# Sensor Network Disposition Facing the Task of Multisensor Cross Cueing

Authors: Ce Pang; Shucai Huang; Yan Zhao; Daozhi Wei; Jinchang Liu
Journal: Mathematical Problems in Engineering
 (2017)

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## Abstract

In order to build the sensor network facing the task of multisensor crossing cueing, the requirements of initiating cueing and being cued are analyzed. Probability theory is used when building models, then probability of sensor cueing in the case of target moving is given, and, after that, the best distance between two sensors is calculated. The operational environment is described by normal distribution function. In the process of distributing sensor network, their elements, operational environment demand of cueing, and the probability of sensor network coverage are considered; then the optimization algorithm of sensor network based on hypothesis testing theory is made. The simulation result indicates that the algorithm can make sensor network which is required. On the basis of that, the two cases, including targets that make linear motion and orbit motion, are used to test the performance of the sensor network, which show that the sensor network can make uninterrupted detection on targets through multisensor cross cuing.


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## Body

## 1. Introduction

Multisensor cross cueing technology is put forward and developed to solve the problem of dynamic management of sensors, meaning that when sensors carry out tasks together, they can cue with each other, and the cued sensors can get the information about targets directly to get further information about targets [1–3]. Multisensor cross cueing can greatly improve the detecting ability of sensors in the intelligence monitoring and scouting system, and it plays a role mainly in two aspects: on one hand, when sensors break down or they cannot detect targets any more, sensors can cue other sensors to hand over target-detecting tasks, by which targets can be detected successively [4]; on the other hand, sensor can cue other sensors to detect targets together so that the detection accuracy can be improved or extra information can be gotten [5].Multisensor cross cueing technology is regarded as the important development trend in the sensor field up to 2015 in America [6]. After making the definition, the function, and the method of multisensor cross cueing [4, 7, 8] clear, the technology enters the application phase. McCarthy Panel [9] uses multisensor cross cueing technology to simulate and verify the scene where SAR and MTI detect the whole target area together. Katsilieris and Narykov make study on the functions of cueing between different kinds of sensors and put forward the sensor-managing methods in the condition of cueing [10, 11]. Salvagnini and Muratore discuss sensor cueing opportunity and methods when there are different kinds of sensors in multiple platforms [12, 13]. Pang et al. make a study on the problem of how the multisensor cross cueing technology is applied on target tracking [14].It is known that there is no introduction on the problem of sensor network deployment facing multisensor cross cueing in the former study, but multisensor cross cueing takes place in the sensor network, requiring good connection of the sensor network to satisfy the need of communication. Whether the performance of the sensor network is well or not can influence the effect of multisensor cross cueing.In this paper, sensors are radars, and the sensor network is built facing multisensor cross cueing. Models are made based on probability theory, and the probability of multisensor cross cueing is defined. The best distance between two sensors is calculated, and the optimization algorithm based on hypothesis test to optimize the sensor network is put forward. In the simulation, the process of building the sensor network and the process of multisensor cross cueing are shown.The probability of multisensor cross cueing models is built based on probability theory, with the best distance between two sensors calculated. The combat environment is described using normal distribution function. After this work, the optimization algorithm based on hypothesis test to optimize the sensor network is put forward. The simulation indicates that the method the paper introduces can get the sensor network to satisfy the need of multisensor cross cueing. What is more, the process of multisensor cross cueing is shown, which indicates that the multisensor cross cueing technology can adapt to the combat reality, making targets detected successively and having a good application prospect.


## 2. Basic Theory of Sensor Cueing

### 2.1. Inspiring Conditions of Cueing between Two Sensors

Assume that the distance between sensorsa and sensor sb is l, the detecting radius and the communicating radius of sa are ra and Ra, and the detecting radius and the communicating radius of sb are rb and Rb. The sufficient condition of cross cueing between sa and sb is(1)Ra≥l,Rb≥l.In this paper, the cueing way between two sensors is “beam cueing,” and the effective cueing is defined as follows: if cross cueing can happen between two sensors and the cued sensor can catch the target, the cueing is effective cueing, or the cueing is invalid cueing. The condition of effective cueing is(2)ra+rb≥l.The happening condition schematic diagram of cross cueing betweensa and sb is as Figure 1 describes.Figure 1
The relationship of two sensors when effective cueing happens.


### 2.2. The Cueing Model between Sensors Based on Probability Theory

Assume thatsa is the cueing sensor and sb is the cued sensor. In order to simplify the model, in this paper, r=ra=Ra=rb=Rb. Assume that when the target is in the area of S0=Sa∩Sb and “A” stands for the event that sa cues sb, in terms of probability theory, then probability of occurrence of A is as follows:(3)PA=S0Sa.In the formula, Sa stands for the detecting area of sa and Sb stands for the detecting area of sb.After geometric calculation, we can get(4)PA=2r2arcos⁡l/2r-lr2-l2/4πr2.Regardl/r as x coordinate and P(A) as y coordinate, and then the relationship of P(A) and l/r is as shown in Figure 2.Figure 2
The Curve of FunctionP(A).


### 2.3. The Multisensor Cross Cueing Model When Targets Move

For the reason that targets move fast when coming, this paper pays attention to the problem of multisensor cross cueing when targets move fast. If a target is flying away from the detecting area ofsa, sa needs to cue other sensors to hand over the task of detecting this target. If sb is determined to accept the task, after sb start to detect the target, sa will not detect the target any more.Firstly, the cueing time is defined as follows.Assume that at the time ofT, the distance of one target and sa is da(T), and the distance of this target and sb is db(T). Assume that, at the time of T+1, the distance of one target and sa is da(T+1), and the distance of this target and sb is db(T+1). When sa is detecting the target, if da(T+1)>da(T) and da(T)>0.7r, sa will produce the need of cueing, and then it will cue other sensors to take over the detecting task. When db(T+1)<db(t) and the target is in the area of S0=Sa∩Sb, sb has the ability to take over the detecting task, and it can be cued by sa.Assume that “B” sands for the event that sb catch the target successfully. As B is carried out after A, in terms of probability theory, the probability of B is as follows:(5)PB=PA∗1-Sa∩SbSb.ForSa=Sb, we can get(6)PB=PA1-PA.Regard l/r as x coordinate and P(B) as y coordinate, and then the relationship of P(B) and l/r is as shown in Figure 3.Figure 3
The Curve of FunctionP(B).In Figure3, we can get max⁡(P(B))=0.25 and P(A)=0.5 and l=0.81r when P(B)=0.25.Whensa needs to cue other sensors, if there are several sensors which can be cued, sa chose the cued sensor based on the probability p(B).In addition, the detecting radius is usually smaller than the communicating radius [15]; that is to say, ra<Ra and rb<Rb.What is more, ignore the assumptionr=ra=Ra=rb=Rb, and then there is(7)PA=ra2arcos⁡l2+ra2-rb2/2lra+rb2arcos⁡l2+rb2-ra2/2lrb-rarb1-ra2+rb2-l2/2rarb2πra2.It can be seen thatp(A) and p(B) are three-dimensional functions of ra, rb, and l, and when l=100, the functions are as Figures 4 and 5 describe.Figure 4
The Curve of FunctionP(A).Figure 5
The Curve of FunctionP(B).


## 2.1. Inspiring Conditions of Cueing between Two Sensors

Assume that the distance between sensorsa and sensor sb is l, the detecting radius and the communicating radius of sa are ra and Ra, and the detecting radius and the communicating radius of sb are rb and Rb. The sufficient condition of cross cueing between sa and sb is(1)Ra≥l,Rb≥l.In this paper, the cueing way between two sensors is “beam cueing,” and the effective cueing is defined as follows: if cross cueing can happen between two sensors and the cued sensor can catch the target, the cueing is effective cueing, or the cueing is invalid cueing. The condition of effective cueing is(2)ra+rb≥l.The happening condition schematic diagram of cross cueing betweensa and sb is as Figure 1 describes.Figure 1
The relationship of two sensors when effective cueing happens.


## 2.2. The Cueing Model between Sensors Based on Probability Theory

Assume thatsa is the cueing sensor and sb is the cued sensor. In order to simplify the model, in this paper, r=ra=Ra=rb=Rb. Assume that when the target is in the area of S0=Sa∩Sb and “A” stands for the event that sa cues sb, in terms of probability theory, then probability of occurrence of A is as follows:(3)PA=S0Sa.In the formula, Sa stands for the detecting area of sa and Sb stands for the detecting area of sb.After geometric calculation, we can get(4)PA=2r2arcos⁡l/2r-lr2-l2/4πr2.Regardl/r as x coordinate and P(A) as y coordinate, and then the relationship of P(A) and l/r is as shown in Figure 2.Figure 2
The Curve of FunctionP(A).


## 2.3. The Multisensor Cross Cueing Model When Targets Move

For the reason that targets move fast when coming, this paper pays attention to the problem of multisensor cross cueing when targets move fast. If a target is flying away from the detecting area ofsa, sa needs to cue other sensors to hand over the task of detecting this target. If sb is determined to accept the task, after sb start to detect the target, sa will not detect the target any more.Firstly, the cueing time is defined as follows.Assume that at the time ofT, the distance of one target and sa is da(T), and the distance of this target and sb is db(T). Assume that, at the time of T+1, the distance of one target and sa is da(T+1), and the distance of this target and sb is db(T+1). When sa is detecting the target, if da(T+1)>da(T) and da(T)>0.7r, sa will produce the need of cueing, and then it will cue other sensors to take over the detecting task. When db(T+1)<db(t) and the target is in the area of S0=Sa∩Sb, sb has the ability to take over the detecting task, and it can be cued by sa.Assume that “B” sands for the event that sb catch the target successfully. As B is carried out after A, in terms of probability theory, the probability of B is as follows:(5)PB=PA∗1-Sa∩SbSb.ForSa=Sb, we can get(6)PB=PA1-PA.Regard l/r as x coordinate and P(B) as y coordinate, and then the relationship of P(B) and l/r is as shown in Figure 3.Figure 3
The Curve of FunctionP(B).In Figure3, we can get max⁡(P(B))=0.25 and P(A)=0.5 and l=0.81r when P(B)=0.25.Whensa needs to cue other sensors, if there are several sensors which can be cued, sa chose the cued sensor based on the probability p(B).In addition, the detecting radius is usually smaller than the communicating radius [15]; that is to say, ra<Ra and rb<Rb.What is more, ignore the assumptionr=ra=Ra=rb=Rb, and then there is(7)PA=ra2arcos⁡l2+ra2-rb2/2lra+rb2arcos⁡l2+rb2-ra2/2lrb-rarb1-ra2+rb2-l2/2rarb2πra2.It can be seen thatp(A) and p(B) are three-dimensional functions of ra, rb, and l, and when l=100, the functions are as Figures 4 and 5 describe.Figure 4
The Curve of FunctionP(A).Figure 5
The Curve of FunctionP(B).


## 3. Build the Sensor Network

### 3.1. Combat Environment Scenarios

Assume that, in the combat environment, the coordinate of our position is(-a,0), the coordinate of the enemy is (a,0), and there are n sensors which need to be deployed to detect targets of the enemy. The distribution of our position and the position of the enemy is described in Figure 6, and the shadow area is what we should watch to detect targets from the enemy.Figure 6
The position relationship of the enemy and our side.Based on the rule that targets should be detected as soon as possible, sensors should be deployed near the enemy, but sensors are so near the enemy that they can be destroyed by the weapons form the enemy. According to the rule of “3σ” [16], assume that, in the rectangular area D, the strategic value of each position obeys the regular as follows:(8)fx,y=12πa/3b/3exp⁡-x22a/32-y22b/32.


### 3.2. The Building Rules of Sensor Network

Building the sensor network, which is the basis for multisensor cross cueing, makes a direct impact on the performance of multisensor cross cueing. In order to satisfy the need of multisensor cross cueing, when building the sensor network, the total number of degrees [17] in the sensor network should remain pretty large, making good connectivity between every sensor.When deploying sensors in the areaD, rules should be obeyed as follows:(1)
Sensors tend to be deployed where there is high strategic value.(2)
In order to satisfy the need of multisensor cross cueing, the distance of each two sensors tends to bel=0.81r.(3)
The coverage of the sensor network should remain large.Rule one is designed to meet the combat environment in this paper; rule two is designed to satisfy the need of multisensor cross cueing; rule three is designed due to the rule in the previous papers.


### 3.3. The Steps of Building Sensor Network

To Build the Earning Degree Function. Assume p1=p(A), p2=p(B), p3=p(C), and the position of si is (xi,yi). There are ki sensors which can communicate directly with si, and the set is ci=si1,si2,…,siki, in which sij is the number j. The probability of cross cueing between si and sij is p2(sij). Assume that, in the position (xi,yi), the strategic value is f(xi,yi), and then the earning degree of si can be calculated as follows:(9)gsi=ω1fxi,yi+ω2∑j=1kip2sij+1-ω1-ω2S4ab.In the function,ω1,ω2∈[0,1], which is the weight, and S is the area which the sensor network covers.In this paper,ω1f(xi,yi) is called strategic earning, ω2∑j=1ki(p2(sij)) is called cueing earning, (1-ω1-ω2)S/4ab is called coverage earning, and g(sis) is called the total earning.To Initialize the Positions of Sensors. At the time of t=0, the grid method [17] is used to initialize the positions of sensors, the area is divided into N×M grids, and, at each vertex, there is one sensor.To Optimize the Positions of Sensors. Assume, at the time of t, the vector, whose direction is from (xi(t),yi(t)) to (0,0), is ei→. si can move through the direction ei→ or -ei→, and the speed is vsi(t), which is calculated as follows:(10)
v
s
i
t
=
f
0,0
-
f
x
i
t
,
y
i
t
f
0,0
v
.In the function, v is a constant value.Move through the directionei→, then the strategic earning of si can increase, and the coverage earning can decrease; move through the direction -ei→, then the strategic earning of si can decrease, and the coverage earning can increase (in the case where each two sensors have common detecting area).According to the statistical detection theory, assume that the caseHk(t)=1 is representative for the total earning increase if one sensor is moving through the direction ei→, and the case Hk(t)=0 is representative for the total earning increase if one sensor is moving through the direction -ei→. Assume that, at the time T, the probability of moving through the direction ei→ is qi(t), and the probability of the increase of the total earning is oi(t)(0.5<oi(t)≤1); assume that the probability of moving through the direction -ei→ is 1-qi(t) and the probability of the increase of the total earning is 1-oi(t). After moving, the total earning of si is f(xi(t+1),yi(t+1)).(1) When f(xi(t+1),yi(t+1))≥f(xi(t),yi(t)), update functions as follows.At the time oft, the probability of the increase of the total earning after moving is(11)uit=qit∗oit+1-qit∗1-oit.At the time oft+1,(12)qit+1=qit∗oituitoit+1=oit.The following is to proveqi(t)<qi(t+1)<1.①(13)qit+1>qit⟸oit⁡qit∗oit+1-qit∗1-oit>1⟸2qit+1oit-qitoit-1<0⟸2+1oitqit-1<0.② The functionqi(t+1)<1 is obviously right.That is to say, if the move at the time oft can prove that Hk(t)=1 is right, then, at the time of t+1, qi(t+1) will increase, and oi(t+1) will be the lager number.(2) When f(xi(t+1),yi(t+1))<f(xi(t), yi(t)), update functions as follows.At the time oft, the probability of the increase of the total earning after moving is(14)uj-t=1-qit∗oit+qit∗1-oit.At the time oft+1,(15)qit+1=qit∗1-oituj-toit+1=1-oit.The following is to prove0<qi(t+1)<qi(t).①(16)qit+1<qit⟸qit∗1-oit1-qit∗oit+qit∗1-oit<qit⟸1-oit1-qit∗oit+qit∗1-oit<1⟸1-qit1-2oit<0∵0.5<oit≤1∴The  function  is  right.② The functionqi(t+1)>0 is obviously right.That is to say, if the move at the time oft cannot prove that Hk(t)=1 is right, then, at the time of t+1, qi(t+1) will decrease, and oi(t+1) will be the smaller number.To Build the Sensor Network. At the time of t=tend, positions of sensors will not change any more and then connect sensors which can communicate with each other to make edges and calculate the weight of each edge according to function (4) and function (9), and, finally, a chart G(V,E,W) can be made, which is the sensor network.


## 3.1. Combat Environment Scenarios

Assume that, in the combat environment, the coordinate of our position is(-a,0), the coordinate of the enemy is (a,0), and there are n sensors which need to be deployed to detect targets of the enemy. The distribution of our position and the position of the enemy is described in Figure 6, and the shadow area is what we should watch to detect targets from the enemy.Figure 6
The position relationship of the enemy and our side.Based on the rule that targets should be detected as soon as possible, sensors should be deployed near the enemy, but sensors are so near the enemy that they can be destroyed by the weapons form the enemy. According to the rule of “3σ” [16], assume that, in the rectangular area D, the strategic value of each position obeys the regular as follows:(8)fx,y=12πa/3b/3exp⁡-x22a/32-y22b/32.


## 3.2. The Building Rules of Sensor Network

Building the sensor network, which is the basis for multisensor cross cueing, makes a direct impact on the performance of multisensor cross cueing. In order to satisfy the need of multisensor cross cueing, when building the sensor network, the total number of degrees [17] in the sensor network should remain pretty large, making good connectivity between every sensor.When deploying sensors in the areaD, rules should be obeyed as follows:(1)
Sensors tend to be deployed where there is high strategic value.(2)
In order to satisfy the need of multisensor cross cueing, the distance of each two sensors tends to bel=0.81r.(3)
The coverage of the sensor network should remain large.Rule one is designed to meet the combat environment in this paper; rule two is designed to satisfy the need of multisensor cross cueing; rule three is designed due to the rule in the previous papers.


## 3.3. The Steps of Building Sensor Network

To Build the Earning Degree Function. Assume p1=p(A), p2=p(B), p3=p(C), and the position of si is (xi,yi). There are ki sensors which can communicate directly with si, and the set is ci=si1,si2,…,siki, in which sij is the number j. The probability of cross cueing between si and sij is p2(sij). Assume that, in the position (xi,yi), the strategic value is f(xi,yi), and then the earning degree of si can be calculated as follows:(9)gsi=ω1fxi,yi+ω2∑j=1kip2sij+1-ω1-ω2S4ab.In the function,ω1,ω2∈[0,1], which is the weight, and S is the area which the sensor network covers.In this paper,ω1f(xi,yi) is called strategic earning, ω2∑j=1ki(p2(sij)) is called cueing earning, (1-ω1-ω2)S/4ab is called coverage earning, and g(sis) is called the total earning.To Initialize the Positions of Sensors. At the time of t=0, the grid method [17] is used to initialize the positions of sensors, the area is divided into N×M grids, and, at each vertex, there is one sensor.To Optimize the Positions of Sensors. Assume, at the time of t, the vector, whose direction is from (xi(t),yi(t)) to (0,0), is ei→. si can move through the direction ei→ or -ei→, and the speed is vsi(t), which is calculated as follows:(10)
v
s
i
t
=
f
0,0
-
f
x
i
t
,
y
i
t
f
0,0
v
.In the function, v is a constant value.Move through the directionei→, then the strategic earning of si can increase, and the coverage earning can decrease; move through the direction -ei→, then the strategic earning of si can decrease, and the coverage earning can increase (in the case where each two sensors have common detecting area).According to the statistical detection theory, assume that the caseHk(t)=1 is representative for the total earning increase if one sensor is moving through the direction ei→, and the case Hk(t)=0 is representative for the total earning increase if one sensor is moving through the direction -ei→. Assume that, at the time T, the probability of moving through the direction ei→ is qi(t), and the probability of the increase of the total earning is oi(t)(0.5<oi(t)≤1); assume that the probability of moving through the direction -ei→ is 1-qi(t) and the probability of the increase of the total earning is 1-oi(t). After moving, the total earning of si is f(xi(t+1),yi(t+1)).(1) When f(xi(t+1),yi(t+1))≥f(xi(t),yi(t)), update functions as follows.At the time oft, the probability of the increase of the total earning after moving is(11)uit=qit∗oit+1-qit∗1-oit.At the time oft+1,(12)qit+1=qit∗oituitoit+1=oit.The following is to proveqi(t)<qi(t+1)<1.①(13)qit+1>qit⟸oit⁡qit∗oit+1-qit∗1-oit>1⟸2qit+1oit-qitoit-1<0⟸2+1oitqit-1<0.② The functionqi(t+1)<1 is obviously right.That is to say, if the move at the time oft can prove that Hk(t)=1 is right, then, at the time of t+1, qi(t+1) will increase, and oi(t+1) will be the lager number.(2) When f(xi(t+1),yi(t+1))<f(xi(t), yi(t)), update functions as follows.At the time oft, the probability of the increase of the total earning after moving is(14)uj-t=1-qit∗oit+qit∗1-oit.At the time oft+1,(15)qit+1=qit∗1-oituj-toit+1=1-oit.The following is to prove0<qi(t+1)<qi(t).①(16)qit+1<qit⟸qit∗1-oit1-qit∗oit+qit∗1-oit<qit⟸1-oit1-qit∗oit+qit∗1-oit<1⟸1-qit1-2oit<0∵0.5<oit≤1∴The  function  is  right.② The functionqi(t+1)>0 is obviously right.That is to say, if the move at the time oft cannot prove that Hk(t)=1 is right, then, at the time of t+1, qi(t+1) will decrease, and oi(t+1) will be the smaller number.To Build the Sensor Network. At the time of t=tend, positions of sensors will not change any more and then connect sensors which can communicate with each other to make edges and calculate the weight of each edge according to function (4) and function (9), and, finally, a chart G(V,E,W) can be made, which is the sensor network.


## 4. The Simulation and the Analysis

In the process of simulation, parameters are as follows:a=50, b=15, M=7, N=3, r=8, q(0)=0.6, o(0)=0.6, v=5, and T=50. In the beginning, sensors are deployed according to grid method [18], and the distribution is as Figure 7 describes. The red circles are sensors, and if there is a line between two sensors, it means cross cueing can happen between the two sensors.Figure 7
Positions of sensors at the beginning of iteration.In the simulation, the value ofω1, ω2 can exert direct influence on the optimized result of the sensor network. If w1=1 and w2=0, the most optimal result is when all sensors are at the position of (0,0); if w1=0 and w2=1, the most optimal result is when each distance of two sensors is 0.81r; if w1=w2=0, the most optimal result is when there is no common area between each two sensors.At the time oft, the sum of degrees of all vertexes is k0=64, and the average distance of all vertexes is l0=11.29.


### 4.1. The Optimization of the Sensor Network

The Optimization of the Sensor Network When
w
1
=
0.99997, w2=0.00003, and w3=0. In this case, the coverage earning is ignored, and the iteration process is as Figure 8 describes.Figure 8
The iteration process of the optimization using the method in this paper.The optimal result is as Figure9 describes.Figure 9
The optimized result of sensor network.In Figure9, the sum of degrees of all vertexes is k1=431, and the average distance of all vertexes is l1=5.76. It can be known that when sensor stops moving, the distance of two sensors is near l=0.81r=0.648.From Figure9, it can be known that when ignoring the coverage earning, all sensors tend to move to the position of (0,0). The detecting area of the sensor network will decrease, and the reason is mainly as follows: the first one is the highest strategic earning at the position of (0,0) attracts every sensor to move to itself; the other one is that sensors move close to try to get more cueing earning. Although all sensors tend to move to the position of (0,0), there is some distance between each two sensors, and the reason is as follows: each sensor tries to adjust the distance with others to 0.81r under rule two.The Optimization of the Sensor Network When
w
1
=
0.99994, w2=0.00003,andw3=0.00003. In this case, the coverage earning is considered, and the iteration process is as Figure 10 describes.Figure 10
The iteration process of the optimization using the method in this paper.The optimal result is as Figure11 describes.Figure 11
The optimized result of sensor network.In Figure11, the sum of degrees of all vertexes is k2=124, and the average distance of all vertexes is l2=9.38.Compared to Figure9, the sensor network can get lager coverage area in Figure 11, it can satisfy the need of multisensor cross cueing, and there are a number of sensors at the position of (0,0) at the same time, which correspond to the combat reality.In this paper, multisensor cross cueing is analyzed based on the sensor network of Figure11. In Figure 11, coordinates of all sensors is as Table 1 describes, and the weight of each edge is as function (17) describes.(17)0.03170.17010.03170.08990.21200.12330.08990.23660.12850.00470.23560.24700.08140.09890.23660.22110.08890.24750.10820.09890.24720.21920.12850.22110.21020.22110.04250.21920.22410.00900.03700.18620.06430.24080.23000.00900.01480.06430.06000.19840.17010.10230.17010.21200.00470.10230.21170.21200.00470.12330.23560.08890.21170.23980.12330.23560.08890.24700.24750.20120.23980.24700.24750.20120.10820.22110.24080.24730.10820.22110.24080.04250.23000.06000.24730.18330.04250.23000.06000.19840.18330.19840.17010.03710.21200.12330.03710.08990.08140.09890.00470.23560.24700.08990.23660.12850.09890.24720.21920.08890.24750.10820.23660.22110.03700.21920.22410.00900.20120.22110.04250.12850.22110.18620.00900.01480.24080.23000.03700.18620.06340.06000.19840.0634Table 1
Coordinates of sensors.
Sensor
Coordinate
1
(
-
35.65
,
10.67
)
2
(
-
21.37,9.16
)
3
(
-
8.74,6.56
)
4
(
-
1.20,3.60
)
5
(
2.92,4.38
)
6
(
12.61,7.57
)
7
(
26.03,9.76
)
8
(
-
35.46
,
0
)
9
(
-
22.89,0
)
10
(
-
13.60,0
)
11
(
-
5.72,0
)
12
(
10.67,0
)
13
(
16.43,0
)
14
(
26.72,0
)
15
(
-
35.65
,
-
10.67
)
16
(
-
21.37
,
-
9.16
)
17
(
-
8.74
,
-
6.56
)
18
(
-
1.20,3.60
)
19
(
2.92
,
-
4.38
)
20
(
12.61
,
-
7.57
)
21
(
26.03
,
-
9.76
)


### 4.2. The Process of Multisensor Cross Cueing

The Process of Multisensor Cross Cueing at the Case When the Target Makes Linear Motion. Assume that the target is a UCAV, at the time of T=0, the target takes off from the position of the enemy (50,0), and the speed is V=0.5/s. The target moves to (-10,0) through the direction of -x, and then it moves back to (50,0) through x. At the time of T, if 0≤T≤120, the coordinate of the target is (50-V∗T,0), and if 120≤T≤240, the coordinate of the target is (-60+V∗T,0).The process of multisensor cross cueing is as Figure12 describes. The horizontal coordinate is the time T, and the vertical coordinate is the sensor which is responsible for the detection to the target.Figure 12
Procession of multisensor cross cueing when the UCAV is coming.The Process of Multisensor Cross Cueing at the Case When the Target Makes Sinusoidal Motion. Assume that the target is a UCAV and, at the time of T=0, the target takes off from the position of the enemy (50,0), making sinusoidal motion. The flight path is y=10sin⁡(0.04x+π), and, at the time of T=0, the coordinate of the target is (50-t,10cos⁡(0.04(50-t)+π)).The process of multisensor cross cueing is as Figure13 describes. The horizontal coordinate is the time T, and the vertical coordinate is the sensor which is responsible for the detection to the target.Figure 13
Procession of multisensor cross cueing when the UCAV is coming.The two simulations can illustrate that the sensor network can make multisensor cross cueing smooth and successive detection to the target.


## 4.1. The Optimization of the Sensor Network

The Optimization of the Sensor Network When
w
1
=
0.99997, w2=0.00003, and w3=0. In this case, the coverage earning is ignored, and the iteration process is as Figure 8 describes.Figure 8
The iteration process of the optimization using the method in this paper.The optimal result is as Figure9 describes.Figure 9
The optimized result of sensor network.In Figure9, the sum of degrees of all vertexes is k1=431, and the average distance of all vertexes is l1=5.76. It can be known that when sensor stops moving, the distance of two sensors is near l=0.81r=0.648.From Figure9, it can be known that when ignoring the coverage earning, all sensors tend to move to the position of (0,0). The detecting area of the sensor network will decrease, and the reason is mainly as follows: the first one is the highest strategic earning at the position of (0,0) attracts every sensor to move to itself; the other one is that sensors move close to try to get more cueing earning. Although all sensors tend to move to the position of (0,0), there is some distance between each two sensors, and the reason is as follows: each sensor tries to adjust the distance with others to 0.81r under rule two.The Optimization of the Sensor Network When
w
1
=
0.99994, w2=0.00003,andw3=0.00003. In this case, the coverage earning is considered, and the iteration process is as Figure 10 describes.Figure 10
The iteration process of the optimization using the method in this paper.The optimal result is as Figure11 describes.Figure 11
The optimized result of sensor network.In Figure11, the sum of degrees of all vertexes is k2=124, and the average distance of all vertexes is l2=9.38.Compared to Figure9, the sensor network can get lager coverage area in Figure 11, it can satisfy the need of multisensor cross cueing, and there are a number of sensors at the position of (0,0) at the same time, which correspond to the combat reality.In this paper, multisensor cross cueing is analyzed based on the sensor network of Figure11. In Figure 11, coordinates of all sensors is as Table 1 describes, and the weight of each edge is as function (17) describes.(17)0.03170.17010.03170.08990.21200.12330.08990.23660.12850.00470.23560.24700.08140.09890.23660.22110.08890.24750.10820.09890.24720.21920.12850.22110.21020.22110.04250.21920.22410.00900.03700.18620.06430.24080.23000.00900.01480.06430.06000.19840.17010.10230.17010.21200.00470.10230.21170.21200.00470.12330.23560.08890.21170.23980.12330.23560.08890.24700.24750.20120.23980.24700.24750.20120.10820.22110.24080.24730.10820.22110.24080.04250.23000.06000.24730.18330.04250.23000.06000.19840.18330.19840.17010.03710.21200.12330.03710.08990.08140.09890.00470.23560.24700.08990.23660.12850.09890.24720.21920.08890.24750.10820.23660.22110.03700.21920.22410.00900.20120.22110.04250.12850.22110.18620.00900.01480.24080.23000.03700.18620.06340.06000.19840.0634Table 1
Coordinates of sensors.
Sensor
Coordinate
1
(
-
35.65
,
10.67
)
2
(
-
21.37,9.16
)
3
(
-
8.74,6.56
)
4
(
-
1.20,3.60
)
5
(
2.92,4.38
)
6
(
12.61,7.57
)
7
(
26.03,9.76
)
8
(
-
35.46
,
0
)
9
(
-
22.89,0
)
10
(
-
13.60,0
)
11
(
-
5.72,0
)
12
(
10.67,0
)
13
(
16.43,0
)
14
(
26.72,0
)
15
(
-
35.65
,
-
10.67
)
16
(
-
21.37
,
-
9.16
)
17
(
-
8.74
,
-
6.56
)
18
(
-
1.20,3.60
)
19
(
2.92
,
-
4.38
)
20
(
12.61
,
-
7.57
)
21
(
26.03
,
-
9.76
)


## 4.2. The Process of Multisensor Cross Cueing

The Process of Multisensor Cross Cueing at the Case When the Target Makes Linear Motion. Assume that the target is a UCAV, at the time of T=0, the target takes off from the position of the enemy (50,0), and the speed is V=0.5/s. The target moves to (-10,0) through the direction of -x, and then it moves back to (50,0) through x. At the time of T, if 0≤T≤120, the coordinate of the target is (50-V∗T,0), and if 120≤T≤240, the coordinate of the target is (-60+V∗T,0).The process of multisensor cross cueing is as Figure12 describes. The horizontal coordinate is the time T, and the vertical coordinate is the sensor which is responsible for the detection to the target.Figure 12
Procession of multisensor cross cueing when the UCAV is coming.The Process of Multisensor Cross Cueing at the Case When the Target Makes Sinusoidal Motion. Assume that the target is a UCAV and, at the time of T=0, the target takes off from the position of the enemy (50,0), making sinusoidal motion. The flight path is y=10sin⁡(0.04x+π), and, at the time of T=0, the coordinate of the target is (50-t,10cos⁡(0.04(50-t)+π)).The process of multisensor cross cueing is as Figure13 describes. The horizontal coordinate is the time T, and the vertical coordinate is the sensor which is responsible for the detection to the target.Figure 13
Procession of multisensor cross cueing when the UCAV is coming.The two simulations can illustrate that the sensor network can make multisensor cross cueing smooth and successive detection to the target.


## 5. Conclusion

In this paper, the probability of multisensor cross cueing model is built based on probability theory, with the best distance between two sensors calculated. The combat environment is described using normal distribution function. After this work, the optimization algorithm based on hypothesis test to optimize the sensor network is put forward. The simulation indicates that the method the paper introduces can get the sensor network to satisfy the need of multisensor cross cueing. What is more, the process of multisensor cross cueing is shown, which indicates that the multisensor cross cueing technology can adapt to the combat reality, making targets detected successively and having a good application prospect.



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*Source: 7372013-2017-06-28.xml*