CN102752761B - Particle swarm-based coverage optimization method of wireless sensor network mobile node - Google Patents

Abstract

Aiming at the disadvantages of a basic particle swarm algorithm on the solving of the coverage optimization problem of a wireless sensor network, in combination with a maximum coverage algorithm, the invention provides a particle swarm-based coverage optimization method of a wireless sensor network mobile node. The algorithm takes a mobile node position vector quantity as an input parameter, and a network coverage rate as a target function, and the positions among nodes can be adjusted by a far module and a near module mentioned in the maximum coverage algorithm, the nodes are enabled to be far away if being distributed densely; and the nodes are enabled to be near if being distributed loosely. In combination with the position adjustment and the particle swarm algorithm, the positions of the nodes and the nearest node can be adjusted in a particle swarm algorithm speed updating formula, and the particle can be guided to be evolved, so that the coverage range of the nodes can be preferably expanded, and the capability of the particle swarm algorithm for searching the globally optimal solution can be enhanced, i.e. the network coverage rate can be improved. Finally, the wireless sensor network coverage optimization problem can be solved by the position adjustment-based particle swarm algorithm.

Description

Based on the mobile node of wireless sensor network coverage optimization method of population

Technical field

The present invention relates in wireless sensor network, based on the method for solving of the optimum Coverage Control collection of static node, belong to sensor technology, wireless communication technology field.

Background technology

Wireless sensor network is by the finite energy be distributed in a large number in monitored area, and has the microsensor node of perception, calculating and communication capacity, the wireless network consisted of Ad hoc mode.Along with the fast development of the technology such as compunication, integrated circuit, the extensive use of wireless sensor network becomes possibility.

Wireless sensor network is usually responsible for the task of monitoring some region and detecting, Coverage Control is a basic problem in wireless sensor network, main research is how under the prerequisite ensureing certain service quality, realize the maximization of network coverage, to provide reliable Monitoring Service.Network coverage control problem can be thought of as network when by condition restrictions such as network node energy, wireless network communication bandwidth, computing abilities, by the means such as node placement and Route Selection, reasonable distribution Internet resources, thus improve perception, the process of network, the service quality such as communication.Optimizing network coverage strategy, for reasonable distribution Internet resources, completes environmental information perception, acquisition and improves Network survivability all having great importance.

Due to the restriction by wireless sensor network operational environment, mostly adopt the random method laying node.Laying in environment random, easily there is coverage hole in the inhomogeneities of Node distribution; Node is once after being deployed in monitored area simultaneously, may, due to the change of environment, cause the covering performance originally reached can not meet the demands.Such as, node failure or its sensing capability weaken, and the appearance etc. of barrier all can have influence on network covering property.

Mobile node, after initial random distribution, in order to reduce overlapping coverage rate and coverage hole, can adjust the position of oneself.The reasonable layout of node location ensures the network coverage and the precondition being communicated with quality, and can provide basis for the reliability of MAC protocol and network scalability.The task of Node distribution optimization is exactly the mobility by node, carries out dynamic conditioning to node location, repairs perception blind area, obtains coverage rate large as far as possible.

A kind of global random searching algorithm that particle cluster algorithm is simulation flock of birds foraging behavior and proposes.In particle cluster algorithm, each alternative solution is called as one " particle ", multiple particle coexists simultaneously, cooperation optimizing (similar flock of birds search of food), each particle in colony is assembled to best position in problem space according to its self best " experience " and the best " experience " of adjacent particles group, search optimal solution.Due to particle cluster algorithm have simply, fast convergence rate, and the feature such as less is required to target function, has caused extensive concern and the research of the numerous scholar of association area in the world.

The present invention, mainly in conjunction with population and innovatory algorithm thereof, optimizes node deployment, improves network covering property, improves the network coverage.

Summary of the invention

Consider the Cost Problems of mobile node in wireless sensor network, how to optimize positions of mobile nodes, and use limited node to arrive maximum coverage, become good problem to study.The present invention is directed to basic particle group algorithm in the deficiency solving radio sensing network coverage optimization problem, in conjunction with maximal cover algorithm, propose the population coverage optimization method that a kind of position-based regulates.

The present invention is based on the mobile node of wireless sensor network coverage optimization method of population, comprise the steps:

Step 1: search volume is j dimension, and population scale is M, initialization particle position, random position and the speed producing each particle, set the distance threshold of node, the distance between node and nearest-neighbors node is less than set distance threshold simultaneously, then away from; When this distance is greater than distance threshold, then close;

Away from module: node A is (x at the coordinate in n moment _n, y _n), and be (x from the nearest neighbors B of node A at the coordinate in n moment _bn, y _bn), node A is (x in the target location in n+1 moment _n+1, y _n+1), if euclidean distance between node pair threshold value is L _th, the step-length of unit interval is d, sensing radius R _s, communication radius R _c, wherein L _th≤ R _c-d,

Known

$\frac{x_{n+1}-x_n}{x_n-x_{\mathrm{bn}}}=\frac{y_{n+1}-y_n}{y_n-y_{\mathrm{bn}}}=\frac{d}{L_n}---\left(1\right)$

Wherein, $L_n=\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}$

When calculating node A away from node b according to formula (1), the target location of node A:

$\left[\begin{array}{c}{x}_{n+1}\\ y_{n+1}\end{array}\right]=\left[\begin{array}{c}d\·\frac{(x_n-x_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+x_n\\ d\·\frac{(y_n-y_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+y_n\end{array}\right]---\left(2\right)$

Near module: be greater than distance threshold between node A and Node B, in the next moment, node A should move to the direction of node b, with the same away from module, sets up similar Mathematical Modeling, the target location of node A:

$\left[\begin{array}{c}{x}_{n+1}\\ y_{n+1}\end{array}\right]=\left[\begin{array}{c}-d\·\frac{(x_n-x_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+x_n\\ -d\·\frac{(y_n-y_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+y_n\end{array}\right]---\left(3\right)$

Step 2: the initial Efficient Coverage Rate calculating whole region, and the local optimum position pbest of each particle of initialization, and the global optimum position gbest of particle when corresponding coverage rate is maximum;

Step 3: calculate the distance between each node in particle i, and the distance threshold of setting compares, and adjust internodal position according to formula (2) and (3), calculates particle i interior joint with the distance changes values of its nearest node

Step 4: upgrade particle position and speed according to formula (4) and (5), and again calculate the network coverage of each particle updated space postpone according to formula (6) ~ (9);

Speed and location updating formula are such as formula (4):

$v_{\mathrm{ij}}^{k+1}=w\left(k\right)\×v_{\mathrm{ij}}\left(k\right)+c_1{r}_{1j}({\mathrm{pbest}}_{\mathrm{ij}}^k-x_{\mathrm{ij}}^k)+c_2{r}_{2j}({\mathrm{gbest}}_{\mathrm{gj}}^k-x_{\mathrm{ij}}^k)+c_3{r}_3{\mathrm{\Δ}}_{\mathrm{ij}}^k---\left(4\right)$

$x_{\mathrm{ij}}^{k+1}=x_{\mathrm{ij}}^k+v_{\mathrm{ij}}^{k+1}---\left(5\right)$

Wherein, c ₁for particulate self-acceleration weight coefficient, c ₂for overall acceleration weight coefficient, c ₃for the acceleration weight coefficient of position adjustments, r _1jand r _2jbe the random number in 0 ~ 1, with be respectively position and the speed of particle i jth dimension in kth time iteration, the two is all limited within the specific limits; the position of the individual extreme value that to be particle i tie up in jth; the position of the individual extreme value that to be colony tie up in jth; W is inertia weight coefficient; it is particle i interior joint with the distance changes values of its nearest node;

If the node s in wireless sensor network _icoordinate be (x _i, y _i), in a two dimensional surface monitored area, the coordinate of arbitrfary point p is (x _p, y _p), then node s _ito the detection probability of impact point p be:

Wherein, d (s _i, p) be sensor node s _iwith the Euclidean distance of impact point p; R _e(0<R _e<R _s) be sensing node Measurement reliability parameter; α ₁=R _e-R _s+ d (s _i, p), α ₂=R _e+ R _s-d (s _i, p); λ ₁, λ ₂, β ₁, β ₂the measurement parameter relevant with sensing node characteristic;

Therefore, the joint-detection probability of n sensor node to impact point p in whole two dimensional surface monitored area is:

$C_p(s_{\mathrm{all}},p)=1-\underset{i=n}{\mathrm{\&Pi;}}(1-C_p(s_i,p))---\left(7\right)$

Wherein, s _allfor the sensor node set of measuring target point; In order to meet coverage requirement, usually require that joint-detection probability is not less than the threshold value c set by network demand _th, then impact point can be by the condition effectively detected:

$\underset{x_p,y_p}{\min }\left\{C_p(s_{\mathrm{all}},p)\right\}\&GreaterEqual;C_{\mathrm{th}}---\left(8\right)$

Region dividing to be measured is become m × n grid, then cell is reduced to pixel, the network coverage is defined as and meets the ratio that cell quantity that formula (7) requires accounts for total cell quantity, that is:

$C_r=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(s_{\mathrm{all}},p)}{m\&times;n}---\left(9\right)$

Step 5: the coverage rate that the coverage rate of each particle updated space postpone is corresponding with the local optimum position pbest of each particle compares, if comparatively large, then upgrades pbest;

Step 6: coverage rate corresponding with gbest for coverage rate corresponding for optimum for the individuality of each particle in colony pbest is compared, if comparatively large, then upgrades gbest;

Step 7: if reach default greatest iteration number, then terminate, and return colony's Optimal Distribution, otherwise return step 2.

This algorithm is with positions of mobile nodes vector for input parameter, and the network coverage is target function, utilize simultaneously mention in maximal cover algorithm away from near module, internodal position is adjusted, as overstocked in distributed between node, then allow node away from; If Node distribution is loose, then node is close.Binding site regulates and particle cluster algorithm, the position considering node and its nearest node in particle cluster algorithm speed more new formula adjusts, and instructs particle evolution, does the coverage contributing to troclia point like this, strengthen the ability of particle cluster algorithm search global optimum, namely improve the network coverage.Finally apply the PSO Algorithm radio sensing network coverage optimization problem based on position adjustments.

Accompanying drawing explanation

Fig. 1 node A is away from Node B schematic diagram;

Fig. 2 node A is near Node B schematic diagram;

Fig. 3 maximal cover algorithm flow;

The particle cluster algorithm coverage optimization flow process that Fig. 4 position-based regulates.

Embodiment

Based on the coverage optimization of improve PSO algorithm

Particle cluster algorithm is simple and be easy to realize, and is applied to by particle cluster algorithm to solve wireless sensor network coverage optimization problem and effectively can improve network covering property, but along with the increase of nodes, dimension increases, and very difficult guarantee obtains globally optimal solution.In addition, particle cluster algorithm is easily absorbed in Local Extremum, limits the hunting zone of particle, can not converge to global extremum point.The present invention is directed to basic particle group algorithm in the deficiency solving radio sensing network coverage optimization problem, give the innovatory algorithm that binding site regulates.

Maximal cover algorithm

For the wireless sensor network be made up of mobile node, maximal cover algorithm, while guarantee Connectivity, is expanded the coverage area as much as possible.Two kinds of modules are had, away from module with near module in algorithm.Distance between node and nearest-neighbors node is less than set distance threshold, then away from; When this distance is greater than distance threshold, then close.

1. away from module

In Selection Model, two nodes are analyzed, and node A is (x at the coordinate in n moment _n, y _n), and be (x from the nearest neighbors B of node A at the coordinate in n moment _bn, y _bn), node A is (x in the target location in n+1 moment _n+1, y _n+1), as shown in Figure 1.And set euclidean distance between node pair threshold value as L _th, the step-length of unit interval is d, sensing radius R _s, communication radius R _c, wherein L _th≤ R _c-d.

According to the geometrical relationship in Fig. 1, known

$\frac{x_{n+1}-x_n}{x_n-x_{\mathrm{bn}}}=\frac{y_{n+1}-y_n}{y_n-y_{\mathrm{bn}}}=\frac{d}{L_n}---\left(1\right)$

Wherein, $L_n=\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}$

When calculating node A away from Node B according to formula (1), the target location of node A:

$\left[\begin{array}{c}{x}_{n+1}\\ y_{n+1}\end{array}\right]=\left[\begin{array}{c}d\&CenterDot;\frac{(x_n-x_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+x_n\\ d\&CenterDot;\frac{(y_n-y_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+y_n\end{array}\right]---\left(2\right)$

2. near module

Corresponding with away from situation, be greater than distance threshold between node A and node b, in the next moment, node A should move to the direction of Node B, with the same away from module, sets up similar Mathematical Modeling, as shown in Figure 2.

Together away from model class seemingly, according to geometrical relationship in figure, the target location of node A is calculated:

$\left[\begin{array}{c}{x}_{n+1}\\ y_{n+1}\end{array}\right]=\left[\begin{array}{c}-d\&CenterDot;\frac{(x_n-x_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+x_n\\ -d\&CenterDot;\frac{(y_n-y_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+y_n\end{array}\right]---\left(3\right)$

This algorithm is simple, and easily realizes, and the flow chart of whole algorithm can be described as shown in Fig. 3.

The coverage optimization of the particle cluster algorithm that position-based regulates

In order to strengthen the ability of particle cluster algorithm search global optimum, namely in order to improve the network coverage.The present invention utilize mention in maximal cover algorithm away from near module, internodal position is adjusted, as overstocked in distributed between node, then allow node away from; If Node distribution is loose, then node is close.Binding site regulates and particle cluster algorithm, incorporates the impact of position vector in particle cluster algorithm speed more new formula.Its speed and location updating formula are such as formula (4):

$v_{\mathrm{ij}}^{k+1}=w\left(k\right)\&times;v_{\mathrm{ij}}\left(k\right)+c_1{r}_{1j}({\mathrm{pbest}}_{\mathrm{ij}}^k-x_{\mathrm{ij}}^k)+c_2{r}_{2j}({\mathrm{gbest}}_{\mathrm{gj}}^k-x_{\mathrm{ij}}^k)+c_3{r}_3{\mathrm{\&Delta;}}_{\mathrm{ij}}^k---\left(4\right)$

$x_{\mathrm{ij}}^{k+1}=x_{\mathrm{ij}}^k+v_{\mathrm{ij}}^{k+1}---\left(5\right)$

Wherein, c ₁for particulate self-acceleration weight coefficient, c ₂for overall acceleration weight coefficient, c ₃for the acceleration weight coefficient of position adjustments, r _1jand r _2jbe the random number in 0 ~ 1, with be respectively position and the speed of particle i jth dimension in kth time iteration, the two is all limited within the specific limits; the position of the individual extreme value that to be particle i tie up in jth; the position of the individual extreme value that to be colony tie up in jth; W is inertia weight coefficient; it is particle i interior joint with the distance changes values (such as formula (2), formula (3)) of its nearest node.

Node Probability Detection model probability is adopted to carry out computing network coverage rate as measurement model.If the node s in wireless sensor network _icoordinate be (x _i, y _i).Assuming that the coordinate of arbitrfary point p is (x in a two dimensional surface monitored area _p, y _p), then node s _ito the detection probability of impact point p be:

Wherein, d (s _i, p) be sensor node s _iwith the Euclidean distance of impact point p; R _e(0<R _e<R _s) be sensing node Measurement reliability parameter; α ₁=R _e-R _c+ d (s _i, p), α ₂=R _e+ R _s-d (s _i, p); λ ₁, λ ₂, β ₁, β ₂the measurement parameter relevant with sensing node characteristic.

Therefore, the joint-detection probability of n sensor node to impact point p in whole two dimensional surface monitored area is:

$C_p(s_{\mathrm{all}},p)=1-\underset{i=n}{\mathrm{\&Pi;}}(1-C_p(s_i,p))---\left(7\right)$

Wherein, s _allfor the sensor node set of measuring target point.In order to meet coverage requirement, usually require that joint-detection probability is not less than the threshold value c set by network demand _th, then impact point can be by the condition effectively detected:

$\underset{x_p,y_p}{\min }\left\{C_p(s_{\mathrm{all}},p)\right\}\&GreaterEqual;C_{\mathrm{th}}---\left(8\right)$

The wireless sensing node monitored area of random laying is normally irregular, cannot use the area coverage of analytic method direct solution network.In order to effective evaluation network covering property, adopt gridding method that Region dividing to be monitored is become grid, more just cell is reduced to a little, analyze the coverage rate of each wireless sensor node to this point, the distance wherein between adjacent mesh is determined by covering precision.

Suppose Region dividing to be measured to become m × n grid, then cell is reduced to pixel.Herein, the network coverage is defined as and meets the ratio that cell quantity that formula (7) requires accounts for total cell quantity, that is:

$C_r=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(s_{\mathrm{all}},p)}{m\&times;n}---\left(9\right)$

The present invention regards the coverage optimization of mobile node in wireless sensor network as with the position of node for input parameter, the network coverage is as the optimization problem of target.Employing formula (9) is as target function, and apply the coverage optimization problem of the PSO Algorithm mobile node based on position adjustments, its flow process as shown in Figure 4.

Algorithm steps is as follows:

Step 1: set search volume as j dimension, definition population scale is M, initialization particle position, and random position and the speed producing each particle, sets the distance threshold of node simultaneously.

Step 2: the initial Efficient Coverage Rate calculating whole region, and the local optimum position pbest of each particle of initialization, and the global optimum position gbest of particle when corresponding coverage rate is maximum.

Step 3: calculate the distance between each node in particle i, and the distance threshold of setting compares, and adjust internodal position according to formula (2) and (3), calculates particle i interior joint with the distance changes values of its nearest node

Step 4: upgrade particle position and speed according to formula (4) and (5), and again calculate the network coverage of each particle updated space postpone according to formula (6) ~ (9).

Step 5: the coverage rate that the coverage rate of each particle updated space postpone is corresponding with the local optimum position pbest of each particle compares, if comparatively large, then upgrades pbest;

Step 6: coverage rate corresponding with gbest for coverage rate corresponding for optimum for the individuality of each particle in colony pbest is compared, if comparatively large, then upgrades gbest;

Step 7: if reach default greatest iteration number, then terminate, and return colony's Optimal Distribution, otherwise return step 2.

Claims (1)

1., based on a mobile node of wireless sensor network coverage optimization method for population, it is characterized in that comprising the steps:

Step 1: search volume is j dimension, and population scale is M, initialization particle position, random position and the speed producing each particle, set the distance threshold of node, the distance between node and nearest-neighbors node is less than set distance threshold simultaneously, then away from; When this distance is greater than distance threshold, then close;

Away from module: node A is (x at the coordinate in n moment _n, y _n), and be (x from the nearest neighbors b of node A at the coordinate in n moment _bn, y _bn), node A is (x in the target location in n+1 moment _n+1, y _n+1), if euclidean distance between node pair threshold value is L _th, the step-length of unit interval is d, sensing radius R _s, communication radius R _c, wherein L _th≤ R _c-d,

Known

$\frac{x_{n+1}-x_n}{x_n-x_{\mathrm{bn}}}=\frac{y_{n+1}-y_n}{y_n-y_{\mathrm{bn}}}=\frac{d}{L_n}---\left(1\right)$

Wherein, $L_n=\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}$

When calculating node A away from node b according to formula (1), the target location of node A:

$\left[\begin{array}{c}{x}_{n+1}\\ y_{n+1}\end{array}\right]=\left[\begin{array}{c}d\&CenterDot;\frac{(x_n-x_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+x_n\\ d\&CenterDot;\frac{(y_n-y_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+y_n\end{array}\right]---\left(2\right)$

Near module: be greater than distance threshold between node A and node b, in the next moment, node A should move to the direction of Node B, with the same away from module, sets up similar Mathematical Modeling, the target location of node A:

$\left[\begin{array}{c}{x}_{n+1}\\ y_{n+1}\end{array}\right]=\left[\begin{array}{c}-d\&CenterDot;\frac{(x_n-x_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+x_n\\ -d\&CenterDot;\frac{(y_n-y_{\mathrm{bn}})}{\sqrt{{(x_n-x_{\mathrm{bn}})}^2+{(y_n-y_{\mathrm{bn}})}^2}}+y_n\end{array}\right]---\left(3\right)$

Step 2: the initial Efficient Coverage Rate calculating whole region, and the local optimum position pbest of each particle of initialization, and the global optimum position gbest of particle when corresponding coverage rate is maximum;

Step 3: calculate the distance between each node in particle i, and the distance threshold of setting compares, and adjust internodal position according to formula (2) and (3), calculates particle i interior joint with the distance changes values of its nearest node

Step 4: upgrade particle position and speed according to formula (4) and (5), and again calculate the network coverage of each particle updated space postpone according to formula (6) ~ (9);

Speed and location updating formula are such as formula (4):

$v_{\mathrm{ij}}^{k+1}=w\left(k\right)\&times;v_{\mathrm{ij}}\left(k\right)+c_1{r}_{1j}({\mathrm{pbest}}_{\mathrm{ij}}^k-x_{\mathrm{ij}}^k)+c_2{r}_{2j}({\mathrm{gbest}}_{\mathrm{gj}}^k-x_{\mathrm{ij}}^k)+c_3{r}_3{\mathrm{\&Delta;}}_{\mathrm{ij}}^k---\left(4\right)$

$x_{\mathrm{ij}}^{k+1}=x_{\mathrm{ij}}^k+v_{\mathrm{ij}}^{k+1}---\left(5\right)$

Wherein, c ₁for particulate self-acceleration weight coefficient, c ₂for overall acceleration weight coefficient, c ₃for the acceleration weight coefficient of position adjustments, r _1jand r _2jbe the random number in 0 ~ 1, with be respectively position and the speed of particle i jth dimension in kth time iteration, the two is all limited within the specific limits; the position of the individual extreme value that to be particle i tie up in jth; the position of the individual extreme value that to be colony tie up in jth; W is inertia weight coefficient; it is particle i interior joint with the distance changes values of its nearest node;

If the node s in wireless sensor network _icoordinate be (x _i, y _i), in a two dimensional surface monitored area, the coordinate of arbitrfary point p is (x _p, y _p), then node s _ito the detection probability of impact point p be:

Wherein, d (s _i, p) be sensor node s _iwith the Euclidean distance of impact point p; R _e(0<R _e<R _s) be sensing node Measurement reliability parameter; α ₁=R _e-R _s+ d (s _i, p), α ₂=R _e+ R _s-d (s _i, p); λ ₁, λ ₂, β ₁, β ₂the measurement parameter relevant with sensing node characteristic;

Therefore, the joint-detection probability of n sensor node to impact point p in whole two dimensional surface monitored area is:

$C_p(s_{\mathrm{all}},p)=1-\underset{i=n}{\mathrm{\&Pi;}}(1-C_p(s_i,p))---\left(7\right)$

Wherein, s _allfor the sensor node set of measuring target point; In order to meet coverage requirement, usually require that joint-detection probability is not less than the threshold value c set by network demand _th, then impact point can be by the condition effectively detected:

$\underset{x_p,y_p}{\min }\left\{C_p(s_{\mathrm{all}},p)\right\}\&GreaterEqual;C_{\mathrm{th}}---\left(8\right)$

Region dividing to be measured is become m × n grid, then cell is reduced to pixel, the network coverage is defined as and meets the ratio that cell quantity that formula (7) requires accounts for total cell quantity, that is:

$C_r=\frac{\underset{x_p=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{y_p=1}{\overset{n}{\mathrm{\&Sigma;}}}{C}_p(s_{\mathrm{all}},p)}{m\&times;n}---\left(9\right)$

Step 5: the coverage rate that the coverage rate of each particle updated space postpone is corresponding with the local optimum position pbest of each particle compares, if comparatively large, then upgrades pbest;

Step 6: coverage rate corresponding with gbest for coverage rate corresponding for optimum for the individuality of each particle in colony pbest is compared, if comparatively large, then upgrades gbest;

Step 7: if reach default greatest iteration number, then terminate, and return colony's Optimal Distribution, otherwise return step 2.