Indiana University-Purdue University Indianapolis (IUPUI) / The lane-keeping system in autonomous vehicles (AV) or even as a part of the advanced driving assistant system (ADAS) is known as one of the primary options of AVs and ADAS. The developed lane-keeping systems work on either computer vision or deep learning algorithms for their lane detection section. However, even the strongest image processing units or the robust deep learning algorithms for lane detection have inaccuracies during lane detection under certain conditions. The source of these inaccuracies could be rainy or foggy weather, high contrast shades of buildings and objects on-street, or faded lines. Since the lane detection unit of these systems is responsible for controlling the steering, even a momentary loss of lane detection accuracy could result in an accident or failure. As mentioned, different lane detection algorithms have been presented based on computer vision and deep learning during the last few years, and each one has pros and cons. Each model may have a better performance in some situations and fail in others. For example, deep learning-based methods are vulnerable to new samples. In this research, multiple models of lane detection are evaluated and used together to implement a robust lane detection algorithm. The purpose of this research is to develop an estimator-based Multiple Model Adaptive Estimation (MMAE) algorithm on the lane-keeping system to improve the robustness of the lane detection system. To verify the performance of the implemented algorithm, the AirSim simulation environment was used. The test simulation vehicle was equipped with one front camera and one back camera used to implement the proposed algorithm. The front camera images are used for detecting the lane and the offset of the vehicle and center point of the lane. The rear camera, which offered better performance in lane detection, was used as an estimator for calculating the uncertainty of each model. The simulation results showed that combining two implemented models with MMAE performed robustly even in those case studies where one of the models failed. The proposed algorithm was able to detect the failures of either of the models and then switch to another good working model to improve the robustness of the lane detection system. However, the proposed algorithm had some limitations; it can be improved by replacing PID controller with an MPC controller in future studies. In addition, in the presented algorithm, two computer vision-based algorithms were used; however, adding a deep learning-based model could improve the performance of the proposed MMAE. To have a robust deep learning-based model, it is suggested to train the network based on AirSim output images. Otherwise, the network will not work accurately due to the differences in the camera's location, camera configuration, colors, and contrast.

The use of visual sensors in providing the necessary information for the autonomous guidance and navigation of the unmanned-air vehicles (UAV) or micro-air vehicles (MAV) applications is inspired by biological systems and is motivated first of all by the reduction of the navigational sensor cost. Also, visual sensors can be more advantageous in military operations since they are difficult to detect. However, the design of a reliable guidance, navigation and control system for aerial vehicles based only on visual information has many unsolved problems, ranging from hardware/software development to pure control-theoretical issues, which are even more complicated when applied to the tracking of maneuvering unknown targets. This dissertation describes guidance law design and implementation algorithms for autonomous tracking of a flying target, when the information about the target's current position is obtained via a monocular camera mounted on the tracking UAV (follower). The visual information is related to the target's relative position in the follower's body frame via the target's apparent size, which is assumed to be constant, but otherwise unknown to the follower. The formulation of the relative dynamics in the inertial frame requires the knowledge of the follower's orientation angles, which are assumed to be known. No information is assumed to be available about the target's dynamics. The follower's objective is to maintain a desired relative position irrespective of the target's motion. Two types of guidance laws are designed and implemented in the dissertation. The first one is a smooth guidance law that guarantees asymptotic tracking of a target, the velocity of which is viewed as a time-varying disturbance, the change in magnitude of which has a bounded integral. The second one is a smooth approximation of a discontinuous guidance law that guarantees bounded tracking with adjustable bounds when the target's acceleration is viewed as a bounded but otherwise unknown time-varying disturbance. In both cases, in order to meet the objective, an intelligent excitation signal is added to the reference commands. These guidance laws are modified to accommodate measurement noise, which is inherently available when using visual sensors and image processing algorithms associated with them. They are implemented on a full scale non-linear aircraft model using conventional block backstepping technique augmented with a neural network for approximation of modeling uncertainties and atmospheric turbulence resulting from the closed-coupled flight of two aerial vehicles. / Ph. D.

As resident space object populations grow, and satellite propulsion capabilities improve, it will become increasingly challenging for space-reliant nations to maintain space situational awareness using current human-in-the-loop methods. This dissertation develops several real-time adaptive approaches to autonomous sensor network management for tracking multiple maneuvering and non-maneuvering satellites with a diversely populated Space Object Surveillance and Identification network. The proposed methods integrate suboptimal Partially Observed Markov Decision Processes (POMDPs) with covariance inflation or multiple model adaptive estimation techniques to task sensors and maintain viable orbit estimates for all targets. The POMDPs developed in this dissertation use information-based and system-based metrics to determine the rewards and costs associated with tasking a specific sensor to track a particular satellite. Like in real-world situations, the population of target satellites vastly outnumbers the available set of sensors. Robust and adaptable tasking algorithms are needed in this scenario to determine how and when sensors should be tasked. The strategies developed in this dissertation successfully track 207 non-maneuvering and maneuvering spacecraft using only 24 ground and space-based sensors. The results show that multiple model adaptive estimation coupled with a multi-metric, suboptimal POMDP can effectively and efficiently task a diverse network of sensors to track multiple maneuvering spacecraft, while simultaneously monitoring a large number of non-maneuvering objects. Overall, this dissertation demonstrates the potential for autonomous and adaptable sensor network command and control for real-world space situational awareness. / Ph. D. / As the number of spacecraft in orbit increase, and satellite propulsion capabilities improve, it will become increasingly difficult for space-reliant nations to keep track of every object orbiting earth using human-in-the-loop methods. Already, the population of target satellites vastly outnumbers the available set of sensors. At any given time, a given network of sensors cannot observe every satellite in orbit, and must manage the available sensors effectively to keep track of every object of interest. The ability to maintain actionable knowledge of every orbiting object of interest is known as space situational awareness. Conventional tracking processes have generally not changed for decades, and were designed when there were far fewer satellites in orbit with little or no ability to maneuver. These methods involve large numbers of operators and engineers who schedule a network of sensors under the assumption that the satellites will not unexpectedly change their orbits for long periods of time. In the near future, traditional space surveillance approaches will become insufficient at maintaining space situational awareness, particularly if more satellites conduct unanticipated maneuvers. This dissertation develops several real-time approaches for controlling a diverse network of ground and space-based sensors that remove the need for human intervention. These fully computer-based command and control processes adapt to dynamic situations and automatically task sensors to rapidly track multiple maneuvering and non-maneuvering satellites. The decision processes used to determine which sensors should be tasked to observe a particular spacecraft compare the amount of information that can be collected in a single observation and the workload a sensor must execute to collect the observation. The command and control strategies developed in this dissertation successfully track 207 non-maneuvering and maneuvering spacecraft using only 24 ground and space-based sensors. The results show that adaptive, fully autonomous sensor network control processes can effectively and efficiently task a diverse set of sensors to track multiple maneuvering spacecraft, while simultaneously monitoring a large number of non-maneuvering objects. Overall, this dissertation demonstrates the potential for adaptive, computer-based sensor network command and control for real-world space situational awareness. This research was supported by the Virginia Tech New Horizons Graduate Scholar Program, the Ted and Karyn Hume Center for National Security and Technology, the DARPA Hallmark program, and the U.S. Joint Warfare Analysis Center.

This thesis paper presents a simultaneous 3D mapping and geolocation of road surface technique that combines local road surface mapping and global camera localization. The local road surface is generated by structure from motion (SFM) with multiple views and optimized by Bundle Adjustment (BA). A system is developed for the global reconstruction of 3D road surface. Using the system, the proposed technique globally reconstructs 3D road surface by estimating the global camera pose using the Adaptive Extended Kalman Filter (AEKF) and integrates it with local road surface reconstruction techniques. The proposed AEKF-based technique uses image shift as prior. And the camera pose was corrected with the sparse low-accuracy Global Positioning System (GPS) data and digital elevation map (DEM). The AEKF adaptively updates the covariance of uncertainties such that the estimation works well in environment with varying uncertainties. The image capturing system is designed with the camera frame rate being dynamically controlled by vehicle speed read from on-board diagnostics (OBD) for capturing continuous data and helping to remove the effects of moving vehicle shadow from the images with a Random Sample and Consensus (RANSAC) algorithm. The proposed technique is tested in both simulation and field experiment, and compared with similar previous work. The results show that the proposed technique achieves better accuracy than conventional Extended Kalman Filter (EKF) method and achieves smaller translation error than other similar other works. / Master of Science / This thesis paper presents a simultaneous three dimensional (3D) mapping and geolocation of road surface technique that combines local road surface mapping and global camera localization. The local road surface is reconstructed by image processing technique with optimization. And the designed system globally reconstructs 3D road surface by estimating the global camera poses using the proposed Adaptive Extended Kalman Filter (AEKF)-based method and integrates with local road surface reconstructing technique. The camera pose uses image shift as prior, and is corrected with the sparse low-accuracy Global Positioning System (GPS) data and digital elevation map (DEM). The final 3D road surface map with geolocation is generated by combining both local road surface mapping and global localization results. The proposed technique is tested in both simulation and field experiment, and compared with similar previous work. The results show that the proposed technique achieves better accuracy than conventional Extended Kalman Filter (EKF) method and achieves smaller translation error than other similar other works.

Discontinuous dynamical systems and multiagent systems are encountered in numerous engineering applications. This dissertation develops stability and dissipativity of nonlinear dynamical systems with discontinuous right-hand sides, optimality of discontinuous feed-back controllers for Filippov dynamical systems, almost consensus protocols for multiagent systems with innaccurate sensor measurements, and adaptive estimation algorithms using multiagent network identifiers. In particular, we present stability results for discontinuous dynamical systems using nonsmooth Lyapunov theory. Then, we develop a constructive feedback control law for discontinuous dynamical systems based on the existence of a nonsmooth control Lyapunov function de fined in the sense of generalized Clarke gradients and set-valued Lie derivatives. Furthermore, we develop dissipativity notions and extended Kalman-Yakubovich-Popov conditions and apply these results to develop feedback interconnection stability results for discontinuous systems. In addition, we derive guaranteed gain, sector, and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear-nonquadratic performance functional for Filippov dynamical systems. Then, we provide connections between dissipativity and optimality of nonlinear discontinuous controllers for Filippov dynamical systems. Furthermore, we address the consensus problem for a group of agent robots with uncertain interagent measurement data, and show that the agents reach an almost consensus state and converge to a set centered at the centroid of agents initial locations. Finally, we develop an adaptive estimation framework predicated on multiagent network identifiers with undirected and directed graph topologies that identifies the system state and plant parameters online.

This thesis investigates using adaptive estimation techniques to determine unknown model parameters such as size and surface material reflectivity, while estimating position, velocity, attitude, and attitude rates of a resident space object. This work focuses on the application of these methods to the space situational awareness problem. This thesis proposes a unique method of implementing a top-level gating network in a dual-layer hierarchical mixture of experts. In addition it proposes a decaying learning parameter for use in both the single layer mixture of experts and the dual-layer hierarchical mixture of experts. Both a single layer mixture of experts and dual-layer hierarchical mixture of experts are compared to the multiple model adaptive estimation in estimating resident space object parameters such as size and reflectivity. The hierarchical mixture of experts consists of macromodes. Each macromode can estimate a different parameter in parallel. Each macromode is a single layer mixture of experts with unscented Kalman filters used as the experts. A gating network in each macromode determines a gating weight which is used as a hypothesis tester. Then the output of the macromode gating weights go to a top level gating weight to determine which macromode contains the most probable model. The measurements consist of astrometric and photometric data from non-resolved observations of the target gathered via a telescope with a charge coupled device camera. Each filter receives the same measurement sequence. The apparent magnitude measurement model consists of the Ashikhmin Shirley bidirectional reflectance distribution function. The measurements, process models, and the additional shape, mass, and inertia characteristics allow the algorithm to predict the state and select the most probable fit to the size and reflectance characteristics based on the statistics of the measurement residuals and innovation covariance. A simulation code is developed to test these adaptive estimation techniques. The feasibility of these methods will be demonstrated in this thesis.

Doctor of Philosophy / Department of Statistics / Weixin Yao / This dissertation contains two projects that are related to varying coefficient models. The traditional least squares based kernel estimates of the varying coefficient model will lose some efficiency when the error distribution is not normal. In the first project, we propose a novel adaptive estimation method that can adapt to different error distributions and provide an efficient EM algorithm to implement the proposed estimation. The asymptotic properties of the resulting estimator is established. Both simulation studies and real data examples are used to illustrate the finite sample performance of the new estimation procedure. The numerical results show that the gain of the adaptive procedure over the least squares estimation can be quite substantial for non-Gaussian errors. In the second project, we propose a unified inference for sparse and dense longitudinal data in time-varying coefficient models. The time-varying coefficient model is a special case of the varying coefficient model and is very useful in longitudinal/panel data analysis. A mixed-effects time-varying coefficient model is considered to account for the within subject correlation for longitudinal data. We show that when the kernel smoothing method is used to estimate the smooth functions in the time-varying coefficient model for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases may lead to wrong conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and a real data application.

Diese Dissertation entwickelt neue lokal adaptive Methoden zur Schaetzung und Vorhersage von Zeitreihendaten. Diese Methoden sind fuer die Volatilitaetsschaetzung von Finanzmarktrenditen und fuer Regressions- und Autoregressionsprobleme konstruiert worden. Die vorgeschlagenen Ansaetze werden als lokal adaptiv bezeichnet, denn, anstatt einen globalen datenerzeugenden Prozess aufzuzwingen, welcher durch eine endliche Anzahl von Parametern beschrieben werden kann, nehmen sie nur an, dass Beobachtungen, welche chronologisch nah bei einander liegen, durch einen konstanten Prozess gut approximiert werden koennen. Diese Prozeduren sind adaptiv, weil sie fuer jede Beobachtung in einer datengesteuerten Art und Weise das Intervall der Zeithomogenitaet,d.h. die Anzahl der chronologisch benachbarten und homogen vergangenen Daten, aussuchen, fuer welchen die Hypothese einer konstanten Struktur nicht verworfen werden kann. Nichtasymptotische theoretische Ergebnisse werden hergeleitet, welche die Optimalitaet der betrachteten Algorithmen zeigen. Vergleiche mit Standardansaetzen verdeutlichen, dass die neuen Prozeduren sich kompetitiv verhalten und eine nuetzliche Alternative bieten, ausserdem liefern intensive Simulationsstudien und Anwendungen an reellen Daten gute Ergebnisse und bezeugen dabei ihre Effektivitaet und praktische Relevanz. / This thesis develops new locally adaptive methods for estimation and forecasting of financial time series data. These methods are mainly tailored for volatility estimation of financial returns and for regression and autoregression problems. The proposed approaches are defined locally adaptive because instead of imposing a stationary data generating process which can be globally described by a finite number of parameters, they only assume that observations which are chronologically close to each other can be well approximated by a constant process. These procedures are adaptive in the sense that for each observation they choose in a data driven way the interval of time homogeneity, i.e. the number of chronologically close and homogeneous past data where the hypothesis of a constant structure can not be rejected. Nonasymptotic theoretical results are derived, which show the optimality of the suggested algorithms. Comparisons with standard approaches demonstrate that the new procedures behave competitively and offer a valuable alternative, furthermore, intensive simulation studies and applications to real data provide good results, confirming their effectiveness and practical relevance.

Dans ce travail, nous nous intéressons à l'estimation d'ensembles convexes dans l'espace Euclidien R^d, en nous penchant sur deux modèles. Dans le premier modèle, nous avons à notre disposition un échantillon de n points aléatoires, indépendants et de même loi, uniforme sur un ensemble convexe inconnu. Le second modèle est un modèle additif de régression, avec bruit sous-gaussien, et dont la fonction de régression est l'indicatrice d'Euler d'un ensemble convexe ici aussi inconnu. Dans le premier modèle, notre objectif est de construire un estimateur du support de la densité des observations, qui soit optimal au sens minimax. Dans le second modèle, l'objectif est double. Il s'agit de construire un estimateur du support de la fonction de régression, ainsi que de décider si le support en question est non vide, c'est-'a-dire si la fonction de régression est effectivement non nulle, ou si le signal observé n'est que du bruit. Dans ces deux modèles, nous nous intéressons plus particulièrement au cas où l'ensemble inconnu est un polytope convexe, dont le nombre de sommets est connu. Si ce nombre est inconnu, nous montrons qu'une procédure adaptative permet de construire un estimateur atteignant la même vitesse asymptotique que dans le cas précédent. Enfin, nous démontrons que ce m$eme estimateur pallie à l'erreur de spécification du modèle, consistant à penser à tort que l'ensemble convexe inconnu est un polytope. Nous démontrons une inégalité de déviation pour le volume de l'enveloppe convexe des observations dans le premier modèle. Nous montrons aussi que cette inégalité implique des bornes optimales sur les moments du volume manquant de cette enveloppe convexe, ainsi que sur les moments du nombre de ses sommets. Enfin, dans le cas unidimensionnel, pour le second modèle, nous donnons la taille asymptotique minimale que doit faire l'ensemble inconnu afin de pouvoir être détecté, et nous proposons une règle de décision, permettant un test consistant du caractère non vide de cet ensemble.

In dieser Arbeit wird die Smallest-Accepted Methode als neue Lepski-Typ Methode für Modellwahl im geordneten Fall eingeführt. In einem ersten Schritt wird die Methode vorgestellt und im Fall von Schätzproblemen mit bekannter Fehlervarianz untersucht. Die Hauptkomponenten der Methode sind ein Akzeptanzkriterium, basierend auf Modellvergleichen für die eine Familie von kritischen Werten mit einem Monte-Carlo-Ansatz kalibriert wird, und die Wahl des kleinsten (in Komplexität) akzeptierten Modells. Die Methode kann auf ein breites Spektrum von Schätzproblemen angewandt werden, wie zum Beispiel Funktionsschätzung, Schätzung eines linearen Funktionals oder Schätzung in inversen Problemen. Es werden allgemeine Orakelungleichungen für die Methode im Fall von probabilistischem Verlust und einer polynomialen Verlustfunktion gezeigt und Anwendungen der Methode in spezifischen Schätzproblemen werden untersucht. In einem zweiten Schritt wird die Methode erweitert auf den Fall einer unbekannten, möglicherweise heteroskedastischen Fehlerstruktur. Die Monte-Carlo-Kalibrierung wird durch eine Bootstrap-basierte Kalibrierung ersetzt. Eine neue Familie kritischer Werte wird eingeführt, die von den (zufälligen) Beobachtungen abhängt. In Folge werden die theoretischen Eigenschaften dieser Bootstrap-basierten Smallest-Accepted Methode untersucht. Es wird gezeigt, dass unter typischen Annahmen unter normalverteilten Fehlern für ein zugrundeliegendes Signal mit Hölder-Stetigkeits-Index s > 1/4 und log(n) (p^2/n) klein, wobei n hier die Anzahl der Beobachtungen und p die maximale Modelldimension bezeichnet, die Anwendung der Bootstrap-Kalibrierung anstelle der Monte-Carlo-Kalibrierung theoretisch gerechtfertigt ist. / In this thesis, the Smallest-Accepted method is presented as a new Lepski-type method for ordered model selection. In a first step, the method is introduced and studied in the case of estimation problems with known noise variance. The main building blocks of the method are a comparison-based acceptance criterion relying on Monte-Carlo calibration of a set of critical values and the choice of the model as the smallest (in complexity) accepted model. The method can be used on a broad range of estimation problems like function estimation, estimation of linear functionals and inverse problems. General oracle results are presented for the method in the case of probabilistic loss and for a polynomial loss function. Applications of the method to specific estimation problems are studied. In a next step, the method is extended to the case of an unknown possibly heteroscedastic noise structure. The Monte-Carlo calibration step is now replaced by a bootstrap-based calibration. A new set of critical values is introduced, which depends on the (random) observations. Theoretical properties of this bootstrap-based Smallest-Accepted method are then studied. It is shown for normal errors under typical assumptions, that the replacement of the Monte-Carlo step by bootstrapping in the Smallest-Accepted method is valid, if the underlying signal is Hölder-continuous with index s > 1/4 and log(n) (p^2/n) is small for a sample size n and a maximal model dimension p.