Extending lifetime of sensor surveillance systems in data fusion model

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1 IEEE WCNC Network Exting lifetime of sensor surveillance systems in data fusion model Xiang Cao Xiaohua Jia Guihai Chen State Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, 2093, P. R. China Department of Computer Science, City University of Hong Kong, HKSAR xiangcao@dislab.nju.edu.cn, jia@cs.cityu.edu.hk, gchen@nju.edu.cn Abstract A critical aspect of the sensor surveillance systems is the network lifetime. Sensors are often battery-powered and they have limited energy constraint. Therefore, it is crucial to ext the network lifetime. However, most existing schemes which ext the lifetime of sensor surveillance systems are based on simplistic sensing models (e.g., the disc model) which do not capture the signal attenuation and the collaboration among sensors. In practice, data fusion has been adopted in a number of sensor systems to improve sensing performance. In this paper, we investigate how to ext the lifetime of sensor surveillance systems in data fusion model. Given a set of sensors and a set of targets in a plane, each target needs to be monitored all the time. The problem of our concern is to schedule the sensors to monitor all the targets, such that the lifetime of this surveillance system is exted. The network lifetime is defined as the time duration when each target is monitored. Our work takes the fact that signal attenuates as the distance increases into consideration. We propose two heuristic algorithms to organize sensors into nondisjoint cover sets and activate them successively. Extensive simulations have been conducted to demonstrate the performance of the algorithms. Keywords-data fusion; energy efficiency; sensor surveillance system; network lifetime I. INTRODUCTION In sensor surveillance system, it consists of a set of wireless sensor nodes and a set of targets. Each target needs to be monitored by sensors all the time. The sensors which are powered by batteries have limited energy constraint and it is not easy to recharge them. Hence, energy efficiency is an important issue. The lifetime of the sensor surveillance system needs to be exted as long as possible. Recently, a lot of research works have been done to ext the lifetime of the sensor surveillance system. Most of them are based on simplistic sensing models [1], [2], [3], [4], [5], [6], [7]. They assumed that the sensing region of a sensor was a disc or a sector with a certain radius r centered at the position of the sensor. The target inside the sensing region of a sensor can be deterministically monitored and vice versa. Although this model allows a geometric treatment to the coverage provided by sensors, it fails to capture the energy attenuation of signals emitted by the targets as distance grows. In other words, the farther the distance between the target and the sensor is, the weaker the signal strength the sensor detect is. Moreover, these works based on the these models do not exploit the collaboration among sensors. Data fusion [8], [9], [] has been adopted to improve the target detection in many research works. The major characteristic of data fusion is to take collaboration among sensors into consideration. By jointly analyzing the signal measurements detected by multiple sensors, a decision is made about whether the target can be monitored. In this model, a target can not be deterministically monitored by a single sensor, instead, the model uses the data sensed by multiple sensors around the target to make a decision. In this paper, the problem we investigate is how to ext the lifetime of the sensor surveillance systems in the data fusion model. Given a set of targets and a set of sensors in a two-dimensional Euclidean plane, each target needs to be monitored by sensors all the time. Our goal is to ext the network lifetime of the system by scheduling the sensors to watch the targets in turn, where the network lifetime is defined as the time duration when each target is monitored. To the best of our knowledge, this work is the first to study the lifetime exting of sensor surveillance systems based on data fusion. Unlike the traditional simplistic sensing model, the key challenge of our work is that when data fusion is employed, the decision whether a target is monitored is depent on the measurements of multiple sensors near the target. Our work takes the advantage of collaborative sensing to monitor the targets and considers both data fusion and signal attenuation of the targets. The rest of this paper is organized as follows. Section II is related work and Section III is the background and problem statement. In Section IV, we propose our solution. Simulation results are in Section V. Finally, we conclude our work in Section VI. II. RELATED WORK There are some research works about how to prolong the lifetime of sensor networks. The basic idea of these papers is to save the energy of sensor nodes by activating them in turn. In [1], Liu et al. determined the workload matrix by using linear programming and achieved the maximal lifetime by decomposing the matrix into a series of scheduling ones. They assumed that every sensor node can monitor at most one target at each time. This work was exted in [2] by considering the communication cost. In [4], Tian and Georganas turned off the sensor node when its neighbors can help it to watch the area by proposing a localized scheduling scheme. In [5], Cardei /11/$ IEEE 641

2 and Du presented a method to divide sensors into a maximal number of disjoint cover sets. They activated the cover sets one by one to ext the network lifetime. In [6], Cardei et al. divided the sensors into nondisjoint cover sets and activated them successively. All the targets could be watched by sensors in each cover set. In [3], [7], Cai et al. investigated the multiple directional cover sets problem to ext the lifetime of the directional sensor networks. They organized directions of sensors into different cover sets and allocated working time to them by using heuristic algorithms. However, all of these works adopted the deterministic model to decide whether a target can be sensed by sensors. They did not consider the attenuation of signal strength of target when distance grows. In contrast, we study the lifetime exting problem based on data fusion model which captures the collaboration of sensors. We take the signal attenuation into consideration as well. Recently, data fusion has been adopted into the research of the wireless sensor networks. In [11], Xing et al. studied the coverage performance of large-scale wireless sensor networks based on collaborative sensing models. Their work showed that data fusion could improve sensing coverage significantly by exploiting the sensors collaboration. In [9], Clouqueur et al. addressed the problem of finding algorithms for collaborative target detection. In [12], Niu and Varshney proposed a decision fusion rule by using the detections reported by local sensors for hypothesis testing. In [13], Tan et al. analyzed the Quality of Surveillance (QoSv) in fusion-based sensor networks. They showed that data fusion was effective in achieving stringent QoSv requirements. In [14], Tan et al. showed the impact of data fusion on real-time detection in sensors networks. They also proposed an adaptive system-level calibration approach to improve sensing performance for sensor networks using data fusion in [15]. In [16], Wang et al. characterized the influence of the number of cooperating sensors on the overall sensing quality. In [17], Yuan et al. proposed fast sensor placement algorithms for target detection based on a probabilistic data fusion model. Research works on data fusion [18], [19], [20] considered spatial distribution of sensors and their limited sensing capability. In practice, some sensor network systems adopted some kind of data fusion schemes to improve the performance of target detection, tracking and classification [18], [19], [21]. III. BACKGROUND AND PROBLEM STATEMENT In this section, we introduce the background of this paper, which includes the sensing model and the data fusion model. Then, we present the problem statement. A. Sensing model In this paper, we assume that sensors detect targets by measuring the energy of signals emitted by the targets. For many physical signals, such as acoustic, seismic and electromagnetic signals, the energy attenuates as the distance from the signal source grows. Suppose the target i emits a signal of energy S, and sensor j is d ij meters away from the target i. The attenuated signal energy w ij of target i at the position of sensor j is given by w ij = S f(d ij ) (1) where f( )is referred as the signal decay function. In this paper, we adopt the signal decay function in the simulations as follows, f(x) = 1 1+x k (2) where k is a decaying factor which typically ranges from 2.0 to 5.0. This signal attenuation model is adopted in the literature [11], [13], [14]. For simplicity, in this paper, we do not consider the influence of noise on the sensor measurements. B. Data fusion model By jointly considering the measurements of multiple sensors, data fusion can improve the performance of detecting targets. In sensor networks, in order to employ data fusion, sensors are often organized into clusters. By fusing the information gathered from the member sensors in the cluster, each cluster head is responsible for making a decision about whether the target is present. In this paper, we adopt the following data fusion model. For every target i, the sensors within a distance of R meters from target i form a cluster and fuse their measurements to decide the presence of the target. R is referred to as the fusion range. A cluster head is elected to make the decision by comparing the sum of measurements reported by member sensors in the fusion range against a detection threshold η. Ifthesumisno less than η, the cluster head decides that the target is present. Otherwise, it decides that the target is not present. C. Problem statement In this paper, we focus on the following problem. Given a two-dimensional Euclidean plane, a set of m targets and a set of n sensors are deployed with known locations. Each target needs to be monitored all the time and each sensor has initial energy reserve. Our goal is to ext the network lifetime of the sensor network, where the network lifetime is defined as the time duration when each target is monitored. We say that a target is monitored if the sensors in its fusion range decide that this target is present based on the data fusion model mentioned above. Our approach is to organize the sensors into a number of nondisjoint sets, such that each set completely monitors all the targets. We denote these sets as the cover sets. These cover sets are activated successively, such that only one set is active at any time. The sensors in the active set are in the active state, while all the other sensors are in the sleep state. IV. OUR SOLUTION In this section, we introduce our solution. The basic idea is to find cover sets one by one. We find and activate only one cover set at a time and let sensors in it work until one of them depletes its energy. Then we find another cover set and activate it. This process is repeated until one or more targets can not be monitored by sensors which have remaining energy. 642

3 In order to find cover sets, we propose two algorithms, a greedy heuristic and a Linear Programming based heuristic. The basic idea of them is to choose as few sensors as possible to form a cover set to monitor all the targets in every step. A. The greedy heuristic chooses cover sets in many iterations. In each iteration, it forms a cover set by selecting sensors one by one. First, targets are sorted according to the number of sensors within their fusion range in the descing order. We start from the target with the largest number of sensors in its fusion range first. We examine whether the chosen target can be monitored by the current set (Initially, the set is empty). If not, we select one sensor at a time into the set until the target can be monitored based on the data fusion model. In this sensor selecting process, the algorithm chooses sensors by considering their distance to the target. The closer the distance between the sensor and the target is, the earlier the sensor will be chosen. When the target can be monitored by the sensors in the set, we move on to next target to continue selecting sensors into the set until all the targets are monitored. We refer the set as a cover set since it can monitor all the targets. Next, the sensors in the cover set will work until one of them depletes its energy. Then, we will find another cover set using the method above until the cover set can not be found. Finally, the algorithm returns the number of cover sets, the cover sets and the total network lifetime. Algorithm 1 illustrates the whole process. Some explanations are as follows. In Algorithm 1, the set U maintains the list of sensors that have the residual energy so that these sensors can participate in the additional cover sets. Since the location of each sensor and target are known, the signal strength of each target that sensor j senses can be computed by using Eqs. (1) and (2). By simply comparing the sum of signal strength that each sensor in set V receives with the threshold η, we can easily determine whether the target can be monitored by sensors in set V.At the last line of Algorithm 1, i, C 1,C 2,..., C i, T represent the number of cover sets, the cover sets and the total network lifetime respectively. B. Linear Programming based heuristic Like Algorithm 1, in this heuristic, we generate the cover sets in many iterations too. In each iteration, we select sensors into a cover set by formalizing it as an Integer Programming. Suppose there are m targets. We set x j as a boolean variable. x j = 1 if sensor j is in the cover set, otherwise x j =0. w ij indicates the signal strength of target i detected by sensor j. w ij can be computed offline by using Eqs. (1) and (2) in the previous section. In this algorithm, if sensor j is out of the fusion range of target i, wesetw ij =0. n represents the number of sensors which have remaining energy and η is the threshold. The optimization problem can be written as: Minimize x j (3) Algorithm 1: U = all sensors; i =0; T =0; while true do V = ; Sort the targets according to the number of sensors within their fusion range in U in the descing order; for all targets do Pick one target at a time; if the target can be monitored by sensors in V then continue for; // move on to the next target; else W = ; Put the sensors within the target s fusion range in U into W ; Sort the sensors in W according to their distance to the target in the ascing order; repeat Select one sensor at a time; W = W {this sensor}; V = V {this sensor}; if the target can be monitored by sensors in V then continue for; // move on to the next target; until W is empty; if the target can not be monitored by sensors in V then break while; i = i +1; C i = V ; Run sensors in C i until one of them s depletes its energy and get the working time t i ; U = U {s}; T = T + t i ; Update the residual lifetime of sensors in C i ; return i, C 1,C 2,..., C i, T ; subject to where w ij x j η, i =1, 2,..., m (4) x j = {0, 1}. (5) 643

4 The objective function (3) minimizes the number of sensors in each cover set. The constraint (4) shows that each target should be monitored. The constraint (5) is the restriction on the x j. To transform this formulation into a Linear Programming (LP), we further apply the relaxation technique: subject to where Minimize x j (6) w ij x j η, i =1, 2,..., m (7) 0 x j 1. (8) Now we introduce our linear programming based heuristic algorithm. In each iteration, we first solve the linear programming formulated above and get the solution x 1,x 2,..., x p. Then, we sort x 1,x 2,..., x p in the descing order and get the new sequence y 1,y 2,..., y p.wepicky 1 first, and set y 1 =1which means we put the sensor that y 1 represents into the cover set. We examine whether sensors in the cover set can monitor all the targets. If not, we continue to set y k =1, k =2,..., p and put more corresponding sensors into the cover set until all targets can be monitored. At this moment, a cover set is formed. Next, like Algorithm 1, we let sensors in the cover set work until one of them depletes its energy. Then we renew the objective function (6) and constraint (7) of the Linear Programming since one sensor has no remaining energy so that it can not be chosen at the next iteration. We continue to find another cover set until it can not be found. In the, the algorithm returns the result. The whole process is illustrated in Algorithm 2. In Algorithm 2, the Linear Programming returns x 1,x 2,..., x p in each iteration. We give an example to show how to select sensors into a cover set given the sequence x 1,x 2,..., x p. Assume there are six sensors and the value of x 1,x 2,..., x 6 are {0.3, 0.8, 0.04, 0.1, 0.6, 0.5}. After sorting, we get the value of the sequence y 1,y 2,..., y 6, which are {0.8, 0.6, 0.5, 0.3, 0.1, 0.04}. According to y 1,y 2,..., y 6, we set y 1 =1first, which means we put sensor s 2 into the cover set. If sensor s 2 can not monitor all the targets based on the data fusion model, then we set y 2 =1and put sensor s 5 into the cover set. We repeat this process until all the targets can be monitored. In this example, suppose three sensors {s 2,s 5,s 6 } can monitor all the targets. The energy reserves of these three sensors are 1.2, 0.9 and 1.1 respectively. We let them work until sensor s 5 depletes its energy. Then we exclude the sensor s 5 from the objective function (6) and constraint (7) of the Linear Programming since in the next Algorithm 2: Linear Programming based heuristic i =0; T =0; while true do V = ; Solve the Linear Programming; if the Linear Programming can not be successful then break while; else Get the Linear Programming solution x 1,x 2,..., x p ; Sort x 1,x 2,..., x p in the descing order and get the new sequence y 1,y 2,..., y p ; for each y k do y k =1; Put the sensor which y k represents into V ; if all the targets can be monitored by sensors in V then break for; if the sensors which y 1,y 2,..., y p represent can not monitor all the targets then break while; i = i +1; C i = V ; Run sensors in C i until one of them s depletes its energy and get the working time t i ; T = T + t i ; Update the residual lifetime of sensors in C i and renew the objective function (6) and constraint (7) of the Linear Programming; return i, C 1,C 2,..., C i, T ; iteration, there only exists five sensors which have remaining energy. V. SIMULATIONS In this section, we first evaluate the performance of the greedy heuristic algorithm and the Linear Programming based heuristic algorithm. Then we give some discussions about our algorithms. We simulate a stationary network with targets and sensor nodes randomly located in a 0m 0m area. The initial energy reserves of sensors are random numbers generated in the range of [0.5,1.5] with the mean of 1. We normalize S (the energy of signal strength which the targets emit) and the threshold η as 1 and 4 respectively. We set the signal decaying factor k as 2. In the following experiments, we vary the number of sensors, the fusion range and the number of targets respectively. 644

5 disc model disc model Network lifetime 15 Network lifetime Number of sensors Number of targets Fig. 1. Network lifetime versus number of sensors with targets, fusion range of 40m and sensing range of 30m Fig. 3. Network lifetime versus the number of targets with 40 sensors, fusion range of 60m and sensing range of 30m disc model Network lifetime 15 Cover sets Fusion range(m) Number of sensors Fig. 2. Network lifetime versus fusion range with targets and 40 sensors Fig. 4. Cover sets versus number of sensors with targets, fusion range of 40m and sensing range of 30m To solve the linear programming, we use the optimization toolbox in Matlab [22]. In the first experiment, we vary the number of sensor nodes between 20 and 70 with an increment of. We set the fusion range as 40m and the number of targets as. In order to analyze the performance of the two heuristic algorithms, we compare them with the traditional simplistic sensing model. We set the sensing range of sensors in simplistic disc model as 30m. In this simulation, we formalize the simplistic disc model as the traditional set cover problem. Like the two heuristic algorithms, we choose cover sets in many iterations. In each iteration, we use the Linear Programming to find as few sensors as possible to form a cover set. We let sensors in the cover set run until one of them depletes its energy and find another cover set until it can not be found. We denote this method as the 0-1 disc model since targets inside the sensing range of the sensor can be monitored deterministically and vice versa. Each algorithm runs 0 times through random placement of sensors and targets. Fig. 1 shows the relation between network lifetime and the number of sensors. The network lifetime will increase as the number of sensors grows. With each number of sensors, we can see that the network lifetime by using the or the is about ten times larger than that in traditional simplistic sensing model. This difference is larger as the number of sensors increases. Next, we investigate the influence of fusion range on the network lifetime in the data fusion model. We set the number of sensors and the number of targets as 40 and respectively. We vary the fusion range in the data fusion model between 50m and 75m with an increment of 5m. Fig. 2 shows the relation between the network lifetime and the fusion range. We can see that the network lifetime increases as the fusion range expands. The reason is that when the fusion range is larger, more sensors can participate in the 645

6 cover set selecting process so that each cover set will contain fewer sensor nodes. This can let more sensors sleep during each iteration and lead to the increase of the total network lifetime. In order to investigate the relation between the network lifetime and the number of targets, we set the number of sensors as 40, the fusion range as 60m and the sensing range as 30m. We vary the number of targets between and 60 with an increment of. Fig. 3 shows the relation between them. As the number of targets increases, the network lifetime will drop. Then, we focus on the number of cover sets. We compare the number of cover sets of greedy heuristic and the LP based heuristic with traditional simplistic disc model. In Fig. 4, the number of cover sets by using and are about twice as large as that under disc model. Too many cover sets may be inefficient (e.g., it may cause sensors to switch between active state and sleep state more frequently.), but compared with the network lifetime improvements shown in Fig. 1, the increase of the number of cover sets is acceptable, especially when the number of sensors is relatively small. In this paper, we propose two algorithms to organize sensors into nondisjoint cover sets to monitor all the targets. We assume that the sensors have different energy reserves. However, in some cases, sensors need to be divided into disjoint cover sets [5]. In this circumstance, it is often assumed that the initial energy reserves of sensors are the same. Our proposed algorithms can easily be exted to deal with the problem of organizing sensors into disjoint cover sets. In each iteration, after the cover set is formed by using our algorithms, the system can exclude the sensors in the cover set from the whole sensors. Then, another cover set can be found among the remaining sensors. This process is repeated until the cover set can not be found. The cover sets found by running our algorithms are disjoint ones. VI. CONCLUSION Saving energy to prolong the network lifetime is always important for sensor surveillance systems. As an effective technique for improving sensing performance, data fusion has been adopted into the wireless sensor networks. In this paper, we address the problem of exting lifetime of sensor surveillance systems based on data fusion model. We propose two heuristic algorithms to find nondisjoint cover sets and activate them successively. We take the fact that signal strength attenuates over distance and collaboration among sensors into consideration. 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