EFFECT OF RIGIDITY ON TRILATERATION TECHNIQUE FOR LOCALIZATION IN WIRELESS SENSOR NETWORKS (original) (raw)

Rigidity, Computation, and Randomization in Network Localization

IEEE INFOCOM, 2004

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.

Further results on sensor network localization using rigidity

Proceeedings of the Second European Workshop on Wireless Sensor Networks, 2005., 2005

Two further results, which extend the previous work on the use of rigidity in sensor network localization, are given, The previous work provided the conditions for the localization of an entire network in which some nodes know their locations and other nodes determine their locations by measuring the distances to their neighbors, First, the paper gives the conditions for partial localization of a subnetwork when an entire network i s not localizable. Second, the paper gives the conditions for localization in which some nodes know their locations and other nodes determine their locations by measuring the bearings (angle of arrivals) to their neighbors rather than the distances. 0-7803-880 1-1/05/$20.00 (c)2005 IEEE.

A Theory of Network Localization

IEEE Transactions on Mobile Computing, 2006

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.

A theoretical analysis of the conditions for unambiguous node localization in sensor networks

2004

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 distances or bearings to their neighbors. Distance information is the separation between two nodes connected by a sensing/communication link. Bearing is the angle between a sensing/communication link and the x-axis of a node's local coordinate system. We construct grounded graphs to model network localization and apply graph rigidity theory and parallel drawings to test the conditions for unique localizability and to construct uniquely localizable networks. We further investigate partially localizable networks.

On the Computational Complexity of Sensor Network Localization

Algorithmic Aspects of Wireless Sensor Networks, 2004

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.

Distributed Localization of Wireless Sensor Network Using Communication Wheel

Algorithms for Sensor Systems, 2020

We study the network localization problem, i.e., the problem of determining node positions of a wireless sensor network modeled as a unit disk graph. In an arbitrarily deployed network, positions of all nodes of the network may not be uniquely determined. It is known that even if the network corresponds to a unique solution, no polynomial-time algorithm can solve this problem in the worst case, unless RP = NP. So we are interested in algorithms that efficiently localize the network partially. A widely used technique that can efficiently localize a uniquely localizable portion of the network is trilateration: starting from three anchors (nodes with known positions), nodes having at least three localized neighbors are sequentially localized. However, the performance of trilateration can substantially differ for different choices of the initial three anchors. In this paper, we propose a distributed localization scheme with a theoretical characterization of nodes that are guaranteed to be localized. In particular, our proposed distributed algorithm starts localization from a strongly interior node and provided that the subgraph induced by the strongly interior nodes is connected, it localizes all nodes of the network except some boundary nodes and isolated weakly interior nodes.

Sensor Network Localization in Constrained 3-D Spaces

2006 International Conference on Mechatronics and Automation, 2006

Localization of sensor nodes is important for many sensor network applications such as distance-based routing and target tracking. This paper presents a localization approach for sensor networks in constrained 3-D space. By assuming that all the original beacon nodes are on the bottom plane, the localization procedure for the entire network is primarily from the bottom to the top and at the same time the localization process is carried out in all directions from the regions where the original beacon nodes are clustered. Simulated results showed that efficiency is improved for network structures whose profiles are cuboid or cone shaped, and whose node distributions are layered or random. The effects of the number of original beacon nodes as well as the node density on the localizing errors and/or the localizing successful rate are explored. Finally, a large scale sensor network is analyzed to verify the propagating trend of localization.

Graphical properties of easily localizable sensor networks

Wireless Networks, 2009

The sensor network localization problem is one of determining the Euclidean positions of all sensors in a network given knowledge of the Euclidean positions of some, and knowledge of a number of inter-sensor distances. This paper identifies graphical properties which can ensure unique localizability, and further sets of properties which can ensure not only unique localizability but also provide guarantees on the associated computational complexity, which can even be linear in the number of sensors on occasions. Sensor networks with minimal connectedness properties in which sensor transmit powers can be increased to increase the sensing radius lend themselves to the acquiring of the needed graphical properties. Results are presented for networks in both two and three dimensions.

Localizability of Wireless Sensor Networks: Beyond Wheel Extension

Lecture Notes in Computer Science, 2013

A network is called localizable if the positions of all the nodes of the network can be computed uniquely. If a network is localizable and embedded in plane with generic configuration, the positions of the nodes may be computed uniquely in finite time. Therefore, identifying localizable networks is an important function. If the complete information about the network is available at a single place, localizability can be tested in polynomial time. In a distributed environment, networks with trilateration orderings (popular in real applications) and wheel extensions (a specific class of localizable networks) embedded in plane can be identified by existing techniques. We propose a distributed technique which efficiently identifies a larger class of localizable networks. This class covers both trilateration and wheel extensions. In reality, exact distance is almost impossible or costly. The proposed algorithm based only on connectivity information. It requires no distance information.

Location and Position Estimation in Wireless Sensor Networks

Current Status and Future Trends, 2012

A wireless sensor network comprises of small sensor nodes each of which consists of a processing device, small amount of memory, battery and radio transceiver for communication. The sensor nodes are autonomous and spatially distributed in an area of investigation. Certain applications and protocols of wireless sensor networks require that the sensor nodes should be aware of their position relative to the sensor network. For it to be significant and to be of value, the data such as temperature, humidity and pressure, gathered by sensor nodes must be ascribed to the relative position from where it was collected. For this to happen, the sensor nodes must be aware of their relative positions. Traditional location finding solutions, such as Global Positioning System, are not feasible for wireless sensor nodes due to multiple reasons. Therefore, new methods, techniques and algorithms need to be developed to solve the problem of location and position estimation of wireless sensor nodes. A number of algorithms and techniques based upon different characteristics and properties of sensor nodes have already been proposed for this purpose. This chapter discusses the basic principles and techniques used in the localization algorithms, categories of these algorithms and also takes a more closer look at a few of the representative localization schemes. be placed at a position with known coordinates. The beacon nodes are also called reference nodes, anchor nodes or landmark nodes. It should be noted that sensor nodes may have symmetric or asymmetric communication links. If two nodes u and v are symmetric then u reaches v and v reaches u as well. In the case of asymmetric communication links, either u reaches v or v reaches u but both u and v do not reach each other simultaneously. Let us now consider a sensor network which is symmetric, two-dimensional and arranged in a square shape. Then this sensor network can be represented as a graph G(V, E) where the set of sensor nodes can be represented as set of vertices as under: V = { v1, v2, …, vn } The set of edges E in the graph G(V, E) comprises of all edges e = (i, j)  E iff vi reaches vj i.e. the distance between vi and vj is less than r where r is the maximum distance between the two nodes after which communication between them ceases to exist i.e. if the distance between two nodes is greater than r, no direct communication between them is possible. In other words, if the distance between two nodes is greater than r, the two nodes are not neighbor nodes. The distance between two neighbor nodes vi and vj is defined as the weight w(e)  r of the edge e = (i, j) between them. It is to be noted that problem of localization is usually solved only for two dimensions with the supposition that when needed or deployed, it could be extended to three dimensions. It is for this reason, we have stated graph G(V, E) to be two-dimensional. Therefore, it can be stated that G is a Euclidean graph in which every sensor node has a coordinate (xi, yi)   2 in a two-dimensional space. The coordinate (xi, yi) represents the location of a node i in the given sensor field. The sensor node localization problem can now be stated as following: Let there be a multihop sensor network represented by a graph G = (V, E). The graph has a set of beacon nodes B with known positions given by (xb, yb) for all b  B. The localization problem requires to find the position set (xd, yd) of as many dumb nodes d D as possible. Finding the location of a node implies finding its latitude, longitude and altitude.