A Statistically Modelling Method for Performance Limits in Sensor Localization

In this paper, we study performance limits of sensor localization from a novel perspective. Specifically, we consider the Cramer-Rao Lower Bound (CRLB) in single-hop sensor localization using measurements from received signal strength (RSS), time of arrival (TOA) and bearing, respectively, but differently from the existing work, we statistically analyze the trace of the associated CRLB matrix (i.e. as a scalar metric for performance limits of sensor localization) by assuming anchor locations are random. By the Central Limit Theorems for $U$-statistics, we show that as the number of the anchors increases, this scalar metric is asymptotically normal in the RSS/bearing case, and converges to a random variable which is an affine transformation of a chi-square random variable of degree 2 in the TOA case. Moreover, we provide formulas quantitatively describing the relationship among the mean and standard deviation of the scalar metric, the number of the anchors, the parameters of communication channels, the noise statistics in measurements and the spatial distribution of the anchors. These formulas, though asymptotic in the number of the anchors, in many cases turn out to be remarkably accurate in predicting performance limits, even if the number is small. Simulations are carried out to confirm our results

Second-order Online Nonconvex Optimization

We present the online Newton's method, a single-step second-order method for online nonconvex optimization. We analyze its performance and obtain a dynamic regret bound that is linear in the cumulative variation between round optima. We show that if the variation between round optima is limited, the method leads to a constant regret bound. In the general case, the online Newton's method outperforms online convex optimization algorithms for convex functions and performs similarly to a specialized algorithm for strongly convex functions. We simulate the performance of the online Newton's method on a nonlinear, nonconvex moving target localization example and find that it outperforms a first-order approach

Neighbor Constraint Assisted Distributed Localization for Wireless Sensor Networks

Localization is one of the most significant technologies in wireless sensor networks (WSNs) since it plays a critical role in many applications. The main idea in most localization methods is to estimate the sensor-anchor distances that are used by sensors to locate themselves. However, the distance information is always imprecise due to the measurement or estimation errors. In this work, a novel algorithm called neighbor constraint assisted distributed localization (NCA-DL) is proposed, which introduces the application of geometric constraints to these distances within the algorithm. For example, in the case presented here, the assistance provided by a neighbor will consist in formulating a linear equality constraint. These constraints can be further used to formulate optimization problems for distance estimation. Then through some optimization methods, the imprecise distances can be refined and the localization precision is improved

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

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

Towards localisation with Doppler radar

In this thesis the author introduces a novel method for Geo Localisation via Doppler Radar. The area of research is in the three dimensional space using amplitude and magnitude measurements. Geo Localisation in mobile applications is a useful technology that enables monitoring and gathering information about objects of interest

Sensor Network Localization with Imprecise Distances

An approach to formulate geometric relations among distances between nodes as equality constraints is introduced in this paper to study the localization problem with imprecise distance information in sensor networks. These constraints can be further used to formulate optimization problems for distance estimation. The optimization solutions correspond to a set of distances that are consistent with the fact that sensor nodes live in the same plane or 3D space as the anchor nodes. These techniques serve as the foundation for most of the existing localization algorithms that depend on the sensors’ distances to anchors to compute each sensor’s location. Keywords: Sensor networks; Localization; Distance geometry; Optimization

Sensor network localization with imprecise distances

An approach to formulate geometric relations among distances between nodes as equality constraints is introduced in this paper to study the localization problem with imprecise distance information in sensor networks. These constraints can be further use