LEACH-MTC ： A Network Energy Optimization Algorithm Constraint as Moving Target Prediction

— When some nodes cooperatively track moving targets in wireless sensor network, some things including network working node selection and network energy consumption are influenced. Thus, this paper proposes an improved algorithm LEACH-MTC (LEACH with Moving Target Constraint) based on low energy adaptive clustering hierarchy protocol (LEACH). Firstly, based on the two-step linearization of the nonlinear dynamic model, the state of nonlinear moving target is predicted by the extended Kalman filter (EKF). Secondly, combining the state prediction of moving target and the performance of collaborative monitoring, this paper constructs an ellipse monitoring area of some working nodes to consist with the direction of the target movement. Subsequently, the node sleep strategy corresponding to the state prediction of moving target is designed. Finally, the cluster head selection strategy is proposed based on energy balance utilizing the state prediction of the moving target. Simulation results show that the proposed LEACH-MTC algorithm can not only ensure the real time consistency between the changing direction of area and the direction of target movement, but also increase the number of working nodes’ survival and reduce the network energy consumption.

modeling, and so on. When the wireless sensor network nodes cooperatively track the moving target, the target motion state (for example, the motion trajectory, speed, direction, etc.) will affect the selection of the network working nodes and the network energy consumption.
In this paper, an improved algorithm named LEACH-MTC (LEACH with Moving Target Constraint) is proposed, this algorithm constructs a time-varying ellipse area in which the nodes are working nodes, these nodes format work node set and are used to monitor moving target. The proposed network node dormancy strategy considers the distance between the working node and the focuses of ellipse area. The proposed cluster head selection threshold considers the distance factor between the working node and the moving target. As a result, for the actual cooperative tracking environment, the proposed LEACH-MTC is more feasible for the realization of the moving target cooperative tracking system. Overall, the main contributions of this paper can be summarized as follows: 1) We timely construct an ellipse monitoring area with the direction changing of the moving target, which constitute a work node set to monitor the moving target. Because using two-step linearization method to linearize nonlinear dynamic system, and utilizing extended Kalman filter (EKF) to predict the moving target state, the shape and size of the ellipse area and the number of nodes contained in the area can all be changed in real time. Above can reduce the number of work nodes, thus reduce the network energy consumption caused by redundant nodes.
2) To reduce the number of working nodes, an improved network node dormancy strategy is proposed to construct working node set under the moving target tracking environment. Besides, according to the network node's own attributes and monitoring environment factors, some network monitoring accuracy indicators are reconstructed. Thus, the monitoring efficiency of system is improved.
3) Based on the working node set and the state prediction of moving target, a new cluster head selection threshold is proposed. Because the number of working nodes is considered to vary in real time, above cluster head selection strategy can be adaptively used to select the cluster head to transmit the collected data.
4) The simulations of this paper are carried out base on MATLAB platform. To better describe the feasibility and effectiveness of LEACH-MTC, we conduct designed simulation to verify the monitoring accuracy by difference working node selection strategies, the number of node survivor, the network residual energy, and so on. We can conclude that the proposed LEACH-MTC yields better performance than traditional methods. The rest of this paper is organized as follows. In the second section, the target nonlinear dynamic model and the target state prediction model are described. In the third section, the new network node dormancy strategy, improved cluster head selection strategy and network monitoring accuracy criterion are designed, respectively. The LEACH-MTC algorithm based on moving target constraints is proposed. In the fourth section, the feasibility and effectiveness of the improved algorithm are simulated and analyzed in terms of saving the number of working nodes and reducing the network energy consumption. The conclusions of this paper are given in the final section.

II. SYSTEM MODEL AND CONVENTIONAL METHOD
In the WSNs, some nodes collaborative observing target may obtain more information. We awaken some nodes in WSNs based on state prediction of target to coordinate observe target. In this section, we present target motion model, target measurement model, energy consumption model of sensor nodes and prediction mechanism of target state, respectively.

A. Nonlinear motion model of target
In a two-dimensional monitoring area, target motion model as following: where  

C. Two-step linearization of target state prediction
Since the motion model of target and the measurement model of target are the equation (2) and (4), and they constitute a nonlinear detection system. They are nonlinear function, thus the standard Kalman filter (KF) is no longer applicable, and the nonlinear filtering problem needs to be approximated as a linear filtering problem, so that a suboptimal solution is obtained.
Therefore, the Extended Kalman Filter (EKF) can be considered to predict or estimate the target state.
In the above nonlinear system, since the nonlinear system needs to be linearized, that is, the Taylor series expansion is used to approximate the nonlinearity, which is transformed into the process of calculating the Jacobian matrix of the Therefore, the linearized system model can be obtained after linearization: where, here, it is important to note that the equation (6) is obtained using two-step linearization. i x 、 i y in   k H are defined as the Xaxis and Y-axis of i s nodes, respectively.
Based on the nonlinear system model (2) and (4), and the linearized system model (5), the state of moving target can be estimated or predicted by the Kalman filter. The main steps are as follows:

D. energy consumption model of sensor nodes
We use first order model described in [15] to model energy consumption of WSNs. Considering l bit data in each data packet, we describe energy consumption of node related to receiving and transmitting one data packet as follows.
Where In WSNs, when some network nodes cooperatively track a target, although the network monitoring performance is improved, the addition of a large number of working nodes will cause redundant measurement information of the target, and also cause waste of the node resources. In order to improve the utilization of nodes and reduce the energy consumption of the network, this section proposes an improved algorithm called LEACH-MTC based on the prediction information of moving targets, and it's flow chart is shown in Fig.1.

Fig.1 LEACH-MTC algorithm flow chart
Based on the LEACH protocol, the LEACH-MTC algorithm uses EKF to obtain the state prediction of moving targets in nonlinear system. In addition, an elliptical coverage area which related to the state prediction is designed to determine the working nodes. Besides, the improved node sleep strategy and the improved cluster head selection strategy are designed under the constraints of moving targets, respectively. Subsequently, three improvements including elliptic coverage construction, node sleep strategy, cluster selection strategy are introduced under some constraints of moving targets.

A. Classical LEACH algorithm
LEACH algorithm [16] is the earliest clustering routing algorithm, which is mainly based on the process wheel and node clustering. This algorithm regards a work cycle as a round, and divides the work process into several rounds, this algorithm periodically executes the work process. Each round contains two processing: the node cluster and the data transfer. In the processing of node clustering, cluster heads of network nodes should be selected first, and a cluster head set should be constructed. Then, cluster heads with hierarchical structured should be formed by each cluster head node and non-cluster head nodes.
Whether some nodes become cluster heads can be judged by the threshold   i Ts , which is as the equation (13) (14) here, p is the ratio of the number of expected cluster head nodes selected to the total number of nodes in the monitoring area.
r is the current network running time (i.e. the number of running rounds). G is the node set that has not been selected as cluster head in the latest round 1 p .
In the cluster stage, each cluster head node sends signals to the network in the form of broadcast. According to the received signal strength, each non-cluster head node chooses the cluster head to join. In order to reduce network energy consumption, non-cluster head nodes are usually added to the nearest cluster head. When all the non-cluster head nodes are added to the corresponding cluster head, all the nodes complete the cluster forming.
In the data transmission stage, cluster member nodes send some monitoring data to the cluster head according to the timing schedule. Then the cluster head fuses the received data and transmits the fusion results to the base station.

B. Construction of elliptical area based on state prediction
Intuitively, reasonably choosing work nodes close to target can effectively reduce redundant information related to observed target, thus enhancing energy efficiency of WSNs. So, we can pre-awaken sleeping nodes nearby direction of moving target to perform monitor work. Specifically, to make sure working nodes (i.e. awakened sleeping nodes) located in direction of moving target, coverage area of awakened sleeping nodes is defined as an ellipse whose major axis coincides with the direction of target moving.
where a and b represent the long semi-axis, the short semi-axis of the elliptical coverage area, respectively.
According to the equations (15) and (16), this paper determines whether the network node in the working state or in the sleep state. The distribution of network nodes as shown in Fig. 3.  Based on the Fig.2 We assume that the shape of the elliptical coverage area formed is related to the target motion velocity, then the semifocal length of the ellipse () ck is received by the equation (18) where  is the weight coefficient. According to the relation between the axis and the focal length of the ellipse, there is a relation is Combining the elliptical coverage area () ab Sk in the equation (14), the ellipse long semiaxis () ak and the short semi-axis () bk are obtained as follows, respectively: Therefore, a strategy of sleep node is developed, which can select working nodes more effectively and cost-effectively, and reduce the number of working nodes and network energy consumption: , the node i s inside the elliptical coverage area, it is in working state and performs the monitoring task, at the same time, this node i s is added to the working node set k G ; , the node i s is not in the elliptical coverage area, it is in a sleep state and does not perform any monitoring task.

D. Cluster head selection strategy based on equilibrium
In this section, round is defined as base unit related to data transmission in network. In each round, after the working node set k G is formed, cluster head selection is performed for all working nodes. In the cluster head selection stage, in order to reduce the probability that nodes with little residual energy or far from the base station become cluster heads, an improved strategy is designed. This strategy takes into some factors including target movement state, the distance between working node and the target, the residual energy rate of working node, and the distance between working node and the base station.
Assuming i s is a working node, we can obtain it's the cluster head selection threshold   wi k Ts  at time k : where k p and k p  represent the expected probability, the compensation probability which the node i s becomes the cluster head, respectively. k n represents the number of surviving nodes in the working node set k G . Therefore, after the cluster head selection threshold is determined using the equation (24), the cluster can be formed by the LEACH protocol framework. Every cluster with working nodes which is self-organized, and the monitoring data of the nodes are processed and transmitted by the cluster head nodes.

E. Network monitoring accuracy
It is assumed that the position of the moving target is where the position of the working node i s is   , ii xy which is fixed deployment.   f  is a function of the working node monitoring accuracy and distance, here,  is a weighting factor.   k V is a Gaussian white noise.
In order to ensure high monitoring accuracy, it is necessary to enable multiple nodes to work simultaneously. Thus, more state information of the moving target can be obtained. But, in order to select the appropriate number of working nodes to reduce network resource, the network monitoring accuracy can be developed by the difference between the actual and the expected value of the selected working node. Besides, represents the measurement error of the working node, and it is as follows: T  T  T  T  1  2  T  TT  2   1  ,  T  ,  100%  T where m represents the number of working nodes at time k .
According to the size of the network monitoring area and the monitoring environment, it can be set that the network monitoring accuracy error can meet the monitoring accuracy requirements as long as it satisfies the threshold of accuracy.

A. Simulation background and parameters
When multiple nodes monitor the moving target, some network nodes in the vicinity of target are selected to perform monitoring tasks. These working nodes need to consume energy for tasks such as information collection, data processing, and communication transmission. Once the remaining energy of one working node is less than zero, it is considered dead and loses itself monitoring ability. Network nodes that are inactive can be considered dormant and they do not consume their own energy.
In this section, performances of proposed method are verified by comparative experiments on MATLAB simulation platform. The main parameters of simulation are shown in Table I. Besides, the proposed algorithm LEACH-MTC is compared to three other LEACH-based algorithms: LEACH [16] , LEACH-DBCH [10] and LEACH-RARE [11] , and conducts performance analysis from the aspects of the working nodes selection, nodes survival number, network residual energy and network monitoring accuracy, and so on.

B. Verification of proposed algorithm
In the comparative simulation, the distribution of network nodes and working nodes corresponding to the four algorithms of LEACH, LEACH-DBCH, LEACH-RARE and LEACH-MTC is shown in Fig. 4.

Fig.4 Node distribution of four algorithms
In Fig.4, □ stands for base station, △ stands for moving target, ◇ stands for working node, * stands for sleep node, curve stands for target trajectory, the target velocity at the current moment is v , and the direction is horizontal. In

a) Working node selection and monitoring accuracy
As the target moves, the network nodes that are working are constantly changing. Fig.5 shows the change of the target position and the working node when the LEACH-MTC algorithm is running in the 1th round, the 300th round, the 600th round and the 800th round, respectively.
In Fig.5, □ stands for base station, △ stands for target, ◇ stands for working node, * stands for sleep node, curve stands for target trajectory. In (a) and (c), when the number of network running rounds is in the 1th round and the 600th round, the number of nodes that are in the working state is 15, and the remaining nodes are in a dormant state. In (b) and (d), when the number of network running rounds is 300th round and 800th round, the number of nodes that are in working state is 16.
Above results indicate that as the target position changes, the long axis, the short axis and the shape of the ellipse also change, besides, the number of working nodes that are in the ellipse area is constantly change.  Table II:  Table II, it can be seen that the number of running rounds is the 1th round, the 300th round, the 600th round, and the 800th round, respectively, the number of working nodes in the elliptical area is not the same, which indicates that as the target position changes, the ellipse area also changes. It can be seen from the changes of the long semi-axes, the short semiaxes and the semi-focal lengths in Table II. This indicates that as the target position changes constantly, the shape of the ellipse area also changes. The analysis of the monitoring accuracy of the network at four moments shows that the monitoring error is less than 5% , which can meet the requirements of network monitoring accuracy. The working nodes need to constantly obtain the moving target state, and as the amount of data processing increases gradually, the energy consumption of the working nodes increases continuously, their residual energy decreases gradually.

b) Number of node survivor and network residual energy
When the residual energy of the working node is less than 0, it is regarded as the dead state, which leads to the reduction of the number of surviving nodes. Length of time from network start running to first nodes death is defined as the life cycle of the network. Fig. 6 shows the changes of the number of the surviving nodes corresponding to the four algorithms. In Fig.6, when the network starts running, there are 100 surviving nodes corresponding to the four algorithms. As the network running time is extended, the energy consumption of the working nodes will become larger and larger, and the remaining energy of the working nodes will gradually decrease. It can be seen from this figure that when the run-time corresponding to the four algorithms run to 407, 365, 814 and 1142, respectively, the four corresponding curves begin to decline, that is, the death nodes begin to appear in the network. By comparing the time of death of the first node of the four algorithms, it can be seen that the LEACH-MTC algorithm has the longest time to appear the first dead node. Therefore, the LEACH-MTC algorithm can effectively extend the time of the first dead node. When the number of running rounds is the same, the curve corresponding to the LEACH-MTC algorithm is above the curve corresponding to the other three algorithms in the whole process, which indicates that the LEACH-MTC algorithm has the largest number of network surviving nodes when the running time is the same. When the network runs to the maximum number of running rounds i.e. 1300 max k  , the number of surviving nodes in the network corresponding to the four algorithms is 4, 4, 51, and 87, respectively. In summary, the LEACH-MTC algorithm makes the number of surviving nodes higher than that of other three algorithms; it effectively increases the number of nodes surviving. Accordingly, Fig.7 shows the variation trend of the total residual energy of network nodes with the working time.

Fig.7 The variation of network residual energy
In Fig.7, the total initial energy of the four algorithms is 100J. As the network running time increases, the energy curves corresponding to the four algorithms all have a downward trend. When the number of running rounds is the same, the curve of the LEACH-MTC algorithm is obviously above the other three curves, which means that the network residual energy of the algorithm is larger than the other three algorithms. When the network runs to the maximum running rounds i.e.