In traditional wireless sensor networks (WSNs), tracking the targets by static sensors is an important and basic application.^[1,2] However, there are several problems. First, due to the limited sensing ranges of sensors, a large number of sensors are deployed in an interested area in order to satisfy the coverage property. But during each sampling time, the target group only occurs in a small region of the interested area, hence the deployment of a large number of sensors is a waste of resources.^[3–5] Second, the energy of sensors is limited, but the tracking process will consume a great deal of energy. When sensors drain their battery power, many problems will appear in the WSNs, such as communication holes and coverage holes.^[6–8] In recent years, with the development of robots and wireless communication, mobile sensors are used in many applications. Compared with static sensors, mobile sensors have some advantages.^[9–11] On one hand, mobile sensors can move to any position according to the requirement of target tracking, so the interested area does not need to be completely covered by sensing ranges of sensors. On the other hand, mobile sensors can move close to targets, so the tracking accuracy is improved.

In this paper, we consider the problem of tracking a target group by a hybrid network including mobile sensors and static sensors. However, there are several challenges in order to solve the problem. First, the problem of tracking a target group is different from tracking multiple targets. A group of targets forming a compact body, named a target group, move together from one location to another for a common goal. The problem of tracking multiple targets focuses on tracking the trajectory of each target. A target group is defined as a lot of targets with related motions including associated velocities, directions, accelerations, etc. Since the number of targets within a target group is large and they are near to each other, it is not necessary and it is difficult to track each target. In this paper, the problem of tracking a target group is modeled on tracking a continuous region covered by the target group. Second, it is worth noting that, to reduce the waste of resources, the number of sensors is limited. Hence, the union of sensing ranges of all the static sensors cannot guarantee full coverage of the interested area. But the static sensors are connected with each other. Generally, sensors have three working modes: sleeping mode, sensing mode, and active mode. When a sensor works in active mode, the energy consumed is the largest among the three modes. To save the energy of static sensors, they only work in low-power sensing mode. Under this mode, static sensors periodically sample the movement of the target group, and they only generate the simplest information, which is a binary digit “1”. Hence, the first problem is how to schedule the minimum number of mobile sensors during each sampling period to guarantee coverage for the region where the target group appears. Therefore, the objective region should be estimated by deficient static sensor resources. The second problem is, during each sampling period, how to assign the locations for the selected mobile sensors as their destinations. The objective is to maximize the average remaining energy of mobile sensors.

The main contribution of this paper is summarized as follows.

(i) In order to reduce the number of sensors participating in the tracking task, the target group is tracked by several mobile sensors cooperating with sparsely distributed static sensors. First, an estimation algorithm is proposed. At the beginning of each sampling period, the region where the target group appears is estimated by static sensors with insufficient information. Then, to satisfy the coverage property of the estimated region, the locations where mobile sensors should move to is decided.

(ii) We propose a distributed scheduling algorithm based on sliding windows. According to the predefined weigh function, the movement priority for each mobile sensor is computed. Then, based on the former deployment result for the estimated region, each selected mobile sensor chooses a suitable location as its destination, so that the movement cost satisfies the predefined objective function.

To summarize, static sensors and mobile sensors are assigned to different tasks. Static sensors are responsible for estimating the region where the target group appears. Mobile sensors are responsible for tracking the target group. When mobile sensors sense the targets, they will generate data packets, and send them to the sink. The data packets generated by mobile sensors contain much more information than those of static sensors.

The rest of this paper is organized as follows. Section 2 states the related works. Section 3 and Section 4 define the target group tracking problem and propose our solutions to the problem. Simulation results and conclusions are given in Section 5 and Section 6, respectively.

Wireless sensor networks are used in many application areas. One application is target tracking, which is used in wildlife surveillance, military affairs, environmental monitoring, and so on. Traditional tracking algorithms are based on static sensors.^[12] Since most sensors should keep in active mode, sensors consume a great deal of energy to track the target and communicate with other sensors.^[13] Hence energy consumption is the main challenge for static sensor networks.^[14,15] In order to solve this problem, prediction algorithms have been proposed in many studies.^[16–18] In Ref. [19], the location of the target in the next time interval is predicted according to the factors including the previous location, the current acceleration, and speed of the target. Based on the prediction result, fewer sensors are activated to track the target. In Ref. [20], sequential Monte Carlo is used to predict the target position. Then, a dynamic collaboration scheme is proposed for camera tracking. The reference [21] focuses on the target group problem based on the static sensors. First, the definition of a target group is proposed, and the tracking problem is modeled as tracking a monitoring region. Then, a Hull–Algorithm and Cir–Algorithm are proposed to estimate the monitoring region based on binary sensors; however, the sensors cannot move close to the targets, thus the tracking solution is less effective than that of mobile sensors.

In static sensor networks, when the energy of the sensors is exhausted, many problems will exist. Hence, in recent years, many researches introduce the mobile sensors. The reference [22] focuses on the target tracking problem based on heterogeneous camera sensor networks, which consist of a lot of static sensors and a small number of mobile camera sensors. Camera sensors are controlled to track the target in a cascading scheme. In the context of target tracking under various scenarios, the authors in Ref. [23] proposed a tracking solution based on a hybrid network, which consists of a few mobile sensors and a large number of fixed sensors. First, fixed sensors detect the appearance of the target and obtain the current location of the target. Second, mobile sensors close to the target are informed to move toward the target. Hence, the mobile sensors are scheduled to track the target coordinating with fixed sensors. Then, the solution is extended for tracking multiple targets. Based on the action force algorithm, mobile sensors are dispatched to track every single target. In this target tracking scheme, static sensors also need to track the targets. Since the energy consumption of tracking targets is larger than that of sensing targets, static sensors consume a great deal of energy during the tracking process. In order to maximize the lifetime of a network, the authors in Ref. [24] computed the sensing radius, communication radius, and locations of sensors, which cooperate to track a target. However, the energy model does not conclude the movement energy of sensors. In Ref. [25], the authors were concerned with the energy-efficient tracking problem in the presence of obstacles. The field is divided into a grid of small cells. The objective is to find the corresponding locations and shortest path for sensors. In order to solve this problem, the grid is converted to a graph, whose edges are weighted according to the energy consumption of sensors. The energy model consists of sensing, movement, and communication energy. Due to the shortcomings of the traditional particle filter algorithm, an improved particle filter algorithm is designed in Ref. [26] for target tracking. First, the location model is constructed with the features of the target as the measurements. Second, the weight of the particle filter algorithm is optimized. Then, the improved particle filter algorithm is adjusted according to the difference between the current and predicted values. The mobile sensors in Ref. [27] are dispatched to track the target based on the estimation result. First, the location of the target is predicted by the online estimation. Second, the assignment problem of the mobile sensors is modeled as an integer linear programming problem. In Ref. [28], the location of the target is estimated by the improved Kalman filter, and a maximum likelihood is used to deal with the sensing nonlinearity. In sum, many existing references have studied the problem of tracking one or multiple targets; however, the number of targets within a target group is large and they are very close to each other, thus many existing tracking algorithms are not suitable for the scenario of tracking a target group.

In this section, some theorems are given as follows.

In this section, we carry out extensive simulation tests to evaluate the performance of our algorithm. The target group tracking algorithm proposed in this paper is called HNTA. In our simulations, we run the algorithms 10 times, and use 10 random trajectories for the logical center of the target group. In each test, sensors are randomly deployed. The simulation results are the averages of 10 tests. The parameters for the network setup are shown in Table 1. The unit energy cost of mobile sensors ΔE, which is specified in Ref. [29], is used in this paper.

Table 1.

Table 1.

Table 1. Simulation parameters. . Parameters Values Interested area size/m2 400 × 400 Number of simulations 10 Velocity of targets/(m/s) 0.3 Velocity of mobile sensors/(m/s) 2 α 1 β 2 γ 2 E/(energy unit per meter) 1 Initial energy of a mobile sensor (energy unit) 1000

Table 1. Simulation parameters. .

Figure 7 focuses on the effect of the number of static sensors on the estimation error. In this experiment, the number of targets is 20. The setting of r_s is 20. We can observe that the estimation error decreases as the number of static sensors increases. With the increase of the number of static sensors, more static sensors have sensed the targets. The sink can obtain more information about the targets. Thus the tracking accuracy is enhanced. We can also find that the estimation error is less than the value of r_s + d_m. This result is consistent with Theorem 3.

Fig. 7.

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	Fig. 7. Number of static sensors versus estimation error.

Figures 8–10 concern the number of sensors tracking the targets. In HNTA, the task of the static sensors is working in the low-power sensing mode to estimate the objective region, while the task of the mobile sensors is tracking the target group. Hence, figures 8–10 evaluate the number of mobile sensors tracking targets in HNTA. We compare our proposed HNTA with the algorithm proposed in Refs. [30] and [31], which are called SOTA and DEETH respectively. In SOTA, the network is organized into several grids. During each sampling period, minimum sensors in a grid are schedule to track the targets.

Fig. 8.

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	Fig. 8. Number of targets versus number of sensors tracking targets.

Figure 8 shows the average number of sensors participating in the tracking task during each sampling time when the number of targets increases from 20 to 60. In this experiment, the number of static sensors and mobile sensors are 500 and 300, respectively. They are randomly deployed in an interested area. Initially, static sensors and mobile sensors are connected, respectively. We can observe that, in HNTA, when the number of targets within a target group increases, the number of mobile sensors selected by the sink to track the targets increases. The reason is that, with the increase in the number of the targets, the estimated objective region is expanded. More sensors are needed to cover the estimated objective region entirely. We can also find that, in SOTA, the number of sensors scheduled to tracking the targets is larger than that of HNTA. In addition, when further increasing the number of targets, the number of sensors for tracking targets in SOTA is significantly increased. This is because, in SOTA, the interested area is divided into grids. When the targets move in a grid, the minimum number of sensors are selected to cover the grid. However, the targets may only occur in a part of a grid, hence the entire coverage of a grid is a waste of resources. When the number of sensors is not large enough, the targets may only occur in a grid. With the increasing number of the targets, the targets will occur in several grids. The sensors in these grids are scheduled to track the targets. Therefore, the number of sensors tracking the targets increases obviously. The number of mobile sensors searching for targets in DEETH is also evaluated. We can find that the number of mobile sensors tracking targets in DEETH is larger than HNTA. After static sensors are deployed, although static sensors are connected with each other, there may be some coverage holes. In this circumstance, the static sensors may only sense some targets, and the other targets cannot be sensed by static sensors. In DEETH, the mobile sensors need to move randomly by the swarm technique to search for them. Thus, in order to find these targets quickly, more sensors need to be schedule in DEETH. However, in HNTA, first, according to the information of static sensors which have sensed targets, the region where the target group may appear is estimated. Then, the mobile sensors only need to cover the estimated region. In another circumstance, when all the targets are sensed by static sensors, in DEETH, for each static sensor which have sensed targets, at least one mobile sensor moves towards it. In HNTA, the deployment solution for mobile sensors in the objective region reduces the overlap of sensing ranges. Then the number of mobile sensors tracking the targets is reduced. Thus, HNTA performs better than DEETH.

Figure 9 evaluates the effect of r_s on the number of sensors tracking the targets. In this experiment, the number of targets is 20. To reflect the relationship of , the settings of (r_c, r_s) are (9,5), (12.6,7), (18,10), and (21.6,12), respectively. We can find that, with the increase of r_s, the performance achieved by HNTA, DEETH, and SOTA trends downward, and HNTA outperforms DEETH and SOTA. The reason is that, when r_s increases, less sensors are dispatched to cover the region where the targets move in.

Fig. 9.

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	Fig. 9. rs versus number of sensors tracking targets.

Fig. 10.

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	Fig. 10. rc/rs versus number of sensors tracking targets.

Figure 10 highlights the effect of the ratio r_c/r_s on the number of sensors tracking the targets. In this experiment, to reflect the relationship from to , the settings of (r_c,r_s) are (10,12), (13,12), (19,12), (22,12), and (28,12), respectively. The number of targets is 20. Compared with , the number of sensors tracking the targets is more when . This is because, in HNTA, the deployment scheme of sensors is illustrated by Fig. 3(a) and Fig. 3(b) when and , respectively. We can also observe that, HNTA performs better than DEETH and SOTA.

The energy consumption of a sensor consists of three parts: energy consumption in the sleeping state, active state, and sensing state. The energy consumed in the sensing state is smaller than that in the active state. In addition, the energy of static sensors is limited, and they cannot change the battery. Hence, in the algorithm proposed in this paper, static sensors work in sensing state to reduce the energy consumption, but mobile sensors work in active state. Static and mobile sensors work together to track the target group. In the other two algorithms, DEETH and RM, mobile sensors also work in the active state. The focus of the three algorithms is the motion strategy of the mobile sensors, and the energy consumption of mobile sensors is much more than that of static sensors. Therefore, in the simulation experiment, we only evaluate the energy consumption of the mobile sensors in the three algorithms, without considering the energy consumption of the static sensors.

Figures 11–12 evaluate the effect of movement strategy on the energy consumption of mobile sensors. The object is during each sampling period, the targets are found by mobile sensors. Figure 11 shows the average remaining energy of sensors when the number of targets changes. The setting of (r_c,r_s) is (20,10). We compare our algorithm with DEETH and a random method designed in Ref. [29], which is called RM. The main idea of the RM is, during each sampling period, the sink randomly selects a location in L for each mobile sensor in S as its destination. In Fig. 11, the average remaining energy of sensors achieved by HNTA is higher than that of RM. The reason is that, the process for a sensor to find its destination is a matching problem. In HNTA, this problem is modeled as a bidirectional choice between L and S. The matching results are obtained according to the priority function. Thus, compared with RM, the HNTA can prolong the network lifetime. In the tests, we evaluate the energy consumption of the searching process in DEETH. We also assume that, in HNTA and DEETH, when a mobile sensor moves towards a location, it moves along the line between them. We can also find that the remaining energy in HNTA is more than in DEETH. The reason is that, in DEETH, when there are some targets not sensed by static sensors, mobile sensors move randomly by the swarm technique to find them. In HNTA, although there are coverage holes, the object region of the target group can also be estimated. Hence, in order to find the targets, the moving distance of mobile sensors in HNTA is shorter than DEETH.

Fig. 11.

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	Fig. 11. Number of targets versus remaining energy of sensors.

Fig. 12.

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	Fig. 12. rs versus remaining energy of sensors.

Figure 12 shows the average remaining energy of sensors when r_s changes. The number of targets is 20. The setting of r_c is 15. We can observe that, HNTA performs better than RM and DEETH. Therefore, the HNTA can effectively balance the energy consumption of mobile sensors.

A target group tracking algorithm based on a hybrid sensor network is proposed in this paper. The objective region is estimated by static sensors, which works in low-power sensing mode. Then, each selected mobile sensor chooses a location as its destination based on the movement algorithm. Algorithm analysis provides the fundamental limits of the estimation algorithm, and the time complexity of the movement algorithm. Simulation results show that this algorithm can decrease the number of mobile sensors tracking the targets, and effectively balance the energy consumption of mobile sensors.