A Movement Control Policy Based On Probabilistic Coverage Model for Mobile Sensor Networks

Zhi Yang, Qian-Nan Li, Min Yu* College of Computer Information Engineering

Jiangxi Normal University Nanchang, Jiangxi, 330022, China

ccxsjjs248@126.com, mosike12@yahoo.com.cn, myu821@163.com

Ya-Li Peng School of Software

Jiangxi Normal University Nanchang, Jiangxi, 330022, China

Linlily2001@sina.com

Abstract—The design problems of localization algorithm, distribution density estimation and node’s moving path for data collection in multi-layers mobile wireless senor network are investigated. To ensure estimating accurately the node density, this paper proposes a new movement control strategy for fusion nodes based on probabilistic coverage model. This method completed the unknown node localization through beacon nodes traversing the monitoring area, and estimated distribution density of nodes in the network based on probabilistic coverage model, and divided the nodes into groups as little as possible, and constructed the short path of the fusion node’s data collection according to the centers of these limited groups. The results of the experiments indicated that the control policy of mobile fusion nodes can reduce greatly network energy, and prolong network lifetime.

Keywords-Mobile wireless sensor network; Probabilistic coverage model; Localization algorithm; Data collection

I. INTRODUCTION Wireless sensor networks normally consist of a large

number of sensor nodes that organize themselves into a multi-hop wireless network. All nodes are powered by battery and have limited storage and computation capability [1, 2]. Many universities and research institutes have launched the applied micro-sensor nodes research, such as the famous UC Berkeley’s Smart Dust[3], Great Duck Island[4], and so on

Combined with the future development direction, multi-layers mobile wireless senor network with stratified idea has a wide application prospect. It contains a large number of nodes having different physical structure or function, and can improve the expansibility of network. In multi-layers networks, common sensor nodes are simple, mainly for the data of perception, and some fusion nodes are in charge of collecting and forwarding data, whose function is stronger. And how to construct the fusion node moving route for collecting and processing real-time sensing information efficiently to get higher network coverage and longer network lifetime becomes an important problem in the field. To meet these challenges, Chong Liu proposed an energy efficient information collection with the ARIMA model [5]. The policy requires sensor nodes to perform data sampling and data transmission periodically. It may incur the implosion of data and information in the networks. David Jea proposed multiple

controlled mobile elements (Data Mules) for data collection [6]. This approach is on the assumptions that the entire network topology is known, but they don’t give the ways to obtain the network topology.

We work on these issues, such as mobile beacon node’s moving path to complete the localization for unknown nodes, the deployment and mobile data collection path of fusion nodes in multi-layers structure of the mobile sensor network. This paper proposes a movement control policy based on probabilistic coverage model for mobile sensor networks. This method first takes advantage of a few mobile beacon nodes to traverse the region through the certain path to complete localization, which is beginning to expand outward in the form of square from the center of the monitoring region, and then this policy based on probabilistic coverage model estimates the distribution density of the nodes in the networks, divides nodes into groups as little as possible to construct a short moving path for data collection, and reduces network energy consumption and prolongs network lifetime.

The remainder of the paper is organized as follows. In section II, we give the background of the research. The movement control policy based on probabilistic coverage model for mobile Sensor Networks is in section III. In Section IV, Simulation results show that this policy can improve performance of the network, reduce the nodes energy consumption, and prolong the network lifetime. Finally, we conclude in Section V.

II. BACKGROUND Combined with the characteristic of the future "smart dust"

sensor nodes in the deployment area, we propose a new type of multi-layers mobile sensor network architecture. In multi-layers mobile WSN, nodes are divided into three layers according to their function: sensor node(S), fusion node (F) and control node(C). The capacity and complexity of the nodes are increased in accordance with the order. Sensor nodes are simple micro-sensor nodes which can drift or be fixed and they are deployed at random in the monitoring region. The function of fusion nodes are much stronger than sensor nodes and can collect and store data, some fusion nodes are in charge of collecting information from their neighbor sensor nodes, the others are used for completing localization of sensor nodes.

978-1-4244-6252-0/11/$26.00 ©2011 IEEE

Control nodes are equivalent to the base stations in the network which are the top layers, and their distribution depend on the size of monitoring field. They can communicate with fusion nodes or with each other to control the whole network, which improved system performance.

This paper focused on the movement policy between fusion nodes and sensor nodes. When sensor nodes are mobile randomly, fusion nodes can move according to the situation that sensor nodes move in monitoring region. We develop an efficient and reliable mobile control policy to collect sensor data in time with the low-power cost.

III. THE MOVEMENT CONTROL POLICY

A. The deployment scheme In the Initial deployment process, sensor nodes and fusion

nodes for collect data will be deployed at random, and fusion nodes for localization will be deployed in the region in accordance with the communication radius. In order to minimize the power cost of sensors, sensor nodes can not exchange information each other, and send the data to the fusion-nodes by single hop communication when fusion-nodes are near enough to collect.

B. Fusion nodes mobile for localization In WSNs, it is meaningless to get sensor data from

unknown position sensor nodes. Therefore, node localization becomes a research hotspot, and to complete sensor nodes localization is an important respect in this paper. Node localization in WSN is the unknown node to communicate with neighbor beacon nodes or with sensor nodes of getting its location, then according to a certain location algorithm to calculate its own position. After the initial deployment, all sensor nodes position is unknown. In this paper, we deploy a few fusion nodes which are used specially for localization. Each fusion node is equipped with Global Positioning System (GPS) or other devices to fix position as a beacon node in the network, which can get its current location information when the nodes are moving. The localization scheme first designs a specific mobile route for fusion nodes. And then make them traverse the entire region in the specific route broadcasting periodically their current location information, which is equivalent to set a virtual beacon node in the poison of broadcasting. If a sensor node within the scope of communication radius of fusion nodes can receive three times or more times the location information, in which the relative distance between fusion node and the current node is equal to the communication radius of the sensor node, and then it can calculate its own position making use of trilateration algorithm or maximum likelihood estimation. The details are presented below.

1) Mobile route designment: In Figure 1, every color line indicates a fusion node’s

mobile route. Each fusion node move back and forward in its own mobile path.

Figure 1. F node’s mobile route for Localization

During the localization phase, sensor nodes can static or move only at tiny rate. Suppose the unknown sensor node’s position coordinates: ( x , y ), and it receive n times location information that the distance is R, these position’s coordinates: ( 1x , 1y ), ( 2x , 2y )… ( nx , ny ), Then one can derive the accurate position according to the constraints, as shown in the following equations:

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according to the (2), and (3).

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The coordinates of unknown node can be calculated by using the standard minimum mean square estimation:

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In this method, we set several fusion nodes that can be capable of getting their own position in the monitoring region, which make most of sensor nodes receive multi-times useful location information in a shorter time. Thus, localization accuracy of this method can be much high.

C. Movement control policy for fusion nodes After localization, we use probabilistic coverage model to

estimate the current density of sensor nodes in the entire monitoring area.

1) Probabilistic Coverage Model Probabilistic coverage model is proposed in [7]. This

model can depict more accurately the capacity of the network coverage. If a node doesn’t have neighbor nodes, the point coverage probability is given by the (4):

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=RpsdRpsdpsad

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),(β

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Where ),( psS is the coverage probability of any point p within the s node’s sensing region. ),( psd is the

geometric distance between the node s and the point p . While α and β are the sensor node’s physical property parameters. Any point’s coverage probability is between 0 and 1. Generally, the value of β is an integer between 1 and 4. α is an adjustable parameter.

In the situation that a node has several neighbor nodes, the point coverage probability can be affected by its neighbor nodes. Suppose that the s node’s neighbor nodes are 1n , 2n ,

…, Nn , p is a any point in the intersection region between s node and all its own neighbor nodes. The p ’s coverage probability is defined in (5).

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iip pnSpsSpC

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Where ),( psS and ),( pnS i are the probability of a node which don’t have neighbor node can be calculated in (4).

After defined the point probability, we can define the node’s coverage probability in the region, which is the smallest value of the point in the sensing region of the node. The probability is defined according to

)](min[)( pCsC pnode = )(sKp ∈∀ (6)

Where the point p is in the sensing region ( )(sK ) of the node s .

Because the sensing region is a continuous geometric plane, we can not calculate all points’ coverage probability in the plane. To calculate the node’s probability, we first introduce the concept of perimeter node. If the node whose border of sensing region is covered by its neighbor nodes’ sensing regions is called perimeter node, else it is called non-perimeter node. As a non-perimeter node, the point q is the

one of the node B ’s sensing region border which not be covered by the neighbor nodes. The node B ’s coverage probability is calculated according to

β]1/[1)()( aRqCBC pnode +== .

Figure 2. Perimeter and non-perimeter node

The method to calculate the perimeter node’s coverage probability was introduced in [7].

According to the definition of node’s coverage probability, we can know that non-perimeter node’s coverage probability is the same. This condition is unsuccessful to estimate the density of sensor nodes with the probabilistic coverage model, because the ability to discriminate coverage among non-perimeter nodes is quite poor. Instead, probabilistic coverage model is slightly modified to take the product of the smallest value of coverage probability of points in the sensing region and the number of its neighbor nodes as the coverage probability, shown in (7).

kmpCsC pnode ×= )](min[)( (7)

Where k is a coefficient, which can be determined by the network, m is the number of its neighbor nodes.

2) Groups of nodes designment After calculating the coverage probability for each sensor

node, we can get a descending sequence of coverage probability of nodes. The position in this sequence indicates that the more front it, the more nodes there are in the node’s surrounding area. Now, we are introducing the trajectory of nodes divided into groups in detail as follows:

a) Selection: To select the position of the sensor node S which coverage probability is the maximum value in sequence as a new group A ’s center.

b) Update: To determine whether two sensors are in the same group, and then to compute the distances between S node and the rest sensors. Namely, whether the distance between two sensors is less than the communication range P . If PSSd j ≤),( , Then they are in the same group.

c) Center Adjustment: To compute the center of all the sensor nodes in the group A , marking the center is AC .

d) Nodes in the new Group are Certain: Because the center of the group A was adjusted, some of the rest sensor nodes may be in this group. Selecting the sensor node to mark in this group, the distance between the node and the center

AC is less than the communication range P , which met the

constraint: PCSd Ai ≤),( .

e) Selection: To select the position of the node which own the greatest value of coverage probability of the rest sensors as a new group’s center position. And return step b to mark the group.

f) End: If all the sensor nodes are marked a symbol of group, the algorithm is over

3) Fusion nodes route Control Nowadays, there are several fusion nodes for collecting

data and some centers of divided groups, we must design an optimal route strategy that fusion nodes can traverse through all the centers of divided groups for just once with low energy consumption, and complete the network data collection task. This problem is similar to sharing access to multiple traveling salesman problem, belonging to a NP-hard problem. It is very difficult to find the shortest moving path to traverse these centers with low energy consumption among the solution space. Thus, we adopt an approximation algorithm to search the shortest route. The algorithm is described in detail as follows: we scan all fusion nodes in multiple rounds. In each round, each fusion node selects the nearest center to traverse and stop for a short time to collect data from the sensors in this group, and update its own position as the location of the nearest center. If there are centers which can not be traversed by fusion nodes, the algorithm is continuing, else the algorithm is over.

IV. SIMULATION We implement the deployment and the mobile control

policy in mobile sensor networks in the WSN simulation platform [11]. Our experiments consider a wireless sensor network of 200 sensor nodes randomly deployed in an 800*600 square monitoring area. The number of fusion nodes for localization is three, and the same number is fusion nodes for collecting data. The sensors are all identical; every sensor has the same kind of battery, and uses the same communication range 30m. As shown in Fig. 3, red solid circles represent fusion nodes; blue solid circles denote sensor nodes in the topology of the network.

Figure 3. The initial deployment in simulation platform

In our experiment, 200 sensor nodes are divided into 50 groups according to the adopted method. In Fig. 4, every circle denotes a group in the network, the blue solid points in each circle denote the sensors in groups. According to the policy in this paper for fusion nodes, the route for each fusion node is showed in Fig. 5.

Figure 4. The sensor nodes for dividing groups

Figure 5. The route for Fusion nodes

In Fig. 6, the x-axis is the number of fusion nodes for collecting data and the y-axis denotes the ratio of the policy’s mathematical expectation E to the total number M of the solution space. The smaller the value of the ratio is, the more excellent the policy is and the shorter route the fusion node traverses. The result shows that, the number of fusion nodes is smaller, the rate is much smaller, and the more excellent is the performance.

Figure 6. E/M for the fusion nodes for collecting data

As shown in Fig. 7, the x-axis indicates the number of fusion nodes for completing localization and the y-axis denotes location error rate. The experiment shows that, the location error rate is less effective in the circumstance to fewer number of fusion nodes.

Figure 7. Location error rate

V. CONCLUSION Under multi-layers mobile sensor network architecture, this

paper proposed a movement control policy based on probabilistic coverage model for fusion nodes. Several fusions as beacon nodes complete localization for the sensors with the path from the center of the monitoring region to expand outward in the form of the square. We estimate sensor node’s density making use of probabilistic coverage model, divide the sensors into groups as little as possible, and construct an effective and reliable moving control policy for fusion nodes taking advantage of the centers of the limited groups. The experiment shown that making fusion nodes as beacon nodes for localization can improve the accuracy for localization, and the moving control policy this paper presented is simple and can be implemented easily. The policy makes the fusion nodes traverse the centers of groups with a shorter route, collect data, and reduce the energy consumption to get the longer network lifetime.

ACKNOWLEDGEMENT This work was supported by both the National Grand

Fundamental Research 973 Program of China No.2006CB303006 and International Science & Technology Cooperation project of Ministry of China No.2010DFA70990. The corresponding author Min Yu is a professor at college of computer information engineering of Jiangxi Normal University. Her main research areas include Wireless Sensor Network, Distributed System and Mobile Computation, Information Security.

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