DisLoc: A Convex Partitioning Based Approach for Distributed 3-D Localization in Wireless Sensor Networks

Accurate localization in wireless sensor networks (WSNs) is fundamental to many applications, such as geographic routing and position-aware data processing. This, however, is challenging in large scale 3-D WSNs due to the irregular topology, such as holes in the path, of the network. The irregular topology may cause overestimated Euclidean distance between nodes as the communication path is bent and accordingly introduces severe errors in 3-D WSN localization. As an effort towards the issue, this paper develops a distributed algorithm to achieve accurate 3-D WSN localization. Our proposal is composed of two steps, segmentation and joint localization. In specific, the entire network is first divided into several subnetworks by applying the approximate convex partitioning. A spatial convex node recognition mechanism is developed to assist the network segmentation, which relies on the connectivity information only. After that, each subnetwork is accurately localized by using the multidimensional scaling-based algorithm. The proposed localization algorithm also applies a new 3-D coordinate transformation algorithm, which helps reduce the errors introduced by coordinate integration between subnetworks and improve the localization accuracy. Using extensive simulations, we show that our proposal can effectively segment a complex 3-D sensor network and significantly improve the localization rate in comparison with existing solutions

Manhattan Cutset Sampling and Sensor Networks.

Cutset sampling is a new approach to acquiring two-dimensional data, i.e., images, where values are recorded densely along straight lines. This type of sampling is motivated by physical scenarios where data must be taken along straight paths, such as a boat taking water samples. Additionally, it may be possible to better reconstruct image edges using the dense amount of data collected on lines. Finally, an advantage of cutset sampling is in the design of wireless sensor networks. If battery-powered sensors are placed densely along straight lines, then the transmission energy required for communication between sensors can be reduced, thereby extending the network lifetime. A special case of cutset sampling is Manhattan sampling, where data is recorded along evenly-spaced rows and columns. This thesis examines Manhattan sampling in three contexts. First, we prove a sampling theorem demonstrating an image can be perfectly reconstructed from Manhattan samples when its spectrum is bandlimited to the union of two Nyquist regions corresponding to the two lattices forming the Manhattan grid. An efficient ``onion peeling'' reconstruction method is provided, and we show that the Landau bound is achieved. This theorem is generalized to dimensions higher than two, where again signals are reconstructable from a Manhattan set if they are bandlimited to a union of Nyquist regions. Second, for non-bandlimited images, we present several algorithms for reconstructing natural images from Manhattan samples. The Locally Orthogonal Orientation Penalization (LOOP) algorithm is the best of the proposed algorithms in both subjective quality and mean-squared error. The LOOP algorithm reconstructs images well in general, and outperforms competing algorithms for reconstruction from non-lattice samples. Finally, we study cutset networks, which are new placement topologies for wireless sensor networks. Assuming a power-law model for communication energy, we show that cutset networks offer reduced communication energy costs over lattice and random topologies. Additionally, when solving centralized and decentralized source localization problems, cutset networks offer reduced energy costs over other topologies for fixed sensor densities and localization accuracies. Finally, with the eventual goal of analyzing different cutset topologies, we analyze the energy per distance required for efficient long-distance communication in lattice networks.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120876/1/mprelee_1.pd

Advances in Robot Navigation

Robot navigation includes different interrelated activities such as perception - obtaining and interpreting sensory information; exploration - the strategy that guides the robot to select the next direction to go; mapping - the construction of a spatial representation by using the sensory information perceived; localization - the strategy to estimate the robot position within the spatial map; path planning - the strategy to find a path towards a goal location being optimal or not; and path execution, where motor actions are determined and adapted to environmental changes. This book integrates results from the research work of authors all over the world, addressing the abovementioned activities and analyzing the critical implications of dealing with dynamic environments. Different solutions providing adaptive navigation are taken from nature inspiration, and diverse applications are described in the context of an important field of study: social robotics

Communication-Efficient Algorithms For Distributed Optimization

This thesis is concerned with the design of distributed algorithms for solving optimization problems. We consider networks where each node has exclusive access to a cost function, and design algorithms that make all nodes cooperate to find the minimum of the sum of all the cost functions. Several problems in signal processing, control, and machine learning can be posed as such optimization problems. Given that communication is often the most energy-consuming operation in networks, it is important to design communication-efficient algorithms. The main contributions of this thesis are a classification scheme for distributed optimization and a set of corresponding communication-efficient algorithms. The class of optimization problems we consider is quite general, since each function may depend on arbitrary components of the optimization variable, and not necessarily on all of them. In doing so, we go beyond the common assumption in distributed optimization and create additional structure that can be used to reduce the number of communications. This structure is captured by our classification scheme, which identifies easier instances of the problem, for example the standard distributed optimization problem, where all functions depend on all the components of the variable. In our algorithms, no central node coordinates the network, all the communications occur between neighboring nodes, and the data associated with each node is processed locally. We show several applications including average consensus, support vector machines, network flows, and several distributed scenarios for compressed sensing. We also propose a new framework for distributed model predictive control. Through extensive numerical experiments, we show that our algorithms outperform prior distributed algorithms in terms of communication-efficiency, even some that were specifically designed for a particular application.Comment: Thesis defended on October 10, 2013. Dual PhD degree from Carnegie Mellon University, PA, and Instituto Superior T\'ecnico, Lisbon, Portuga

On the Performance and Linear Convergence of Decentralized Primal-Dual Methods

This dissertation studies the performance and linear convergence properties of primal-dual methods for the solution of decentralized multi-agent optimization problems. Decentralized multi-agent optimization is a powerful paradigm that finds applications in diverse fields in learning and engineering design. In these setups, a network of agents is connected through some topology and agents are allowed to share information only locally. Their overall goal is to seek the minimizer of a global optimization problem through localized interactions. In decentralized consensus problems, the agents are coupled through a common consensus variable that they need to agree upon. While in decentralized resource allocation problems, the agents are coupled through global affine constraints. Various decentralized consensus optimization algorithms already exist in the literature. Some methods are derived from a primal-dual perspective, while other methods are derived as gradient tracking mechanisms meant to track the average of local gradients. Among the gradient tracking methods are the adapt-then-combine implementations motivated by diffusion strategies, which have been observed to perform better than other implementations. In this dissertation, we develop a novel adapt-then-combine primal-dual algorithmic framework that captures most state-of-the-art gradient based methods as special cases including all the variations of the gradient-tracking methods. We also develop a concise and novel analysis technique that establishes the linear convergence of this general framework under strongly-convex objectives. Due to our unified framework, the analysis reveals important characteristics for these methods such as their convergence rates and step-size stability ranges. Moreover, the analysis reveals how the augmented Lagrangian penalty term, which is utilized in most of these methods, affects the performance of decentralized algorithms. Another important question that we answer is whether decentralized proximal gradient methods can achieve global linear convergence for non-smooth composite optimization. For centralized algorithms, linear convergence has been established in the presence of a non-smooth composite term. In this dissertation, we close the gap between centralized and decentralized proximal gradient algorithms and show that decentralized proximal algorithms can also achieve linear convergence in the presence of a non-smooth term. Furthermore, we show that when each agent possesses a different local non-smooth term then global linear convergence cannot be established in the worst case. Most works that study decentralized optimization problems assume that all agents are involved in computing all variables. However, in many applications the coupling across agents is sparse in the sense that only a few agents are involved in computing certain variables. We show how to design decentralized algorithms in sparsely coupled consensus and resource allocation problems. More importantly, we establish analytically the importance of exploiting the sparsity structure in coupled large-scale networks

Algorithmen für Topologiebewusstsein in Sensornetzen

This work deals with algorithmic and geometric challenges in wireless sensor networks (WSNs). Classical algorithm theory, with a single processor executing one sequential program while having access to the complete data of the problem at hand, does not suit the needs of WSNs. Instead, we need distributed protocols where nodes collaboratively solve problems that are too complex for a single node. First we analyze a location problem, where the nodes obtain a sense of the network topology and their position in it. Computing coordinates in a global coordinate system is NP-hard in almost all relevant variants. So we present a completely new approach instead. The network builds clusters and constructs an abstract graph that closely reflects the topology of the network region. The resulting topology awareness suits the needs of some applications much better than the coordinate-based approach. In the second part, we present a novel flow problem, which adds battery constraints to dynamic network flows. Given a time horizon, we seek a flow from source to sink that maximizes the total amount of delivered data. As there is no prior work on this problem, we also analyze it in a centralized setting. We prove complexity results for several variants and present approximation schemes. The third part introduces the WSN simulator Shawn. By letting the user choose among different geometric communication models and data structures for the resulting graph, Shawn can adapt to many different setups, including mobile ones. Due to its design, Shawn is much faster than comparable simulation environments.Die vorliegende Arbeit beschäftigt sich mit algorithmischen und geometrischen Fragestellungen in Sensornetzwerken. Im Gegensatz zur klassischen Algorithmik, bei der ein einzelner Prozessor sequenziell Anweisungen abarbeitet und vollen Zugriff auf die Probleminstanz hat, werden hier verteilte Protokolle benötigt, bei denen die Knoten gemeinsam eine Aufgabe bewältigen, zu der sie allein nicht in der Lage wären. Zuerst untersuchen wir das grundlegende Problem, wie Sensorknoten ein Bewusstsein für ihre Position erlangen können. Motiviert daraus, dass das Problem, Koordinaten für ein globales Koordinatensystem zu bestimmen, in fast allen Varianten NP-schwer ist, wird ein vollkommen neuer Ansatz skizziert, bei dem das Netzwerk selbständig geometrische Cluster bildet und einen abstrakten Graphen konstruiert, der die Topologie des zugrunde liegenden Gebiets sehr genau widerspiegelt. Das sich daraus ergebende Positionsbewusstsein ist für einige Anwendungen dem klassischen euklidischen Ansatz deutlich überlegen. Der zweite Teil widmet sich einem Flussproblems für Sensornetzwerke, dass klassische dynamische Flüsse um Batteriebeschränkungen erweitert. Gesucht ist ein Fluss, der für gegebenen Zeithorizont die Datenmenge maximiert, die von einer Quelle zur Senke geschickt werden kann. Dieses Problem wird auch im zentralisierten Modell untersucht, da keine Vorarbeiten existieren. Wir beweisen Komplexitäten von Problemvarianten und entwickeln Approximationsschemata. Der dritte Teil stellt den Netzwerksimulator Shawn vor. Da der Benutzer zwischen verschiedenen geometrischen Kommunikationsmodellen wählen kann und das Speichermodell für den daraus resultierenden Graphen an den verfügbaren Speicher sowie an Simulationsparameter wie eventuell mögliche Mobilität der Knoten anpassen kann, ist Shawn hochflexibel und gleichzeitig deutlich schneller als vergleichbare Simulationsumgebungen