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Thesis (Ph. D.)--Oregon State University, 1969. / Typescript. Includes bibliographical references (leaves 76-79). Also available on the World Wide Web.

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.

Detection of biological and chemical threats is an important consideration in the modern national defense policy. Much of the testing and evaluation of threat detection technologies is performed without appropriate uncertainty quantification. This paper proposes an approach to analyzing the effect of threat concentration on the probability of detecting chemical and biological threats. The approach uses a probit semi-parametric formulation between threat concentration level and the probability of instrument detection. It also utilizes a bayesian adaptive design to determine at which threat concentrations the tests should be performed. The approach offers unique advantages, namely, the flexibility to model non-monotone curves and the ability to test in a more informative way. We compare the performance of this approach to current threat detection models and designs via a simulation study.

The topic of this thesis is occupancy mapping for mobile robots, with an emphasis on a novel method for continuous occupancy mapping using Gaussian processes. In the new method, spatial correlation is accounted for in a natural way, and an a priori discretization of the area to be mapped is not necessary as within most other common methods. The main contribution of this thesis is the construction of a Gaussian process library for C++, and the use of this library to implement the continuous occupancy mapping algorithm. The continuous occupancy mapping is evaluated using both simulated and real world experimental data. The main result is that the method, in its current form, is not fit for online operations due to its computational complexity. By using approximations and ad hoc solutions, the method can be run in real time on a mobile robot, though not without losing many of its benefits.

The proliferation of renewables, electric vehicles, and power electronic devices calls for innovative approaches to learn, optimize, and plan the power system. The uncertain and volatile nature of the integrated components necessitates using swift and probabilistic solutions. Gaussian process regression is a machine learning paradigm that provides closed-form predictions with quantified uncertainties. The key property of Gaussian processes is the natural ability to integrate the sensitivity of the labels with respect to features, yielding improved accuracy. This dissertation tailors Gaussian process regression for three applications in power systems. First, a physics-informed approach is introduced to infer the grid dynamics using synchrophasor data with minimal network information. The suggested method is useful for a wide range of applications, including prediction, extrapolation, and anomaly detection. Further, the proposed framework accommodates heterogeneous noisy measurements with missing entries. Second, a learn-to-optimize scheme is presented using Gaussian process regression that predicts the optimal power flow minimizers given grid conditions. The main contribution is leveraging sensitivities to expedite learning and achieve data efficiency without compromising computational efficiency. Third, Bayesian optimization is applied to solve a bi-level minimization used for strategic investment in electricity markets. This method relies on modeling the cost of the outer problem as a Gaussian process and is applicable to non-convex and hard-to-evaluate objective functions. The designed algorithm shows significant improvement in speed while attaining a lower cost than existing methods. / Doctor of Philosophy / The proliferation of renewables, electric vehicles, and power electronic devices calls for innovative approaches to learn, optimize, and plan the power system. The uncertain and volatile nature of the integrated components necessitates using swift and probabilistic solutions. This dissertation focuses on three practically important problems stemming from the power system modernization. First, a novel approach is proposed that improves power system monitoring, which is the first and necessary step for the stable operation of the network. The suggested method applies to a wide range of applications and is adaptable to use heterogeneous and noisy measurements with missing entries. The second problem focuses on predicting the minimizers of an optimization task. Moreover, a computationally efficient framework is put forth to expedite this process. The third part of this dissertation identifies investment portfolios for electricity markets that yield maximum revenue and minimum cost.

There are several methods to measure surface evenness for car roads, but almost none for bike paths. Accordingly, VTI (the Swedish National Road and Transport Research Institute) have created a smartphone application which uses the accelerometers in the phone to measure the vibration from the road. This report’s aim is to analyze the data collected using this application, investigate if the data is repeatable, to find factors that are important for evenness and perform classification of bike paths as even or wiggly. Two main methods were used, Gaussian process and wavelets. Gaussian process was used to classify bike paths and wavelets to investigate the repeatability and see how many trips are needed to get a consistent result. The results show that the two different smartphones gave quite different results; one smartphone indicated almost twice as high RMS values (measure of vibration) than the other. The GPS positions of smartphones were quite good, except under a tunnel and close to high buildings. Some short section of the road gave very high or very low RMS values, but the general standard of all investigated bike paths were too even to detect any significant differences between the paths. The results show that there’s some unexplained variance in the turns, but the effect of the turns hasn’t been tested. The wavelets analysis show that around 15 trips were needed to get a consistent result. The report contains a description of a designed experiment that will continue this project. This new data will be collected in a more carefully to make a better separation between good and bad cycle routes by the RMS value. / <p>Uppdragsgivare: VTI (Anna Niska och Leif Sjögren)</p>

This report deals with reconstruction of strain fields within deformed materials. The method relies upon data generated from Bragg edge measurements, in which information is gained from neutron beams that are sent through the sample. The reconstruction has been made by modelling the strain field as a Gaussian process, assigned a covariance structure customized by incorporation of the so-called equilibrium constraints. By making use of an approximation scheme well suited for the problem, the complexity of the computations has been significantly reduced. The results from numerical simulations indicates a better performance as compared to previous work in this area.

<p>Bayesian nonparametric models, such as the Gaussian process and the Dirichlet process, have been extensively applied for target kinematics modeling in various applications including environmental monitoring, traffic planning, endangered species tracking, dynamic scene analysis, autonomous robot navigation, and human motion modeling. As shown by these successful applications, Bayesian nonparametric models are able to adjust their complexities adaptively from data as necessary, and are resistant to overfitting or underfitting. However, most existing works assume that the sensor measurements used to learn the Bayesian nonparametric target kinematics models are obtained a priori or that the target kinematics can be measured by the sensor at any given time throughout the task. Little work has been done for controlling the sensor with bounded field of view to obtain measurements of mobile targets that are most informative for reducing the uncertainty of the Bayesian nonparametric models. To present the systematic sensor planning approach to leaning Bayesian nonparametric models, the Gaussian process target kinematics model is introduced at first, which is capable of describing time-invariant spatial phenomena, such as ocean currents, temperature distributions and wind velocity fields. The Dirichlet process-Gaussian process target kinematics model is subsequently discussed for modeling mixture of mobile targets, such as pedestrian motion patterns. </p><p>Novel information theoretic functions are developed for these introduced Bayesian nonparametric target kinematics models to represent the expected utility of measurements as a function of sensor control inputs and random environmental variables. A Gaussian process expected Kullback Leibler divergence is developed as the expectation of the KL divergence between the current (prior) and posterior Gaussian process target kinematics models with respect to the future measurements. Then, this approach is extended to develop a new information value function that can be used to estimate target kinematics described by a Dirichlet process-Gaussian process mixture model. A theorem is proposed that shows the novel information theoretic functions are bounded. Based on this theorem, efficient estimators of the new information theoretic functions are designed, which are proved to be unbiased with the variance of the resultant approximation error decreasing linearly as the number of samples increases. Computational complexities for optimizing the novel information theoretic functions under sensor dynamics constraints are studied, and are proved to be NP-hard. A cumulative lower bound is then proposed to reduce the computational complexity to polynomial time.</p><p>Three sensor planning algorithms are developed according to the assumptions on the target kinematics and the sensor dynamics. For problems where the control space of the sensor is discrete, a greedy algorithm is proposed. The efficiency of the greedy algorithm is demonstrated by a numerical experiment with data of ocean currents obtained by moored buoys. A sweep line algorithm is developed for applications where the sensor control space is continuous and unconstrained. Synthetic simulations as well as physical experiments with ground robots and a surveillance camera are conducted to evaluate the performance of the sweep line algorithm. Moreover, a lexicographic algorithm is designed based on the cumulative lower bound of the novel information theoretic functions, for the scenario where the sensor dynamics are constrained. Numerical experiments with real data collected from indoor pedestrians by a commercial pan-tilt camera are performed to examine the lexicographic algorithm. Results from both the numerical simulations and the physical experiments show that the three sensor planning algorithms proposed in this dissertation based on the novel information theoretic functions are superior at learning the target kinematics with</p><p>little or no prior knowledge</p> / Dissertation

Gaussian processes can be used as priors on functions. The need for a flexible, principled, probabilistic model of functional relations is common in practice. Consequently, such an approach is demonstrably useful in a large variety of applications. Two challenges of Gaussian process modelling are often encountered. These are dealing with the adverse scaling with the number of data points and the lack of closed form posteriors when the likelihood is non-Gaussian. In this thesis, we study variational inference as a framework for meeting these challenges. An introductory chapter motivates the use of stochastic processes as priors, with a particular focus on Gaussian process modelling. A section on variational inference reviews the general definition of Kullback-Leibler divergence. The concept of prior conditional matching that is used throughout the thesis is contrasted to classical approaches to obtaining tractable variational approximating families. Various theoretical issues arising from the application of variational inference to the infinite dimensional Gaussian process setting are settled decisively. From this theory we are able to give a new argument for existing approaches to variational regression that settles debate about their applicability. This view on these methods justifies the principled extensions found in the rest of the work. The case of scalable Gaussian process classification is studied, both for its own merits and as a case study for non-Gaussian likelihoods in general. Using the resulting algorithms we find credible results on datasets of a scale and complexity that was not possible before our work. An extension to include Bayesian priors on model hyperparameters is studied alongside a new inference method that combines the benefits of variational sparsity and MCMC methods. The utility of such an approach is shown on a variety of example modelling tasks. We describe GPflow, a new Gaussian process software library that uses TensorFlow. Implementations of the variational algorithms discussed in the rest of the thesis are included as part of the software. We discuss the benefits of GPflow when compared to other similar software. Increased computational speed is demonstrated in relevant, timed, experimental comparisons.