We consider the problem of localizing wireless devices in an ad-hoc network embedded in a d-dimensional Euclidean space. Obtaining a good estimation of where wireless devices are located is crucial in wireless network applications including environment monitoring, geographic routing and topology control. When the positions of the devices are unknown and only local distance information is given, we need to infer the positions from these local distance measurements. This problem is particularly challenging when we only have access to measurements that have limited accuracy and are incomplete. We consider the extreme case of this limitation on the available information, namely only the connectivity information is available, i.e., we only know whether a pair of nodes is within a fixed detection range of each other or not, and no information is known about how far apart they are. Further, to account for detection failures, we assume that even if a pair of devices is within the detection range, it fails to detect the presence of one another with some probability and this probability of failure depends on how far apart those devices are. Given this limited information, we investigate the performance of a centralized positioning algorithm MDS-MAP introduced by , and a distributed positioning algorithm, introduced by , called HOP-TERRAIN. In particular, for a network consisting of n devices positioned randomly, we provide a bound on the resulting error for both algorithms. We show that the error is bounded, decreasing at a rate that is proportional to R Rc, where Rc is the critical detection range when the resulting random network starts to be connected, and R is the detection range of each device.
Perhaps a more practical and interesting case is when there is no central infrastructure. @cite_34 identifies a common three-phase structure of three, popular, distributed sensor-localization algorithms, namely robust positioning @cite_8 , ad-hoc positioning @cite_13 and N-hop multilateration @cite_7 . Table illustrates the structure of these algorithms. In the first phase, nodes share information to collectively determine the distances from each of the nodes to a number of anchors. Anchors are special nodes with a priori knowledge of their own position in some global coordinate system. In the second phase, nodes determine their position based on the estimated distances to the anchors provided by the first phase and the known positions of the anchors. In the last phase, the initial estimated positions are iteratively refined. It is empirically demonstrated that these simple three-phase distributed sensor-localization algorithms are robust and energy-efficient @cite_34 . However, depending on which method is used in each phase, there are different tradeoffs between localization accuracy, computation complexity and power requirements. In @cite_39 , a distributed algorithm-called the Gradient algorithm- was proposed; it is similar to ad-hoc positioning @cite_13 but uses a different method for estimating the average distance per hop.
@cite_7 @cite_8 @cite_39 @cite_34 @cite_13
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This paper studies the problem of determining the node locations in ad-hoc sensor networks. We compare three distributed localization algorithms (Ad-hoc positioning, Robust positioning, and N-hop multilateration) on a single simulation platform. The algorithms share a common, three-phase structure: (1) determine node-anchor distances, (2) compute node positions, and (3) optionally refine the positions through an iterative procedure. We present a detailed analysis comparing the various alternatives for each phase, as well as a head-to-head comparison of the complete algorithms. The main conclusion is that no single algorithm performs best; which algorithm is to be preferred depends on the conditions (range errors, connectivity, anchor fraction, etc.). In each case, however, there is significant room for improving accuracy and or increasing coverage. The localization of sensor nodes is a fundamental problem in sensor networks and can be implemented using powerful and expensive beacons. Beacons, the fewer the better, can acquire their position knowledge either from GPS devices or by virtue of being manually placed. In this paper, we propose a distributed method to localization of sensor nodes using a single moving beacon, where sensor nodes compute their position estimate based on the range-free technique. Two parameters are critical to the location accuracy of sensor nodes: the radio transmission range of the beacon and how often the beacon broadcasts its position. Theoretical analysis shows that these two parameters determine the upper bound of the estimation error when the traverse route of the beacon is a straight line. We extend the position estimate when the traverse route of the beacon is randomly chosen in a real-world situation, where the radio irregularity might cause a node to miss some crucial coordinate information from the beacon. We further point out that the movement pattern of the beacon plays a pivotal role in the localization task for sensors. To minimize estimation errors, sensor nodes can carry out a variety of algorithms in accordance with the movement of the beacon. Simulation results compare variants of the distributed method in a variety of testing environments. Real experiments show that the proposed method is feasible and can estimate the location of sensor nodes accurately, given a single moving beacon. This paper describes a distributed, linear-time algorithm for localizing sensor network nodes in the presence of range measurement noise and demonstrates the algorithm on a physical network. We introduce the probabilistic notion of robust quadrilaterals as a way to avoid flip ambiguities that otherwise corrupt localization computations. We formulate the localization problem as a two-dimensional graph realization problem: given a planar graph with approximately known edge lengths, recover the Euclidean position of each vertex up to a global rotation and translation. This formulation is applicable to the localization of sensor networks in which each node can estimate the distance to each of its neighbors, but no absolute position reference such as GPS or fixed anchor nodes is available. We implemented the algorithm on a physical sensor network and empirically assessed its accuracy and performance. Also, in simulation, we demonstrate that the algorithm scales to large networks and handles real-world deployment geometries. Finally, we show how the algorithm supports localization of mobile nodes. This paper focuses on the principled study of distance reconstruction for distance-based node localization. We address an important issue in node localization by showing that a highly incomplete set of inter-node distance measurements obtained in ad-hoc node deployments carries sufficient information for the accurate reconstruction of the missing distances, even in the presence of noise and sensor node failures. We provide an efficient and provably accurate algorithm for this reconstruction, and we show that the resulting error is bounded, decreasing at a rate that is inversely proportional to radicn, the square root of the number of nodes in the region of deployment. Although this result is applicable to many localization schemes, in this paper we illustrate its use in conjunction with the popular multidimensional scaling algorithm. Our analysis reveals valuable insights and key factors to consider during the sensor network setup phase, to improve the quality of the position estimates A distributed algorithm for determining the positions of nodes in an ad-hoc, wireless sensor network is explained in detail. Details regarding the implementation of such an algorithm are also discussed. Experimentation is performed on networks containing 400 nodes randomly placed within a square area, and resulting error magnitudes are represented as percentages of each node’s radio range. In scenarios with 5 errors in distance measurements, 5 anchor node population (nodes with known locations), and average connectivity levels between neighbors of 7 nodes, the algorithm is shown to have errors less than 33 on average. It is also shown that, given an average connectivity of at least 12 nodes and 10 anchors, the algorithm performs well with up to 40 errors in distance measurements. Evolving networks of ad-hoc wireless sensing nodes rely heavily on the ability to establish position information. The algorithms presented herein rely on range measurements between pairs of nodes and the a priori coordinates of sparsely located anchor nodes. Clusters of nodes surrounding anchor nodes cooperatively establish confident position estimates through assumptions, checks, and iterative refinements. Once established, these positions are propagated to more distant nodes, allowing the entire network to create an accurate map of itself. Major obstacles include overcoming inaccuracies in range measurements as great as spl plusmn 50 , as well as the development of initial guesses for node locations in clusters with few or no anchor nodes. Solutions to these problems are presented and discussed, using position error as the primary metric. Algorithms are compared according to position error, scalability, and communication and computational requirements. Early simulations yield average position errors of 5 in the presence of both range and initial position inaccuracies. We demonstrate that it is possible to achieve accurate localization and tracking of a target in a randomly placed wireless sensor network composed of inexpensive components of limited accuracy. The crucial enabler for this is a reasonably accurate local coordinate system aligned with the global coordinates. We present an algorithm for creating such a coordinate system without the use of global control, globally accessible beacon signals, or accurate estimates of inter-sensor distances. The coordinate system is robust and automatically adapts to the failure or addition of sensors. Extensive theoretical analysis and simulation results are presented. Two key theoretical results are: there is a critical minimum average neighborhood size of 15 for good accuracy and there is a fundamental limit on the resolution of any coordinate system determined strictly from local communication. Our simulation results show that we can achieve position accuracy to within 20 of the radio range even when there is variation of up to 10 in the signal strength of the radios. The algorithm improves with finer quantizations of inter-sensor distance estimates: with 6 levels of quantization position errors better than 10 are achieved. Finally we show how the algorithm gracefully generalizes to target tracking tasks. We consider the problem of node positioning in ad hoc networks. We propose a distributed, infrastructure-free positioning algorithm that does not rely on GPS (Global Positioning System). Instead, the algorithm uses the distances between the nodes to build a relative coordinate system in which the node positions are computed in two dimensions. Despite the distance measurement errors and the motion of the nodes, the algorithm provides sufficient location information and accuracy to support basic network functions. Examples of applications where this algorithm can be used include Location Aided Routing [10] and Geodesic Packet Forwarding [2]. Another example are sensor networks, where mobility is less of a problem. The main contribution of this work is to define and compute relative positions of the nodes in an ad hoc network without using GPS. We further explain how the proposed approach can be applied to wide area ad hoc networks. Since ad hoc and sensor networks can be composed of a very large number of devices, the scalability of network protocols is a major design concern. Furthermore, network protocols must be designed to prolong the battery lifetime of the devices. However, most existing routing techniques for ad hoc networks are known not to scale well. On the other hand, the so-called geographical routing algorithms are known to be scalable but their energy efficiency has never been extensively and comparatively studied. In a geographical routing algorithm, data packets are forwarded by a node to its neighbor based on their respective positions. The neighborhood of each node is constituted by the nodes that lie within a certain radio range. Thus, from the perspective of a node forwarding a packet, the next hop depends on the width of the neighborhood it perceives. The analytical framework proposed in this paper allows to analyze the relationship between the energy efficiency of the routing tasks and the extension of the range of the topology knowledge for each node. A wider topology knowledge may improve the energy efficiency of the routing tasks but increases the cost of topology information due to signaling packets needed to acquire this information. The problem of determining the optimal topology knowledge range for each node to make energy efficient geographical routing decisions is tackled by integer linear programming. It is shown that the problem is intrinsically localized, i.e., a limited topology knowledge is sufficient to make energy efficient forwarding decisions. The leading forwarding rules for geographical routing are compared in this framework, and the energy efficiency of each of them is studied. Moreover, a new forwarding scheme, partial topology knowledge forwarding (PTKF), is introduced, and shown to outperform other existing schemes in typical application scenarios. A probe-based distributed protocol for knowledge range adjustment (PRADA) is finally introduced that allows each node to efficiently select online its topology knowledge range. PRADA is shown to rapidly converge to a near-optimal solution. The recent advances in MEMS, embedded systems and wireless communication technologies are making the realization and deployment of networked wireless microsensors a tangible task. In this paper we study node localization, a component technology that would enhance the effectiveness and capabilities of this new class of networks. The n-hop multilateration primitive presented here, enables ad-hoc deployed sensor nodes to accurately estimate their locations by using known beacon locations that are several hops away and distance measurements to neighboring nodes. To prevent error accumulation in the network, node locations are computed by setting up and solving a global non-linear optimization problem. The solution is presented in two computation models, centralized and a fully distributed approximation of the centralized model. Our simulation results show that using the fully distributed model, resource constrained sensor nodes can collectively solve a large non-linear optimization problem that none of the nodes can solve individually. This approach results in significant savings in computation and communication, that allows fine-grained localization to run on a low cost sensor node we have developed. In this paper, we describe a global distributed solution that enables the simultaneous performance of time synchronization and positioning in ultra-wideband (UWB) ad hoc networks. On the one hand, the proposed synchronization scheme basically relies on cooperative two-way-ranging time-of-arrival transactions and a diffusion algorithm that ensures the convergence of clock parameters to average reference values in each node. Although the described solution is generic at first sight, its sensitivity to time-of-arrival accuracy imposes the choice of an impulse-radio ultra-wideband physical layer in the very context. On the other hand, a distributed algorithm coupled with this synchronization scheme mitigates the impact of non-line-of-sight ranging errors on positioning accuracy without any additional protocol hook. More particularly, the realistic UWB ranging error models we use take into account UWB channel effects, as well as detection noises and relative clock drifts. Then, it is demonstrated that a cooperative and distributed maximization of the log-likelihood of range estimates can reduce the uncertainty on estimated positions in comparison with classical distributed weighted least squares approaches. Finally, the proposed distributed maximum log-likelihood algorithm proves to preserve a reasonable level of complexity in each node by approximating asynchronously the positive gradient direction of the log-likelihood function. For both distributed synchronization and positioning algorithms, simulation results are provided to illustrate the relevance of such a solution. Distributed algorithms for multi-robot systems rely on network communications to share information. However, the motion of the robots changes the network topology, which affects the information presented to the algorithm. For an algorithm to produce accurate output, robots need to communicate rapidly enough to keep the network topology correlated to their physical configuration. Infrequent communications will cause most multi-robot distributed algorithms to produce less accurate results, and cause some algorithms to stop working altogether. The central theme of this work is that algorithm accuracy, communications bandwidth, and physical robot speed are related. This thesis has three main contributions: First, I develop a prototypical multi-robot application and computational model, propose a set of complexity metrics to evaluate distributed algorithm performance on multi-robot systems, and introduce the idea of the robot speed ratio, a dimensionless measure of robot speed relative to message speed in networks that rely on multi-hop communication. The robot speed ratio captures key relationships between communications bandwidth, mobility, and algorithm accuracy, and can be used at design time to trade off between them. I use this speed ratio to evaluate the performance of existing distributed algorithms for multi-hop communication and navigation. Second, I present a definition of boundaries in multi-robot systems, and develop new distributed algorithms to detect and characterize them. Finally, I define the problem of dynamic task assignment, and present four distributed algorithms that solve this problem, each representing a different trade-off between accuracy, running time, and communication resources. All the algorithms presented in this work are provably correct under ideal conditions and produce verifiable real-world performance. They are self-stabilizing and robust to communications failures, population changes, and other errors. All the algorithms were tested on a swarm of 112 robots. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.) This paper presents a new approach for the challenging problem of geo-localization using image matching in a structured database of city-wide reference images with known GPS coordinates. We cast the geo-localization as a clustering problem of local image features. Akin to existing approaches to the problem, our framework builds on low-level features which allow local matching between images. For each local feature in the query image, we find its approximate nearest neighbors in the reference set. Next, we cluster the features from reference images using Dominant Set clustering, which affords several advantages over existing approaches. First, it permits variable number of nodes in the cluster, which we use to dynamically select the number of nearest neighbors for each query feature based on its discrimination value. Second, this approach is several orders of magnitude faster than existing approaches. Thus, we obtain multiple clusters (different local maximizers) and obtain a robust final solution to the problem using multiple weak solutions through constrained Dominant Set clustering on global image features, where we enforce the constraint that the query image must be included in the cluster. This second level of clustering also bypasses heuristic approaches to voting and selecting the reference image that matches to the query. We evaluate the proposed framework on an existing dataset of 102k street view images as well as a new larger dataset of 300k images, and show that it outperforms the state-of-the-art by 20 and 7 percent, respectively, on the two datasets. This paper considers the problem of designing power efficient routing with guaranteed delivery for sensor networks with known distances between neighbors but unknown geographic locations. We propose Hector, a hybrid energy efficient tree-based optimized routing protocol, based on two sets of virtual coordinates. One set is based on rooted tree coordinates, and the other is based on hop distances toward several landmarks. In our algorithm, the node currently holding the packet forwards it to its neighbor that optimizes ratio of power cost over distance progress with landmark coordinates, among nodes that reduce landmark coordinates and do not increase tree coordinates. If such a node does not exist then forwarding is made to the neighbor that reduces tree based distance and optimizes power cost over tree distance progress ratio. Our simulations show the superiority of our algorithm over existing alternatives while guaranteeing delivery, and only up to 30 additional power compared to centralized shortest weighted path algorithm. In this paper we present a prototype system for image based localization in urban environments. Given a database of views of city street scenes tagged by GPS locations, the system computes the GPS location of a novel query view. We first use a wide-baseline matching technique based on SIFT features to select the closest views in the database. Often due to a large change of viewpoint and presence of repetitive structures, a large percentage of matches (> 50 ) are not correct correspondences. The subsequent motion estimation between the query view and the reference view, is then handled by a novel and efficient robust estimation technique capable of dealing with large percentage of outliers. This stage is also accompanied by a model selection step among the fundamental matrix and the homography. Once the motion between the closest reference views is estimated, the location of the query view is then obtained by triangulation of translation directions. Approximate solutions for cases when triangulation cannot be obtained reliably are also described. The presented system is tested on the dataset used in ICCV 2005 Computer Vision Contest and is shown to have higher accuracy than previous reported results. Each node in a wireless multi-hop network can adjust the power level at which it transmits and thus change the topology of the network to save energy by choosing the neighbors with which it directly communicates. Many previous algorithms for distributed topology control have assumed an ability at each node to deduce some location-based information such as the direction and the distance of its neighbor nodes with respect to itself. Such a deduction of location-based information, however, cannot be relied upon in real environments where the path loss exponents vary greatly leading to significant errors in distance estimates. Also, multipath effects may result in different signal paths with different loss characteristics, and none of these paths may be line-of-sight, making it difficult to estimate the direction of a neighboring node. In this paper, we present Step Topology Control (STC), a simple distributed topology control algorithm which reduces energy consumption while preserving the connectivity of a heterogeneous sensor network without use of any location-based information. The STC algorithm avoids the use of GPS devices and also makes no assumptions about the distance and direction between neighboring nodes. We show that the STC algorithm achieves the same or better order of communication and computational complexity when compared to other known algorithms that also preserve connectivity without the use of location-based information. We also present a detailed simulation-based comparative analysis of the energy savings and interference reduction achieved by the algorithms. The results show that, in spite of not incurring a higher communication or computational complexity, the STC algorithm performs better than other algorithms in uniform wireless environments and especially better when path loss characteristics are non-uniform. It is often useful to know the geographic positions of nodes in a communications network, but adding GPS receivers or other sophisticated sensors to every node can be expensive. We present an algorithm that uses connectivity information who is within communications range of whom to derive the locations of the nodes in the network. The method can take advantage of additional information, such as estimated distances between neighbors or known positions for certain anchor nodes, if it is available. The algorithm is based on multidimensional scaling, a data analysis technique that takes O(n3) time for a network of n nodes. Through simulation studies, we demonstrate that the algorithm is more robust to measurement error than previous proposals, especially when nodes are positioned relatively uniformly throughout the plane. Furthermore, it can achieve comparable results using many fewer anchor nodes than previous methods, and even yields relative coordinates when no anchor nodes are available. This paper develops an optimal decentralized algorithm for sparse signal recovery and demonstrates its application in monitoring localized phenomena using energy-constrained large-scale wireless sensor networks. Capitalizing on the spatial sparsity of localized phenomena, compressive data collection is enforced by turning off a fraction of sensors using a simple random node sleeping strategy, which conserves sensing energy and prolongs network lifetime. In the absence of a fusion center, sparse signal recovery via decentralized in-network processing is developed, based on a consensus optimization formulation and the alternating direction method of multipliers. In the proposed algorithm, each active sensor monitors and recovers its local region only, collaborates with its neighboring active sensors through low-power one-hop communication, and iteratively improves the local estimates until reaching the global optimum. Because each sensor monitors the local region rather than the entire large field, the iterative algorithm converges fast, in addition to being scalable in terms of transmission and computation costs. Further, through collaboration, the sensing performance is globally optimal and attains a high spatial resolution commensurate with the node density of the original network containing both active and inactive sensors. Simulations demonstrate the performance of the proposed approach. We show that the coarse-grained and fine-grained localization problems for ad hoc sensor networks can be posed and solved as a pattern recognition problem using kernel methods from statistical learning theory. This stems from an observation that the kernel function, which is a similarity measure critical to the effectiveness of a kernel-based learning algorithm, can be naturally defined in terms of the matrix of signal strengths received by the sensors. Thus we work in the natural coordinate system provided by the physical devices. This not only allows us to sidestep the difficult ranging procedure required by many existing localization algorithms in the literature, but also enables us to derive a simple and effective localization algorithm. The algorithm is particularly suitable for networks with densely distributed sensors, most of whose locations are unknown. The computations are initially performed at the base sensors, and the computation cost depends only on the number of base sensors. The localization step for each sensor of unknown location is then performed locally in linear time. We present an analysis of the localization error bounds, and provide an evaluation of our algorithm on both simulated and real sensor networks. Given a set of sensor nodes V where each node wants to broadcast a message to all its neighbors that are within a certain broadcasting range, the local broadcasting problem is to schedule all these requests in as few timeslots as possible. In this paper, assuming the more realistic physical interference model and no knowledge of the topology, we present three distributed local broadcasting algorithms where the first one is for the asynchronized model and the other two are for the synchronized model. Under the asynchronized model, nodes may join the execution of the protocol at any time and do not have access to a global clock, for which we give a distributed randomized algorithm with approximation ratio O(log2 n). This improves the state-of-the-art result given in [14] by a logarithmic factor. For the synchronized model where communications among nodes are synchronous and nodes can perform physical carrier sensing, we propose two distributed deterministic local broadcasting algorithms for synchronous and asynchronous node wakeups, respectively. Both algorithms have approximation ratio O(log n).