Approximate convex decomposition based localization in wireless sensor networks

Accurate localization in wireless sensor networks is the foundation for many applications, such as geographic routing and position-aware data processing. An important research direction for localization is to develop schemes using connectivity information only. These schemes primary apply hop counts to distance estimation. Not surprisingly, they work well only when the network topology has a convex shape. In this paper, we develop a new Localization protocol based on Approximate Convex Decomposition (ACDL). It can calculate the node virtual locations for a large-scale sensor network with arbitrary shapes. The basic idea is to decompose the network into convex subregions. It is not straight-forward, however. We first examine the influential factors on the localization accuracy when the network is concave such as the sharpness of concave angle and the depth of the concave valley. We show that after decomposition, the depth of the concave valley becomes irrelevant. We thus define concavity according to the angle at a concave point, which can reflect the localization error. We then propose ACDL protocol for network localization. It consists of four main steps. First, convex and concave nodes are recognized and network boundaries are segmented. As the sensor network is discrete, we show that it is acceptable to approximately identify the concave nodes to control the localization error. Second, an approximate convex decomposition is conducted. Our convex decomposition requires only local information and we show that it has low message overhead. Third, for each convex subsection of the network, an improved Multi-Dimensional Scaling (MDS) algorithm is proposed to compute a relative location map. Fourth, a fast and low complexity merging algorithm is developed to construct the global location map. Our simulation on several representative networks demonstrated that ACDL has localization error that is 60%-90% smaller as compared with the typical MDS-MAP algorithm and 20%-30% - maller as compared to a recent state-of-the-art localization algorithm CATL.Department of ComputingRefereed conference pape

Distributed Maximum Likelihood Sensor Network Localization

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks

DisLoc: A Convex Partitioning Based Approach for Distributed 3-D Localization in Wireless Sensor Networks

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