Localization in wireless sensor networks with gradient descent

Localization of wireless sensor networks is aimed at determining the positions of all sensors in a network, usually given a few connected anchor nodes' positions and certain relative measurements, where the latter could be pairwise distance measurements among directly connected neighbors as considered in this paper. In this paper we investigate neighborhood collaboration based distributed cooperative localization of all sensors in a particular network with the so-called `convex hull constraint': all nodes in such a network are either position-known anchors or sensors to be localized, and every sensor is inside the convex hull of its neighbors. For such a practically widely seen thus important class of localizable wireless sensor networks, we propose three iterative self-positioning algorithms, for independent implementation at all individual sensors of the considered network. Analysis and simulation study show that when iteratively running at all sensors of the considered network, i) the first one of our proposed iterative self-positioning algorithms leads to global convergence, where the converged solution is the correct positions of all sensors in the absence of measurement error, but might not be optimum if there exist measurement errors; ii) the second algorithm suffers from local convergence, but once correctly converged the converged solution would be the least squares (LS) solution; iii) the third algorithm, a combined version that switches between the former two algorithms' iterations efficiently and independently at individual sensors based on locally collected information, globally converges to the LS solution, as long as the measurement errors are sufficiently small such that the converged solution by the first algorithm is well inside the correctly converging area of the second algorithm.

Sensor localization in wireless sensor networks is an important component of many applications. Previous work has demonstrated how localization can be achieved using various methods. In this paper we focus on achieving fine-grained localization that does not require external infrastructure, specialized hardware support, or excessive sensor resources. We use a real sensor network and provide measurements on the actual system. We adopt a localization approach that relies on acoustic sounds and clock synchronization. The contribution of our work is achieving consistent sound pulse detection at each sensor and precise range estimation using a high-precision clock synchronization implementation. We first describe our technique and then we evaluate our approach using a real setup. Our results show that our approach achieves an average clock synchronization accuracy of 5μs. We verify this accuracy using an external global clock via an interrupt mechanism. Our sound detection technique is able to consistently identify sound pulses up to 10m distances in indoor environments. Combining the two techniques, we find that our localization method results in accurate range estimation with an average error of 11cm in distances up to 7m and in consistent range estimation up to 10m in various indoor environments.

A fundamental problem in wireless sensor networks is localization -- the determination of the geographical locations of sensors. Most existing localization algorithms were designed to work well either in networks of static sensors or networks in which all sensors are mobile. In this paper, we propose two localization algorithms, MSL and MSL*, that work well when any number of sensors are static or mobile. MSL and MSL* are range-free algorithms -- they do not require that sensors are equipped with hardware to measure signal strengths, angles of arrival of signals or distances to other sensors. We present simulation results to demonstrate that MSL and MSL* outperform existing algorithms in terms of localization error in very different mobility conditions. MSL* outperforms MSL in most scenarios, but incurs a higher communication cost. MSL outperforms MSL* when there is significant irregularity in the radio range. We also point out some problems with a well known lower bound for the error in any range-free localization algorithm in static sensor networks.

Sensor localization is a fundamental and crucial issue for wireless sensor networks operation and management. Accurate self-localization capability is highly desirable in wireless sensor network. A fundamental problem in distance-based sensor network localization is whether a given sensor network is uniquely localizable or not. Flip ambiguity is a main problem that can make the sensor network not uniquely localized. It causes large errors in the location estimates. This paper proposes a method in which the localization is done through two steps. During the first step, tabu search (TS) is used to obtain an accurate estimation of the nodes' location. During the second step, simulated annealing algorithm (SAA) is used to refine the location estimates of those nodes that are likely to have flip ambiguity problem. The simulation results confirm that the proposed algorithm has better performance than that of the existing algorithms.

This chapter describes one of the major challenges in technology advancement of Wireless Sensor Networks (WSNs), i.e., Localization in WSNs. In recent years, sensor node localization is an emerging research area in WSNs. The sensor data become useless, if we do not know the location of the reporting node. Coordinates determination of the sensor node is a challenging problem and it is referred as localization problem. The nodes which has unknown coordinates is termed as target Nodes. Various localization methods can be utilized to find out the location of sensor nodes, those coordinates are not known in a system/network. Efficient WSN localization can be treated as multi-dimensional optimization problem which can be addressed through population based stochastic techniques, which involves the minimization of a function of differences between Euclidean and measured distance between sensor nodes. In this chapter various connectivity, range information and mobility based localization algorithms have been discussed. For optimizing the results of these algorithms, various computational intelligence (CI) based optimizing algorithms like Particle Swarm Optimization, Biogeography Based Optimization, Firefly Algorithm and Genetic Algorithm have been discussed. A choice between these algorithm is influenced by the localization accuracy expected to be and convergence rate.

SummaryIndoor localization in wireless sensor networks is a challenging task. Static localization and moving target monitoring are addressed using ensemble learning method and received signal strength indicator. The suggested strategy combines several regression trees to have better performance. This solution has been experimentally evaluated using real measurements in an office room. The performance results have been analyzed through a comparison with learning‐based localization algorithms currently available in the literature. The analysis shows that the adopted solution is simple in term of computation, accurate and robust to environmental variation.

In this paper, a distributed algorithm for localization and tracking in wireless sensor network is designed and implemented. Combining the fingerprint approach and subgradient optimization, the proposed algorithm, called golf algorithm, uses different strategies to attain fast movement for tracking a moving object and a fine tune to approach a stationary object, like a drive and a putt on the putting green in the golf. Based on the WLS objective function, a recursive form for both the fingerprint approach and subgradient optimization is derived and can be accomplished by anchor nodes in collaboration. From simulation results, we can see the proposed algorithm has better estimation performance than the conventional decentralized algorithms to localize a stationary or moving target in large wireless sensor networks. In addition, its hardware architecture is designed. The CORDIC operation is employed to compute the vector norm. Parallel processing is used to handle the calculation of fingerprint data. The tracking trajectories of the floating-point program and fixed-point hardware implementation are shown to be quite similar with small finite precision effect, which verifies the feasibility of this hardware solution.

The paper describes a concept of software tool for development of nodes localization in large wireless sensor network. The basic module is the event driven simulator that enables loading position of wireless network nodes, description of the behavior of nodes, description of the environment and modeling of wave propagation in defined space. Node localization and deployment problem in wireless sensor network are supported by implemented algorithms.

We propose a novel approach to the source localization and tracking problem in wireless sensor networks. By applying minimax approximation and semidefinite relaxation, we transform the traditionally nonlinear and nonconvex problem into convex optimization problems for two different source localization models involving measured distance and received signal strength. Based on the problem transformation, we develop a fast low-complexity semidefinite programming (SDP) algorithm for two different source localization models. Our algorithm can either be used to estimate the source location or be used to initialize the original nonconvex maximum likelihood algorithm.

Localization, the determination of geographical location of sensors is a fundamental problem in wireless sensor networks. In this paper we consider a static wireless network in which the nodes are static-non moving. We propose a positioning method which combines linear frequency modulation continuous wave (FMCW) technique and time frequency difference of arrival (TFDA) method. We conduct simulation experiments to evaluate the performance of these methods. The relationships among measurement resolution, the sweep bandwidth and the sampling frequency are investigated. Results show that the proposed method achieves good performance on position accuracy.

Recent works show that the Hilbert curve path for mobile-beacon-based localization in sensor networks has better accuracy than other approaches, such as randomized and circular paths. In this paper, the modified Hilbert curve path is introduced, and its theoretical lower bound error, compared with the basic Hilbert curve path, has been shown using Cramér–Rao lower bound analysis. It is shown that the proposed approach has a more uniform localization accuracy across all the nodes in the environment than the basic Hilbert approach. The simulation results show that this approach, combined with inter-node communication, provides better and close to uniform accuracy compared with previously proposed approaches.

In this paper, we propose a new maximum-likelihood (ML) target location estimator which uses quantized sensor data and wireless channel statistics in a wireless sensor network. The novelty of our approach comes from the fact that imperfect channel statistics between wireless sensors and the fusion center are incorporated in the localization algorithm. We call this approach target localization. Furthermore, we derive the Cramer-Rao lower bound as a performance bound for our channel-aware ML estimator. Simulation results are presented to show that the performance of the channel-aware ML location estimator is quite close to its theoretical performance bound even with relatively small number of sensors and it has superior performance compared to that of the channel-unaware ML estimator.

Similar to many technological developments, wireless sensor networks have emerged from military needs and found its way into civil applications. Today wireless sensor networks has become a key technology for different kinds of smart environments and an intense research effort is currently underway to enable the application of wireless sensor networks for a wide range of industrial problems. Wireless networks are of a particular importance when a large number of sensor nodes have to be deployed and/or in hazardouse situations. The research field in this paper is supposed to be on this issue that a lot of these sensors are distributed randomly and just a few of them are aware of their position [e.g. by GPS]. The purpose is to determine the best way that allows all the nodes to find their position. This paper presents an effective geometric algorithm for localization. Result of implementation show that this algorithm can be a better substitution for current methods because of lower expense and simple implementation.

Accurate localization in wireless sensor networks (WSNs) is fundamental to many applications, such as geographic routing and position-aware data processing. This, however, is challenging in large scale 3-D WSNs due to the irregular topology, such as holes in the path, of the network. The irregular topology may cause overestimated Euclidean distance between nodes as the communication path is bent and accordingly introduces severe errors in 3-D WSN localization. As an effort towards the issue, this paper develops a distributed algorithm to achieve accurate 3-D WSN localization. Our proposal is composed of two steps, segmentation and joint localization. In specific, the entire network is first divided into several subnetworks by applying the approximate convex partitioning. A spatial convex node recognition mechanism is developed to assist the network segmentation, which relies on the connectivity information only. After that, each subnetwork is accurately localized by using the multidimensional scaling-based algorithm. The proposed localization algorithm also applies a new 3-D coordinate transformation algorithm, which helps reduce the errors introduced by coordinate integration between subnetworks and improve the localization accuracy. Using extensive simulations, we show that our proposal can effectively segment a complex 3-D sensor network and significantly improve the localization rate in comparison with existing solutions.

In recent years node localization in wireless sensor networks (WSNs) has attracted much attention due to the increase of usage and applications of WSNs. Many algorithms and techniques for locating sensor nodes have been proposed in the literature. A recent algorithm, which is based on a given set of pairwise distance estimates among nodes and the target, generates a map of node locations. This algorithm, known as FastMap, uses projections onto orthogonal hyperplanes to find the coordinates successively. In this paper, we analytically study the performance of the FastMap algorithm for 2D positioning. Moreover a modified version of FastMap with better performance is proposed and analyzed. The analysis shows that the optimum anchor placement should be at the edge of the network.