Sensor Network Localization Problem Research Articles

Loraine – an interior-point solver for low-rank semidefinite programming

The aim of this paper is to introduce a new code for the solution of large-and-sparse linear semidefinite programs (SDPs) with low-rank solutions or solutions with few outlying eigenvalues, and/or problems with low-rank data. We propose to use a preconditioned conjugate gradient method within an interior-point SDP algorithm and an efficient preconditioner fully utilizing the low-rank information. The efficiency is demonstrated by numerical experiments using the truss topology optimization problems, Lasserre relaxations of the MAXCUT problems and the sensor network localization problems.

A Hybrid STA Based on Nelder–Mead Simplex Search and Quadratic Interpolation

State transition algorithm (STA) is a metaheuristic method for global optimization. However, due to the insufficient utilization of historical information, it still suffers from slow convergence speed and low solution accuracy on specific problems in the later stages. This paper proposes a hybrid STA based on Nelder–Mead (NM) simplex search and quadratic interpolation (QI). In the exploration stage, NM simplex search utilizes the historical information of STA to generate promising solutions. In the exploitation stage, QI utilizes the historical information to enhance the local search capacity. The proposed method uses an eagle strategy to maximize the efficiency and stability. The proposed method successfully combines the merits of the three distinct approaches: the powerful exploration capacity of STA, the fast convergence speed of NM simplex search and the strong exploitation capacity of QI. The hybrid STA is evaluated using 15 benchmark functions with dimensions of 20, 30, 50 and 100. Moreover, the results are statistically analyzed using the Wilcoxon signed-rank sum test. In addition, the applicability of the hybrid STA to solve real-world problems is assessed using the wireless sensor network localization problem. Compared with six state-of-the-art metaheuristic methods, the experimental results demonstrate the superiority and effectiveness of the proposed method.

Efficient Rigid Body Localization Based on Euclidean Distance Matrix Completion for AGV Positioning Under Harsh Environment

In real-world applications for automatic guided vehicle (AGV) navigation, the positioning system based on the time-of-flight (TOF) measurements between anchors and tags is confronted with the problem of insufficient measurements caused by blockages to radio signals or lasers, etc. Mounting multiple tags at different positions of the AGV to collect more TOFs is a feasible solution to tackle this difficulty. Vehicle localization by exploiting the measurements between multiple tags and anchors is a rigid body localization (RBL) problem, which estimates both the position and attitude of the vehicle. However, the state-of-the-art solutions to the RBL problem do not deal with missing measurements, and thus will result in degraded localization availability and accuracy in harsh environments. In this paper, different from these existing solutions for RBL, we model this problem as a sensor network localization problem with missing TOFs. To solve this problem, we propose a new efficient RBL solution based on Euclidean distance matrix (EDM) completion, abbreviated as ERBL-EDMC. Firstly, we develop a method to determine the upper and lower bounds of the missing measurements to complete the EDM reliably, using the known relative positions between tags and the statistics of the TOF measurements. Then, based on the completed EDM, the global tag positions are obtained from a coarse estimation followed by a refinement step assisted with inter-tag distances. Finally, the optimal vehicle position and attitude are obtained iteratively based on the estimated tag positions from the previous step. Theoretical analysis and simulation results show that the proposed ERBL-EDMC method effectively solves the RBL problem with incomplete measurements. It obtains the optimal positioning results while maintaining low computational complexity compared with the existing RBL methods based on semi-definite relaxation.

A Multi-Strategy Improved Sparrow Search Algorithm for Solving the Node Localization Problem in Heterogeneous Wireless Sensor Networks

Aiming at the problems of slow convergence and low accuracy of the traditional sparrow search algorithm (SSA), a multi-strategy improved sparrow search algorithm (ISSA) was proposed. Firstly, the golden sine algorithm was introduced in the location update of producers to improve the global optimization capability of SSA. Secondly, the idea of individual optimality in the particle swarm algorithm was introduced into the position update of investigators to improve the convergence speed. At the same time, a Gaussian disturbance was introduced to the global optimal position to prevent the algorithm from falling into the local optimum. Then, the performance of the ISSA was evaluated on 23 benchmark functions, and the results indicate that the improved algorithm has better global optimization ability and faster convergence. Finally, ISSA was used for the node localization of HWSNs, and the experimental results show that the localization algorithm with ISSA has a smaller average localization error than that of the localization algorithm with other meta-heuristic algorithms.

A block coordinate descent method for sensor network localization

The problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank constraint into a product of two matrices via the Burer–Monteiro factorization. Then, we add the difference of the two matrices, with a penalty parameter, to the objective function, thereby reformulating SNL as an unconstrained multiconvex optimization problem, to which we apply the block coordinate descent method. In this paper, we also provide theoretical analyses of the proposed method and show that each subproblem that is solved sequentially by the block coordinate descent method can also be solved analytically, with the sequence generated by our proposed algorithm converging to a stationary point of the objective function. We also give a range of the penalty parameter for which the two matrices used in the factorization agree at any accumulation point. Numerical experiments confirm that the proposed method does inherit the rank constraint and that it estimates sensor positions faster than other methods without sacrificing the estimation accuracy, especially when the measured distances contain errors.

A hybrid fuzzy weighted centroid and extreme learning machine with crow‐particle optimization approach for solving localization problem in wireless sensor networks

SummaryThe sensor nodes localization is very advantageous in wireless sensor network (WSN). This allows effective data transfer between the sensor node networks. Therefore, it saves energy and prolongs network life. Here, a hybrid FWCELM‐CPO method is proposed for solving the sensor node localization problem in WSN. The proposed hybrid method is executed in MATLAB, and the performance is analyzed with different existing algorithms like centroid, fuzzy centroid, and ELM. The simulation results show that the proposed FWCELM‐CPO method attains the higher detection rate of 14.117%, 5.435%, and 11.494%, higher segmentation accuracy of 9.556%, 26.41%, and 16%, lower execution time of 66.667%, 75%, and 70.37%, higher segmented region of 65.957%, 20%, and 44.444%, and higher precision of 34.72%, 18.29%, and 8.78% compared to the existing algorithms. The simulation results demonstrate that the proposed method can be able to find the optimal global solutions efficiently with accurately.

STRONG: Synchronous and asynchronous robust network localization, under non-Gaussian noise

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data — data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where, despite the abundance of technical literature, prior research seldom considered outlier data. We propose robust, fast, and distributed network localization algorithms, resilient to high-power noise, but also precise under regular Gaussian noise. We use a Huber M-estimator, thus obtaining a robust (but nonconvex) optimization problem. We convexify and change the problem representation, to allow for distributed robust localization algorithms: a synchronous distributed method that has optimal convergence rate and an asynchronous one with proven convergence guarantees. A major highlight of our contribution lies on the fact that we pay no price for provable distributed computation neither in accuracy, nor in communication cost or convergence speed. Simulations showcase the superior performance of our algorithms, both in the presence of outliers and under regular Gaussian noise: our method exceeds the accuracy of alternative approaches, distributed and centralized, even under heavy additive and multiplicative outlier noise.

Cooperative Localization Using Distance Measurements for Mobile Nodes.

This paper considers the two-dimensional (2D) anchorless localization problem for sensor networks in global positioning system (GPS)-denied environments. We present an efficient method, based on the multidimensional scaling (MDS) algorithm, in order to estimate the positions of the nodes in the network using measurements of the inter-node distances. The proposed method takes advantage of the mobility of the nodes to address the location ambiguity problem, i.e., rotation and flip ambiguity, which arises in the anchorless MDS algorithm. Knowledge of the displacement of the moving node is used to produce an analytical solution for the noise-free case. Subsequently, a least squares estimator is presented for the noisy scenario and the associated closed-form solution derived. The simulations show that the proposed algorithm accurately and efficiently estimates the locations of nodes, outperforming alternative methods.

Alternating Minimization Based First-Order Method for the Wireless Sensor Network Localization Problem

We propose an algorithm for the Wireless Sensor Network localization problem, which is based on the well-known algorithmic framework of Alternating Minimization. We start with a non-smooth and non-convex minimization, and transform it into an equivalent smooth and non-convex problem, which stands at the heart of our study. This paves the way to a new method which is globally convergent: not only does the sequence of objective function values converge, but the sequence of the location estimates also converges to a unique location that is a critical point of the corresponding (original) objective function. The proposed algorithm has a range of fully distributed to fully centralized implementations, which all have the property of global convergence. The algorithm is tested over several network configurations, and it is shown to produce more accurate solutions within a shorter time relative to existing methods.

A Geometric Approach for Distributed Multi-Hop Target Localization in Cooperative Networks

This work addresses target localization problem in cooperative distributed sensor networks, in which all sensors are capable of measuring Received Signal Strength (RSS), but only some are appropriately equipped to measure Angle Of Arrival (AOA) of the received signal. A novel approach based on simple geometry and multi-hopping is proposed, which allows for natural conversion of the problem into a Generalized Trust Region Sub-Problem (GTRS). The proposed algorithm comprises three main steps, each of them with linear computational cost in the number of neighbors, making it suitable for real-time applications. Our simulation results validate the performance of the new algorithm, surpassing some significantly more complex ones, and almost achieving a lower bound set by an existing algorithm which uses some (unrealistic) assumptions in its favor.

Sensor Network Localization via Alternating Rank Minimization Algorithms

Sensor network localization (SNL) is to determine physical coordinates of all sensors in a network given global coordinates of anchors and available measurements among sensors and anchors. Two challenges related to SNL are to find conditions leading to a uniquely localizable network and develop effective and efficient methods to solve SNL problems. This work first proves that infinitesimal rigidity, together with some mild conditions, is sufficient for unique localizability of a network considering additional relationships between nonadjacent sensors. On the other hand, solving an SNL problem is generally NP-hard due to its nonconvex constraints. Instead of ignoring the rank constraint used in existing relaxation methods, we convert the rank constraint in the SNL problem into its equivalent constraints and solve it alternatively by proposing the alternating rank minimization algorithm (ARMA). We start with the centralized ARMA to solve the exact SNL problem. Next, to improve the scalability for solving large-scale SNL problems, ARMA is extended in a distributed manner by decomposing the original problem into a group of subproblems, which can be solved independently. Finally, simulation cases are provided for both centralized and distributed ARMA to validate the improved localization accuracy, efficiency, and robustness by being compared to the state-of-the-art localization methods.

Performance of Elephant Herding Optimization and Tree Growth Algorithm Adapted for Node Localization in Wireless Sensor Networks.

Wireless sensor networks, as an emerging paradigm of networking and computing, have applications in diverse fields such as medicine, military, environmental control, climate forecasting, surveillance, etc. For successfully tackling the node localization problem, as one of the most significant challenges in this domain, many algorithms and metaheuristics have been proposed. By analyzing available modern literature sources, it can be seen that the swarm intelligence metaheuristics have obtained significant results in this domain. Research that is presented in this paper is aimed towards achieving further improvements in solving the wireless sensor networks localization problem by employing swarm intelligence. To accomplish this goal, we have improved basic versions of the tree growth algorithm and the elephant herding optimization swarm intelligence metaheuristics and applied them to solve the wireless sensor networks localization problem. In order to determine whether the improvements are accomplished, we have conducted empirical experiments on different sizes of sensor networks ranging from 25 to 150 target nodes, for which distance measurements are corrupted by Gaussian noise. Comparative analysis with other state-of-the-art swarm intelligence algorithms that have been already tested on the same problem instance, the butterfly optimization algorithm, the particle swarm optimization algorithm, and the firefly algorithm, is conducted. Simulation results indicate that our proposed algorithms can obtain more consistent and accurate locations of the unknown target nodes in wireless sensor networks topology than other approaches that have been proposed in the literature.

RSS-Based Target Localization in Underwater Acoustic Sensor Networks via Convex Relaxation.

The received signal strength (RSS) based target localization problem in underwater acoustic wireless sensor networks (UWSNs) is considered. Two cases with respect to target transmit power are considered. For the first case, under the assumption that the reference of the target transmit power is known, we derive a novel weighted least squares (WLS) estimator by using an approximation to the RSS expressions, and then transform the originally non-convex problem into a mixed semi-definite programming/second-order cone programming (SD/SOCP) problem for reaching an efficient solution. For the second case, there is no knowledge on the target transmit power, and we treat the reference power as an additional unknown parameter. In this case, we formulate a WLS estimator by using a further approximation, and present an iterative ML and mixed SD/SOCP algorithm for solving the derived WLS problem. For both cases, we also derive the closed form expressions of the Cramer–Rao Lower Bounds (CRLBs) on root mean square error (RMSE). Computer simulation results show the superior performance of the proposed methods over the existing ones in the underwater acoustic environment.

Efficient Deterministic Algorithm for Huge-Sized Noisy Sensor Localization Problems via Canonical Duality Theory

This paper presents a new deterministic method and a polynomial-time algorithm for solving general huge-sized sensor network localization problems. The problem is first formulated as a nonconvex minimization, which was considered as an NP-hard based on conventional theories. However, by the canonical duality theory, this challenging problem can be equivalently converted into a convex dual problem. By introducing a new optimality measure, a powerful canonical primal-dual interior (CPDI) point algorithm is developed which can solve efficiently huge-sized problems with hundreds of thousands of sensors. The new method is compared with the popular methods in the literature. Results show that the CPDI algorithm is not only faster than the benchmarks but also much more accurate on networks affected by noise on the distances.

An exact penalty method for semidefinite-box-constrained low-rank matrix optimization problems

AbstractThis paper considers a matrix optimization problem where the objective function is continuously differentiable and the constraints involve a semidefinite-box constraint and a rank constraint. We first replace the rank constraint by adding a non-Lipschitz penalty function in the objective and prove that this penalty problem is exact with respect to the original problem. Next, for the penalty problem we present a nonmonotone proximal gradient (NPG) algorithm whose subproblem can be solved by Newton’s method with globally quadratic convergence. We also prove the convergence of the NPG algorithm to a first-order stationary point of the penalty problem. Furthermore, based on the NPG algorithm, we propose an adaptive penalty method (APM) for solving the original problem. Finally, the efficiency of an APM is shown via numerical experiments for the sensor network localization problem and the nearest low-rank correlation matrix problem.

Phase Retrieval via Sensor Network Localization

The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast theoretical and algorithmic literature on the latter to tackle the former. Leveraging this connection, we develop a two-stage algorithm for phase retrieval that can provably recover the desired signal. In both sparse and dense settings, our proposed algorithm improves upon prior approaches simultaneously in the number of required measurements for recovery and the reconstruction time. We present numerical results to corroborate our theory and to demonstrate the efficiency of the proposed algorithm. As a side result, we propose a new form of phase retrieval problem and connect it to the complex rigidity theory proposed by Gortler and Thurston (in: Connelly R, Ivic Weiss A, Whiteley W (eds) Rigidity and symmetry, Springer, New York, pp 131–154, 2014).

Average Quasi-Consensus Algorithm for Distributed Constrained Optimization: Impulsive Communication Framework.

This paper presents the impulsive average quasi-consensus algorithm for distributed constrained convex optimization. First, the constrained optimization problem can be transformed into an unconstrained problem using the interior point method, and then a distributed algorithm is modeled by means of impulsive differential equation. In the framework of the continuous-time gradient method and algebraic graph theory, each agent can deal with one local objective function with local constraints. At the impulsive instants, each agent can communicate with its neighboring agents over the network. Under certain conditions, the impulsive average quasi-consensus is achieved. It is shown that the state of average quasi-consensus is the optimal solution of the aforementioned unconstrained optimization problem, and the state of each agent can also reach the neighborhood of the optimal solution. Finally, two numerical examples show the effectiveness of the proposed impulsive average quasi-consensus algorithm. Moreover, the feasibility of the approach is verified by an application to one sensor network localization problem.

Efficient linear fusion of partial estimators

Many signal processing applications require performing statistical inference on large datasets, where computational and/or memory restrictions become an issue. In this big data setting, computing an exact global centralized estimator is often either unfeasible or impractical. Hence, several authors have considered distributed inference approaches, where the data are divided among multiple workers (cores, machines or a combination of both). The computations are then performed in parallel and the resulting partial estimators are finally combined to approximate the intractable global estimator. In this paper, we focus on the scenario where no communication exists among the workers, deriving efficient linear fusion rules for the combination of the distributed estimators. Both a constrained optimization perspective and a Bayesian approach (based on the Bernstein–von Mises theorem and the asymptotic normality of the estimators) are provided for the derivation of the proposed linear fusion rules. We concentrate on finding the minimum mean squared error (MMSE) global estimator, but the developed framework is very general and can be used to combine any type of unbiased partial estimators (not necessarily MMSE partial estimators). Numerical results show the good performance of the algorithms developed, both in problems where analytical expressions can be obtained for the partial estimators, and in a wireless sensor network localization problem where Monte Carlo methods are used to approximate the partial estimators.

Rigid graph-based three-dimension localization algorithm for wireless sensor networks

This paper investigates the node localization problem for wireless sensor networks in three-dimension space. A distributed localization algorithm is presented based on the rigid graph. Before location, the communication radius is adaptively increasing to add the localizability. The localization process includes three steps: firstly, divide the whole globally rigid graph into several small rigid blocks; secondly, set up the local coordinate systems and transform them to global coordinate system; finally, use the quadrilateration iteration technology to locate the nodes in the wireless sensor network. This algorithm has the advantages of low energy consumption, low computational complexity as well as high expandability and high localizability. Moreover, it can achieve the unique and accurate localization. Finally, some simulations are provided to demonstrate the effectiveness of the proposed algorithm.

A Support Vector Learning-Based Particle Filter Scheme for Target Localization in Communication-Constrained Underwater Acoustic Sensor Networks.

Target localization, which aims to estimate the location of an unknown target, is one of the key issues in applications of underwater acoustic sensor networks (UASNs). However, the constrained property of an underwater environment, such as restricted communication capacity of sensor nodes and sensing noises, makes target localization a challenging problem. This paper relies on fractional sensor nodes to formulate a support vector learning-based particle filter algorithm for the localization problem in communication-constrained underwater acoustic sensor networks. A node-selection strategy is exploited to pick fractional sensor nodes with short-distance pattern to participate in the sensing process at each time frame. Subsequently, we propose a least-square support vector regression (LSSVR)-based observation function, through which an iterative regression strategy is used to deal with the distorted data caused by sensing noises, to improve the observation accuracy. At the same time, we integrate the observation to formulate the likelihood function, which effectively update the weights of particles. Thus, the particle effectiveness is enhanced to avoid “particle degeneracy” problem and improve localization accuracy. In order to validate the performance of the proposed localization algorithm, two different noise scenarios are investigated. The simulation results show that the proposed localization algorithm can efficiently improve the localization accuracy. In addition, the node-selection strategy can effectively select the subset of sensor nodes to improve the communication efficiency of the sensor network.