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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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... 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): ...
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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. ...
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... 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. ...
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... 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. ...
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