Biological systems, processes, and applications present modeling challenges in the form of system complexity, limited steady-state availability, and limited measurements. One primary issue is the lack of well-estimated parameters. This thesis presents two contributions in the area of modeling and parameter estimation for these kinds of biological processes. The primary contribution is the development of an adaptive parameter estimation process that includes parameter selection, evaluation, and estimation, applied along with modeling of cell growth in culture. The second contribution shows the importance of parameter estimation for evaluation of experiment and process design. / Thesis / Master of Applied Science (MASc)

This thesis presents a validation study of the research by Hassett (2011). It examined the permanent canines’ cervical diameters using established measurement techniques set forth by Hillson et al. (2005) to determine sex in a known population of male and female adults and juveniles. The present study combined the Maxwell Collection, housed at University of New Mexico, and the Hamann-Todd Collection, housed at the Cleveland Museum of Natural History, as the known-sex sample. The sample included 642 permanent canines resulting in 862 measurements from 218 individuals. There were 120 males and 98 females between the ages of 12 and 98 years old. Of the 218 individuals, 148 were White, 62 were Black, 2 were Hispanic, 1 was Native American, and 5 were an unknown ancestry. The measurements used were the cervical mesiodistal diameter and the cervical buccolingual diameter of each upper and lower, right and left canine. The author hypothesized that research conducted on this known age skeletal collection sample would support Hassett (2011), who concluded that the cervical diameter of the canine is sexually dimorphic and can be used to predict sex accurately. In addition, it was predicted that there would not be a significant statistical difference between adult and juvenile permanent canine measurements. An intra-observer error test found that original and repeated measures were not statistically different from one another. Statistical analysis found that adults and juveniles did not have significantly different measurements, so the two samples were combined into one larger known-sex sample. The accuracy of all the functions for both sexes using the cervical diameter method is between 80.2% and 87.5%. The fourth function’s formula, which uses both diameters from one maxillary canine and one mandibular canine, had the best overall accuracy of 87.1%. The accuracy of all the functions for males was between 81.1% and 91.7% and for females the accuracy was between 74.8% and 89.7%. Analysis also indicated that no tooth nor measurement proved to be a better predictor of sex; therefore, any tooth and measurement can be used to estimate sex. The author believes that this validation will allow further research into the applicability of the permanent canine using cone-beam computed tomography to determine sex in juveniles whose permanent canines have not yet erupted. This determination is highly significant, given the dearth of usable techniques to sex juvenile human remains.

Analysis of measured data is often required when there is no deep understanding of the mathematics that accurately describes the process being measured. Additionally, realistic estimation of the derivative of measured data is often useful. Current techniques of accomplishing this type of data analysis are labor intensive, prone to significant error, and highly dependent on the expertise of the engineer performing the analysis. The ?Self-Smoothing Functional Estimation? (SSFE) algorithm was developed to automate the analysis of measured data and to provide a reliable basis for the extraction of derivative information. In addition to the mathematical development of the SSFE algorithm, an example is included in Chapter III that illustrates several of the innovative features of the SSFE and associated algorithms. Conclusions are drawn about the usefulness of the algorithm from an engineering perspective and additional possible uses are mentioned.

In order for a robot to operate autonomously in an environment, it must be able to locate itself within it. A robot's position and orientation cannot be directly measured by physical sensors, so estimating it is a non-trivial problem. Some sensors provide this information, such as the Global Navigation Satellite System (GNSS) and Motion capture (Mo-cap). Nevertheless, these sensors are expensive to set up, or they are not useful in environments where autonomous vehicles are often deployed. Our proposal explores a new approach to sensing for relative motion and position estimation. It consists of one vision sensor and a marker that utilizes moiré phenomenon to estimate the position of the vision sensor by using Convolutional Neural Networks (CNN) trained to estimate the position from the pattern shown on the marker. We share the process of data collection and training of the network and share the hyperparameter search method used to optimize the structure of the network. We test the trained network in a setup to evaluate its ability in estimating position. The system achieved an average absolute error of 1 cm, showcasing a method that could be used to overcome the current limitations of vision approaches in pose estimation.

Group testing is a procedure that splits samples into multiple groups based on some specific grouping criterion and then tests each group. It is usually used in identifying affected individuals or estimating the population proportion of affected individuals. Improving precision of group testing and saving cost of experiment are two crucial tasks for investigators. Cost-efficiency is a ratio of precision to cost; hence improving cost-efficiency is as crucial as improvement of precision and cost saving. In this thesis, retesting will be considered as a method to improve precision and cost-efficiency, and save cost. Retesting is an extension of group testing. It uses two or more group testing stages, and testing original samples in all of the stages. Hepworth and Watson (2015) proposed a two-stage group testing procedure where two stages have equal group sizes, and the number of groups of the second stage is based on the number of positive groups in the first stage. In this thesis, our main goal is estimating a proportion p under the circumstance of unequal group sizes in two stages, and discovering the most cost-efficient experiment design. Analytical solutions of precision will be provided; we will use these analytical solutions with simulations to analyse some experimental designs, and discover whether doing one group testing only is precise enough or not and if it is worth retesting for each design. In the end, we will combine all these analyses and identify the optimal experiment design. / Thesis / Master of Science (MSc)

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