Group-Lasso on Splines for Spectrum Cartography

The unceasing demand for continuous situational awareness calls for innovative and large-scale signal processing algorithms, complemented by collaborative and adaptive sensing platforms to accomplish the objectives of layered sensing and control. Towards this goal, the present paper develops a spline-based approach to field estimation, which relies on a basis expansion model of the field of interest. The model entails known bases, weighted by generic functions estimated from the field's noisy samples. A novel field estimator is developed based on a regularized variational least-squares (LS) criterion that yields finitely-parameterized (function) estimates spanned by thin-plate splines. Robustness considerations motivate well the adoption of an overcomplete set of (possibly overlapping) basis functions, while a sparsifying regularizer augmenting the LS cost endows the estimator with the ability to select a few of these bases that ``better'' explain the data. This parsimonious field representation becomes possible, because the sparsity-aware spline-based method of this paper induces a group-Lasso estimator for the coefficients of the thin-plate spline expansions per basis. A distributed algorithm is also developed to obtain the group-Lasso estimator using a network of wireless sensors, or, using multiple processors to balance the load of a single computational unit. The novel spline-based approach is motivated by a spectrum cartography application, in which a set of sensing cognitive radios collaborate to estimate the distribution of RF power in space and frequency. Simulated tests corroborate that the estimated power spectrum density atlas yields the desired RF state awareness, since the maps reveal spatial locations where idle frequency bands can be reused for transmission, even when fading and shadowing effects are pronounced.Comment: Submitted to IEEE Transactions on Signal Processin

Super-resolved localisation in multipath environments

In the last few decades, the localisation problems have been studied extensively. There are still some open issues that remain unresolved. One of the key issues is the efficiency and preciseness of the localisation in presence of non-line-of-sight (NLoS) path. Nevertheless, the NLoS path has a high occurrence in multipath environments, but NLoS bias is viewed as a main factor to severely degrade the localisation performance. The NLoS bias would often result in extra propagation delay and angular bias. Numerous localisation methods have been proposed to deal with NLoS bias in various propagation environments, but they are tailored to some specif ic scenarios due to different prior knowledge requirements, accuracies, computational complexities, and assumptions. To super-resolve the location of mobile device (MD) without prior knowledge, we address the localisation problem by super-resolution technique due to its favourable features, such as working on continuous parameter space, reducing computational cost and good extensibility. Besides the NLoS bias, we consider an extra array directional error which implies the deviation in the orientation of the array placement. The proposed method is able to estimate the locations of MDs and self-calibrate the array directional errors simultaneously. To achieve joint localisation, we directly map MD locations and array directional error to received signals. Then the group sparsity based optimisation is proposed to exploit the geometric consistency that received paths are originating from common MDs. Note that the super-resolution framework cannot be directly applied to our localisation problems. Because the proposed objective function cannot be efficiently solved by semi-definite programming. Typical strategies focus on reducing adverse effect due to the NLoS bias by separating line-of-sight (LoS)/NLoS path or mitigating NLoS effect. The LoS path is well studied for localisation and multiple methods have been proposed in the literature. However, the number of LoS paths are typically limited and the effect of NLoS bias may not always be reduced completely. As a long-standing issue, the suitable solution of using NLoS path is still an open topic for research. Instead of dealing with NLoS bias, we present a novel localisation method that exploits both LoS and NLoS paths in the same manner. The unique feature is avoiding hard decisions on separating LoS and NLoS paths and hence relevant possible error. A grid-free sparse inverse problem is formulated for localisation which avoids error propagation between multiple stages, handles multipath in a unified way, and guarantees a global convergence. Extensive localisation experiments on different propagation environments and localisation systems are presented to illustrate the high performance of the proposed algorithm compared with theoretical analysis. In one of the case studies, single antenna access points (APs) can locate a single antenna MD even when all paths between them are NLoS, which according to the authors’ knowledge is the first time in the literature.Open Acces

Fail-Safe Vehicle Pose Estimation in Lane-Level Maps Using Pose Graph Optimization

Die hochgenaue Posenschätzung autonomer Fahrzeuge sowohl in HD-Karten als auch spurrelativ ist unerlässlich um eine sichere Fahrzeugführung zu gewährleisten. Für die Serienfertigung wird aus Kosten- und Platzgründen bewusst auf hochgenaue, teure Einzelsensorik verzichtet und stattdessen auf eine Vielzahl von Sensoren, die neben der Posenschätzung auch von anderen Modulen verwendet werden können, zurückgegriffen. Im Fokus dieser Arbeit steht die Unsicherheitsschätzung, Bewertung und Fusion dieser Sensordaten. Die Optimierung von Posengraphen zur Fusion von Sensordaten zeichnet sich, im Gegensatz zu klassischen Filterverfahren, wie Kalman oder Partikelfilter, durch seine Robustheit gegenüber Fehlmessungen und der Flexibilität in der Modellierung aus. Die Optimierung eines Posengraphen wurde erstmalig auf mobilen Roboterplattformen zur Lösung sogenannter SLAM-Probleme angewendet. Diese Verfahren wurden immer weiter entwickelt und im speziellen auch zur rein kamerabasierten Lokalisierung autonomer Fahrzeuge in 3D-Punktwolken erfolgreich emonstriert. Für die Entwicklung und Freigabe sicherheitsrelevanter Systeme nach ISO 26262 wird neben der Genauigkeit jedoch auch eine Aussage über die Qualität und Ausfallsicherheit dieser Systeme gefordert. Diese Arbeit befasst sich, neben der Schätzung der karten- und spurrelativen Pose, auch mit der Schätzung der Posenunsicherheit und der Integrität der Sensordaten zueinander. Auf Grundlage dieser Arbeit wird eine Abschätzung der Ausfallsicherheit des Lokalisierungsmoduls ermöglicht. Motiviert durch das Projekt Ko-HAF werden zur Lokalisierung in HD-Karten lediglich Spurmarkierungen verwendet. Die speichereffiziente Darstellung dieser Karten ermöglicht eine hochfrequente Aktualisierung der Karteninhalte durch eine Fahrzeugflotte. Der vorgestellte Ansatz wurde prototypisch auf einem Opel Insignia umgesetzt. Der Testträger wurde um eine Front- und Heckkamera sowie einen GNSS-Empfänger erweitert. Zunächst werden die Schätzung der karten-und spurrelativen Fahrzeugpose, der GNSS-Signalauswertung sowie der Bewegungsschätzung des Fahrzeugs vorgestellt. Durch einen Vergleich der Schätzungen zueinander werden die Unsicherheiten der einzelnen Module berechnet. Das Lokalisierungsproblem wird dann durch einen Optimierer gelöst. Mithilfe der berechneten Unsicherheiten wird in einem nachgelagerten Schritt eine Bewertung der einzelnen Module durchgeführt. Zur Bewertung des Ansatzes wurden sowohl hochdynamische Manöver auf einer Teststrecke als auch Fahrten auf öffentlichen Autobahnen ausgewertet

Distributive Time Division Multiplexed Localization Technique for WLANs

This thesis presents the research work regarding the solution of a localization problem in indoor WLANs by introducing a distributive time division multiplexed localization technique based on the convex semidefinite programming. Convex optimizations have proven to give promising results but have limitations of computational complexity for a larger problem size. In the case of localization problem the size is determined depending on the number of nodes to be localized. Thus a convex localization technique could not be applied to real time tracking of mobile nodes within the WLANs that are already providing computationally intensive real time multimedia services. Here we have developed a distributive technique to circumvent this problem such that we divide a larger network into computationally manageable smaller subnets. The division of a larger network is based on the mobility levels of the nodes. There are two types of nodes in a network; mobile, and stationery. We have placed the mobile nodes into separate subnets which are tagged as mobile whereas the stationary nodes are placed into subnets tagged as stationary. The purpose of this classification of networks into subnets is to achieve a priority-based localization with a higher priority given to mobile subnets. Then the classified subnets are localized by scheduling them in a time division multiplexed way. For this purpose a time-frame is defined consisting of finite number of fixed duration time-slots such that within the slot duration a subnet could be localized. The subnets are scheduled within the frames with a 1:n ratio pattern that is within n number of frames each mobile subnet is localized n times while each stationary subnet consisting of stationary nodes is localized once. By using this priority-based scheduling we have achieved a real time tracking of mobile node positions by using the computationally intensive convex optimization technique. In addition, we present that the resultant distributive technique can be applied to a network having diverse node density that is a network with its nodes varying from very few to large numbers can be localized by increasing frame duration. This results in a scalable technique. In addition to computational complexity, another problem that arises while formulating the distance based localization as a convex optimization problem is the high-rank solution. We have also developed the solution based on virtual nodes to circumvent this problem. Virtual nodes are not real nodes but these are nodes that are only added within the network to achieve low rank realization. Finally, we developed a distributive 3D real-time localization technique that exploited the mobile user behaviour within the multi-storey indoor environments. The estimates of heights by using this technique were found to be coarse. Therefore, it can only be used to identify floors in which a node is located

Trajectory optimization and motion planning for quadrotors in unstructured environments

Trajectory optimization and motion planning for quadrotors in unstructured environments Coming out from university labs robots perform tasks usually navigating through unstructured environment. The realization of autonomous motion in such type of environments poses a number of challenges compared to highly controlled laboratory spaces. In unstructured environments robots cannot rely on complete knowledge of their sorroundings and they have to continously acquire information for decision making. The challenges presented are a consequence of the high-dimensionality of the state-space and of the uncertainty introduced by modeling and perception. This is even more true for aerial-robots that has a complex nonlinear dynamics a can move freely in 3D-space. To avoid this complexity a robot have to select a small set of relevant features, reason on a reduced state space and plan trajectories on short-time horizon. This thesis is a contribution towards the autonomous navigation of aerial robots (quadrotors) in real-world unstructured scenarios. The first three chapters present a contribution towards an implementation of Receding Time Horizon Optimal Control. The optimization problem for a model based trajectory generation in environments with obstacles is set, using an approach based on variational calculus and modeling the robots in the SE(3) Lie Group of 3D space transformations. The fourth chapter explores the problem of using minimal information and sensing to generate motion towards a goal in an indoor bulding-like scenario. The fifth chapter investigate the problem of extracting visual features from the environment to control the motion in an indoor corridor-like scenario. The last chapter deals with the problem of spatial reasoning and motion planning using atomic proposition in a multi-robot environments with obstacles

Uma nova relaxação quadrática para variáveis binárias com aplicações a confiabilidade de redes de energia elétrica, a segmentação de imagens médicas de nervos e a problemas de geometria de distâncias

Orientador: Christiano Lyra FilhoTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: Como o título sugere, o foco desta pesquisa é o desenvolvimento de uma nova relaxação quadrática para problemas binários, sua formalização em resultados teóricos, e a aplicação dos novos conceitos em aplicações à confiabilidade de redes de energia elétrica, à segmentação de imagens médicas de nervos e à problemas de geometria de distâncias. Modelos matemáticos contendo va-riáveis de decisões binárias podem ser usados para encontrar as melhores soluções em processos de tomada de decisões, normalmente caracterizando problemas de otimização combinatória difíceis. A solução desses problemas em aplicações de interesse prático requer um grande esforço computacional; por isso, ao longo dos últimos anos, têm sido objeto de pesquisas na área de metaheurísticas. As ideias aqui desenvolvidas abrem novas perspectivas para a abordagem desses problemas apoiando-se em métodos de otimização não-lineares, área que vem sendo povoada por "solvers" muito eficientes. Inicialmente, explorando aspectos formais, a relaxação desenvolvida é parti-cularizada para um problema de otimização quadrática binária irrestrita. O relaxamento permite o desenvolvimento de três estruturas para abordar esta classe de problemas, e explora a convexidade da função objetivo para obter melhorias computacionais. Estudos de casos compararam o relaxamento proposto com os relaxamentos similares apresentados na literatura. Foram desenvolvidas três aplicações para os desenvolvimentos teóricos da pesquisa. A primeira aplicação envolve a melhoria da confiabilidade de redes de energia elétrica. Especificamente, aborda o problema de definir a melhor alternativa para a alocação de sensores na rede, o que permite reduzir os efeitos de ocorrências indesejáveis e ampliar a resiliência das redes. A segunda aplicação envolve o problema de segmentação de imagens médicas associadas a estruturas de nervos. A abordagem proposta interpreta o problema de segmentação como um problema de otimização binária, onde medir cada axônio significa encontrar um ciclo Hamiltoniano, um caso do problema do caixeiro viajante; a solução desses problemas fornece a estatística descritiva para um conjunto de axônios, incluindo o número (de axônios), os diâmetros e as áreas ocupadas. A última aplicação elabora um modelo matemático para o problema de geometria de distâncias sem designação, área ainda pouco estudada e com muitos aspectos em aberto. A relaxação desenvolvida na pesquisa permitiu resolver instâncias com mais de vinte mil variáveis binárias. Esses resultados são bons indicadores dos benefícios alcançáveis com os aspectos teóricos da pesquisa, e abrem novas perspectivas para as aplicações, que incluem inovações em nanotecnologia e bioengenhariaAbstract: As the title suggests, the focus this research is the development of a new quadratic relaxation for binary problems, its formalization in theoretical results, and the application of the new concepts in applications to the reliability of electric power networks, segmentation of nerve root images, and distance geometry problems. Mathematical models with binary decision variables can be used to find the best solutions for decision-making process, usually leading to difficult combinatorial optimization problems. The solution to these problems in practical applications requires a high computational effort; therefore, over the past years it has been the subject of research in the area of metaheuristics. The ideas developed in this thesis open new perspectives for addressing these problems using nonlinear optimization approaches, an area that has been populated by very efficient solvers. The initial developments explore the formal aspects of the relaxation in the context of a quadratic unconstrained binary optimization problem. The use of the proposed relaxation allows to create three structures to deal with this class of problems, and explores the objective function convexity to improve the computational performance. Case studies compare the proposed relaxation with the previous relaxations proposed in the literature. Three new applications were developed to explore the theoretical developments of this research. The first application concerns the improvement of the reliability of electric power distribution networks. Specifically, it deals with the problem of defining the best allocation for remote fault sensor, allowing to reduce the consequence of the faults and to improve the resilience of the networks. The second application explores the segmentation of medical images related to nerve root structures. The proposed approach regards the segmentation problem as a binary optimization problem, where measuring each axon is equivalent to finding a Hamiltonian cycle for a variant of the traveling salesman problem; the solution to these problems provides the descriptive statistics of the axon set, including the number of axons, their diameters, and the area used by each axon. The last application designs a mathematical model for the unassigned distance geometry problem, an incipient research area with many open problems. The relaxation developed in this research allowed to solve instances with more than twenty thousand binary variables. These results can be seen as good indicators of the benefits attainable with the theoretical aspects of the research, and opens new perspectives for applications, which include innovations in nanotechnology and bio-engineeringDoutoradoAutomaçãoDoutora em Engenharia Elétrica148400/2016-7CNP

Statistical Filtering for Multimodal Mobility Modeling in Cyber Physical Systems

A Cyber-Physical System integrates computations and dynamics of physical processes. It is an engineering discipline focused on technology with a strong foundation in mathematical abstractions. It shares many of these abstractions with engineering and computer science, but still requires adaptation to suit the dynamics of the physical world. In such a dynamic system, mobility management is one of the key issues against developing a new service. For example, in the study of a new mobile network, it is necessary to simulate and evaluate a protocol before deployment in the system. Mobility models characterize mobile agent movement patterns. On the other hand, they describe the conditions of the mobile services. The focus of this thesis is on mobility modeling in cyber-physical systems. A macroscopic model that captures the mobility of individuals (people and vehicles) can facilitate an unlimited number of applications. One fundamental and obvious example is traffic profiling. Mobility in most systems is a dynamic process and small non-linearities can lead to substantial errors in the model. Extensive research activities on statistical inference and filtering methods for data modeling in cyber-physical systems exist. In this thesis, several methods are employed for multimodal data fusion, localization and traffic modeling. A novel energy-aware sparse signal processing method is presented to process massive sensory data. At baseline, this research examines the application of statistical filters for mobility modeling and assessing the difficulties faced in fusing massive multi-modal sensory data. A statistical framework is developed to apply proposed methods on available measurements in cyber-physical systems. The proposed methods have employed various statistical filtering schemes (i.e., compressive sensing, particle filtering and kernel-based optimization) and applied them to multimodal data sets, acquired from intelligent transportation systems, wireless local area networks, cellular networks and air quality monitoring systems. Experimental results show the capability of these proposed methods in processing multimodal sensory data. It provides a macroscopic mobility model of mobile agents in an energy efficient way using inconsistent measurements