Accurate and low-cost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. Low-power wireless sensors may be many hops away from any other sensors with a priori location information. In cooperative localization, sensors work together in a peer-to-peer manner to make measurements and then form a map of the network. Various application requirements (such as scalability, energy efficiency, and accuracy) will influence the design of sensor localization systems. In this article, we describe measurement-based statistical models useful to describe time-of-arrival (TOA), angle-of-arrival (AOA), and received-signal-strength (RSS) measurements in wireless sensor networks. Wideband and ultra-wideband (UWB) measurements, and RF and acoustic media are also discussed. Using the models, we show how to calculate a Cramér-Rao bound (CRB) on the location estimation precision possible for a given set of measurements. This is a useful tool to help system designers and researchers select measurement technologies and evaluate localization algorithms. We also briefly survey a large and growing body of sensor localization algorithms. This article is intended to emphasize the basic statistical signal processing background necessary to understand the state-of-the-art and to make progress in the new and largely open areas of sensor network localization research.

Abstract — This paper presents a study of how empirical ranging characteristics affect multihop localization in wireless sensor networks. We use an objective metric to evaluate a well-established parametric model of ranging called Noisy Disk: if the model accurately predicts the results of a real-world deployment, it sufficiently captures ranging characteristics. When the model does not predict accurately, we systematically replace components of the model with empirical ranging characteristics to identify which components contribute to the discrepancy. We reveal that both the connectivity and noise components of Noisy Disk fail to accurately represent real-world ranging characteristics and show that these shortcomings affect localization in different ways under different circumstances. I.

Determining the positions of the sensor nodes in a network is essential to many network functionalities such as routing, coverage and tracking, and event detection. The localization problem for sensor networks is to reconstruct the positions of all of the sensors in a network, given the distances between all pairs of sensors that are within some radius r of each other. In the past few years, many algorithms for solving the localization problem were proposed, without knowing the computational complexity of the problem. In this paper, we show that no polynomial-time algorithm can solve this problem in the worst case, even for sets of distance pairs for which a unique solution exists, unless RP = NP. We also discuss the consequences of our result and present open problems.

We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior–point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in R 2 using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable sub–networks in the input network. 1

An SDP relaxation based method is developed to solve the localization problem in sensor networks using incomplete and inaccurate distance information. The problem is set up to find a set of sensor positions such that given distance constraints are satisfied. The nonconvex constraints in the formulation are then relaxed in order to yield a semidefinite program which can be solved efficiently. The basic model is extended in order to account for noisy distance information. In particular, a maximum likelihood based formulation and an interval based formulation are discussed. The SDP solution can then also be used as a starting point for steepest descent based local optimization techniques that can further refine the SDP solution. We also describe the extension of the basic method to develop an iterative distributed SDP method for solving very large scale semidefinite programs that arise out of localization problems for large dense networks and are intractable using centralized methods. The performance evaluation of the technique with regard to estimation accuracy and computation time is also presented by the means of extensive simulations. Our SDP scheme also seems to be applicable to solving other Euclidean geometry problems where points are locally connected.

In many applications of wireless ad hoc and sensor networks, position-awareness is of great importance. Often, as in the case of geometric routing, it is sufficient to have virtual coordinates, rather than real coordinates. In this paper, we address the problem of obtaining virtual coordinates based on connectivity information. In particular, we propose the first approximation algorithm for this problem and discuss implementational aspects.

Sensor positioning is a crucial part of many location-dependent applications that utilize wireless sensor networks (WSNs). Current localization approaches can be divided into two groups: range-based and range-free. Due to the high costs and critical assumptions, the range-based schemes are often impractical for WSNs. The existing range-free schemes, on the other hand, suffer from poor accuracy and low scalability. Without the help of a large number of uniformly deployed seed nodes, those schemes fail in anisotropic WSNs with possible holes. To address this issue, we propose the Rendered Path (REP) protocol. To the best of our knowledge, REP is the only range-free protocol for locating sensors with constant number of seeds in anisotropic sensor networks.

Several protocols have been proposed to defend against wormholes in ad hoc networks by adopting positioning devices, synchronized clocks, or directional antennas. In this paper, we propose a mechanism, MDS-VOW, to detect wormholes in a sensor network. MDS-VOW first reconstructs the layout of the sensors using multi-dimensional scaling. To compensate the distortions caused by distance measurement errors, a surface smoothing scheme is adopted. MDS-VOW then detects the wormhole by visualizing the anomalies introduced by the attack. The anomalies, which are caused by the fake connections through the wormhole, bend the reconstructed surface to pull the sensors that are faraway to each other. Through detecting the bending feature, the wormhole is located and the fake connections are identified. The contributions of MDS-VOW are: (1) it does not require the sensors to be equipped with special hardware, (2) it adopts and combines the techniques from social science, computer graphics, and scientific visualization to attack the problem in network security. We examine the accuracy of the proposed mechanism when the sensors are deployed in a circle area and one wormhole exists in the network. The results show that MDS-VOW has a low false alarm ratio when the distance measurement errors are not large.

Abstract — Knowing the positions of the nodes in a network is essential to many next generation pervasive and sensor network functionalities. Although many network localization systems have recently been proposed and evaluated, there has been no systematic study of partially localizable networks, i.e., networks in which there exist nodes whose positions cannot be uniquely determined. There is no existing study which correctly identifies precisely which nodes in a network are uniquely localizable and which are not. This absence of a sufficient uniqueness condition permits the computation of erroneous positions that may in turn lead applications to produce flawed results. In this paper, in addition to demonstrating the relevance of networks that may not be fully localizable, we design the first framework for two dimensional network localization with an efficient component to correctly determine which nodes are localizable and which are not. Implementing this system, we conduct comprehensive evaluations of network localizability, providing guidelines for both network design and deployment. Furthermore, we study an integration of traditional geographic routing with geographic routing over virtual coordinates in the partially localizable network setting. We show that this novel cross-layer integration yields good performance, and argue that such optimizations will be likely be necessary to ensure acceptable application performance in partially localizable networks. I.

In this paper we provide a theoretical foundation for the problem of network localization in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors. We construct grounded graphs to model network localization and apply graph rigidity theory to test the conditions for unique localizability and to construct uniquely localizable networks. We further study the computational complexity of network localization and investigate a subclass of grounded graphs where localization can be computed efficiently. We conclude with a discussion of localization in sensor networks where the sensors are placed randomly.