中 華 大 學 碩 士 論 文
A Study on the Coverage Problem in Directional Sensor Networks with Rotatable Sensors
系 所 別：資訊工程學系碩士班 學號姓名：M09402045 徐 寅 鐘 指導教授：梁 秋 國 博士
中 華 民 國 101 年 2 月
最近幾年來，由於科技的進步，大量微小、可無線傳輸及自主運作的感測器紛紛 問世並帶來了許多應用，例如戰地的偵查、醫院中病人的照護、或是探測危險區域的 環境資訊。但在這些感測網路的應用中，感測器佈署狀態之覆蓋率高低必定會影響後 續應用的優劣，以至於感測網路的覆蓋問題受到很多學者的注意並引起廣泛的討論。
在無線感測網路中覆蓋問題可以大致上分為兩類：分別為監測感興趣區域的區域 覆蓋問題及監測特定目標物的目標物覆蓋問題。在此之前已經有許多的學者在研究此 類型的問題，但都假設感測器具有全方向的感測能力，而現實生活中由於技術或是硬 體的限制，大多數的感測器的感測區域是呈現一個有角度的扇形區域。一個有向性感 測 網 路 是 由 許 多 有 向 性 感 測 器 所 組 成 ， 此 類 型 感 測 器 跟 傳 統 的 全 向 性 (Omni-directional) 感測器不同之處，在於有向性的感測器都有限制的感測角度跟固定 的感測半徑，只具備感測一個近似於扇形的區域能力。
在本篇論文中，我們定義目標物覆蓋問題為使用最小的旋轉角度來達到最大的目 標物覆蓋率，並提出兩個分散式貪婪演算法來解決此問題。第一種演算法的精神為限 制感測器最大旋轉角度來保證原先覆蓋的目標物還將會被覆蓋，其二則為尋找感測器 在其感測圓型區域中最大覆蓋目標物數量之方向為優先考量之方法。另一方面針對區 域覆蓋問題，我們提出了尋找最少覆蓋方向優先考量之演算法，使得感測器在旋轉後 可以減少與其他感測器的重疊。有別於前人尋找相鄰鄰居的夾角角平分線或是與鄰居 感測圓之切點當作旋轉之方向，此方法是在整圓周中找尋最少被鄰居覆蓋之圓周方向 來旋轉。透過實驗模擬，利用我們提出的旋轉角度之技巧，確實可以有效來提高目標 物覆蓋率或是區域覆蓋的覆蓋率。
In wireless sensor networks (WSNs), many applications in military and civilian operations, such as environmental monitoring, battlefield surveillance, health care and volcanoes monitoring become more popular in recent years, since more powerful sensors with high capabilities are being designed at rapidly decreasing costs. However, the coverage of sensor deployment which is good or bad must be affect these applications, so the coverage problem in sensor network has received a lot of attention from many researchers and has been widely discussed.
The overage problem can be broadly divided into two categories: target coverage problem and area coverage problem. Most of the past work on the problem is based on the assumption of omni-directional sensors that have an omni-angle of sensing range. In real-world, most sensors may have a limited angle of sensing range due to technical constraints or cost considerations. s
In this thesis, we propose a Maximum Coverage with Rotatable Sensors (MCRS) problem in which coverage in terms of the number of targets to be covered is maximized whereas the rotated angles of sensors are minimized. We present two distributed greedy algorithm solutions for the MCRS problem. The second objective is to solve the area coverage problem. We proposed a greed algorithm to decrease the overlapping area and maximize the area coverage of a randomly deployed directional sensor network. Finally, simulation results show that the proposed algorithms are more effective than the previous methods of the coverage rate.
Keywords: Directional Sensor Networks, Target Coverage Problem, Area Coverage Problem.
一開始，並沒有想過要念研究所，只是因為周遭的朋友都在準備考試，也跟 著一起去補習準備。成為一個研究生後，才發現以前的讀書方法只是用來應付考 試，那種在短時間內死背硬記，但其實根本就不懂裡面的道理是什麼。在這途中 我迷惘了，個性變成怯懦，臉上失去笑容，最怕被人問到的問題就是什麼時候要 畢業。就選擇先去服兵役換個時空看能不能找回曾經的自信。最後憑著不想認輸 的心態，回來繼續完成學業。
我必須誠摯的感謝我的指導教授梁秋國老師，在老師平常的言傳身教中，學 習到很多待人處事的方式，以及堅持對自己心中信念的堅持。有一句老師常說的 話，讓我印象非常深刻，就是不要把論文上面寫的每一句話或演算法的每一個步 驟都當作是對的，使我會開始反思每件事情背後的因果關係，不論是研究上或是 日常看的事情。
在論文口試階段，承蒙口試委員成功大學的張燕光博士、高雄大學的嚴力行 博士與本校王俊鑫博士的鼓勵與疏漏處之指正，使得本論文更趨完備，在此深致 謝意。因為在你們的幫忙和提醒，使得本論文能夠更趨完整和嚴謹。
Table of Contents
Chapter 1 Introduction ... 1
Chapter 2 Related Works ... 7
2.1 The Target Coverage Problem ... 8
2.1.1 Distributed Greedy Algorithm for the MCMS Problem ... 8
2.1.2 Weighted Centralized Greedy Algorithm ... 11
2.2 The Area Coverage Problem ... 15
2.2.1 The Coverage Rate of Expected Value ... 16
2.2.2 Face Away Algorithm ... 17
Chapter 3 Directional Sensing Model with Rotatable Sensor ... 20
3.1 Directional Sensing Model ... 20
3.2 Target in Sector (TIS) test ... 23
3.3 Assumptions for Proposed Algorithms. ... 23
Chapter 4 Our Proposed Scheme for Target Coverage Problem ... 25
4.1 Preliminary and Problem Definition ... 25
4.2 The Definition of the Weight Function ... 27
4.3 Distributed Maximal Rotatable Angle algorithm ... 28
4.4 Distributed Maximal Coverage First Algorithm ... 31
4.5 Simulation Environment and Simulation Results ... 34
4.5.1 Coverage Rate vs. the Number of Sensors... 34
4.5.2 Coverage Rate per Angle vs. the Number of Sensors ... 36
4.5.3 Active Sensor Rate vs. the Number of Sensors ... 37
Chapter 5 Our Proposed Scheme for Area Coverage Problem ... 38
5.1 Preliminary ... 38
5.2 The Definition of the Weight Function ... 40
5.3 Distributed Minimum Overlapping-Angle First Algorithm ... 43
5.4 Simulation Environment and Simulation Results ... 46
5.4.1 Coverage rate vs. the Number of Sensors ... 46
5.4.2 Coverage rate vs. Sensing Radius ... 48
5.4.3 Coverage rate vs. Sensing Angles ... 49
Chapter 6 Conclusions ... 51
References ... 52
List of Figures
Figure 1.1 An example of wireless sensor network. ... 1
Figure 1.2 An example for target coverage problem with rotatable sensors. ... 4
Figure 1.3 An example for area coverage problem with rotatable sensors. ... 5
Figure 2.1 An example of DGA with 2 sensors. ... 9
Figure 2.2 An example of DGA with 3 sensors. ... 10
Figure 2.3 An example of MCN value... 12
Figure 2.4 An example of the weight of orientation. ... 13
Figure 2.5 The final result of the case in Figure 2.3. ... 14
Figure 2.6 The initial deployment & the relationship of six sensors. ... 18
Figure 2.7 An example of the sensor s2. ... 18
Figure 2.8 The new working direction of sensor s1 and s6. ... 19
Figure 2.9 The final result of FA algorithm. ... 19
Figure 3.1 The common directional sensing model. ... 20
Figure 3.2 The directional sensing model of a switchable sensor. ... 21
Figure 3.3 The directional sensing model of rotatable sensors. ... 22
Figure 4.1 An example for a sensor to cover more targets by rotating its direction. 26 Figure 4.2 Minimize Rotatable with small angles. ... 27
Figure 4.3 An example for MRA policy. ... 28
Figure 4.4 the initial deployment of four sensors. ... 29
Figure 4.5 The step by step of the DMRA ... 30
Figure 4.6 An example for MCF policy... 32
Figure 4.7 The main difference between MCF & MRA policy. ... 32
Figure 4.8 The table of Experimental parameter. ... 34
Figure 4.9 The Coverage Rate vs. the Number of Sensors. ... 35
Figure 4.10 The Coverage Rate per Angle vs. the Number of Sensors. ... 36
Figure 4.11 The Active Sensor Rate (%) vs. the Number of Sensors. ... 37
Figure 5.1 An disadvantage of FA algorithm. ... 39
Figure 5.2 The relationship between two sensors. ... 41
Figure 5.3 Two example for case 3. ... 42
Figure 5.4 An example of executing MOAF algorithm ... 44
Figure 5.5 The result of MOAF compares with FA... 45
Figure 5.6 The experimental parameters ... 46
Figure 5.7 The Coverage rate vs. the Number of Sensors with α=40∘ ... 47
Figure 5.8 The Coverage rate vs. the Number of Sensors with α=50∘ ... 47
Figure 5.9 Coverage rate vs. Sensing radius with N=100. ... 48
Figure 5.10 Coverage rate vs. Sensing radius with N=200. ... 49
Figure 5.11 Coverage rate vs. Sensing Angles with N=100 ... 50
Figure 5.12 Coverage rate vs. Sensing Angles with N=150 ... 50
Chapter 1 Introduction
Wireless sensor network (WSN) is a new and essential technology, because this network can monitor environmental conditions, such as temperature, humidity, vibration, sound, pollutants or interested targets and send collected information to users wirelessly and cooperatively. Generally speaking, as Figure 1.1 shows, a wireless sensor network consists of users, one or some base stations and a large number of autonomous sensors. Each sensor is equipped with some sensing modules which are capable of sensing some information or monitoring some entity in the environment, a microprocessor for processing the sensing data and a radio transceiver for wireless communication [1, 2].
Figure 1.1 An example of wireless sensor network.
In recent years, the wireless sensor networks have received a lot of attention due to their wide applications in military and civilian operations, such as environmental
monitoring, battlefield surveillance, and habitat monitoring, etc [3, 4]. There are two kinds of deployment schemes in wireless sensor network: deterministic deployment and random deployment. Deterministic deployment is often used in an indoor environment, such as security monitoring in a museum. However, in many situations the interested regions may be a battlefield, a disaster area, a forest or the high dangerous field where human cannot reach. In these environments, the sensors cannot be deployed in a specific location precisely. The sensors may be dropped randomly from aircrafts. Hence, the initial deployment of randomly deployed sensors is difficult to achieve a good coverage. In these cases of poor coverage, the application must be affected by the bad quality of collected data, so how to enhance the coverage rate after sensors deployed is a fundamental problem and has been studied by many researchers.
The overage problems can be broadly divided into two categories. One is the target coverage problem and the other is the area coverage problem. Most of the past work to solve the coverage problems is based on the assumption of omni-directional sensors . This kind of sensor nodes has a circular disk of sensing range. In real-world, many kinds of sensors have a limited angle of sensing area due to the technical constraints or cost considerations. There are many kinds of directional sensors, such as infrared sensors , video sensors  and ultrasonic sensors . The sensing angles of infrared sensor are about 30∘to 110∘ and the angles of ultrasonic sensor are about 15∘to 60∘. Hence, the directional sensor node has a sector-like sensing area and the smaller sensing angle than the omni-directional one.
However, many methods to solve the coverage problem in conventional sensor networks are not suitable in directional sensor networks. For target coverage problem, this is because a directional sensor has a limited angle of sensing area and does not
even cover all targets which are located in its sensing range, and for area coverage problem, the directional sensor cannot not cover all circular sensing area at the same time. Hence, to design an algorithm to enhance coverage rate in a directional sensor network is a much more difficult problem than the past work.
In this paper, we are interested in improving the coverage rate for a randomly deployed directional sensor network. In general, the first goal is to propose an algorithm to cover more number of interested targets than the initial deployment for solving the target coverage problem. The second objective is to improve the coverage rate for the area coverage problem.
In the past, researchers have proposed several ways to improve the sensing abilities of a directional sensor. The first way is to put several directional sensors on one sensor node, each of which is faced to different direction to model an omni-directional sensor. One example using this way is in , where four pairs of ultrasonic sensors are equipped on a single node to detect ultrasonic signals from any directions. The second way is to place the sensor node onto a mobile device so that the node can move around. However, moving sensors will cost much energy so that the sensor's lifetime will be shortened. In reality, moving a sensor node for 1 meter consumes almost 30 times more energy than transmitting 1K bytes of data . The third way is to equip the sensor node with a device that enables the node to rotate to different directions. Due to its low hardware and low energy overhead, the rotation ability can be easily incorporated into sensor nodes. In this study, we adopt the assumption that our sensor nodes can face to different directions.
For simplicity, we consider the following assumptions and notations in this paper.
In the directional sensor model, the sensing region of a directional sensor is a
sector-like area of the sensing disk centered at the sensor with a sensing radius. When the sensors are randomly deployed, each sensor initially faces to a randomly selected direction. Each sensor node equips exactly one sensor on it. Thus, we do not distinguish the terms sensor and node in the rest of the paper. Moreover, for target coverage problem, some interested targets are randomly deployed in the given region.
When a target is both located in the direction and the sensing region of a sensor, we say that the target is covered by the sensor.
In order to improve the coverage for a randomly deployed directional sensor network, each sensor is equipped with a device that enables the sensor to rotate with some degrees to face on another sensing direction. Hence, we are interested in finding a way for each sensor to rotate with some degrees to cover more targets than it is initially deployed. The problem is called the Maximum Coverage with Rotatable Sensors (MCRS) problem. In this paper, we are asked to develop a method that can maximize the number of covered targets whereas the total rotated degrees are minimized to save energy.
Figure 1.2 An example for target coverage problem with rotatable sensors.
As Figure 1.2 (a) shows, many targets may not be covered by sensors at initial deployment. If each sensor has the ability to rotate its direction, the number of uncovered targets may be decreased to achieve a good coverage as shown in Figure 1.2 (b).
Figure 1.3 An example for area coverage problem with rotatable sensors.
Area coverage problem is still an essential issue in a directional sensor network.
The coverage region of a directional sensor is determined by both its location and its direction of sensing radius. When a sensor works in one direction, we call the sensing range of the working direction as its coverage region. The coverage region of different sensors may be overlapped with each other after they are randomly deployed.
Therefore, we need an algorithm to rotate sensors to face to certain directions to maximize the covered area of the whole network.
The other goal is to maximize the area coverage of a randomly deployed directional sensor network. The problem of rotating working-direction to cover maximal regions, called Maximum Directional Area Coverage (MDAC) problem, has been proved to be NP-complete . As Figure 1.3 (a) shows, the initial deployment may have many overlapping regions. If each sensor has an ability to rotate its direction, the overlapping regions may be decreasing to achieve a good coverage as
shown in Figure 1.3 (b).
In this paper, we present two angle adjustment algorithms, namely the Distributed Maximal Rotatable Angles (DMRA) scheme and the Distributed Maximum Coverage First (DMCF) scheme, for the MCRS problem. Simulation results show the performance of our proposed angle adjustment algorithms. On the other sides, we also propose a greedy algorithm for the area coverage problem with rotatable sensors. Simulation results show that our proposed algorithms outperform the previously proposed Face-away (FA) algorithm .
The rest of the thesis is organized as follows: Chapter 2 introduces some related literatures dealing with directional sensor networks. In Chapter 3, the directional sensing model is formally defined and some notations and assumptions are also introduced. In Chapter 4, the proposed angle adjustment algorithms for target coverage problem are presented. In Chapter 5, we will explain the angle adjustment algorithms for area coverage problem. Finally, some concluding remarks are given in Chapter 6.
Chapter 2 Related Works
To collect data from the environment is the main function of wireless sensor applications. Each application collects different types of data for different goals. It reflects how well the environment is monitored, and serves as a basis for applications such as physical phenomenon or target detection, classification and tracking. However, most of the sensor applications need maximum coverage with minimum number of sensors. Thus, the coverage problem in wireless sensor networks has been researched extensively in the past decades.
The coverage problems can be broadly divided into two categories: one is the target coverage problem and the other is the area coverage problem, each of which requires different strategies for the solution. In the area coverage problem, we are focused on the coverage performance on the covered region, while in the target coverage problem the coverage performance on the number of covered targets is discussed. In this thesis, we pay our attention to the both coverage problems.
Therefore, in the following, we will discuss the recent works related to the coverage problem. In Section 2.1, the previous works for the target coverage problem will be discussed, and then the related studies for the area coverage problem are described in Section 2.2.
2.1 The Target Coverage Problem
In WSNs, some sensor applications are only interested in stationary target points, such as buildings, doors, flags, and boxes. Stationary targets can be located anywhere in the observed area. To cover only the interested targets instead of the whole area, researchers have defined target-based coverage problems. Many studies have focused on the maximization of covered stationary targets with a minimum number of sensors .
Then, we will introduce two different previous approaches by using switchable directional sensors. In Section 2.1.1, the MCMS Problem will be described and the centralized greedy algorithm is proposed to solve the problem. In Section 2.1.2, the weighted centralized greedy algorithm chooses the possible orientations with the larger weights and can cover targets as much as possible. However, in the two studies, the sensing models are always based on assumption of the switchable sensor.
2.1.1 Distributed Greedy Algorithm for the MCMS Problem
In , the authors proposed the Maximum Coverage with Minimum Sensors (MCMS) problem. Under the random deployment strategy, not all targets are covered by the initial deployment. The objective is to change the initial orientations in order to cover as many targets as possible.
The MCMS problem can be defined as follows: Given a set of targets, and a set of homogenous sensors, each of which is randomly deployed in a 2-D region. Each
sensor has several possible orientations. The problem is to look for a minimum number of directional sensors with appropriate directions that maximize the number of targets to be covered. The authors first show that the MCMS problem is NP-hard by proving that MCMS is a sub-problem of Max-Cover Problem.
The authors presented a distributed greedy algorithm to solve the MCMS problem. This method has some assumptions:
All sensors are homogenous, and each sensor holds in one state of active, transient and inactive state.
A directional sensor can acquire the location knowledge on targets within maximum sensing ranges, and can identify whether a target is in the sensor’s certain sector or not.
The network is a connected topology and no communication errors occur.
Sensor si receives a coverage message sent by its sensing neighbor sensors. The coverage message contains the sensor ID, location, orientation, priority. Priority is a distinct value assigned to the sensor. (e.g., a hash function value of ID).
Figure 2.1 An example of DGA with 2 sensors.
Acquired targets of sensor si mean these targets are not covered by any sensors with high priority than the priority of si. According to the information carried in the coverage message, sensor computes the number of acquired targets in its each orientation.
For the example shown in Figure 2.1, if the priority of sensor s1 is bigger than the s2, the number of acquired targets in sector s1,6 is 2, and the number in sector s1,3 is 1. On the contrary, if the priority of the sensor s1 is less than the s2, the number of acquired targets in sector s1,6 is 0, and the number in sector s1,3 is 1.
Figure 2.2 An example of DGA with 3 sensors.
In the second case as shown in Figure 2.2, suppose the priority of s1 is less than the priority of s2. The sensor s1 applies the greedy principle of maximizing the number of acquired targets, switches to orientation s1,3 and then sends a coverage message as well to updating its state in sensing neighborhood.
Suppose another sensor s3 with higher priority (than sensor s1) covers the target as shown in the Figure 2.1(b). No acquired target available for sensor s1, the sensor s1 activates a transition timer, with duration Tw. The timer is canceled if new coverage
information from the neighbors arrives and changes the maximum number of acquired targets to a non-zero value. Note that the purposes of setting the timer are to prevent finalizing its decision before its sensing neighbors with high priorities and to transfer its state to inactive when the timer expires.
We discovered the disadvantage of DGA that each sensor only considers the maximal number of acquired targets within its working directions. However, a sensor does not take into account whether the target has been covered repeatedly by its neighbor sensors. Hence, in order to enhance the target’s coverage rate, the target is covered with less number of sensors, and has the higher priority to be selected.
2.1.2 Weighted Centralized Greedy Algorithm
In this researcher , the problem is how to select orientations of sensor nodes so as to cover the targets as much as possible. It is similar to the MCMS problem. To yield a better coverage result, the authors proposed a weighted centralized greedy algorithm to solve the problem.
The proposed method adds a weight function to consider the importance of targets. The importance of targets is the maximum number of sensor nodes which covers the target (MCN Value). For example in Figure 2.3, the target t1 and t2 are covered by sensor s3 and s4, so the MCN of target t1 is 2, and the MCN of target t2 is 2, too. Similarly, the target t6 is covered by three sensors, so the MCN value is 3.
Figure 2.3 An example of MCN value.
Then, the weight of the target tk denoted by w(tk), where w(tk) > 0 could be defined in Equation (2.1). Where m is the total number of targets and α is the positive factor to adjust the target weight. The weight of a target is lower. It means the target with the bigger MCN value, which is the target covered by much number of sensors would have a lower priority to cover it first by a sensor.
Let di,j denote the jth orientation of the sensor si. The weight of the orientation di,j denoted W(di,j), where W(di,j) ≥ 0 could be defined by Equations (2.2). If the set of targets covered in the orientation di,j. If the set of target in the orientation di,j is empty, then the orientation weight is zero.
The detail of WCGA follows. At first, WCGA will compute the weight of all targets, and the weight of all directions. Then, it selects the working direction of sensor with the maximal weight until all sensors have selected its direction.
For the example in Figure 2.4, we assume the value of α*m is 1, the target t4, t5 and t6 are covered by sensor s1, the target t5, t6 and t10 are covered by sensor s2, the target t2, t3, t4, t7, t8 and t9 are covered by sensor s3 and the target t7, t8, t9 and t10 are covered by sensor s4.
Figure 2.4 An example of the weight of orientation.
For consideration of sensor s1, the MCN of target t4 is 2 because t4 is covered by sensor s1 and s3. As Equation (2), the weight of the orientation is 3. In the other orientation, the MCN of target t5 is 2, and the MCN of target t6 is 2, too, so the weight of the orientation is 2.5. In this case, the sector with the maximum weight is the sector of sensor s3 which covers the target t2 and t3. So the s3 will switch its orientation to this
sector. After all sensors select the orientation according to the scheme, the final result shows in Figure 2.5.
Figure 2.5 The final result of the case in Figure 2.3.
Both of the two algorithms are based on the assumption of switchable sensors. In our work, we use the rotatable sensor to discuss the coverage problem. The rotatable angle is more flexible, the considerations are not the same with the two related work, so it’s unfair to compare our simulation results with the two algorithms. This is because our sensor can rotate any degrees for maximum number of targets.
2.2 The Area Coverage Problem
The wireless sensor networks have received a lot of attention due to their wide applications in military and civilian operations, such as environmental monitoring, battlefield surveillance, and habitat monitoring, etc. There are two kinds of deployment schemes in wireless sensor network: deterministic deployment and random deployment.
Deterministic deployment is often used in an indoor environment, such as security monitoring in a museum. However, in many situations, the sensors always are dropped randomly from aircrafts. Hence, the initial deployment of randomly deployed sensors is difficult to achieve a good coverage. In these cases of poor coverage, the application must be affected by the bad quality of collected data, so how to enhance the coverage rate after sensors deployed is a fundamental problem and has been studied by many researchers.
In the area coverage problem, we are focused on the coverage performance on the covered region, while in the target coverage problem the coverage performance on the number of covered targets is discussed. In this thesis, we also pay our attention to the area coverage problem. Therefore, in the following, we only discuss the recent works related to area coverage problem.
Then, we will review two different previous approaches that use switchable directional sensors. In Section 2.2.1, the coverage rate of expected value will be described. In Section 2.1.2, each sensor faces away from all its neighboring sensors by finding the direction with the fewest neighboring sensors and pointing in that direction.
2.2.1 The Coverage Rate of Expected Value
In , the authors discuss that many directional sensors can be deployed in order to achieve coverage rate p in a distributed directional sensor network. For a randomly deployed sensor networks, for example, sensors are dropped by an airplane, it is difficult and impossible to guarantee 100 percentages coverage of the monitored area even if the node density is very high. Their goal is to focus in investigating the coverage problem that directional sensor networks can guarantee coverage rate at least p percentages.
Assume that the area of the monitored region is S, and there are no two sensors located at exactly the same position and sensing region. Notice that a directional sensor with angles α covers a sensing area of αr2. Assume that the sensors are randomly deployed in the monitored region, and the locations of sensors obey uniform distribution. After N directional sensors are deployed, the probability that the targeted region is covered is given by
In a special case, when the offset angle is 180 degrees, the sensing range must be the same with the omni-directional sensor. The coverage probability for deploying N sensors is simply as the Equation (2.6).
Naturally, if the coverage rate of a given area is required to be at least p percentages, the number of deployed directional sensors should be represented in Equation (2.7):
Here, we use a case to illustrate the coverage of expect value. In a 500*500 square meters field, we want to deploy the directional nodes with the sensing radius 50m and the offset angel 60º for gathering the visual information. If the required coverage rate is at least 80%, we can calculate the number of node to be deployed as follows:
2.2.2 Face Away Algorithm
In , the authors proposed a greedy solution named the Face-Away (FA) algorithm to achieve the maximal area coverage rate in the interested region. The FA algorithm works in a very simple manner.
Each sensor knows the direction in which their neighbors are located (within sensing range R), the FA algorithm simply determines the largest angle between adjacent directions and draws the bisector to that angle. Sensors then simply point in the direction of the bisector making it their new working direction. It is unlike other papers to assume that the distances of sensing neighbors are 2R.
If the locations of neighbor sensors are known, each sensor will determine the sequence of neighbor sensors, which are sorted by the angles which are formed by the two closely neighbors sensor. And then, each directional sensor will choose the bisector of the maximum angle to be a new working direction. At last, each sensor switches the center line of field of view to the new working direction.
Here, we demonstrate an example for the Face Away algorithm. In Figure 2.6, there are six sensors, namely s1, s2, s3, s4, s5 and s6. The initial relationship of neighbor sensors is shown on the table. At the same time, all sensors compute the maximum angle of neighbor sensors, and change the working direction to the bisector line of the maximum angle.
s1 s2 s3 s4 s5 s6
s1 V V V V V
s2 V V V V
s3 V V V
s4 V V
s5 V V V
s6 V V V
Figure 2.6 The initial deployment & the relationship of six sensors.
Figure 2.7 An example of the sensor s2.
Figure 2.8 The new working direction of sensor s1 and s6.
In Figure 2.7, it is easy to see that the maximum angle is between sensors s5 and s3 and the angle of counterclockwise rotation is smaller than the angle of clockwise rotation. So, the sensor s2 will rotate its working direction to the bisector line counterclockwise. In Figure 2.8, the sensor s1 and s6 will rotate to the new working direction by using the same policy. The final result of this case is shown on Figure 2.9.
Figure 2.9 The final result of FA algorithm.
Directional Sensing Model with Rotatable Sensor
In this chapter, we shall present some notations, assumptions and the definition for the coverage problem. First, the directional sensing model is discussed in Section 3.1. Next, we will explain how to determine whether a target is covered by a directional sensor in Section 3.2. Finally, the assumptions used in the paper will be described in Section 3.3.
3.1 Directional Sensing Model
Unlike an omni-directional sensor node, a directional sensor, such as infrared sensor, ultrasonic sensor and video sensor, has a limited angle of working direction and thus it cannot monitor the whole circular area. We assume each sensor will face to a randomly selected direction after initial deployed and can rotate their sensing direction in the applications.
Figure 3.1 The common directional sensing model.
The common directional sensing model for 2D spaces is illustrated in Figure 3.1.
The sensing model of a directional sensor s can be denoted by a 4-tuple (S, r, D, α). S is the position of the sensor node; r is the sensing radius; D is the working direction and α is the offset angle of view. The special case of this model, where the offset angle = 180∘can be described as omni-directional sensing model.
Figure 3.2 The directional sensing model of a switchable sensor.
The direction to which a directional sensor faces is the working direction of this sensor. Most of the past work is based on the assumption of sensors which may have disjoint working directions. These directions can be combined to generate the full circular view. It means a sensor node has several fixed directional sensors on it, each of which faces to different orientation. As the Figure 3.2 shows, for example the sensor s1 has four switchable directions to change but just face to one direction at the same time.
In our study, we use the rotatable sensor nodes as shown in Figure 3.3. These sensor nodes cannot use more sensors and may spend less power than the moving sensors. Each rotatable sensor is equipped with a device (like a stepper motor or other device) that gives the sensor the ability to rotate to face other directions. If sensors can rotate its direction, it will decrease the overlapping regions to enhance the coverage
α α D
D' s(x, y)
Figure 3.3 The directional sensing model of rotatable sensors.
We adopt the following notations with rotatable sensors in rotatable directional sensing model throughout the thesis:
：The working direction denotes the center line of field of view.
：The angle of the Field Of View (FOV).
：The offset angle of the field of view on both sides of direction.
：The sensing radius of a sensor.
：The number of sensors.
：The number of targets.
：The ith target, 1 ≤ i ≤ N.
：The jth target, 1 ≤ j ≤ M.
3.2 Target in Sector (TIS) test
In , with each choice of orientation, a certain subset of targets is covered by the directional sensor. The relationship of a directional sensor, its orientation, and a target can be determined by a Target in Sector (TIS) test.
First, calculate the distance from the directional sensor s to the target t and verify whether the distances are less than the sensing radius or not.
Then, check whether the angle between the vector and is within the FOV of the directional sensor s.
A target t is said to be covered by the sensor s if and only if the both conditions are satisfied. Moreover, a region is said to be covered by a sensor s, if and only if for any point p in region, p is covered by s. Note that the mathematical sensing model of s is the binary model. This model guarantees that the target is detected if it is located anywhere within the defined sector of one sensor.
3.3 Assumptions for Proposed Algorithms.
We make the following assumptions of our models in this paper:
Each directional sensor is homogeneous, such as: sensing angle, sensing radius, communication radius.
Each directional sensor is randomly placed on a uniform 2-dimensional surface, has an ability to rotate its direction and cannot move around.
The transmission range is greater than or equal to the twice times of sensing radius such that sensing neighbors can communicate with each other and no communication errors occur..
Our Proposed Scheme for Target Coverage Problem
In this chapter, we proposed two distributed greedy algorithms to solve the Maximum Coverage with Rotatable Sensors (MCRS) problem in which coverage in terms of the number of targets to be covered is maximized whereas the rotated angles of sensors are minimized. At first, each sensor determines its weight of working direction and order of priority. Then the sensor with the highest order than its neighbor sensors can rotates its angle first in order to cover as many targets as possible which results in higher coverage rate.
Section 4.1 describes the definition of the target coverage problem. Section 4.2 describes the detailed solutions for Distributed Maximal Rotatable Angle (DMRA) scheme. The Distributed Maximum Coverage First (DMCF) scheme is shown in Section 4.3. In Section 4.4, we compare the experimental result in term of coverage rate of our algorithms where the directions are rotatable, against those methods in 
and  where the directions are not rotatable.
4.1 Preliminary and Problem Definition
For simplicity, we consider the following assumptions and notations in this chapter. In the directional sensing model, the sensing region of a directional sensor is
a sector-like area of the sensing disk centered at the sensor with a sensing radius.
When the sensors are randomly deployed, each sensor initially faces to a randomly selected direction. Moreover, some interested targets are randomly deployed in the given region. When a target is both located in the direction and the sensing region of a sensor, we say that the target is covered by the sensor. Each sensor node equips exactly one sensor on it and we assume the sensor can detect the information of targets within in its sensing range.
Maximizing number of targets to be covered is the first issue of Maximum Coverage with Rotatable Sensors (MCRS) problem. As we know that, sensor nodes cannot monitor the target even if it is within the sensing radius in a directional sensor network.
For example, In Figure 4.1(a), there are nine targets randomly located in the region but only two targets are covered within the sensing radius of sensors. Suppose that, after the three sensors rotate the sensing direction with some degrees to new working direction. Thus, it is to see that in the region, increasing four targets will be covered by sensor, as shown in Figure 4.1 (b).
Figure 4.1 An example for a sensor to cover more targets by rotating its direction.
The second issue is to minimize the rotatable angles. In most application in WSNs, the power of each sensor is limited. By using the stepper motor or other devices to rotate the sensor with more angles will make the sensor died quickly. So we hope the sensor can cover more targets but rotate with small angles. In the case as shown in Figure 4.2, we will choose the smaller angle to rotate counterclockwise.
(a) Initial deployment (b) Counterclockwise (with small angle)
(c) Clockwise (with large angle) Figure 4.2 Minimize Rotatable with small angles.
4.2 The Definition of the Weight Function
With the MCN value for each target, we can define the target weight as follows to indicate the priority of a target. It can be seen that when a target has a lower MCN value, it implies that the target node can be covered by fewer sensor nodes. Therefore, the target would have higher priority to be covered by a sensor. We use the idea to define the priorities of sensors to be chosen for rotating angles.
In this section, two kinds of weight functions are defined, one is the target and the other is the working direction weight. One priority function has been defined by using the working direction weight. If sensor s has a lower P(s), it implies that the targets inside the direction of s can be covered by fewer other sensors.
The weight of target: Let t be a target and w(t) be the target weight of t.
Then, w(t) = MCN(t).
The weight of working direction: Let D be a unit vector of a sensor s and W(D) be the direction weight of D. Then, W(D) = w(t), for all target t located inside the direction D of sensor s. If there is no target located inside direction D, then W(D) = 0.
The priority of sensor: P(s) be the priority value of s. Then, P(s) = W(D) / k, where W(D) is the direction weight of D and k is the number of targets located inside the direction D of sensor s. If there is no target located inside direction D of sensor s, then P(s) = 0.
4.3 Distributed Maximal Rotatable Angle algorithm
Maximal rotatable angle policy: The objective is to keep those targets in the original direction in the final direction after rotating sensors. One target can be covered after a sensor rotates its working direction, but some originally covered targets may become uncovered. So we need to limit the maximal rotatable angles.
Figure 4.3 An example for MRA policy.
Next we give an example to explain how to limit the maximal angles. Figure 4.3(a) shows the initial deployment. In Figure 4.3 (b), to keep t3 in the final direction, the maximal angle to rotate clockwise is α1. In Figure 4.3 (c), to keep t4 in the final direction, the maximal angle to rotate counterclockwise is α2. For this case we will choose α1 to be the final rotated angles, because s1 can cover two more targets.
The process of our DMRA scheme is to apply the MRA policy on every sensor to rotate effectively to cover more targets. The order of the chosen sensors to apply the MRA policy may result in different performance in term of the target coverage rate.
The proposed DMRA scheme consists of three major steps: compute the priority of each sensor, choose the sensor with the highest priority in local region, and apply the MRA policy on the chosen sensor to rotate. After a sensor has been rotated, the priorities of remaining sensors will be re-calculated and the whole process is repeated for the remaining sensors until there is no remaining sensor.
Figure 4.4 the initial deployment of four sensors.
Here, we demonstrate an example for the proposed DMRA algorithm. In Figure 4.4, there are four sensors, namely s1, s2, s3 and s4. Initially, s1 covers no targets, s2
covers targets t9 and t11, s3 covers targets t7 and t15, and s4 covers targets t1 and t8. Thus, t5
t12 t13 t14
the priority values of s1, s2, s3 and s4 are 0, 2, 1.5, and 1.5, respectively. We can find that s1 and s4 have the highest priority since they have the smallest priority value than their neighboring sensors. Therefore, sensor s1 first rotates to cover more targets and in the same time s4 initializes a back-off time as a value uniformly distributed and goes to listen.
Figure 4.5 The step by step of the DMRA
It should be noticed that, in this case, sensor s1 covers no targets in the very t5
t12 t13 t14
t12 t13 t14
t1 t2 t11
t1 t2 t11
beginning, it will rotate its direction until reach the first target, for example in this case is t10. After it covers the first target, the maximal rotatable angle will be the angle of its direction and the sensor will rotate its maximal rotatable angle to cover more targets. If no other sensors transmit the start-rotated message before the back-off time expires, s4 will be allowed to send the start-rotated message to its neighbors and utilize the MRA policy to rotate. This strategy is to prevent several adjacent sensors from rotating simultaneously. In this case, sensor s1 will cover targets t7, t10 and t14, and sensor s4 will cover targets t1, t2 and t8.
4.4 Distributed Maximal Coverage First Algorithm
Maximal coverage first policy: Try to cover the maximal number of targets after rotating sensor. Do not limit the rotated angles.
In this section, we propose another greedy algorithm for MCRS problem.
Although we can get a better coverage by applying the previous DMRA algorithm, there is a limitation on MRA policy. In the previous section, the original covered targets should be kept in the final coverage regardless of whether the rotation has been applied or not. We want to remove the limitation in order to cover more targets. This means that each sensor looks for the direction that can cover the most targets regardless the rotation angles.
Figure 4.6 An example for MCF policy.
It is possible that a better coverage can be obtained by uncovering some original targets and covering new targets. In Figure 4.6, sensor s1 covers two targets t3 and t4 within its original direction. However, we can find a better coverage which covers t5, t6 and t7 by rotating some degrees clockwise. Note that target t3 and t4 will be uncovered by the sensor s1 in order to cover more targets. The idea is called the Maximal Coverage First (MCF) policy.
(a).The s3 rotates by using the MCF. (b).The s3 rotates by using the MRA.
Figure 4.7 The main difference between MCF & MRA policy.
t1 t2 t11
t1 t2 t11
Basically, the procedure of DMCF algorithm is much the same as the DMRA algorithm. The main difference between them is in the rotation policy. In the DMCF algorithm, we do not limit the rotation angles while in DMRA algorithm the rotation angles are limited by MRA policy. Therefore, we will only demonstrate an example to show how the DMCF algorithm works and skip the detailed procedures.
After sensor s1 and s4 are rotated, the priority values of sensors s2 and s3 are updated to 1.5 and 1, respectively. In Figure 4.7, the coverage of sensor s2 remains t9 and t11. The sensor s3 can find the maximal coverage of covering targets t3, t5, t12 and t13. Note that sensor s3 uncovers target t15 to get a better coverage.
4.5 Simulation Environment and Simulation Results
In this section, through a set of simulation results show the performance of our proposed algorithms. We discuss how the number of directional sensor nodes influence on the performance of DMRA and DMCF.
The experimental environment of our simulation is a two-dimensional plane with the size R×R, where R = 100 meters. The positions of sensor and target nodes are randomly distributed, but any two sensor nodes cannot be located in the same position.
Each sensor has the same sensing radius which is R/10 = 10 meters.
All sensor nodes are identical and each sensor node is aware of its own location and can detect target nodes within the sensing range. Any two of the sensor nodes can communicate with each other and no communication errors and collisions are occurred. After all sensor nodes and target nodes are spread in the area, all nodes are unable to move. Furthermore, in our experiments, we have done two different scenarios, which have 400 and 800 targets randomly deployed in the area, respectively.
For both cases, the number of sensor nodes is varying from 50 to 225. In the following, we show the simulation results for the above purposes.
Network sizes: 100x100(m2)
Sensing radius: 50m
Sensing angle: 60
The number of directional sensors: 50 ,75,100,125,150,175,200,225 Figure 4.8 The table of Experimental parameter.
4.5.1 Coverage Rate vs. the Number of Sensors
First, we present the simulation result of the coverage rate for the two different rotating approaches. The Coverage Rate (CR) is used to measure the ratio of target
nodes that can be covered in the network. The coverage rate can be calculated by using the following equation, where m, mc, and mout represent the total number of targets, the number of covered targets and the number of uncovered targets which means no sensor could detect it by rotating any degrees, respectively.
Figure 4.9 The Coverage Rate vs. the Number of Sensors.
It should be noticed that the higher coverage rate is obtained, the better performance of coverage is achieved. We evaluate the proposed approaches and compare their performance. The experimental result is shown in Figure 4.9. It is easy to see that the DMCF scheme can achieve the higher coverage rate than the DMRA scheme. It justifies that we can rotate the sensing direction to get a better coverage rate. This is because that if we allow the sensors to rotate its sensing direction with a large angle; these sensors can cover as many targets as possible.
50 75 100 125 150 175 200 225
Coverage Rate (%)
Number of Sensors
4.5.2 Coverage Rate per Angle vs. the Number of Sensors
However, we are also interested in finding the benefit of coverage with regard to the rotated angles. Therefore, we compare the coverage rate after rotating sensors by unit angle with DMRA and DMCF schemes. In the second experiment, we focused on the performance of the coverage rate for each sensor after rotating a unit of angle.
Figure 4.10 shows the experimental results.
Figure 4.10 The Coverage Rate per Angle vs. the Number of Sensors.
We can see that the coverage rate per angle of DMRA approach has better benefit than that of DMCF approach. This means that the rotating scheme in DMRA approach can achieve more efficient result than DMCF approach in term of the coverage rate.
But the DMCF approach can achieve better coverage rate by using more angles than DMRA approach.
0.00 0.01 0.02 0.03 0.04 0.05
50 75 100 125 150 175 200 225
Coverage Rate Per Angle (%)
Number of Sensors
DMRA-400 DMCF-400 DMRA-800 DMCF-800