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. 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. 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. 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. Many ad hoc network protocols and applications assume the knowledge of geographic location of nodes. The absolute position of each networked node is an assumed fact by most sensor networks which can then present the sensed information on a geographical map. Finding position without the aid of GPS in each node of an ad hoc network is important in cases where GPS is either not accessible, or not practical to use due to power, form factor or line of sight conditions. Position would also enable routing in sufficiently isotropic large networks, without the use of large routing tables. We are proposing APS --- a localized, distributed, hop by hop positioning algorithm, that works as an extension of both distance vector routing and GPS positioning in order to provide approximate position for all nodes in a network where only a limited fraction of nodes have self positioning capability. 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 Wireless sensor networks are widely adopted in many location-sensitive applications including disaster management, environmental monitoring, military applications where the precise estimation of each node position is inevitably important when the absolute positions of a relatively small portion as anchor nodes of the underlying network were predetermined. Intrinsically, localization is an unconstrained optimization problem based on various distance path measures. Most of the existing localization methods focus on using different heuristic-based or mathematical techniques to increase the precision in position estimation. However, there were recent studies showing that nature-inspired algorithms like the ant-based or genetic algorithms can effectively solve many complex optimization problems. In this paper, we propose to adapt an evolutionary approach, namely a micro-genetic algorithm, as a post-optimizer into some existing localization methods such as the Ad-hoc Positioning System (APS) to further improve the accuracy of their position estimation. Obviously, our proposed MGA is highly adaptable and easily integrated into other localization methods. Furthermore, the remarkable improvements attained by our proposed MGA on both isotropic and anisotropic topologies of our simulation tests prompt for several interesting directions for further investigation. 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. Localization is crucial for wireless ad hoc and sensor networks. As the distance-measurement ranges are often less than that of the communication range for many ranging systems, most communication-dense wireless networks are often localization-sparse. Consequently, most existing algorithms fail to provide accurate localization supports. In order to address this issue, by introducing a concept of component, we propose to group nodes into components, so that nodes are able to better share their ranging and anchor knowledge. This design, CALL, relaxes two essential restrictions in localization: node ordering and anchor distribution. We evaluate the effectiveness of CALL through extensive simulations. The results show that CALL locates 80 nodes in a network with average degree 7.5 and 5 percent anchors, which outperforms the state of the art design Sweeps about 20 . 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. With the advent of Substation Computer Systems dedicated to protection, control and data logging functions in a Substation, it becomes possible to develop new applications which can utilize the processing power available within the substation. The microcomputer based Symmetrical Component Distance Relay (SCDR) described in the references cited at the end of this paper possesses certain characteristics which facilitate real-time monitoring of positive sequence voltage phasor at the local power system bus. With a regression analysis the frequency and rate-of-change of frequency at the bus can also be determined from the positive sequence voltage phase angle. This paper describes the theoretical basis of these computations and describes results of experiments performed in the AEP power system simulation laboratory. Plans for future field tests on the AEP system are also outlined. In this paper we address the problem of estimating the poses of a team of agents when they do not share any common reference frame. Each agent is capable of measuring the relative position and orientation of its neighboring agents, however these measurements are not exact but they are corrupted with noises. The goal is to compute the pose of each agent relative to an anchor node. We present a strategy where, first of all, the agents compute their orientations relative to the anchor. After that, they update the relative position measurements according to these orientations, to finally compute their positions. As contribution we discuss the proposed strategy, that has the interesting property that can be executed in a distributed fashion. The distributed implementation allows each agent to recover its pose using exclusively local information and local interactions with its neighbors. This algorithm has a low memory load, since it only requires each node to maintain an estimate of its own orientation and position. 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. MDS-MAP is a recent localization method based on multidimensional scaling (MDS). It uses connectivity information - who is within communications range of whom - to derive the locations of the nodes in the network, and can take advantage of additional data, such as estimated distances between neighbors or known positions for certain anchor nodes, if they are available. However, MDS-MAP is an inherently centralized algorithm and is therefore of limited utility in many applications. In this paper, we present a new variant of the MDS-MAP method, which we call MDS-MAP(P) standing for MDS-MAP using patches of relative maps, that can be executed in a distributed fashion. Using extensive simulations, we show that the new algorithm not only preserves the good performance of the original method on relatively uniform layouts, but also performs much better than the original on irregularly-shaped networks. The main idea is to build a local map at each node of the immediate vicinity and then merge these maps together to form a global map. This approach works much better for topologies in which the shortest path distance between two nodes does not correspond well to their Euclidean distance. We also discuss an optional refinement step that improves solution quality even further at the expense of additional computation. We describe an SDP relaxation based method for the position estimation problem in wireless sensor networks. The optimization problem is set up so as to minimize the error in sensor positions to fit distance measures. Observable gauges are developed to check the quality of the point estimation of sensors or to detect erroneous sensors. The performance of this technique is highly satisfactory compared to other techniques. Very few anchor nodes are required to accurately estimate the position of all the unknown nodes in a network. Also the estimation errors are minimal even when the anchor nodes are not suitably placed within the network or the distance measurements are noisy. Many ad hoc network protocols and applications assume the knowledge of geographic location of nodes. The absolute location of each networked node is an assumed fact by most sensor networks which can then present the sensed information on a geographical map. Finding location without the aid of GPS in each node of an ad hoc network is important in cases where GPS is either not accessible, or not practical to use due to power, form factor or line of sight conditions. Location would also enable routing in sufficiently isotropic large networks, without the use of large routing tables. We are proposing APS - a distributed, hop by hop positioning algorithm, that works as an extension of both distance vector routing and GPS positioning in order to provide approximate location for all nodes in a network where only a limited fraction of nodes have self location capability. We study a slotted version of the Aloha Medium Access (MAC) protocol in a Mobile Ad-hoc Network (MANET). Our model features transmitters randomly located in the Euclidean plane, according to a Poisson point process and a set of receivers representing the next-hop from every transmitter. We concentrate on the so-called outage scenario, where a successful transmission requires a Signal-to-Interference-and-Noise (SINR) larger than some threshold. We analyze the local delays in such a network, namely the number of times slots required for nodes to transmit a packet to their prescribed next-hop receivers. The analysis depends very much on the receiver scenario and on the variability of the fading. In most cases, each node has finite-mean geometric random delay and thus a positive next hop throughput. However, the spatial (or large population) averaging of these individual finite mean-delays leads to infinite values in several practical cases, including the Rayleigh fading and positive thermal noise case. In some cases it exhibits an interesting phase transition phenomenon where the spatial average is finite when certain model parameters (receiver distance, thermal noise, Aloha medium access probability) are below a threshold and infinite above. To the best of our knowledge, this phenomenon, which we propose to call the wireless contention phase transition, has not been discussed in the literature. We comment on the relationships between the above facts and the heavy tails found in the so-called "RESTART" algorithm. We argue that the spatial average of the mean local delays is infinite primarily because of the outage logic, where one transmits full packets at time slots when the receiver is covered at the required SINR and where one wastes all the other time slots. This results in the "RESTART" mechanism, which in turn explains why we have infinite spatial average. Adaptive coding offers another nice way of breaking the outage RESTART logic. We show examples where the average delays are finite in the adaptive coding case, whereas they are infinite in the outage case. Time-based localization approaches attract a lot of interest due to their high accuracy and potentially low cost for wireless sensor networks (WSNs). However, time-based localization is tightly coupled with clock synchronization. Thus, the reliability of timestamps in time-based localization becomes an important yet challenging task to deal with. In this paper, we propose robust time-based localization strategies to locate a target node with the help of anchors (nodes with known positions) in asynchronous networks. Two kinds of asynchronous networks are considered: one only with clock offsets, labeled quasi-synchronous networks, whereas the other with not only clock offsets but also clock skews, labeled fully asynchronous networks. A novel ranging protocol is developed for both networks, namely asymmetric trip ranging (ATR), to reduce the communication load and explore the broadcast property of WSNs. Regardless of the reliability of the timestamp report from the target node, closed-form least-squares (LS) estimators are derived to accurately estimate the target node position. As a result, we counter the uncertainties caused by the target node by ignoring the timestamps from this node. Furthermore, in order to simplify the estimator in fully asynchronous networks, localization and synchronization are decoupled. A simple yet efficient method is proposed to first Calibrate the Clock Skews of the anchors, and then Estimate the Node Position (CCS-ENP). Finally, Cramer-Rao bounds (CRBs) and simulation results corroborate the efficiency of our localization schemes. Localization is one of the substantial issues in wireless sensor networks. Several approaches, including range-based and range-free, have been proposed to calculate positions for randomly deployed sensor nodes. With specific hardware, the range-based schemes typically achieve high accuracy based on either node-to-node distances or angles. On the other hand, the range-free mechanisms support coarse positioning accuracy with the less expense. This paper describes a range-free localization scheme using mobile anchor points. Each anchor point equipped with the GPS moves in the sensing field and broadcasts its current position periodically. The sensor nodes obtaining the information are able to compute their locations. With the scheme, no extra hardware or data communication is needed for the sensor nodes. Moreover, obstacles in the sensing fields can be tolerated. The localization mechanism has been implemented in the network simulator ns-2. The simulation results show that our scheme performed better than other range-free mechanisms. An adaptive rule-based algorithm, SpaseLoc, is described to solve localization problems for ad hoc wireless sensor networks. A large problem is solved as a sequence of very small subproblems, each of which is solved by semidefinite programming relaxation of geometric optimization model. The subproblems are generated according to a set of sensor anchor selection rules and a priority list. Computational results compared with existing approaches show that the SpaseLoc algorithm scales well and provides excellent, positioning accuracy. A dynamic version of the SpaseLoc method is developed for estimating proving sensors locations in a real-time environment. The method uses dynamic distance measurement updates among sensors, and utilizes SpaseLoc for static sensor localization. Further computational results are presented, along with an application to bus transit systems. Ways to deploy sensor localization algorithms in clustered distributed environments are also studied, permitting application to arbitrarily large networks. In addition, we extend the algorithm to solving sensor localizations in 3D space. A preprocessor is developed to enable SpaseLoc: for localization of networks without absolute position information.* *Joint research conducted in the Dept of Management Science and Engineering, Stanford University. This paper considers the noisy range-only network localization problem in which measurements of relative distances between agents are used to estimate their positions in networked systems. When distance information is noisy, existence and uniqueness of location solution are usually not guaranteed. It is well known that in presence of distance measurement noise, a node may have discontinuous deformations (e.g., flip ambiguities and discontinuous flex ambiguities). Thus, there are two issues that we consider in the noisy localization problem. The first one is the location estimate error propagated from distance measurement noise. We compare two kinds of analytical location error computation methods by assuming that each distance is corrupted with independent Gaussian random noise. These analytical results help us to understand effects of the measurement noises on the position estimation accuracy. After that, based on multidimensional scaling theory, we propose a distributed localization algorithm to solve the noisy range network localization problem. Our approach is robust to distance measurement noise, and it can be implemented in any random case without considering the network setup constraints. Moreover, a refined version of distributed noisy range localization method is developed, which achieves a good tradeoff between computational effort and global convergence especially in large-scale networks.