Ce Pang,Gong-guo Xu,Gan-lin Shan,Yun-pu Zhang

Army Engineering University,Hebei Shijiazhuang,050003,China

ABSTRACT This paper mainly studied the problem of energy conserving in wireless sensor networks for target tracking in defensing combats.Firstly,the structures of wireless sensor nodes and networks were illustrated;Secondly,the analysis of existing energy consuming in the sensing layer and its calculation method were provided to build the energy conserving objective function;What’s more,the other two indicators in target tracking,including target detection probability and tracking accuracy,were combined to be regarded as the constraints of the energy conserving objective function.Fourthly,the three energy conserving approaches,containing optimizing the management scheme,prolonging the time interval between two adjacent observations,and transmitting the observations selectively,were introduced;In addition,the improved lion algorithm combined with the Logistic chaos sequence was proposed to obtain sensor management schemes.Finally,simulations had been made to prove the effectiveness of the proposed methods and algorithm.

1.Introduction

Wireless sensor networks(WSN)are used to obtain and collect information[1-3]in combats,providing the essential data to be processed.And wireless sensor networks(WSN)have been widely applied and become an important portion of the sensing layer nowadays.There are some advantages in wireless sensors,including a small volume,a low price and a high sensitivity.Therefore,wireless sensors have become a kind of crucial component and been applied to a variety of scenarios,for Example,health monitoring in human’s body,fire warning in the forest,failure detection in the industrial production,target tracking in the military field and so on.Once information has been gathered by a sensor network,it will be sent to the data collector through communication devices.And combined with the agent technology,a wireless sensor can execute orders from the controlling center or react to the environment by itself according to reacting rules.

In spite of advantages mentioned above,there are still some shortcomings in WSNs,such as the susceptibility by the electromagnetic interference,the limitation of the sensing scope,the limitation of the communication distance,and the limitation of the energy.Especially,a wireless sensor is usually powered by a battery.Once the battery is run out of,this wireless sensor will stop working and be ineffective.So,the topic of energy efficiency in a WSN has been a hot topic and attracted researchers around the world[4,5].

Target searching and tracking in defensing combats is one of critical issues and attractive applications for WSNs[6].This paper applies WSNs to monitor an defensing area which may be intruded by unfriendly targets.The topic of this paper is mainly focused on how to make the WSN perform well in the constraint of energy.

The energy resources are constrained and limited in WSNs.It’s difficult to replace batteries of sensors.Reducing the energy consumption can expand the lifetime of a WSN.The issue of energy efficiency for target detection or tracking in WSNs has been discussed in many former studies.Reference[7]applied mobile sensors with limited sensing ranges to track moving targets and saved energy to extend the lifetime of the wireless sensor network in the centralized structure.It minimized the energy cost with the constraint of target tracking performance,which ensured that each target could be tracked by one sensor at least.Reference[8]studied the problem of space surveillance using WSNs.Then it compared the performances of the genetic fuzzy tree approach and the neural network approach in the balance of energy consumption and target tracking errors.The simulation result illustrated that the latter approach was better.Reference[9]divided the surveillance area into little grids,then it reduced the energy consumption and enhanced the accuracy of node locations.After the sensor scheduling function was built,a tracking recovery strategy was also described to enhance the robustness of the tracking system.Reference[10]studied the problem how to extend the lifetime of WSNs and regarded the problem as a Linear Programming.After those,it built the fitness function based on four conflicting objectives,including the minimum number of selected sensor nodes,full coverage,connectivity and energy efficiency.Finally,it proposed an improved genetic algorithm(GA)to obtain sensor controlling orders.Reference[11]mainly made full use of energy in an WSN,and proposed a fuzzy data fusion method to do some favor for energy efficiency.Reference[12]saved energy and combined the Firefly algorithm and Hierarchical Maximum Likelihood for sensor scheduling in a WSN with perfect results in simulation.Reference[13]and reference[14]were mainly focused on energy-efficient target tracking in underwater wireless sensor networks with the distributed fusion framework.They saved the energy and minimized the target tracking accuracy at the same time.Reference[13]proposed an improved square root particle filter to improve the target tracking accuracy and employed the self-adaptive artificial fish swarm algorithm to optimize the sensor scheduling problem.What the outstanding point in Ref.[14]was that it combined the artificial measurements with observations from sensors,and its effectiveness had been proved by some simulation examples.Reference[15]used the clustering scheme and selected the best sensor cluster heads under the limitation of energy in a WSN.The energy was mainly consumed during the communication between the heads and other nodes in clusters.The simulation results showed that the proposed cluster-based method,selecting the nodes on the edge of a cluster as the head,outperformed the performer ones,regarding the center of the cluster as the head,in prolonging the network lifetime by about 20%.What’s more,reference[16-18]also applied the cluster approach on the distributed wireless sensor networks and calculated the cluster head through optimization algorithms.Reference[19]and Reference[20]regarded the sensor controlling problem as a Partially Observable Markov Decision Process(POMDP).Then they made balances between the sensor consumption and target tracking performance.After building the sensor controlling model,they also designed greedy algorithms to calculate the sensor controlling orders.The shortness of them was that their sensor management schemes were suboptimal.Compared with the regular approaches,the POMDP based methods depended on the prior information more tightly.This indicated that once the prior information was not accurate,the method would be ineffective.

It can be seen that from the references introduced above the distributed structure of networks outperforms the centralized structure in energy efficiency[21,22].The reason is that it saves communication energy from sensor nodes to the information fusion center by remarkably reducing the communication distances.However,due to just utilizing the local information from several sensor nodes,the errors of distributed sensor networks may be larger than the ones of centralized sensor networks.However,if the energy efficiency problem plays a more important role in what we are concerned about,the distributed structure should be adopted.

What’s more,although there have been lots of researches about energy efficiency in WSNs as mentioned above,they nearly all concentrated on the problem how to select sensor nodes to obtain observations in advance obeying the minimum energy consumption rule.For Example,at time instantk,the sensor scheduling scheme of time instantk+1 is produced based on the predictions.The method is called optimizing the sensor management schemes.However,after the measurement has been obtained,they seldom control sensors.That is to say,all observations will be transmitted to the cluster head[23](information center).In fact,the predictions and the real values may be different and not all observations should be transmitted to the cluster head.The reason is that there may be errors in the observation because of sensing failures,natural interference or other random interruptions.We should find the inaccurate observations and let them not be transmitted to the cluster head.Two advantages exist in this step,and they are forbidding the transmission energy consumption which is the main consumption[24]and making the fusion result more accurate.

In addition,in the formal sensor management methods,they calculate sensor management schemes and schedule sensors once at each time instant.This may lead to energy wasting.And the reason is that there is no need to schedule new nodes to obtain observations if the tracking accuracy is perfect and satisfied with the demand.This case exists when the target is moving in a straight line.

Based on the former analysis,this paper proposes a new sensor management method in distributed WSNs.The proposed sensor management conducts energy conserving not only by optimizing the management scheme,but also by prolonging the time interval between two adjacent observations and transmitting the observations selectively.The other sections are organized as follows.Section II introduces the problem formulation.Section III describes the indicators to assess the performance of the sensor management methods.Section IV describes the mentioned three cautions to conserve energy.Section V makes some simulations to illustrate the effectiveness of the proposed sensor management methods before Section VI concludes this paper.

2.Problem formulation

A wireless sensor network is taken into consideration firstly.In this section,we introduce the related knowledge about the basic sensor management approach,including the structure of a wireless sensor node,the distributed wireless sensor networks,and the distributed Kalman filter used to estimate the states of targets.

2.1.The structure of a wireless sensor node

The structure of sensor nodes used in this paper is as Fig.1 shows.A wireless sensor is made up of six portions.

Transmitter/receiver module:This module is used to transmit or receive information about targets.That is to say,it can receive the observations from other sensor nodes,or transmit its observation and calculation result to other sensor nodes;

Sensing module:The sensing module can sense the states and collect information about targets.In this paper,the sensing module is made up of active sensors,which usually emit electromagnetic waves and receive radio signals to detect targets;

Fig.1.The structure of a wireless sensor node.

GPS module:With this module,the sensor node can sense and know the position of itself,the positions of other nodes and other position information in the network;

Data processing center:In this module,the signals from the sensing module or the receiver module are processed.The data processing center generates the estimation of the targets’motion state and the sensor management schemes.The processing results will be transmitted to the data storage module or the data transmitter;

Data storage module:This module stores information from the data processing center and the receiver;

Battery:The battery provides energy for other modules.

Based on the six portions,there are five kinds of working modes in one sensor node as follows and their relationship is in Fig.2.

Sleeping mode:In this mode,the sensor modes will stop working and keep in a low level of energy consumption;

Sensing mode:This mode indicates that the sensor node is working to detect targets,and the motion states of targets can be obtained;

Listening mode:In this mode,the sensor node is receiving observations or the calculation results from other sensor nodes;

Communicating mode:The information on the targets’motion states obtained by this sensor node or its calculation results can be broadcast if the sensor node is in the communication node;

Calculating mode:In this mode,the sensor node is processing signals to estimate the states of targets or calculating the sensor management schemes.

2.2.The distributed structure of wireless sensor networks

A wireless sensor network composed by the sensor nodes mentioned above can be shown in Fig.3.

In the cluster-based sensor management method,there are two kinds of sensor nodes in the WSN,and they are sleeping nodes and working nodes.In addition,the working nodes in a cluster can also be divided into two categories,heading nodes and the usual tasking nodes.Note thekth cluster as Ckand its heading node ashk∈Ck.

Before the target is detected,all sensor nodes are in the sleeping mode.As Fig.3 shows,the data flow from time instantk-1 to time instantk+1 in the sensor network can be described as follows.

Fig.3.The structure of a wireless sensor network.

(2)All sensor nodes in the kth clusterchange into the sensing mode and obtain observations about the target motion state at time instant k;

(3)All sensor nodes in the kth clusterchange into calculating mode and estimate the target motion state through EKF,fusing the predictionand their observations.The fusion results arewhere the variableis the estimation of the motion state of targettby sensor

Fig.2.T he relationship of five working modes.

(4)All tasking nodes in the setchange into the communicating mode and transmit their fusion results to the kth heading nodethen they will change into the sleeping mode;

(5)The heading node receives the transmitted information from other tasking nodes.After the heading nodehas received all results from all tasking nodes,it will change into the calculating mode.Then three steps should be taken.And the first one is to fuse all received information to estimate the target motion state with the resultThe second step is to predict the target motion state of time instantk+1,which can be noted asThe third one is to calculate the sensor management scheme of time instantk+1 based on the prediction.That is to say,thek+1 cluster should be determined at time instantk.Note thek+1th cluster as

(6)Choose the heading sensor node inand note it as as

(8)Setk=k+1,and go back to(2).

2.3.The distributed Kalman filter

In the distributed WSN,there is no global fusion center,but a local fusion center in the heading node.At time instantk,for targett,there is the estimation of its motion statewhereis the mean value andis its covariance matrix.

The state transmission matrix of targettis noted as F,where the variableTis the time interval.

At time instantk+1,the motion state of targettcan be denoted as:

where the variable W is the process noise,and obeys the Gaussian functionG(0，Q);The variable Q is the covariance;The variableqis a known scalar which represents the intensity of the process noise[25].

When the target is moving in a straight line,there are F=

And when the target state is augmented with the turning rateφ(k),there are

At time instantk+1,the observation from sensorsto targettcan be expressed as:

where theh(·)is the observation function,and there isthis paper;The variable(xs，ys)is the coordinate of sensors;The matrix V is the observation noise,which obeys the Gaussian functionG(0，R);The variable R is the covariance and there is R=diagThe variablepsis the sensing probability of sensors,for the reason that sensors are not always obtaining correct and effective observations due to sensing failures,natural interference or other random interruptions[26].

When the target is moving in a single mode,the EKF[27,28](Expanded Kalman Filter)is used to estimate the target motion state.However,when the target is maneuvering,IMM[29,30]is applied.

In the EKF,the matrix H denotes the Jacobian matrix after linearization.

The EKF used by all tasking sensors to estimate the target motion states is as follows:

3.The indicators in sensor management

This section is mainly on our proposed distributed sensor management in energy efficiency.Firstly,the analysis on the energy consumption in the sensor management is provided.Obviously,it is easy to find effective cautions to save energy once the case where energy is consumed largely is acquired.After that,the other two indicators applied to measure the tracking performance,including the target detection probability and tracking accuracy,are introduced.

3.1.The analysis of sensor consumption in target tracking

In target tracking,there are four steps where energy is mainly consumed using the wireless sensor network as follows.

(1)In the sensing mode,energy is consumed to obtain mea

surement.Letrdenote the sensing radius of sensors.

Assume that the variableEsdenote the energy consumed in an observation for one sensor,and it is a constant value for each sensor node.

(2)In the communicating mode,energy is consumed to transmit information or control orders.LetRdenote the communicating radius of sensors,andDdenote the distance between different sensors.

A sensor node transmitsbbits information with the energy consumption as follows[31]:

where the variablesetandedare determined by the specifications of the transmitter in sensor nodes;The variableκis a constant and depends on the channel characteristics,and there isκ=2.

Usually,there isR=2r.

(3)In the listening mode,energy is consumed to receive data and controlling orders.

A sensor node receivesbbits information with the energy consumption as follows[31]:

where the variableeris decided by the specifications of receivers.

In this paper,it is assumed that the information containing the target motion stateis equal tobbits.

(4)In the calculating mode,energy is consumed to fuse the information or compute the sensor management scheme.

Assume that the energyEcwill be consumed in an observation for one sensor,andEcis a constant value for each sensor node.In general,the energyEcis smaller than any of the other three kinds of energy consumption.

For a cluster,the total energy consumption at time instantkis as follows.

where the variablenk+1is the number of sensor nodes ink+1th cluster at time instantk+1.

The energy consumption should be as small as possible.

Based on the description above,it can be seen that once the number of sensors gets less in a cluster,the energy consumption from sensing,communicating,listening and calculating will also be less.That is to say,we can select sensor nodes as less as we can in satisfying the requirement of detection probability and tracking accuracy.

Besides that,in the whole sensor tracking time periodΩ,it can be seen that the less the number of observations is,the less energy consumption there is.So we should also reduce the time of observations as much as possible in satisfying the requirement of detection probability and tracking accuracy.

What’s more,the majority of energy consumption occurs in the information transmission,and the heading nodes are communication junctions playing an important effect on the communication.They receive information from the former heading nodes and the tasking nodes in this cluster,and transmit information to nodes in the next cluster.Obviously,if we set a proper node as the heading node obeying the rule of reducing the communication energy consumption as much as possible after a cluster is determined,the total energy consumption will also be reduced.

What’s more,although the nodes in clusters obtain observations of target motion states,not all fusion results based on Eq.(3)should be transmitted to the heading nodes to be further fused.At least in two cases the fusion results need not to be offered to the heading nodes.They are when the fusion resultfrom sensorsiis much similar to the prediction valueandwhen the error in the local fusion resultis pretty large because of sensing failures,natural interference or other random interruptions.In the first case,the final fusion result will be almost the same no matter the provided information is the local fusion resultor the prediction valueThen the informationneed not to be transmitted to save communication energy.In the second case,it will not only cause energy wasting,but also expand the error in the final fusion results after transmitting the informationto the heading node.

3.2.The target detection probability

At time instantk,the Gaussian distributionof targettis as Fig.4 shows.Letdenote the covered area by the distribution

The probability density function is

Let the variableStkdenote the covered region by the distribution of targettat time instantk.Assume that in the sensing region of a sensor,the detection probability ispd,and all sensors’detection probabilities are the same.That is to say,there is the detection probability at the point(x，y)from sensorsas follows:

If point(x，y)is in the sensing area ofn*ktargets at the same time,the joint detection probability at this point can be calculated by:

Then the target detection probability for targettcan be calculated by:

The target detection probability should be as large as possible,leading to the fact that there should be sensors as many as possible to detect the target.

3.3.The target tracking accuracy

The target tracking accuracy at time instantkis formally defined as follows:

However,at time instantk,the sensor management scheme is produced forward for time instantk+1 without observations.It’s difficult to evaluate the performance of sensors without observations.So Eq.(11)will be useless to assess whether this senor performs well or not in sensing.To overcome this default,we replace the matrixwhich is the PCRLB[33]of sensorsfor targettand doesn’t need observations to assess the sensing performance.PCRLB is the inverse of the Fisher matrix[34]and can be calculated by Ref.[35]:

where there are:

Then the fusion rule based on Eq.(4)is as follows:

The target tracking accuracy should be as small as possible.

4.The algorithm of sensor management

The rest of this paper will discuss how to save energy through the three kinds of cautions mentioned above,and they are prolonging the time interval between two adjacent observations,selecting the most proper sensor nodes to track targets and transmitting the observations selectively.

4.1.Prolong the time interval between two adjacent observations,which is also called caution 1

This section discusses when to get observations from sensors to estimate the target motion states.

LetΘ=｛1，2，…，T｝denote the observing sequence.The relationship ofΘand the time periodΩ=｛1，2，…，K｝is as Fig.5 shows.

There needn’t be observations at each time instant.For Example,when the target is moving along a straight line,its positions can be well predicted.Then the time interval between two adjacent observations should be longer.

In practice,the time interval between two adjacent observations is between the range ofT∈[Tmin，Tmax][36].Tminmust be larger than the sum of the processing time in sensors,including the observing time,the calculating time and so on.The time intervalΔTbetween each two time instant should also be satisfied to the requirement.What’s more,Tmaxcannot be too large to locate targets.

where parameterσis a variable,then the predictioncan be calculated by:

whereΔTis the time interval,andσvis the variable in Qk.

Then the prediction of the tracking accuracy can be calculated by:

Let us denote the equation above as the functionThen there is:

It’s easy to find that there isthus the functiong(·)is a monotonic function.When there isthe time intervalcan be the biggest valueTmaxunder the requirementwhere the variableρ?is the threshold value.

Tmaxcan be calculated by solving the following equation:

To change this issue into the optimization problem,the solutions of Eq.(18)can be seen equal to the ones which satisfy the following optimization function.

4.2.Select the most proper sensor nodes to track targets,which is called caution 2

This section discusses the problem of how to select the most proper sensor nodes to observe targets.

In sensor scheduling,when the sensor management scheme of time instantkis calculated at time instantk-1,not only energy consumption at time instantkis taken into consideration,but also the communicating energy consumption of the heading node in thek-1th cluster should be considered,for the reason that the scheduled sensor nodes at time instantkneed to receive informationfrom the heading nodemeaning that the positions of selected nodes for time instantkhave an influence on the communicating energy consumption of the heading nodeSimilarly,the predictionshould also be predicted and the sensor clusterof time instantk+1 should also be taken into consideration,for the reason that the positions of nodes in the set ofalso affect the communicating energy consumption of the heading node

The communicating energy consumption that the clusterproduces is shown in Fig.6.

Above all,the objective function in sensor management at time instantkis as follows:Subjects to:

where the variablesρpandρ?are the threshold values.

When making up the cluster of time instantk,there isNknodes to be selected,and for the cluster of time instantk+1,there isNk+1nodes.Taking into the heading node into consideration,the total number of chosen sensor management schemes isNk(2Nk-1)(2Nk+1-1).

The calculation speed of the optimization algorithm should be faster in sensor scheduling due to a real-time combat situation.

When two or more clusters are fighting for the same sensor node,that node will enter into any of them randomly.

C Do not transmit the observations to the head nodes as much as possible,which is called caution 3.

This section discusses the problem whether observations obtained by sensors should be transmitted into the heading node in a cluster to be further fused.

Shannon entropy[37,38]is usually used to describe the information amount in an event.Let the variabledenote the prior probability of targett’s motion state before obtaining observation anddenote the posterior probability of targett’s motion state after sensorsifused its observations.The information gain based on Shannon entropy is as follows.

Renyi entropy is the generalized form of Shannon entropy.When the probability of the random variable Xchanges fromf1tof2,its Renyi entropy is defined as:

where the variableαis a parameter[39].

In target tracking,the information gain after fusing observations can be calculated by the following equation.

Fig.6.The communicating energy consumption in clusters.

There is a case where the information gain in Eq.(23)fromis too small,which is noted as Υα(p1｜｜p0)≤κland means that there are little difference between them.In this case,we try not to let sensorsitransmit the informationto the heading node in order to conserve energy with little influence on the final fusion resultThe variableκlis the low threshold.

There is another case where the information gain in Eq.(23)fromis too high,which is noted asΥα(p1｜｜p0)≥κhand means that there is much difference between them.It can be seen that noise and error exist in the observationin this case.There may be two possible reasons for this case.The first one is that the sensor nodesihas been broken down so that there isin Eq.(2).The second one is that the noise in the environment is too high that there isIn another word,the effective observation has been drowned in the noise.In this case,we also try not to let sensorsitransmit the informationto the heading node in order to conserve energy and make the final fusion result more accurate.The variableκhis the high threshold.

Example.Assume that a target is moving in a straight line,and at time instantk,the target state is Xk=[10 3 10 3]’.The estimation isThere are the variables At time instantk+1,the target state changes to be Xk=[13.26 3 12.39 3]’.The observations changing with the variablegare as Fig.7(a)and Fig.7(b)show.The relationship ofκl,κhandΥα(p1｜｜p0)is shown in Fig.7(c).

As Fig.7 shows,we only transmit the informationfrom sensorsito the heading sensor node when there is κl＜Υα(p1｜｜p0)＜κh.In other case,the heading node will replaceintelligently without receiving any information from sensorsi.

Fig.7.The communicating energy consumption in clusters.

4.3.The sensor management process in target tracking

In this paper,to obtain solutions from Eqs.(19)and(20),we propose the improved lion algorithm.

The lion algorithm was a new intelligence and bionic algorithm from the lions’action proposed by B.R.Rajakumar in 2012[40,41].Due to the higher evolutionary intelligence and evolutionary mechanism,the lion algorithm shows a strong advantage inoptimization calculation.This paper not only introduces but also improves the lion algorithm.

Table 1The process of the algorithm.

Fig.8.The detection region and distribution of sensors.

In the lion algorithm,there are four kinds of lions,namely,leading lions,wandering lions,female lions(hunting lion)and young lion(following lion).Their actions include wanderingbehavior,mating behavior,defensive behavior and migration behavior.

Table 2The Parameter Set.

Table 3The sensor management algorithm.

In the lion algorithm,the lion with the best fitness(the best objective function value)is chosen from the crowd to be the leading lion.The female lions are responsible for catching prey.Once the female lions find a better position whose fitness value is better than the leading lion,it will be occupied by the leading lion.Young lions follow female lions to learn how to predate prey or are feed by the leading lion.When young lions grow up,they will be sent into exile by the leading lion,and be wandering lions.The wandering lions predate prey beyond the domain occupied by the leading lion,and once a wandering lion finds a better position whose fitness is better than the position occupied by the leading lion,it will fight with the leading lion and kill it,then it becomes the new leading lion and processes the mating action.

Fig.9.The simulation result when a single target moves in a straight line.

In order to further improve the optimization ability of the algorithm,the Logistic chaos sequence is applied to generate the initial positions in the algorithm initialization.The Logistic chaos sequence can ensure that all initial positions distribute all around the solution space.The map equation of Logistic is as follows:

Fig.10.The simulation result when a single target moves in a maneuvering mode.

Table 4The estimated locations using different algorithms.

where the variableεis the controlling parameter;The variablezois the threshold variable;The variableois the calculation time.

The calculation process is shown as Table 1 shows.

5.Simulations

This section conducts some simulations to illustrate the effectiveness of the method and algorithm proposed in this paper.

The simulations are conducted in Matlab 2018.The simulation environment is in a square of 100×100 m2.100 sensor nodes distribute in the detection region as Fig.8 shows.

The time interval between two time instants isΔT=1 s.The other parameters are as Table 2 shows.

We compare five sensor management algorithms which are named as Table 3 shows.

The algorithm 1 with no optimization caution means that all sensors whose detection ranges cover the target will observe the target at the same time,and the heading sensor node is selected randomly.

The Error of estimation is defined as follows:

The simulation is divided into three portions,the scene of a single target moving,the scene of multiple target moving,and the simulation of the improved lion algorithm to prove its effectiveness.

5.1.The scene of single target tracking

To fully illustrate the effectiveness of the proposed method in different scenes where targets move in different modes,this section is divided into two simulation scenes where a target moves in a straight line and in a maneuvering mode.

20 Monte Carlo experiments have been conducted,and Fig.9 and Fig.10 show the simulation results in the two scenes separately.Figs.9(a)and Fig.10(a)show targets’moving trajectories;Figs.9(b)and Fig.10(b)show the target detection probability changing with time;Figs.9(c)and Fig.10(c)show the target tracking accuracy changing with time;Figs.9(d)and Fig.10(d)show the Error changing with time;Figs.9(e)and Fig.10(e)show the observation time intervals changing with time;Figs.9(f)and Fig.10(f)show the sensing energy consumption changing with time;Figs.9(g)and Fig.10(g)show the communication energy consumption changing with time;Figs.9(h)and Fig.10(h)show the total energy consumption changing with time.The locations of targets at different time instants are shown as Table 4 and Table 5 show.

It can be seen that from both of the different two simulation cases,algorithm 5 which includes the three energy conserving cautions performs the best among all sensor management methods,with the lowest energy consumption as Fig.9(f),Fig.9(g),Fig.9(h),Fig.10(f),Fig.10(g),and Fig.10(h)show.Under the requirement of conserving energy mostly,algorithm 5 still has perfect target tracking performances,with nearly the same target detection probability,tracking accuracy and Error with algorithm 3 and algorithm 4 as Fig.9(b),Fig.9(c),Fig.9(d),Fig.10(b),Fig.10(c),and Fig.10(d)show.What’s more,although the target detection probability and tracking accuracy are a little worse than algorithm 1 and algorithm 2,the two kind of values are still in the demanding limits.That is to say,algorithm 5 can conserve energy and satisfy the target detection and tracking requirement at the same time.This conclusions can be also addressed by Tables 4 and 5.The total numbers of observations by algorithm 5 is 25 and 26 as Figs.9(e)and Fig.10(e)show.It can be seen from Fig.9(h)that the total energy consumption can be reduced by 64.00% in algorithm 2,52.00% in algorithm 3,7.20% in algorithm 4,and 98.24% in algorithm 5 compared with algorithm 1 separately.It can be seen from Fig.10(h)that the total energy consumption can be reduced by 65.57%in algorithm 2,50.82%in algorithm 3,16.39%in algorithm 4,and 81.15% in algorithm 5 compared with algorithm 1 separately.

Fig.11.The target’s moving trajectories.

Fig.12.The simulation results in multiple target tracking.

In addition,applying a single energy conserving caution,such as prolonging the time interval between two adjacent observations,selecting the most proper sensor nodes to track targets or transmitting the observations selectively,can also save energy in varying degrees.Compared with algorithm 1,algorithm 2 can save sensing energy and communicating energy simultaneously as Fig.9(f),Fig.9(g),Fig.10(f)and Fig.10(g)show,for the reason that it prolonging the time interval and in the perspective of the whole sensor tracking process,the frequency of observations is reduced sharply.Reducing one time of observation can avoid both sensing and communicating.The total numbers of observations by algorithm 2 are 21 and 23 as Figs.9(e)and Fig.10(e)show.Compared with algorithm 1,algorithm 3 can also save sensing energy and communicating energy simultaneously as Fig.9(f),Fig.9(g),Fig.10(f)and Fig.10(g)show.The reason is that optimizing the sensor management schemes can reduce the number of scheduled sensors,and once a sensor node is left unused,its sensing and communicating energy can be conserved.Compared with algorithm 1,algorithm 3 can only conserve communicating energy as Fig.9(f),Fig.9(g),Fig.10(f)and Fig.10(g)show.The three single cautions can be sequenced as algorithm 4＞algorithm 3＞algorithm 2 in the total energy conserving as Figs.9(h)and Fig.10(h)show.The three single cautions can also satisfy the target detection and tracking requirement as Fig.9(b),Fig.9(c),Fig.9(d),Fig.10(b),Fig.10(c),and Fig.10(d)show.

Table 6The estimated locations using different algorithms.

5.2.The scene of multiple target tracking

To fully illustrate the effectiveness of the proposed method,this section also applies the proposed method on a multi-target tracking scene.In this simulation,the number of targets is three,and the three targets’moving trajectories are as Fig.11 shows.

20 Monte Carlo experiments have been conducted,and the simulation results are as Fig.12 shows.The locations of targets at different time instants are shown as Table 6 shows.

Fig.12(a)-(c)show the Error of three targets;Fig.12(d)-(f)show the instant sensing energy consuming,the instant communicating energy consumption and the instant total energy consumption;Fig.12(g)-(i)show the accumulative sensing energy consumption,the accumulative communicating energy consumption and the accumulative total energy consumption.In this simulation,algorithm 1,algorithm 3 and algorithm 5 are compared in energy conserving.

In the multi-target tracking scene,algorithm 5 still performs the best among the three algorithms.It can be seen from Fig.12(h)that the total energy consumption can be reduced by 40.04% in algorithm 3 and 81.64% in algorithm 5 compared with algorithm 1 separately.

Only by combing the three energy conserving cautions,can the energy consumption achieve the least energy consumption.Obviously,it is needed to manage sensor nodes so that they can conserve energy in order to prolong the working life of sensor networks.

5.3.The simulation on the improved lion algorithm

In this section,the improved lion algorithm is proved to be effective when solving the optimization problems in Eq.(19)and Eq.(20).

The Genetic Algorithm(GA)[42],the Artificial Bee Colony Algorithm(ABC)[43],and the basic Lion Algorithm(BLA)are compared with the improved Lion Algorithm(ILA)in simulation.

In the first simulation,two functions are taken as examples:

20 Monte Carlo experiments have been conducted,and the simulation results are as Fig.13 and Fig.14 show.Figs.13(a)and Fig.14(a)show the changes of time intervals,which is the required results,and Figs.13(b)and Fig.14(b)show the changes of function values.The final calculation results are respectivelyΔT=0.01 and ΔT=0.82.It can be seen that the ILA outperforms the other three algorithm in convergence rate and solution quality.

In the simulation,the sensor management schemes at time instantk=0 in Fig.9(a single target tracking)and in Fig.10(multitarget tracking)are calculated separately.20 Monte Carlo experiments have been conducted,and the simulation results are as Fig.15 shows.

Fig.13.The comparison of four algorithms in solving F1.

Fig.14.The comparison of four algorithms in solving F2.

Fig.15.The comparison of four algorithms in optimizing the sensor scheduling schemes.

In solving the problem of Eq.(20),Fig.15 can also show that the ILA is better than any other algorithms in calculation rate and the solution quality.Obviously,after being improved,the solutions in the original step can distribute all over the solution space,which is the defect of the basic lion algorithm.Therefore,the improved lion algorithm can search for solutions quickly and jump out of the local optimization to find the optimal one.

6.Conclusions

This paper studied the problem of energy conserving in wireless sensor networks for defensing combats.Energy plays an important role in WSNs.Once the energy is run out of,the sensing layer will stop working.So it is significant to conserve energy to prolong the working life of WSNs.The constructions of the wireless sensor nodes and networks were introduced firstly.After that,the optimized indicators in target tracking,including the energy consuming,the detection probability and the tracking accuracy,were proposed.After them,the sensor scheduling objective function was built.Then this paper controlled the energy consuming by three kinds of cautions,optimizing the management scheme,which was also the normal method used in the former papers,prolonging the time interval between two adjacent observations,which could conserve the sensing and communicating energy,and transmitting the observations selectively,which could conserve the communicating energy.The latter two methods were newly proposed by this paper.To obtain sensor management schemes from objective functions,the improved lion algorithm combined with the Logistic chaos sequence was proposed.The simulation results showed the effectiveness of the proposed methods and algorithm.It also indicated that the three cautions could all conserve energy.

Future work will be focused on the following areas.Firstly,other methods of energy conserving to prolong its working time will be studied;Secondly,the application of the proposed energy conserving method will be expanded from 2-D environment to 3-D environment;Lastly,the proposed method would be experimentally validated on a physical sensor network in the laboratory and outdoor settings.

Funding

This research was funded NSFC(Natural Science Foundation of China),grant number 61573374.

Declaration of competing interest

There is no conflicts for this paper with other researches.

AcknowledgmentThis research was funded by(Defense Pre-Research Fund Project of China),grant number 012015012600A2203,and NSFC(Natural Science Foundation of China),grant number 61573374.