Sensor Network Localization Problem Research Articles

A Security Localization method based on Threshold and Vote for wireless sensor networks

In this paper, we address wireless sensor network localization problems that have high reliability in an environment where physical node destruction is possible. We propose a new security localization algorithm TVSL (Threshold and Vote Security Localization) for wireless sensor network (WSN). This algorithm improves the safety performance of positioning process of nodes in WSN by using the threshold idea and vote with sensor nodes. The advantage of this algorithm is that no additional hardware is needed, easy integration with other localization algorithms, and the safety performance of localization algorithm is improved obviously. From the simulation of this algorithm, we get the expected results.

A Security Localization Method in Wireless Sensor Networks

In this paper, we address wireless sensor network localization problems that have high reliability in an environment where physical node destruction is possible. We propose a range-independent location algorithm called security location based on genetic algorithm (GASL) that allows sensors to passively determine their location with high reliability, without increasing the number of reference points, or the complexity of the hardware of each reference point or node. In GASL, sensors determine their location based on the optimization of select function by the reliability by aim at some reference point process location compute confirm and remainder energy and distance of node to reference point. By combining the communication range constraints imposed by the physical medium with computationally efficient cryptographic primitives that secure the beacon transmissions. We show that GASL is robust against diversified known attacks and mostly unknown attacks on WSN, such as the wormhole attack, the sybil attack, and inject misdate attack, etc. Finally, our performance evaluation shows that GASL leads to significant improvement in location accuracy and security compared with state of the art range independent location schemes.

Force-directed approaches to sensor localization

As the number of applications of sensor networks increases, so does the interest in sensor network localization, that is, in recovering the correct position of each node in a network of sensors from partial connectivity information such as adjacency, range, or angle between neighboring nodes. In this article, we consider the anchor-free localization problem in sensor networks that report possibly noisy range information and angular information about the relative order of each sensor's neighbors. Previously proposed techniques seem to successfully reconstruct the original positions of the nodes for relatively small networks with nodes distributed in simple regions. However, these techniques do not scale well with network size and yield poor results with nonconvex or nonsimple underlying topology. Moreover, the distributed nature of the problem makes some of the centralized techniques inapplicable in distributed settings. To address these problems we describe a multiscale dead-reckoning (MSDR) algorithm that scales well for large networks, can reconstruct complex underlying topologies, and is resilient to noise. The MSDR algorithm takes its roots from classic force-directed graph layout computation techniques. These techniques are augmented with a multiscale extension to handle the scalability issue and with a dead-reckoning extension to overcome the problems arising with nonsimple topologies. Furthermore, we show that the distributed version of the MSDR algorithm performs as well as, if not better than, its centralized counterpart, as shown by the quality of the layout, measured in terms of the accuracy of the computed pairwise distances between sensors in the network.

Energy Aware Iterative Source Localization for Wireless Sensor Networks

In this paper, the source localization problem in wireless sensor networks is investigated where the location of the source is estimated based on the quantized measurements received from sensors in the field. An energy efficient iterative source localization scheme is proposed where the algorithm begins with a coarse location estimate obtained from measurement data from a set of anchor sensors. Based on the available data at each iteration, the posterior probability density function (pdf) of the source location is approximated using an importance sampling based Monte Carlo method and this information is utilized to activate a number of non-anchor sensors. Two sensor selection metrics namely the mutual information and the posterior Cramér-Rao lower bound (PCRLB) are employed and their performance compared. Further, the approximate posterior pdf of the source location is used to compress the quantized data of each activated sensor using distributed data compression techniques. Simulation results show that with significantly less computation, the PCRLB based iterative sensor selection method achieves similar mean squared error (MSE) performance as compared to the state-of-the-art mutual information based sensor selection method. By selecting only the most informative sensors and compressing their data prior to transmission to the fusion center, the iterative source localization method reduces the communication requirements significantly and thereby results in energy savings.

Minimum cost localization problem in wireless sensor networks

Localization is a fundamental problem in wireless sensor networks. Current localization algorithms mainly focus on checking the localizability of a network and/or how to localize as many nodes as possible given a static set of anchor nodes and distance measurements. In this paper, we study a new optimization problem, minimum cost localization problem, which aims to localize all sensors in a network using the minimum number (or total cost) of anchor nodes given the distance measurements. We show this problem is very challenging and then present a set of greedy algorithms using both trilateration and local sweep operations to address the problem. Extensive simulations have been conducted and demonstrate the efficiency of our algorithms.

Sensor network localization using kernel spectral regression

This paper addresses the localization problem in wireless sensor networks using signal strength. We use a kernel function to measure the similarities between sensor nodes. The kernel matrix can be ...

Sensor network localization using kernel spectral regression

AbstractThis paper addresses the localization problem in wireless sensor networks using signal strength. We use a kernel function to measure the similarities between sensor nodes. The kernel matrix can be naturally defined in terms of the signal strength matrix. We show that the relative locations of sensor nodes can be obtained by solving a dimension reduction problem. To capture the structure of the whole network, we use the kernel spectral regression (KSR) method to estimate the relative locations of the sensor nodes. Given sufficient anchor nodes, the relative locations can be aligned to global locations. The key benefits of adopting KSR are that it allows us to define a graph to optimally preserve the topological structure of the sensor network, and a kernel function can capture the nonlinear relationship in the signal space. Simulation results show that we can achieve small average location error with a small number of anchors. We also compare our method with several related methods, and the results show that KSR is more efficient than the others in our simulated sensor networks. Copyright © 2009 John Wiley & Sons, Ltd.

Timing-Based Mobile Sensor Localization in Wireless Sensor and Actor Networks

In this paper, localization problem in wireless sensor and actor networks (WSAN) is addressed. In WSAN, the performance of event detection and tracking highly depends on the exact location information of the events that must be reported along with the event features. Having precise location information of the sensor nodes, actors are able to execute actions more effectively in the region of detected events. In this context, the accurate localization of sensor nodes is essential with respect to the actors. Particularly, the problem becomes much more complicated when the sensor nodes as well as the anchor nodes (actors) are mobile. In order to localize the mobile sensor nodes relative to the actors, a novel Timing-based Mobile Sensor Localization (TMSL) algorithm is introduced. In TMSL, sensor nodes determine their distance from actors by using propagation time and speed of RF signal. In order to determine distance from the actors, actors actively broadcast reference beacons in a pattern of intervals adaptively defined according to the mobility of sensor nodes and the required level of localization accuracy. These reference beacons carry the interval numbers in which they were transmitted. The interval numbers are then used by the sensor nodes to calculate the start time of the beacons locally which is then used to determine the propagation time. TMSL does neither require nor assume any time synchronization among the sensor nodes or with the actors. Performance evaluations clearly show that TMSL is adaptive to velocity of mobile sensor and actor nodes and can be configured according to the required localization accuracy in order to avoid overhead raised due to high velocity.

(Robust) Edge-based semidefinite programming relaxation of sensor network localization

Recently Wang, Zheng, Boyd, and Ye (SIAM J Optim 19:655–673, 2008) proposed a further relaxation of the semidefinite programming (SDP) relaxation of the sensor network localization problem, named edge-based SDP (ESDP). In simulation, the ESDP is solved much faster by interior-point method than SDP relaxation, and the solutions found are comparable or better in approximation accuracy. We study some key properties of the ESDP relaxation, showing that, when distances are exact, zero individual trace is not only sufficient, but also necessary for a sensor to be correctly positioned by an interior solution. We also show via an example that, when distances are inexact, zero individual trace is insufficient for a sensor to be accurately positioned by an interior solution. We then propose a noise-aware robust version of ESDP relaxation for which small individual trace is necessary and sufficient for a sensor to be accurately positioned by a certain analytic center solution, assuming the noise level is sufficiently small. For this analytic center solution, the position error for each sensor is shown to be in the order of the square root of its trace. Lastly, we propose a log-barrier penalty coordinate gradient descent method to find such an analytic center solution. In simulation, this method is much faster than interior-point method for solving ESDP, and the solutions found are comparable in approximation accuracy. Moreover, the method can distribute its computation over the sensors via local communication, making it practical for positioning and tracking in real time.

Explicit Sensor Network Localization using Semidefinite Representations and Facial Reductions

The sensor network localization (SNL) problem in embedding dimension r consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the sensors (called anchors). Current solution techniques relax this problem to a weighted, nearest, (positive) semidefinite programming (SDP) completion problem by using the linear mapping between Euclidean distance matrices (EDM) and semidefinite matrices. The resulting SDP is solved using primal-dual interior point solvers, yielding an expensive and inexact solution. This relaxation is highly degenerate in the sense that the feasible set is restricted to a low dimensional face of the SDP cone, implying that the Slater constraint qualification fails. Cliques in the graph of the SNL problem give rise to this degeneracy in the SDP relaxation. In this paper, we take advantage of the absence of the Slater constraint qualification and derive a technique for the SNL problem, with exact data, that explicitly solves the corresponding rank restricted SDP problem. No SDP solvers are used. For randomly generated instances, we are able to efficiently solve many huge instances of this NP-hard problem to high accuracy by finding a representation of the minimal face of the SDP cone that contains the SDP matrix representation of the EDM. The main work of our algorithm consists in repeatedly finding the intersection of subspaces that represent the faces of the SDP cone that correspond to cliques of the SNL problem.

Universal Rigidity and Edge Sparsification for Sensor Network Localization

Owing to their high accuracy and ease of formulation, there has been great interest in applying convex optimization techniques, particularly that of semidefinite programming (SDP) relaxation, to tackle the sensor network localization problem in recent years. However, a drawback of such techniques is that the resulting convex program is often expensive to solve. In order to speed up computation, various edge sparsification heuristics have been proposed, whose aim is to reduce the number of edges in the input graph. Although these heuristics do reduce the size of the convex program and hence make it faster to solve, they are often ad hoc in nature and do not preserve the localization properties of the input. As such, one often has to face a tradeoff between solution accuracy and computational effort. In this paper, we propose a novel edge sparsification heuristic that can provably preserve the localization properties of the original input. At the heart of our heuristic is a graph decomposition procedure, which allows us to identify certain sparse generically universally rigid subgraphs of the input graph. Our computational results show that the proposed approach can significantly reduce the computational and memory complexities of SDP-based algorithms for solving the sensor network localization problem. Moreover, it compares favorably with existing speedup approaches, both in terms of accuracy and solution time.

Probabilistic localization in sensor networks using distributed Kalman Filter

In recent years sensor networks have interested fields such as environment monitoring, surveillance and other distributed applications for data elaboration. This interest has been based on the decentralized approach in treating the information. However it is still a challenge to manipulate such streams of data when the dimension of the net becomes large despite computational capabilities and consumption constraints. In most of applications, location awareness is fundamental to accomplish common tasks. In this paper a probabilistic approach to solve localization problem in wireless sensor networks is presented. The algorithm, based on the Kalman Filter, estimates the sensors' location by an adaptive behavior. The technique proposed allows a reduction of the computation burden respect to the traditional Kalman Filter showing, as explained in simulations and real world experiments, good performances.

Formal Theory of Noisy Sensor Network Localization

Graph theory has been used to characterize the solvability of the sensor network localization problem. If sensors correspond to vertices and edges correspond to sensor pairs between which the distance is known, a significant result in the theory of range-based sensor network localization is that if the graph underlying the sensor network is generically globally rigid and there is a suitable set of anchors at known positions, then the network can be localized, i.e., a unique set of sensor positions can be determined that is consistent with the data. In particular, for planar problems, provided the sensor network has three or more noncollinear anchors at known points, all sensors are located at generic points, and the intersensor distances corresponding to the graph edges are precisely known rather than being subject to measurement noise, generic global rigidity of the graph is necessary and sufficient for the network to be localizable (in the absence of any further information). In practice, however, distance measurements will never be exact, and the equations whose solutions deliver sensor positions in the noiseless case in general no longer have a solution. This paper then argues that if the distance measurement errors are not too great and otherwise the associated graph is generically globally rigid and there are three or more noncollinear anchors, the network will be approximately localizable, in the sense that estimates can be found for the sensor positions which are near the correct values; in particular, a bound on the position errors can be found in terms of a bound on the distance errors. The sensor positions in this case can be found by minimizing a cost function which, although nonconvex, does have a global minimum.

3D Underwater Sensor Network Localization

We transform the 3D underwater sensor network (USN) localization problem into its 2D counterpart by employing sensor depth information and a simple projection technique. We first prove that a nondegenerative projection preserves network localizability. We then prove that given a network and a constant k, all of the geometric k-lateration localization methods are equivalent. Based on these results, we design a purely distributed bilateration localization scheme for 3D USNs termed as underwater sensor positioning (USP). Through extensive simulations, we show that USP has the following nice features: (1) improved localization capabilities over existing 3D methods, (2) low storage and computation requirements, (3) predictable and balanced communication overhead, and (4) robustness to errors from the underwater environment.

An range-free localization scheme for large scale underwater wireless sensor networks

In this paper, we study an area localization problem in large scale underwater wireless sensor networks (UWSNs). The limited bandwidth, the severely impaired channel and the cost of underwater equipment all make the underwater localization problem very challenging. Exact localization is very difficult for UWSNs in deep underwater environment. We propose a range free method based on mobile detachable elevator transceiver (DET) and 3D multi-power area localization scheme (3D-MALS) to address the challenging problem. In the proposed scheme, the ideas of 2D multi-power area localization scheme (2D-ALS) and utilizing DET are used to achieve the simplicity, location accuracy, scalability and low cost performances. The DET can rise and get down to broadcast its position. And it is assumed that all the underwater nodes underwater have pressure sensors and know their z coordinates. We evaluate the performances of 2D-ALS and our proposed 3D-MALS schemes under both ideal and non-ideal channel propagation conditions, in terms of localization error and localization ratio. The simulation results show that our proposed scheme is much more efficient than the 2D-ALS.

Efficient localization for large-scale underwater sensor networks

In this paper, we study the localization problem in large-scale underwater sensor networks. The adverse aqueous environments, the node mobility, and the large network scale all pose new challenges, and most current localization schemes are not applicable. We propose a hierarchical approach which divides the whole localization process into two sub-processes: anchor node localization and ordinary node localization. Many existing techniques can be used in the former. For the ordinary node localization process, we propose a distributed localization scheme which novelly integrates a 3-dimensional Euclidean distance estimation method with a recursive location estimation method. Simulation results show that our proposed solution can achieve high localization coverage with relatively small localization error and low communication overhead in large-scale 3-dimensional underwater sensor networks.

Force-directed hybrid PSO–SNTO algorithm for acoustic source localization in sensor networks

As a smart combination of particle swarm optimization (PSO) and sequential number-theoretic optimization (SNTO), a new hybrid PSO–SNTO algorithm is proposed to handle the initialization dependence of basic PSO algorithm. We then apply the hybrid algorithm to the acoustic source localization problem in sensor networks, which is modeled as a maximum likelihood estimation problem. Furthermore, a heuristic method based on virtual force is used to direct the particles of PSO to the global optimum, which can efficiently speed up the algorithm convergence. Simulation results demonstrate that the hybrid algorithm can achieve robust convergence with sophisticated estimation performance, and the convergence rate can be largely enhanced with the assistance of the force-directed heuristics.

Exploiting Sparsity in SDP Relaxation for Sensor Network Localization

A sensor network localization problem can be formulated as a quadratic optimization problem (QOP). For QOPs, semidefinite programming (SDP) relaxation by Lasserre with relaxation order 1 for general polynomial optimization problems (POPs) is known to be equivalent to the sparse SDP relaxation by Waki et al. with relaxation order 1, except for the size and sparsity of the resulting SDP relaxation problems. We show that the sparse SDP relaxation applied to the QOP is at least as strong as the Biswas-Ye SDP relaxation for the sensor network localization problem. A sparse variant of the Biswas-Ye SDP relaxation, which is equivalent to the original Biswas-Ye SDP relaxation, is also derived. We compare numerically the sparse SDP relaxation applied to the QOP, the Biswas-Ye SDP relaxation, its sparse variant, and the edge-based SDP relaxation by Wang et al. to confirm the effectiveness of the proposed techniques for exploiting the sparsity in SDP relaxation for sensor network localization problems. The sparse SDP relaxation applied to the QOP is much faster than the Biswas-Ye SDP relaxation, and the sparse variant of the Biswas-Ye SDP relaxation outperforms all other SDP relaxations in speed.

Sequential Localization of Sensor Networks

The sensor network localization problem with distance information is to determine the positions of all sensors in a network, given the positions of some of the sensors and the distances between some pairs of sensors. A definition is given for a sensor network in the plane to be “sequentially localizable.” It is shown that the graph of a sequentially localizable network must have a “bilateration ordering,” and a polynomial time algorithm is given for deciding whether or not a network's graph has such an ordering. A provably correct algorithm is given which consists of solving a sequence of quadratic equations, and it is shown that the algorithm can localize any localizable network in the plane whose graph has a bilateration ordering.

Distributed sensor network localization using SOCP relaxation

The goal of the sensor network localization problem is to determine positions of all sensor nodes in a network given certain pairwise noisy distance measurements and some anchor node positions. This paper describes a distributed localization algorithm based on second-order cone programming relaxation. We show that the sensor nodes can estimate their positions based on local information. Unlike previous approaches, we also consider the effect of inaccurate anchor positions. In the presence of anchor position errors, the localization is performed in three steps. First, the sensor nodes estimate their positions using information from their neighbors. In the second step, the anchors refine their positions using relative distance information exchanged with their neighbors and finally, the sensors refine their position estimates. We demonstrate the convergence of the algorithm numerically. Simulation study, for both uniform and irregular network topologies, illustrates the robustness of the algorithm to anchor position and distance estimation errors, and the performance gains achievable in terms of localization accuracy, problem size reduction and computational efficiency.