In this thesis, we propose a statistical framework for estimating correlation between sensor systems measuring diverse physical phenomenon. We consider systems that measure at different temporal frequencies and measure responses with different dimensionalities. Our goal is to provide estimates of correlation between all pairs of sensors and use this information to flag potentially anomalous readings. Our anomaly detection method consists of two primary components: dimensionality reduction through projection and Gaussian process (GP) regression. We use non-metric multidimensional scaling to project a partially observed and potentially non-definite covariance matrix into a low dimensional manifold. The projection is estimated in such a way that positively correlated sensors are close to each other and negatively correlated sensors are distant. We then fit a Gaussian process given these positions and use it to make predictions at our observed locations. Because of the large amount of data we wish to consider, we develop methods to scale GP estimation by taking advantage of the replication structure in the data. Finally, we introduce a semi-supervised method to incorporate expert input into a GP model. We are able to learn a probability surface defined over locations and responses based on sets of points labeled by an analyst as either anomalous or nominal. This allows us to discount the influence of points resembling anomalies without removing them based on a threshold. / Ph. D.

We study an informative path planning problem where the goal is to minimize the time required to learn a spatial field. Specifically, our goal is to ensure that the mean square error between the learned and actual fields is below a predefined value. We study three versions of the problem. In the placement version, the objective is to minimize the number of measurement locations. In the mobile robot version, we seek to minimize the total time required to visit and collect measurements from the measurement locations. A multi-robot version is studied as well where the objective is to minimize the time required by the last robot to return back to a common starting location called depot. By exploiting the properties of Gaussian Process regression, we present constant-factor approximation algorithms that ensure the required guarantees. In addition to the theoretical results, we also compare the empirical performance using a real-world dataset with other baseline strategies. / M. S. / We solve the problem of measuring a physical phenomenon accurately using a team of robots in minimum time. Examples of such phenomena include the amount of nitrogen present in the soil within a farm and concentration of harmful chemicals in a water body etc. Knowing accurately the extent of such quantities is important for a variety of economic and environmental reasons. For example, knowing the content of various nutrients in the soil within a farm can help the farmers to improve the yield and reduce the application of fertilizers, the concentration of certain chemicals inside a water body may affect the marine life in various ways. In this thesis, we present several algorithms which can help robots to be deployed efficiently to quantify such phenomena accurately. Traditionally, robots had to be teleoperated. The algorithms proposed in this thesis enable robots to work more autonomously.

Navigation of autonomous underwater vehicles (AUVs) in the subsea environment is particularly challenging due to the unavailability of GPS because of rapid attenuation of electromagnetic waves in water. As a result, the AUV requires alternative methods for position estimation. This thesis describes a terrain-aided navigation approach for an AUV where, with the help of a prior depth map, the AUV localizes itself using altitude measurements from a multibeam DVL. The AUV simultaneously builds a probabilistic depth map of the seafloor as it moves to unmapped locations. The main contribution of this thesis is a new, scalable, and on-line terrain-aided navigation solution for AUVs which does not require the assistance of a support surface vessel. Simulation results on synthetic data and experimental results from AUV field trials in Panama City, Florida are also presented. / Master of Science

Many tasks in machine learning require learning some kind of input-output relation (function), for example, recognising handwritten digits (from image to number) or learning the motion behaviour of a dynamical system like a pendulum (from positions and velocities now to future positions and velocities). We consider this problem using the Bayesian framework, where we use probability distributions to represent the state of uncertainty that a learning agent is in. In particular, we will investigate methods which use Gaussian processes to represent distributions over functions. Gaussian process models require approximations in order to be practically useful. This thesis focuses on understanding existing approximations and investigating new ones tailored to specific applications. We advance the understanding of existing techniques first through a thorough review. We propose desiderata for non-parametric basis function model approximations, which we use to assess the existing approximations. Following this, we perform an in-depth empirical investigation of two popular approximations (VFE and FITC). Based on the insights gained, we propose a new inter-domain Gaussian process approximation, which can be used to increase the sparsity of the approximation, in comparison to regular inducing point approximations. This allows GP models to be stored and communicated more compactly. Next, we show that inter-domain approximations can also allow the use of models which would otherwise be impractical, as opposed to improving existing approximations. We introduce an inter-domain approximation for the Convolutional Gaussian process - a model that makes Gaussian processes suitable to image inputs, and which has strong relations to convolutional neural networks. This same technique is valuable for approximating Gaussian processes with more general invariance properties. Finally, we revisit the derivation of the Gaussian process State Space Model, and discuss some subtleties relating to their approximation. We hope that this thesis illustrates some benefits of non-parametric models and their approximation in a non-parametric fashion, and that it provides models and approximations that prove to be useful for the development of more complex and performant models in the future.

<p>Mapping is a central and common task in robotics research. Building an accurate map without human assistance provides several applications such as space missions, search and rescue, surveillance and can be used in dangerous areas. One application for robotic mapping is to measure changes in terrain volume. In Sweden there are over a hundred landfills that are regulated by laws that says that the growth of the landfill has to be measured at least once a year.</p><p>In this thesis, a preliminary study of methods for measuring terrain volume by the use of an Unmanned Aerial Vehicle (UAV) and a Light Detection And Ranging (LIDAR) sensor is done. Different techniques are tested, including data merging strategies and regression techniques by the use of Gaussian Processes. In the absence of real flight scenario data, an industrial robot has been used fordata acquisition. The result of the experiment was successful in measuring thevolume difference between scenarios in relation to the resolution of the LIDAR. However, for more accurate volume measurements and better evaluation of the algorithms, a better LIDAR is needed.</p> / <p>Kartering är ett centralt och vanligt förekommande problem inom robotik. Att bygga en korrekt karta av en robots omgivning utan mänsklig hjälp har en mängd tänkbara användningsområden. Exempel på sådana är rymduppdrag, räddningsoperationer,övervakning och användning i områden som är farliga för människor. En tillämpning för robotkartering är att mäta volymökning hos terräng över tiden. I Sverige finns det över hundra soptippar, och dessa soptippar är reglerade av lagar som säger att man måste mäta soptippens volymökning minst en gång om året.</p><p>I detta exjobb görs en undersökning av möjligheterna att göra dessa volymberäkningarmed hjälp av obemannade helikoptrar utrustade med en Light Detectionand Ranging (LIDAR) sensor. Olika tekniker har testats, både tekniker som slår ihop LIDAR data till en karta och regressionstekniker baserade på Gauss Processer. I avsaknad av data inspelad med riktig helikopter har ett experiment med en industri robot genomförts för att samla in data. Resultaten av volymmätningarnavar goda i förhållande till LIDAR-sensorns upplösning. För att få bättre volymmätningaroch bättre utvärderingar av de olika algoritmerna är en bättre LIDAR-sensor nödvändig.</p>

Mapping is a central and common task in robotics research. Building an accurate map without human assistance provides several applications such as space missions, search and rescue, surveillance and can be used in dangerous areas. One application for robotic mapping is to measure changes in terrain volume. In Sweden there are over a hundred landfills that are regulated by laws that says that the growth of the landfill has to be measured at least once a year. In this thesis, a preliminary study of methods for measuring terrain volume by the use of an Unmanned Aerial Vehicle (UAV) and a Light Detection And Ranging (LIDAR) sensor is done. Different techniques are tested, including data merging strategies and regression techniques by the use of Gaussian Processes. In the absence of real flight scenario data, an industrial robot has been used fordata acquisition. The result of the experiment was successful in measuring thevolume difference between scenarios in relation to the resolution of the LIDAR. However, for more accurate volume measurements and better evaluation of the algorithms, a better LIDAR is needed. / Kartering är ett centralt och vanligt förekommande problem inom robotik. Att bygga en korrekt karta av en robots omgivning utan mänsklig hjälp har en mängd tänkbara användningsområden. Exempel på sådana är rymduppdrag, räddningsoperationer,övervakning och användning i områden som är farliga för människor. En tillämpning för robotkartering är att mäta volymökning hos terräng över tiden. I Sverige finns det över hundra soptippar, och dessa soptippar är reglerade av lagar som säger att man måste mäta soptippens volymökning minst en gång om året. I detta exjobb görs en undersökning av möjligheterna att göra dessa volymberäkningarmed hjälp av obemannade helikoptrar utrustade med en Light Detectionand Ranging (LIDAR) sensor. Olika tekniker har testats, både tekniker som slår ihop LIDAR data till en karta och regressionstekniker baserade på Gauss Processer. I avsaknad av data inspelad med riktig helikopter har ett experiment med en industri robot genomförts för att samla in data. Resultaten av volymmätningarnavar goda i förhållande till LIDAR-sensorns upplösning. För att få bättre volymmätningaroch bättre utvärderingar av de olika algoritmerna är en bättre LIDAR-sensor nödvändig.

Les simulations par ordinateur sont un outil de grande importance pour les mathématiciens appliqués et les ingénieurs. Elles sont devenues plus précises mais aussi plus compliquées. Tellement compliquées, que le temps de lancement par calcul est prohibitif. Donc, plusieurs aspects de ces simulations sont mal compris. Par exemple, souvent ces simulations dépendent des paramètres qu'ont une valeur inconnue.Un metamodèle est une reconstruction de la simulation. Il produit des réponses proches à celles de la simulation avec un temps de calcul très réduit. Avec ce metamodèle il est possible d'étudier certains aspects de la simulation. Il est construit avec peu de données et son objectif est de remplacer la simulation originale.Ce travail est concerné avec la construction des metamodèles dans un cadre particulier appelé multi-fidélité. En multi-fidélité, le metamodèle est construit à partir des données produites par une simulation objective et des données qu'ont une relation avec cette simulation. Ces données approximées peuvent être générés par des versions dégradées de la simulation ; par des anciennes versions qu'ont été largement étudiées ou par une autre simulation dans laquelle une partie de la description est simplifiée.En apprenant la différence entre les données il est possible d'incorporer l'information approximée et ce ci peut nous conduire vers un metamodèle amélioré. Deux approches pour atteindre ce but sont décrites dans ce manuscrit : la première est basée sur des modèles avec des processus gaussiens et la seconde sur une décomposition à base d'ondelettes. La première montre qu'en estimant la relation il est possible d'incorporer des données qui n'ont pas de valeur autrement. Dans la seconde, les données sont ajoutées de façon adaptative pour améliorer le metamodèle.L'objet de ce travail est d'améliorer notre compréhension sur comment incorporer des données approximées pour produire des metamodèles plus précis. Travailler avec un metamodèle multi-fidélité nous aide à comprendre en détail ces éléments. A la fin une image globale des parties qui forment ce metamodèle commence à s'esquisser : les relations et différences entres les données deviennent plus claires. / A very important tool used by applied mathematicians and engineers to model the behavior of a system are computer simulations. They have become increasingly more precise but also more complicated. So much, that they are very slow to produce an output and thus difficult to sample so that many aspects of these simulations are not very well understood. For example, in many cases they depend on parameters whose value isA metamodel is a reconstruction of the simulation. It requires much less time to produce an output that is close to what the simulation would. By using it, some aspects of the original simulation can be studied. It is built with very few samples and its purpose is to replace the simulation.This thesis is concerned with the construction of a metamodel in a particular context called multi-fidelity. In multi-fidelity the metamodel is constructed using the data from the target simulation along other samples that are related. These approximate samples can come from a degraded version of the simulation; an old version that has been studied extensively or a another simulation in which a part of the description is simplified.By learning the difference between the samples it is possible to incorporate the information of the approximate data and this may lead to an enhanced metamodel. In this manuscript two approaches that do this are studied: one based on Gaussian process modeling and another based on a coarse to fine Wavelet decomposition. The fist method shows how by estimating the relationship between two data sets it is possible to incorporate data that would be useless otherwise. In the second method an adaptive procedure to add data systematically to enhance the metamodel is proposed.The object of this work is to better our comprehension of how to incorporate approximate data to enhance a metamodel. Working with a multi-fidelity metamodel helps us to understand in detail the data that nourish it. At the end a global picture of the elements that compose it is formed: the relationship and the differences between all the data sets become clearer.

published_or_final_version / abstract / Statistics and Actuarial Science / Master / Master of Philosophy

Scalable autonomy requires a robot to be able to recognize and contend with the uncertainty in its knowledge of the world stemming from its noisy sensors and actu- ators. The regions it chooses to explore, and the paths it takes to get there, must take this uncertainty into account. In this thesis we outline probabilistic approaches to represent that world; to construct plans over it; and to determine which part of it to explore next. We present a new technique to create probabilistic cost maps from overhead im- agery, taking into account the uncertainty in terrain classification and allowing for spatial variation in terrain cost. A probabilistic cost function combines the output of a multi-class classifier and a spatial probabilistic regressor to produce a probability density function over terrain for each grid cell in the map. The resultant cost map facilitates the discovery of not only the shortest path between points on the map, but also a distribution of likely paths between the points. These cost maps are used in a path planning technique which allows the user to trade-off the risk of returning a suboptimal path for substantial increases in search speed. We precompute a probability distribution which precisely approximates the true distance between any grid cell in the map and goal cell. This distribution under- pins a number of A* search heuristics we present, which can characterize and bound the risk we are prepared to take in gaining search efficiency while sacrificing optimal path length. Empirically, we report efficiency increases in excess of 70% over standard heuristic search methods. Finally, we present a global approach to the problem of robotic exploration, uti- lizing a hybrid of a topological data structure and an underlying metric mapping process. A ‘Gap Navigation Tree’ is used to motivate global target selection and occluded regions of the environment (‘gaps’) are tracked probabilistically using the metric map. In pursuing these gaps we are provided with goals to feed to the path planning process en route to a complete exploration of the environment. The combination of these three techniques represents a framework to facilitate robust exploration in a-priori unknown environments.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science. Johannesburg, 30th May 2014. / The Multi-Angle Imaging SpectroRadiometer (MISR) is an Earth observation instrument operated by NASA on its Terra satellite. The instrument is unique in imaging the Earth’s surface from nine cameras at different angles. An extended system MISR-HR, has been developed by the Joint Research Centre of the European Commission (JRC) and NASA, which derives many values describing the interaction between solar energy, the atmosphere and different surface characteristics. It also generates estimates of data at the native resolution of the instrument for 24 of the 36 camera bands for which on-board averaging has taken place prior to downloading of the data. MISR-HR data potentially yields high value information in agriculture, forestry, environmental studies, land management and other fields. The MISR-HR system and the data for the African continent have also been provided by NASA and the JRC to the South African National Space Agency (SANSA). Generally, satellite remote-sensing of the Earth’s surface is characterised by irregularity in the time-series of data due to atmospheric, environmental and other effects. Time-series methods, in particular for vegetation phenology applications, exist for estimating missing data values, filling gaps and discerning periodic structure in the data. Recent evaluations of the methods established a sound set of requirements that such methods should satisfy. Existing methods mostly meet the requirements, but choice of method would largely depend on the analysis goals and on the nature of the underlying processes. An alternative method for time-series exists in Gaussian Processes, a long established statistical method, but not previously a common method for satellite remote-sensing time-series. This dissertation asserts that Gaussian Process regression could also meet the aforementioned set of time-series requirements, and further provide benefits of a consistent framework rooted in Bayesian statistical methods. To assess this assertion, a data case study has been conducted for data provided by SANSA for the Kruger National Park in South Africa. The requirements have been posed as research questions and answered in the affirmative by analysing twelve years of historical data for seven sites differing in vegetation types, in and bordering the Park. A further contribution is made in that the data study was conducted using Gaussian Process software which was developed specifically for this project in the modern open language Julia. This software will be released in due course as open source.