Scientific Programming

Volume 2017 (2017), Article ID 4769710, 8 pages

https://doi.org/10.1155/2017/4769710

## 3D Localization Algorithm Based on Voronoi Diagram and Rank Sequence in Wireless Sensor Network

School of Information, Beijing Wuzi University, Beijing, China

Correspondence should be addressed to Xi Yang; moc.361@gnuoyxy

Received 23 September 2016; Revised 29 November 2016; Accepted 26 December 2016; Published 22 January 2017

Academic Editor: Wenbing Zhao

Copyright © 2017 Xi Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Accurate nodes’ localization is a key problem in wireless sensor network (WSN for short). This paper discusses and analyzes the effects of Voronoi diagram in 3D location space. Then it proposes Sequence Localization Correction algorithm based on 3D Voronoi diagram (SLC3V), which introduces 3D Voronoi diagram to divide the 3D location space and constructs the rank sequence tables of virtual beacon nodes. SLC3V uses RSSI method between beacon nodes as a reference to correct the measured distance and fixes the location sequence of unknown nodes. Next, it selects optimal parameter* N* and realizes the weighted location estimate with* N* valid virtual beacon nodes by normalization process of rank correlation coefficients. Compared with other sequence location algorithms, simulation experiments show that it can improve the localization accuracy for nodes in complex 3D space with less measurements and computational costs.

#### 1. Introduction

Due to its broad applications, researchers have been concerned with wireless sensor network (WSN). As one of the key technologies of the Internet of Things, WSN has been widely applied in various fields, such as military affairs, wise industries, environmental monitor, and smart home. The location information of wireless sensor nodes is needed in many applications. And location information can be used to self-organize, manage networks, select the optimal route, determine the occurrence area of the monitoring events, track moving targets, and so on. Therefore, node localization is attractive in wireless sensor network and plays a key role in the application of wireless sensor network [1–3].

Due to the characteristics of wireless sensor network, traditional localization methods in computer network cannot be directly applied, such as Global Positioning System (GPS).

Only a few sensor nodes can be equipped with GPS module or predeployed in a specific location if the operation cost and maintenance cost are taken into consideration. These nodes can know their own coordinates and assist other nodes to realize self-localization.

Localization accuracy directly affects the application effects, so great attentions have been paid to the localization problem. And many researchers have put forward many theories and efficient solutions.

In the past, most of the researches only paid much attention to the self-localization in 2D space with beacon nodes, which know their own location information beforehand (for example, [4, 5]). And current localization algorithms in 2D can be classified into two kinds: range-based algorithm and range-free algorithm [6, 7]. For range-based algorithms, distances are commonly computed by using different parameters such as time, angles, or signal strength and the location is estimated on the basis of the distances. For the range-free algorithms, unknown nodes calculate their approximate locations by using information from a few beacon nodes.

With the mature technology and market promotion, beacon nodes may be dynamic and localization will expand from the two-dimensional (2D) space to three-dimensional (3D) space.

As we all know, wireless sensor nodes are deployed in real environment, which is three-dimensional. And many applications often need three-dimensional location information. Localization in 3D space is more difficult than in 2D space. In addition, more factors should be considered in 3D localization, such as the environmental changes, the insufficient number of beacon nodes, and various disturbing effects in the signal transmission process.

Now, 3D localization has become a current research trend and one of the hot problems. Many researchers extend 2D localization technologies into 3D space, such as tetrahedral centroid localization algorithm and 3D DV-Hop, APIT, RSSI location, and partial filter, which have achieved good results and have been used to some extent.

Currently, localization algorithms in 3D space can include two categories: hierarchical location and nonhierarchical location. In hierarchical location, nodes are mostly deployed in the interior of the monitoring buildings. In this condition, users or networks only need the floor information of unknown node replacing the specific coordinate value. Some of the proposals [8, 9] in this category are discussed in greater detail. However, nodes may be deployed underwater or in hills in nonhierarchical location. Users often need to estimate the specific coordinate value. Such approaches are depicted in [10–12].

In this paper, we introduce Voronoi diagram into localization algorithm and propose a new Sequence Localization Correction algorithm based on Voronoi diagram, which can be used in 3D space. The new algorithm divides location space with 3D Voronoi diagram, corrects the measured distance, and fixes location sequence of unknown nodes, which reduces the space partition complexity and raises localization accuracy. In order to reduce the effects of the number of real beacon nodes, SL3CV selects optimal parameter* N* to determine the number of valid virtual beacon nodes in the last localization estimation, which also improves the localization accuracy. The localization estimation of unknown nodes can be calculated through the weights based on the optimal location sequence table of virtual beacon nodes.

This paper includes 5 sections. The concepts of 3D Voronoi diagram and location sequences are described in Section 2. Section 3 describes and analyzes the localization procedures of SLC3V algorithm in 3D space. This paper analyzes and compares the proposed localization algorithm with other algorithms through an exhaustive systematic performance study and simulation experiments in Section 4. Finally, this paper concludes in Section 5.

#### 2. Related Techniques

##### 2.1. 3D Voronoi

There are many space partition methods. Voronoi diagram is a kind of partition method, which divides the space into a number of subregions. Now Voronoi diagram is widely used in various fields, such as geographical information system, information system, and meteorology. Many researchers use Voronoi diagram to study the coverage problem in WSN.

Voronoi diagram divides the plane into many regions. We are given a finite set of points , , in the Euclidean plane. Let be any point in the space. Let denote the Euclidean distance with and , . Then

Voronoi diagram divides the plane into regions (Voronoi region) around each generator point , which makes any point in Voronoi region satisfy the following condition: Then is the sets of Voronoi region .

We find that 2D Voronoi diagram includes many continuous polygons, which are composed of a set of perpendicular bisectors. And all perpendicular bisectors are vertical to the connection lines between two adjacent points. With the increase of dimension, the formation of Voronoi cells has changed into high dimensional polyhedron. Therefore a Voronoi cell in 3D space is a 3D polyhedron.

After divided, any point in any given Voronoi cell is closer to the corresponding Voronoi site than other Voronoi sites. And all Voronoi cells combine together without overlapping and seams in [13, 14].

Because of the practicability of 3D Voronoi diagram, there are many computational methods developed to divide 3D discrete point set. In order to decrease the computational complexity, many researchers proposed various fast generation methods of 3D Voronoi diagram.

Figure 1 shows the 3D Voronoi diagram of 20 scattered points in the 3D closed space, in which the dots are 20 discrete points randomly deployed.