Eigenvector Synchronization, Graph Rigidity and the Molecule Problem

The graph realization problem has received a great deal of attention in recent years, due to its importance in applications such as wireless sensor networks and structural biology. In this paper, we extend on previous work and propose the 3D-ASAP algorithm, for the graph realization problem in $\mathbb{R}^3$, given a sparse and noisy set of distance measurements. 3D-ASAP is a divide and conquer, non-incremental and non-iterative algorithm, which integrates local distance information into a global structure determination. Our approach starts with identifying, for every node, a subgraph of its 1-hop neighborhood graph, which can be accurately embedded in its own coordinate system. In the noise-free case, the computed coordinates of the sensors in each patch must agree with their global positioning up to some unknown rigid motion, that is, up to translation, rotation and possibly reflection. In other words, to every patch there corresponds an element of the Euclidean group Euc(3) of rigid transformations in $\mathbb{R}^3$, and the goal is to estimate the group elements that will properly align all the patches in a globally consistent way. Furthermore, 3D-ASAP successfully incorporates information specific to the molecule problem in structural biology, in particular information on known substructures and their orientation. In addition, we also propose 3D-SP-ASAP, a faster version of 3D-ASAP, which uses a spectral partitioning algorithm as a preprocessing step for dividing the initial graph into smaller subgraphs. Our extensive numerical simulations show that 3D-ASAP and 3D-SP-ASAP are very robust to high levels of noise in the measured distances and to sparse connectivity in the measurement graph, and compare favorably to similar state-of-the art localization algorithms.Comment: 49 pages, 8 figure

Distributed Maximum Likelihood Sensor Network Localization

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks

Distributed Algorithms for Stochastic Source Seeking With Mobile Robot Networks

Autonomous robot networks are an effective tool for monitoring large-scale environmental fields. This paper proposes distributed control strategies for localizing the source of a noisy signal, which could represent a physical quantity of interest such as magnetic force, heat, radio signal, or chemical concentration. We develop algorithms specific to two scenarios: one in which the sensors have a precise model of the signal formation process and one in which a signal model is not available. In the model-free scenario, a team of sensors is used to follow a stochastic gradient of the signal field. Our approach is distributed, robust to deformations in the group geometry, does not necessitate global localization, and is guaranteed to lead the sensors to a neighborhood of a local maximum of the field. In the model-based scenario, the sensors follow a stochastic gradient of the mutual information (MI) between their expected measurements and the expected source location in a distributed manner. The performance is demonstrated in simulation using a robot sensor network to localize the source of a wireless radio signal

Reference Nodes Selection for Anchor-Free Localization in Wireless Sensor Networks

Dizertační práce se zabývá návrhem nového bezkotevního lokalizačního algoritmu sloužícího pro výpočet pozice uzlů v bezdrátových senzorových sítích. Provedené studie ukázaly, že dosavadní bezkotevní lokalizační algoritmy, pracující v paralelním režimu, dosahují malých lokalizačních chyb. Jejich nevýhodou ovšem je, že při sestavení množiny referenčních uzlu spotřebovávají daleko větší množství energie než algoritmy pracující v inkrementálním režimu. Paralelní lokalizační algoritmy využívají pro určení pozice referenční uzly nacházející se na protilehlých hranách bezdrátové sítě. Nový lokalizační algoritmus označený jako BRL (Boundary Recognition aided Localization) je založen na myšlence decentralizovaně detekovat uzly ležící na hranici síti a pouze z této množiny vybrat potřebný počet referenčních uzlu. Pomocí navrženého přístupu lze znažně snížit množství energie spotřebované v průběhu procesu výběru referenčních uzlů v senzorovém poli. Dalším přínosem ke snížení energetických nároku a zároveň zachování nízké lokalizační chyby je využití procesu multilaterace se třemi, eventuálně čtyřmi referenčními body. V rámci práce byly provedeny simulace několika dílčích algoritmu a jejich funkčnost byla ověřena experimentálně v reálné senzorové síti. Navržený algoritmus BRL byl porovnán z hlediska lokalizační chyby a počtu zpracovaných paketů s několika známými lokalizačními algoritmy. Výsledky simulací dokázaly, že navržený algoritmus představuje efektivní řešení pro přesnou a zároveň nízkoenergetickou lokalizaci uzlů v bezdrátových senzorových sítích.The doctoral thesis is focused on a design of a novel anchor free localization algorithm for wireless sensor networks. As introduction, the incremental and concurrent anchor free localization algorithms are presented and their performance is compared. It was found that contemporary anchor free localization algorithms working in the concurrent manner achieve a low localization error, but dissipate signicant energy reserves. A new Boundary Recognition Aided Localization algorithm presented in this thesis is based on an idea to recognize the nodes placed on the boundary of network and thus reduce the number of transmission realized during the reference nodes selection phase of the algorithm. For the position estimation, the algorithm employs the multilateration technique that work eectively with the low number of the reference nodes. Proposed algorithms are tested through the simulations and validated by the real experiment with the wireless sensor network. The novel Boundary Recognition Aided Localization algorithm is compared with the known algorithms in terms of localization error and the communication cost. The results show that the novel algorithm presents powerful solution for the anchor free localization.