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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 ) 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.

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All content in this area was uploaded by Markus P. J. Fromherz on Sep 25, 2012

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... Compared with range-based localization using the TOA, TDOA, RSS, and AOA measurements, the range-free method makes no assumption about the availability or validity of such information and only utilizes connectivity information to locate a BN. For a UDN, such as a wireless sensor network (WSN) or Internet of Things (IoT), nodes are usually low-cost and low-power and have no ability to obtain high-precision measurements of the TOA, TDOA, RSS, or AOA [26], [29]. Because of the hardware limitations and power constraints of nodes, range-free localization is often a preferred solution for UDNs [27]. ...

... A well-known method of range-free localization is centroid-based localization (CL) [28], where the centroid of the RNs detecting a BN is estimated as the BN's position. A location method based on multidimensional scaling (MDS) was proposed for range-free localization in WSNs [29]. Based on the connectivity matrix, the MDS method provides a relative position estimate for the WSN. ...

... where f r is the PDF of the range between the RNs and BN. Using different f r , the theoretical variance of CL with an arbitrary node distribution can be calculated using (29) and (30). For the Gaussian node distribution, f r can be obtained from (4): ...

Performance analysis of connectivity-based geolocation in ultra-dense networks (UDNs) is a very important task. Although several performance analyses have been presented for range-free localization, determining the best achievable positioning accuracy of range-free localization remains an open problem. In this paper, we first derive the Cramer-Rao lower bound (CRLB) for the performance evaluation of rangefree localization. All the current performance analyses in the literature for range-free localization are used to evaluate the real performance of a given algorithm, whereas the proposed CRLB provides a benchmark to evaluate the performance of any unbiased range-free location algorithm and determines the physical impossibility of the variance of an unbiased estimator being less than the bound. To the best of our knowledge, this is the first time in the literature that the CRLB for range-free localization has been derived. Second, the theoretical variance of centroid-based localization (CL) with an arbitrary node distribution is derived in this paper. In contrast to the existing theoretical variance of CL for uniform node distribution, the proposed theoretical variance can be used to evaluate the performance of CL in the case of an arbitrary node distribution. Additionally, characteristics of the proposed CRLB and theoretical variance are given in this paper. Finally, an optimal estimator based on a maximum likelihood estimator (MLE) is proposed to improve positioning accuracy. Since both prior information on the spatial node distribution and the connectivity property are effectively utilized in our algorithm, the proposed method performs better than the CL method and can asymptotically attain the CRLB.

... An alternative approach is to attach only a few sensor nodes with GPS receivers, which are termed as "beacons" [13]. Thus, a number of localization methods VOLUME 4, 2016 based on multidimensional scaling (MDS) could be applied, such as ranging-based MDS [14], MDS-MAP [15], MDS-MAP(P) [16] and ranging and angle of arrival (AoA)-based SMDS [17]. MDS is a technique projecting high-dimensional data onto a low-dimensional space to obtain the relative coordinates of objects, which has the advantages of high localization accuracy, especially in the case of small number of beacons, and robust to ranging errors. ...

... However, MDS is a centralized algorithm and requires the network nodes being fully connected, which is difficult to be always satisfied in practice. In order to make MDS be able to work in partially connected network, Yi Shang et al. proposed the improved MDS-MAP algorithm [15], where shortest path algorithm is used when the distances between directly connected terminals are unknown. Although MDS-MAP provides a trade-off between availability and solution accuracy, it can not work well in irregularly-shaped networks, where the shortest path distance between two nodes does not correlate well with their true Euclidean distance. ...

With the widespread application of Internet of things (IoT), the interference problem becomes more and more serious, which results in not only the poor network performance but also the increased energy consumption of IoT nodes. Therefore, in this paper, we investigate the problem of how to locate the interference sources and infer their communication relationships in the cognitive radio IoT (CR-IoT) deployment scenario. First, we utilize MDS-MAP(P) algorithm with dynamic power control to realize cooperative self-localization of the CR-IoT nodes, which is more energy-efficient than all the IoT nodes equipped with global positioning system (GPS) receivers. Then, we propose a non-cooperative localization method to determine the inference sources with the angle of arrivals (AoAs) measured by the CR-IoT nodes. Finally, the communication relationship between interference sources can be inferred based on the association rule of signals. The network simulation results validate that the proposed methods can locate the interference sources accurately with low energy consumption and correctly infer their communication relationships, which is helpful for the interrupted CR-IoT nodes to take a specific opportunistic transmission policy to reduce their energy consumption.

... As a matter of fact, several linearization techniques have been proposed, such as the classical Newton method. To avoid the local minima introduced to the system by the Newton method, alternative linearization algorithms [17] , multidimensional scaling [18] , semidefinite programming [19] , second-order cone programming [20] , and linearized least squares methods [21][22][23] were also proposed. ...

The quality of measurement data is critical to the accuracy of both outdoor and indoor localization methods. Due to the inevitable measurement error, the analytics on the error data is critical to evaluate localization methods and to find the effective ones. For indoor localization, Received Signal Strength (RSS) is a convenient and low-cost measurement that has been adopted in many localization approaches. However, using RSS data for localization needs to solve a fundamental problem, that is, how accurate are these methods? The reason of the low accuracy of the current RSS-based localization methods is the oversimplified analysis on RSS measurement data. In this proposed work, we adopt a generalized measurement model to find optimal estimators whose estimated error is equal to the Cramér-Rao Lower Bound (CRLB). Through mathematical techniques, the key factors that affect the accuracy of RSS-based localization methods are revealed, and the analytics expression that discloses the proportional relationship between the localization accuracy and these factors is derived. The significance of our discovery has two folds: First, we present a general expression for localization error data analytics, which can explain and predict the accuracy of range-based localization algorithms; second, the further study on the general analytics expression and its minimum can be used to optimize current localization algorithms.

... 3) Spectrum Layer: Utilizing spectrum scanning [10], the network reports device adjacencies. Through RSSI-based network localization [16] [17], vehicle speed and direction are deduced. As the TCP termination point, and the layer handling medium access, an open SSID is broadcast with its default VLAN utilizing a null route. ...

While direct allocation of spectrum and evolved medium access protocols provide a base for ubiquitous wireless connectivity, the existing TCP/IP and OSI models were designed for wired networks and do not address open interconnection of air interfaces. Without an interconnection model for the air interface, existing network designs continue to tie wireless medium access to that of the backhaul provider for ownership of access and identity trust, resulting in limitations on functionality and coverage. In this paper, we propose a novel solution to access ownership and identity trust by extending the TCP network standard, under a new model we propose, named TCP-Air which integrates distributed ledger technologies directly at the air interface. Further, we present two use cases of the TCP-Air model, demonstrating applications not feasible under existing permissioned-access network designs.

Let Xv for v∈V be a family of n iid uniform points in the square . Suppose first that we are given the random geometric graph , where vertices u and v are adjacent when the Euclidean distance dE(Xu,Xv) is at most r. Let n3/14≪r≪n1/2. Given G (without geometric information), in polynomial time we can with high probability approximately reconstruct the hidden embedding, in the sense that “up to symmetries,” for each vertex v we find a point within distance about r of Xv; that is, we find an embedding with “displacement” at most about r. Now suppose that, instead of G we are given, for each vertex v, the ordering of the other vertices by increasing Euclidean distance from v. Then, with high probability, in polynomial time we can find an embedding with displacement .

In this paper, we investigate the feasibility of environment
sensing with non-geotagged sensor data. There is a need
for such environment sensing with non-geotagged data to reduce
the data volume and power consumption of rapidly growing
networks of connected devices. We propose a straightforward
method using proximity-based localization to first obtain sensor’s
relative locations, and then applying a transformation to obtain
their absolute locations using anchor sensors, whose location
are known. First, sensors for detecting the target objects are
deployed in an observation area. Each sensor transmits data
including the sensor identifier to a cloud server when it detects
an object nearby. The data from each sensor are not geotagged
and the locations of sensors are not known in advance. In
this work, we show that the information about the objects
(e.g., the number of objects) in the field can be obtained by
localizing the sensors based on their responses to the objects
traversing the field. The key idea is that sensors simultaneously
detecting the target object are in close proximity. Each time
an object traverses the field, it provides information on the
relative locations of the sensors. Based on the information on
the relative locations of the sensors, a map of the relative or
absolute locations of sensors can be constructed by solving a
nonlinear optimization problem. Once the sensor location map is
constructed, we can then obtain information on the objects in the
field. We demonstrate the feasibility of the proposed approach
with simulation experiments.

The hop count matrices are very helpful in obtaining the location information of sensing nodes in Internet of Things (IoT). However, in some scenarios, the hop count matrices cannot be completely observed due to abnormal termination of flooding process, or some of the entries are contaminated by false information in external malicious attacks. Therefore, it is very important to recover the missing hop count matrices. However, to the best of our knowledge, there is no specific algorithm used in the current research to recover the hop count matrices, which would cause the positioning accuracy to be seriously deteriorated. In this paper, for the scenarios of the entries partially observed in the hop count matrices, the hop count matrices recovery schemes, namely, HCMR-NBC and HCMR-MC, are proposed. The former, HCMR-NBC, is to learn the internal relations of different sensing node pairs in the hop count matrices. It is a simple and fast approach which utilizes the feature with single dimension to predict the missing hop count values between the sensing nodes. The latter, HCMR-MC, is to transform the problem of the matrices recovery to the one of matrices completion. Compared with the previous SVT and BLMC algorithms, the proposed algorithms have great advantages in terms of the reconstruction performance and the computation complexity.

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

A method for estimating unknown node positions in a sensor network
based exclusively on connectivity-induced constraints is described.
Known peer-to-peer communication in the network is modeled as a set of
geometric constraints on the node positions. The global solution of a
feasibility problem for these constraints yields estimates for the
unknown positions of the nodes in the network. Providing that the
constraints are tight enough, simulation illustrates that this estimate
becomes close to the actual node positions. Additionally, a method for
placing rectangular bounds around the possible positions for all unknown
nodes in the network is given. The area of the bounding rectangles
decreases as additional or tighter constraints are included in the
problem. Specific models are suggested and simulated for isotropic and
directional communication, representative of broadcast-based and optical
transmission respectively, though the methods presented are not limited
to these simple cases

Instrumenting the physical world through large networks of
wireless sensor nodes, particularly for applications like environmental
monitoring of water and soil, requires that these nodes be very small,
lightweight, untethered, and unobtrusive. The problem of localization,
that is, determining where a given node is physically located in a
network, is a challenging one, and yet extremely crucial for many of
these applications. Practical considerations such as the small size,
form factor, cost and power constraints of nodes preclude the reliance
on GPS of all nodes in these networks. We review localization techniques
and evaluate the effectiveness of a very simple connectivity metric
method for localization in outdoor environments that makes use of the
inherent RF communications capabilities of these devices. A fixed number
of reference points in the network with overlapping regions of coverage
transmit periodic beacon signals. Nodes use a simple connectivity
metric, which is more robust to environmental vagaries, to infer
proximity to a given subset of these reference points. Nodes localize
themselves to the centroid of their proximate reference points. The
accuracy of localization is then dependent on the separation distance
between two-adjacent reference points and the transmission range of
these reference points. Initial experimental results show that the
accuracy for 90 percent of our data points is within one-third of the
separation distance. However, future work is needed to extend the
technique to more cluttered environments

The recent advances in MEMS, embedded systems and wireless communication technologies are making the realization and deployment of networked wireless microsensors a tangible task. Vital to the success of wireless microsensor networks is the ability of microsensors to ``collectively perform sensing and computation''. In this paper, we study one of the fundamental challenges in sensor networks, node localization. The collaborative multilateration 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.

A computer program is described that is designed to reconstruct the metric configuration of a set of points in Euclidean space on the basis of essentially nonmetric information about that configuration. A minimum set of Cartesian coordinates for the points is determined when the only available information specifies for each pair of those points—not the distance between them—but some unknown, fixed monotonic function of that distance. The program is proposed as a tool for reductively analyzing several types of psychological data, particularly measures of interstimulus similarity or confusability, by making explicit the multidimensional structure underlying such data.

This paper considers two problems which at first sight appear to
be quite distinct: localizing a robot in an unknown environment and
calibrating an embedded sensor network. We show that both of these can
be formulated as special cases of a generalized localization problem. In
the standard localization problem, the aim is to determine the pose of
some object (usually a mobile robot) relative to a global coordinate
system. In our generalized version, the aim is to determine the pose of
all elements in a network (both fixed and mobile) relative to an
arbitrary global coordinate system. We have developed a physically
inspired 'mesh-based' formalism for solving such problems. This paper
outlines the formalism, and describes its application to the concrete
tasks of multirobot mapping and calibration of a distributed sensor
network. The paper presents experimental results for both tasks obtained
using a set of Pioneer mobile robots equipped with scanning laser
range-finders

We present a new approach to the problem of simultaneously
localizing a group of mobile robots capable of sensing each other. Each
of the robots collects sensor data regarding its own motion and shares
this information with the rest of the team during the update cycles. A
single estimator, in the form of a Kalman filter, processes the
available positioning information from all the members of the team and
produces a pose estimate for each of them. The equations for this
centralized estimator can be written in a decentralized form thus
allowing this single Kalman filter to be decomposed into a number of
smaller communicating filters, each of them processing local data for
most of the time. The resulting decentralized estimation scheme
constitutes a unique mean for fusing measurements collected from a
variety of sensors with minimal communication and processing
requirements. The distributed localization algorithm is applied to a
group of 3 robots and the improvement in localization accuracy is
presented. Finally, a comparison to the equivalent distributed
information filter is provided