CN113347561B - Multidimensional scale node positioning method based on improved particle swarm - Google Patents
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Abstract
The invention provides a multidimensional scaling node positioning method based on improved particle swarm. The invention adopts two kinds of sensor nodes: the anchor node positions itself through GPS, the unknown node communicates with adjacent anchor node and realizes its own positioning through network topology, and particle swarm algorithm with cross operation is introduced in the coordinate conversion stage, including step 1: an initialization stage; step 2: clustering; step 3: a relative positioning stage of nodes in the cluster; step 4: an inter-cluster fusion stage; step 5: and a coordinate conversion stage. The invention can adapt to wireless sensor networks with various shapes in practical application, optimize coordinate conversion parameters of absolute coordinates and relative coordinates, and achieve the purposes of improving the accuracy of absolute coordinates of unknown nodes in the network and improving the positioning accuracy.
Description
Technical Field
The invention relates to a multidimensional scaling node positioning method based on improved particle swarm, and belongs to the technical field of wireless sensor network application.
Background
A wireless sensor network (Wireless Sensor Network, WSN) is a dynamic network area consisting of a large number of sensor nodes exploiting the multi-hop ad hoc nature and network topology. The nodes are randomly deployed in the area to be monitored with small-scale batteries as energy sources and have certain computing and communication capabilities. The deployment mode of the sensor nodes is not unique, or the sensor nodes can be deployed manually through aerial delivery and broadcast of an airplane or by mechanical projection. The nodes in the network cooperate with each other, and after the operations such as monitoring, collecting, analyzing and processing the data information of the area to be monitored are performed, the data information is received and transmitted by using the Internet, so that the real-time performance of information acquisition of users is ensured. The variety of application scenes and information types requires that the sensor is also rich and various in variety, such as temperature and humidity sensors, light sensors and the like applied to modern agriculture; the pressure sensor and the sound sensor are applied to national defense safety; the formaldehyde sensor and the smoke sensor are applied to intelligent home. The nature of the sensor network and the manner in which the sensor nodes are deployed are such that the location of each sensor node is random. Geographic location information is an essential item in obtaining monitoring information, for example, in military security, geographic information of both enemy teams and my teams is extremely critical; before natural disasters such as earthquake disasters, forest fires and the like, rescue can be rapidly and accurately carried out only by acquiring accurate geographical position information; or when people find vacant parking spaces in underground parking lots at ordinary times, accurate geographic position information is also needed. Therefore, the node positioning technology is an important technology in WSNs, and numerous scientific researchers participate in promoting the development of the positioning technology.
The node location algorithm is based on the location information of anchor nodes deployed with a global positioning system (Global Positioning System, GPS), and the nodes communicate with each other to estimate the location of an unknown node. Wireless sensor network positioning algorithms can be broadly divided into two categories: ranging-based and non-ranging-free based. The former positioning premise is that information such as distance or angle among nodes is known, and positioning accuracy is high. And distance information is indirectly obtained according to the information such as network connectivity and relevance based on a non-ranging positioning algorithm, so that the cost is low, but the positioning accuracy is relatively poor.
MDS-MAP is used as a classical positioning algorithm which can be applied to ranging and non-ranging, and by virtue of the classical positioning algorithm, the advantages of less requirement on anchor nodes, low hardware cost and the like gradually become great heat when people select the positioning algorithm. The basic idea is to obtain a distance matrix between nodes by using a shortest path algorithm. And processing the distance matrix by using a metric or non-metric multidimensional scaling algorithm to obtain the relative coordinates of the nodes in the network according to whether the distances among the nodes are measurable, and finally converting the relative coordinates of the nodes in the whole network into absolute coordinates by linear transformation by utilizing absolute coordinate information of anchor nodes.
In practical applications, the centralized MDS-MAP is often limited in use due to poor expansion performance, so that the distributed MDS algorithm is used more recently. There are four main phases of the distributed MDS node location algorithm: a clustering stage, a positioning stage in a cluster, an inter-cluster fusion stage and a coordinate conversion stage. The current coordinate conversion stage only takes the real coordinates of the anchor node as the absolute coordinates thereof, and utilizes a coordinate conversion formula to solve the parameters of coordinate conversion. However, the coordinate conversion parameters obtained by different anchor nodes are different, and the inability to unify the parameter standards can bring about larger positioning errors. It is extremely important to propose a positioning algorithm that is optimized for the coordinate transformation parameters of the coordinate transformation stage.
Disclosure of Invention
The invention aims to provide a multidimensional scaling node positioning method based on an improved particle swarm, which is improved on the basis of the existing distributed multidimensional scaling positioning method, and a particle swarm optimization algorithm with cross operation is introduced to optimize coordinate conversion parameters of absolute coordinates and relative coordinates so as to improve the accuracy of absolute coordinates of unknown nodes in a network and improve the positioning accuracy.
In order to achieve the above purpose, the invention provides a multidimensional scaling node positioning method based on improved particle swarm, comprising the following specific implementation steps: two sensor nodes, namely an anchor node and an unknown node, are adopted, the anchor node positions itself through GPS, the unknown node communicates with the adjacent anchor node and realizes the self positioning through network topology, a particle swarm algorithm with cross operation is introduced in the coordinate conversion stage, and the method mainly comprises the following stages:
step 1: initializing a wireless sensor network, wherein each node in the network obtains a distance matrix of adjacent nodes through an RSSI ranging method;
step 2: in the clustering stage, clustering integration is carried out on the wireless sensor network, and the wireless sensor network after the clustering integration is divided into a plurality of clusters taking cluster heads as calculation centers;
step 3: in the relative positioning stage of the nodes in the cluster, a generalized square distance matrix is calculated according to the input distance matrix, and singular value decomposition is carried out on the generalized square distance matrix subjected to the decentralization treatment by using a classical MDS algorithm to obtain the relative coordinates of the nodes in the cluster;
step 4: in the inter-cluster fusion stage, a cluster with more common nodes in the cluster is selected to be fused with adjacent clusters, and then a least square method-based inter-cluster coordinate registration method is adopted to carry out coordinate registration on each cluster so as to achieve the fusion; repeating the steps until all nodes are fused;
step 5: and in the coordinate conversion stage, the absolute coordinates and the relative coordinates of the anchor nodes are utilized, the acquisition of the coordinate conversion parameters is optimized by utilizing a particle swarm optimization algorithm with cross operation, and the relative coordinates of each unknown node are converted into the absolute coordinates.
As a further improvement of the present invention, in step 1, the wireless sensor network is initialized by taking into account a shadow model of environmental factor changes:
wherein P is R (m) represents the signal power received by the receiving end, P T Representing the signal power at the transmitting end, PL (m 0 ) Represents the distance m from the transmitting end 0 The path loss at which m represents the distance between the transmitting end and the receiving end, m 0 Represents the reference distance, eta represents the channel attenuation factor, the value range is 2-4, X δ ＝N(0,δ 2 ) Is a random variable of the debilitating component of RSSI to obtain a distance matrix [ m ] of neighboring nodes ij ]。
As a further improvement of the present invention, in step 2: the clustering stage adopts a rapid clustering method to perform clustering and inspect the public nodes, and the clustering stage comprises the following steps:
step 21: node k randomly generates a timer t k ＝rand(0,t max ) And empty the cluster head list MyHeader to which the user belongs at the moment
Step 22: when the timer of the node ends, the node broadcasts a message to announce that the node becomes a cluster head, and the message contains a type identifier msgtype=header and a node identification ID;
step 23: if node k receives message msgtype=leader before timer is finished, stopping timing, adding node identification ID of the leader node to own myleader list, and then broadcasting a connection request message by node k, wherein the connection request message contains type identifier msgtype=join and node identification ID;
step 24: if only the cluster head uses the MSGTYPE=join response message, the cluster head checks a MyHeader list of the connection request message, and if the list contains an ID of the cluster head, the cluster head stores the message; the Cluster head stores the connection request message into a self Cluster-reactant list, wherein the connection request message comprises a node identification ID and a MyHeader list, and then the Cluster head broadcasts and confirms a message, and the Cluster head comprises a type identifier (MSGTYPE=ack), a Cluster head ID and a Cluster-reactant list;
step 25: when node k receives message msgtype=ack, checking the Cluster head ID of the Cluster where itself is located, if the ID is in the Cluster head list, it will store the message and update the Cluster-remmber list;
step 26: the cluster head checks whether the cluster has enough public nodes with the adjacent clusters, if not, the two-hop adjacent nodes are cached to serve as member nodes of the cluster, and the sufficient public nodes are ensured to be fused among the clusters.
As a further improvement of the present invention, in step 3: distance matrix [ m ] between nodes in relative positioning stage of nodes in cluster ij ]Using the square of the P-dimensional space as input and decomposing the relative map between the output nodes by using the singular values to make the P-dimensional space have n nodes X i I=1, …, n, the square of the euclidean distance between adjacent nodes is D 2 ＝m ij 2 Matrix B represents the node inner product and the uniqueness of the solution is achieved by classical multidimensional scaling algorithm (MDS) by transferring the node center coordinates to the origin of coordinates, D 2 Double-decentering is performed, both sides being multiplied by a center matrix H, where h=e-n -1 1, E represents an n-order identity matrix, the inner product B is represented by a p-dimensional coordinate matrix X form, the rank of the matrix B represents the coordinate dimension p, then singular value decomposition is carried out on the matrix B, the characteristic values are arranged according to the order of magnitude, and the first p maximum characteristic values lambda are taken 1 λ 2 ,…,λ p Then, a diagonal matrix Λ is formed, and the corresponding eigenvector e is formed 1 ,e 2 ,…e p And forming an N multiplied by P dimensional matrix V, and finally representing the coordinates of all nodes as follows by an MDS algorithm:
X＝V·Λ 1/2 。
as a further improvement of the present invention, in step 4: in the inter-cluster fusion stage, one cluster A with more public nodes is selected to be fused with an adjacent cluster B, a least square method-based inter-cluster coordinate registration method is adopted to perform coordinate registration on each cluster to achieve fusion, the steps are repeated until all nodes in a network are contained, n public nodes are shared in the cluster A and the cluster B, a rotation matrix of coordinates of the public nodes in local maps of the cluster A and the cluster B is represented by Q, the rotation matrix Q is solved by a least square method, then the cluster B is fused to the cluster A, and the formula of the cluster B fused to the cluster A is as follows:
X A ＝s×Q(X B )+x 0
where s is a scaling factor, x 0 Is a translation vector.
As a further improvement of the present invention, in step 5: the coordinate conversion stage comprises the following steps:
step 51: setting an adaptability function of the evaluation;
step 52: calculating the speed by using a new particle motion formula, generating a new guide vector by using arithmetic crossover, differential evolution crossover and selection operation, and substituting the new guide vector into the particle motion formula by adopting a guide vector substitution strategy;
step 53: calculating a new fitness function according to the new guide vector generated in the step 52, and judging the fitness of the particles by using the sum of the distance differences between the real coordinates and the estimated coordinates of all anchor nodes as the new fitness function;
step 54: judging whether the preset precision or the maximum iteration times are reached, if so, converting the relative coordinates of all unknown nodes into absolute coordinates through the coordinate conversion parameters after the optimization; if not, repeating step 52 and step 53 in sequence.
As a further improvement of the invention, in step 51, setting an adaptive fitness function of the valuation further comprises:
step 511: taking the anchor node parameter combination as a particle, and constructing a proper fitness function by using the absolute coordinates and the relative coordinates of the anchor nodes:
wherein (x) 1 ,x 2 ) Is the anchor node relative coordinates, (y) 1 ,y 2 ) As absolute coordinates of anchor node, deltax 1 ,Δx 2 For translation vector, alpha is rotation angle, t is turnover parameter;
step 512: setting an error function f (Deltax 1 ,Δx 2 α, t) to measure the degree of difference between the actual coordinates (X, Y) of the anchor node and the estimated absolute coordinates (X, Y), the formula is:
wherein N is the number of anchor nodes, A= [ (x) i cosα-ty i sinα)+Δx 1 -X i ] 2 ，B＝[(x i sinα+ty i cosα)+Δx 2 -Y i ] 2 ，f(Δx 1 ,Δx 2 The smaller the α, t), the better the parameter optimization effect, the smaller the positioning error, the error function f (Δx) 1 ,Δx 2 Alpha, t) is used as an fitness function of a particle swarm optimization algorithm to search for the population optimum P g 。
As a further improvement of the present invention, the particle motion formula in step 52 is specifically:
in the search space in D-dimension, one particle i has two vectors, one is the velocity vector V i ＝(v i1 ,v i2 ,…v id ,…v iD ) The other is the position vector X i ＝(x i1 ,x i2 ,…x id ,…x iD ) The position and speed vectors of each particle are randomly initialized according to the space to be searched, and then the two parameters are iteratively searched and updated by using an updating formula of the position and the speed, wherein the updating formula is as follows:
v id ＝wv id +cr d (GV id -x id )
wherein w is an inertia factor with positive value, c is an acceleration factor, r d Is uniformly distributed in [0,1 ]]Random number, GV between i Then called the pilot vector, the variable t represents the number of iterations, d represents one of the dimensions, d e 1,2]。
As a further development of the invention, the vector GV is guided in step 52 i The construction method comprises the following steps:
step 521: arithmetic crossover
Let two particles P i And P j Crossover is performed to generate a new velocity vector V id ：
Before the crossover operation is performed, the historical optimum position (P 1 ,P 2 ,…,P N ) Performing random permutation to optimize P for the group g Performing more detailed local search around;
step 522: differential evolution crossover
Differential evolutionary cross-action on velocity vector V i And a target vector T i Generating a new vector U i ：
Wherein CR is a crossover factor
Step 523: selection operation
Evaluating a newly generated vector U by means of an fitness function i And taking the evaluation result as a guide vector:
step 524: alternative strategies
And selecting the guiding vector with the best adaptability to replace the current guiding vector, and changing the position and the speed of the particles to be out of local optimum.
The beneficial effects of the invention are as follows: compared with a distributed MDS node positioning algorithm, the method optimizes the coordinate conversion parameters of the absolute coordinates and the relative coordinates by introducing a particle swarm optimization algorithm with cross operation, so that the accuracy of the absolute coordinates of unknown nodes in a network is improved, the error rate can be effectively reduced, and the positioning accuracy is improved.
Drawings
Fig. 1 is a flow chart of the present method.
Fig. 2 is a node distribution diagram of the present method in a rectangular monitoring area.
FIG. 3 is a graph of the node distribution of the present method in the type C monitoring region.
FIG. 4 is a graph comparing the positioning errors of the present invention with the MDS-MAP, MDS-MAP (P) and FC-MDS algorithms in different anchor node ratios in a rectangular region.
FIG. 5 is a graph comparing the positioning errors of the present invention with the MDS-MAP, MDS-MAP (P) and FC-MDS algorithms under different node connectivity in a rectangular region.
FIG. 6 is a graph comparing the positioning errors of the present invention with the MDS-MAP, MDS-MAP (P) and FC-MDS algorithm at different anchor node ratios in the C-type region.
FIG. 7 is a graph showing the comparison of the positioning errors of the present invention with three algorithms MDS-MAP, MDS-MAP (P) and FC-MDS at different node communication levels in the C-type region.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in detail with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1, the invention discloses a multidimensional scaling node positioning method based on improved particle swarm, which adopts two sensor nodes, namely an anchor node and an unknown node, wherein the anchor node positions itself through a GPS, the unknown node communicates with adjacent anchor nodes and realizes self positioning through network topology, a particle swarm algorithm (a particle swarm optimization with crossover operation, PSOCO) with cross operation is introduced in a coordinate conversion stage, and the method mainly comprises the following stages:
step 1: an initialization stage: initializing a wireless sensor network, wherein each node in the network obtains a distance matrix [ m ] of adjacent nodes by a RSSI (received signal strength indication (Received Signal Strength Indicator) positioning technology) ranging method ij ]A shadow model is used that fully accounts for environmental factor changes, as shown in the following:
wherein P is R (m) represents the signal power received by the receiving end, P T Representing the signal power at the transmitting end, PL (m 0 ) Indicating distance from transmitting end d 0 The path loss at which m represents the distance between the transmitting end and the receiving end, m 0 Represents the reference distance, eta represents the channel attenuation factor, the value range is 2-4, X δ ＝N(0,δ 2 ) A random variable, expressed as a debilitating component of RSSI, is obtained for a distance matrix [ m ] of adjacent nodes ij ]。
Step 2: clustering: and carrying out cluster integration on the wireless sensor network, and dividing the wireless sensor network after cluster integration into a plurality of clusters taking the cluster heads as the computing centers.
The clustering method adopts a rapid clustering method similar to a three-way handshake transmission control protocol, and adds a step of checking a public node before finishing, thereby improving the reliability of the algorithm, and mainly comprises the following steps:
step 21: node k randomly generates a timer t k ＝rand(0,t max ) And empty the cluster head list MyHeader to which the user belongs at the moment
Step 22: when the timer of the node ends, the node broadcasts a message to announce that the node becomes a cluster head, and the message contains a type identifier msgtype=header and a node identification ID;
step 23: if node k receives message msgtype=leader before timer is finished, stopping timing, adding node identification ID of the leader node to own myleader list, and then broadcasting a connection request message by node k, wherein the connection request message contains type identifier msgtype=join and node identification ID;
step 24: only the cluster head uses the MSGTYPE=join response message, the cluster head checks the MyHeader list of the connection request message, and if the list contains the ID of the cluster head, the cluster head stores the message; the Cluster head stores the connection request message into a self Cluster-reactant list, wherein the connection request message comprises a node identification ID and a MyHeader list, and then the Cluster head broadcasts and confirms a message, and the Cluster head comprises a type identifier (MSGTYPE=ack), a Cluster head ID and a Cluster-reactant list;
step 25: when node k receives message msgtype=ack, checking the Cluster head ID of the Cluster where itself is located, if the ID is in the Cluster head list, it will store the message and update the Cluster-remmber list;
step 26: the cluster head checks whether the cluster has enough public nodes with the adjacent clusters, if not, the two-hop adjacent nodes are cached to serve as member nodes of the cluster, and the sufficient public nodes are ensured to be fused among the clusters.
The cluster head is operated to buffer the two-hop neighbor nodes to form clusters through the above clustering, so that the number of public nodes is ensured, and meanwhile, the following locating stage in the clusters is also padded.
Step 3: relative positioning stage of nodes in a cluster: calculating a generalized square distance matrix according to the input distance matrix, and performing singular value decomposition on the generalized square distance matrix subjected to the decentralization treatment by using a classical MDS (multidimensional scaling, multidimensional scale analysis) algorithm to obtain relative coordinates of nodes in the cluster;
distance matrix [ m ] between nodes ij ]The relative map between the output nodes is decomposed using singular values as input.
Will D 2 ＝m ij 2 Double centring, i.e. D 2 The two sides are multiplied by a central matrix H, which is defined as follows:
H＝E-n -1 1 (formula 2)
Wherein E is an n-order identity matrix, and the double-centering matrix B is
Singular value decomposition is carried out on the matrix B, the eigenvalues are arranged according to the order of magnitude, and the first p maximum eigenvalues lambda are taken 1 λ 2 ,…,λ p Then, a diagonal matrix Λ is formed, and the corresponding eigenvector e is formed 1 ,e 2 ,…e p An n×p dimensional matrix V is composed, represented by equation 4:
B＝VΛV T (equation 4)
Λ＝diag(λ 1 ,λ 2 ,…,λ p ) (equation 5)
V＝[e 1 ,e 2 ,…,e p ](equation 6)
Finally, the coordinates of all nodes are expressed by an MDS algorithm through a formula 7:
X＝V·Λ 1/2 (equation 7)
One cluster A with more public nodes and the adjacent cluster B are selected for fusion, so that more local mapping is beneficial to the fusion operation between clusters. The local map is extended by combining other maps, and finally is covered on the global map.
In order to avoid the high collinearity of the common nodes, adopting a least square method-based inter-cluster coordinate registration method to perform coordinate registration on each cluster so as to achieve fusion, and repeating the steps until all nodes in a network are included. Let n common nodes in cluster a and cluster B, the coordinates of the common nodes in the local maps of cluster a and cluster B are expressed by equation 8 and equation 9, respectively:
X public ＝[x 1 ,x 2 ,…,x n ] T (equation 8)
X ′ public ＝[x 1 ′ ,x 2 ′ ,…,x n ′ ] T (equation 9)
The rotation matrix is denoted by Q, which is solved by the least squares method:
Q＝(A T A)\(A T b) (equation 10)
The least square inter-cluster coordinate registration method can avoid errors caused by higher co-linearity degree of common nodes, and the cluster B is fused into the cluster A by using the formula 11, wherein s is a scaling factor and x is 0 Is a translation vector:
X A ＝s×Q(X B )+x 0 (equation 11)
Step 5: coordinate conversion stage: the method comprises the following steps of:
step 51: setting an adaptability function of the evaluation;
step 52: calculating the speed by using a new particle motion formula, generating a new guide vector by using arithmetic crossover, differential evolution crossover and selection operation, and substituting the new guide vector into the particle motion formula by adopting a guide vector substitution strategy;
step 53: calculating a new fitness function according to the new guide vector generated in the step 52, and judging the fitness of the particles by using the sum of the distance differences between the real coordinates and the estimated coordinates of all anchor nodes as the new fitness function;
step 54: judging whether the preset precision or the maximum iteration times are reached, if so, converting the relative coordinates of all unknown nodes into absolute coordinates through the coordinate conversion parameters after the optimization; if not, repeating step 52 and step 53 in sequence. The iteration number is also a preset value, and is determined according to the requirement, and the iteration number is 50 in the invention.
Step 51: setting an evaluative fitness function further includes:
step 511: the fitness function is a key that the particle swarm optimization algorithm can be realized and applied to different scenes, the anchor node parameter combination is regarded as a particle, and the absolute coordinate and the relative coordinate of the anchor node are utilized to construct the proper fitness function. In the two-dimensional space, four conversion parameters, namely two translation vectors, a rotation angle and a scaling parameter, are needed in the absolute coordinate and relative coordinate conversion relation model. As represented by equation 12:
in (x) 1 ,x 2 ) Is the anchor node relative coordinates, (y) 1 ,y 2 ) As absolute coordinates of anchor node, deltax 1 ,Δx 2 For translation vector, α is rotation angle, and t is flipping parameter.
Step 512: setting an error function f (Deltax 1 ,Δx 2 α, t) to measure the degree of difference between the actual coordinates (X, Y) of the anchor node and the estimated absolute coordinates (X, Y), expressed by equation 13, N being the number of anchor nodes. f (Deltax) 1 ,Δx 2 The smaller the α, t), the better the parameter optimization effect, and the smaller the positioning error. The error function f (Deltax 1 ,Δx 2 Alpha, t) is used as an fitness function of a particle swarm optimization algorithm to search for the population optimum P g 。
A＝[(x i cosα-ty i sinα)+Δx 1 -X i ] 2 (equation 14)
B＝[(x i sinα+ty i cosα)+Δx 2 -Y i ] 2 (equation 15)
Step 52: the particle swarm optimization algorithm with cross operation is specifically:
in the search space in the D dimension, one particle i has two vectors. First is velocity vector V i ＝(v i1 ,v i2 ,…v id ,…v iD ). The other is the position vector X i ＝(x i1 ,x i2 ,…x id ,…x iD ). The random initialization operation is performed on the position and velocity vectors of each particle by the space required for searching. Then updating the formula of the position and the speed to two parametersAnd carrying out iterative search update, wherein the update formula is as follows:
v id ＝wv id +cr d (GV id -x id ) (equation 16)
Wherein w is an inertia factor with positive value, c is an acceleration factor, r d Is uniformly distributed in [0,1 ]]Random number, GV between i Then it is referred to as a steering vector.
The scheme can enable particles to perform more efficient searching, the whole is optimized by searching more potential areas, and the variable t represents the iteration number d and represents one dimension in the dimensions, and d epsilon [1,2].
Well-established GV i Is the key point of the algorithm, GV i The construction is realized mainly by the following steps:
step 521: arithmetic crossover
The main function of the operation arithmetic cross operation is to let two particles P i And P j Crossover is performed to generate a new velocity vector V id ：
V id ＝r 1 P i +(1-r 1 )P j (equation 18)
Before the crossover operation is performed, the historical optimum position (P 1 ,P 2 ,…,P N ) Random permutation is carried out, and the permutation formula is as follows:
the crossing operation leads the elements corresponding to the upper layer of particles and the lower layer of particles to generate various offspring derivatization. As the number of iterations increases, P i And P j Also the crossover probability of (1) should be increased to correspond to P g A more detailed local search is made around. Defining variable R as a dynamic adjustment strategy for reflecting the replacement of individual history optima by group history optima in the replacement processQuantity:
wherein Maxiter is the maximum iteration number, t is the iterated number, and N is the total number of particles.
Step 522: differential evolution crossover
Unlike arithmetic interleaving, differential interleaving acts on velocity vector V i And a target vector T i Generating a new vector U i . Since the performance of the particle swarm optimization algorithm is better when cr=0.05, the CR is taken as 0.05.
Step 523: selection operation
The newly generated vector is evaluated by the fitness function as a guide vector.
Step 524: alternative strategies
Parameter G represents GV i Stopping the update of the termination algebra, if the algebra is terminated, the guide vector is also in the local optimum, and many researches show that when G is taken to be 5 or 7, the guide vector has good forward benefit. In this context, g=7 is taken, after it is determined that the particle may be trapped in the local optimum, the fitness sorting is performed by using 0.5×n randomly selected guide vectors, the guide vector with the best fitness replaces the current guide vector, and the position and speed of the particle are changed to leave the local optimum.
Initializing coordinate conversion parameters randomly generated in the range, combining the coordinate parameters of each anchor node into a particle, and determining the delta x of the particle speed 1 ,Δx 2 Alpha is randomly generated in 10% of optimizing space, and t is unchanged. Generating guide vectors using crossover and selection operations, evaluating fitness values of each particle using fitness functions, computing a further calculationNew P i And P g Updating the particle position and velocity using equations 16 and 17; and judging whether the overall optimal precision is met or the maximum iteration number is reached, if so, continuing to execute, and if not, jumping to the fitness function evaluation. And performing coordinate transformation on the unknown node by the optimized parameters.
The multi-dimensional scale node positioning algorithm based on the improved particle swarm is used for carrying out comparison analysis on the positioning errors of different anchor node proportions and different node connectivity under different monitoring areas, and experimental parameter selection comprises the following steps:
100 nodes are randomly deployed in the area to be monitored. Wherein the number of unknown nodes is 90, the number of anchor nodes is 10, the proportion of anchor nodes is 10, and in the figure, "o" represents an unknown node and "×" represents an anchor node. The area to be monitored is a regular rectangular area of 1000m×1000m and a C-shaped irregular area of 1000m×1000m hollow 400m×700m, and specific simulation parameters are shown in table 1.
Table 1 simulation parameter configuration table
Experiment 1: comparing the method of the present invention with three algorithms, MDS-MAP (the originally proposed multidimensional scaling positioning algorithm), MDS-MAP (P) (the once-distributed modified multidimensional scaling positioning algorithm) and FC-MDS (Fast clustering-based multidimensional scaling, the multidimensional scaling analysis based Fast aggregation algorithm), positioning errors at different anchor node ratios.
Referring to fig. 4 and 5, the positioning error of the present invention is smaller than the other three positioning schemes, regardless of the rectangular region or the C-type region at different anchor node ratios, wherein PFC-MDS (PSOCO-FC-MDS) is the custom name of the method.
Experiment 2: comparing the method of the invention with three algorithms of MDS-MAP, MDS-MAP (P) and FC-MDS, and positioning errors under different node connectivity.
Referring to fig. 6 and 7, the positioning error of the present invention is smaller than that of the other three positioning schemes, whether in the rectangular area or the C-shaped area under different node connectivity.
The invention improves on the basis of the existing distributed multidimensional scale positioning method, introduces a particle swarm optimization algorithm with cross operation, optimizes coordinate conversion parameters of absolute coordinates and relative coordinates, and is used for improving the precision of absolute coordinates of unknown nodes in a network and improving the positioning precision.
The above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention.
Claims (5)
1. The multidimensional scale node positioning method based on improved particle swarm adopts two sensor nodes, namely an anchor node and an unknown node, wherein the anchor node positions itself through GPS, and the unknown node communicates with adjacent anchor nodes and realizes self positioning through network topology.
Step 1: initializing a wireless sensor network, wherein each node in the network obtains a distance matrix of adjacent nodes through an RSSI ranging method;
step 2: in the clustering stage, clustering integration is carried out on the wireless sensor network, and the wireless sensor network after the clustering integration is divided into a plurality of clusters taking cluster heads as calculation centers;
step 3: in the relative positioning stage of the nodes in the cluster, a generalized square distance matrix is calculated according to the input distance matrix, and singular value decomposition is carried out on the generalized square distance matrix subjected to the decentralization treatment by using a classical MDS algorithm to obtain the relative coordinates of the nodes in the cluster;
step 4: in the inter-cluster fusion stage, a cluster with more common nodes in the cluster is selected to be fused with adjacent clusters, and then a least square method-based inter-cluster coordinate registration method is adopted to carry out coordinate registration on each cluster so as to achieve the fusion; repeating the steps until all nodes are fused;
step 5: in the coordinate conversion stage, the absolute coordinates and the relative coordinates of the anchor nodes are utilized, the acquisition of the coordinate conversion parameters is optimized by utilizing a particle swarm optimization algorithm with cross operation, and the relative coordinates of each unknown node are converted into the absolute coordinates, and the method specifically comprises the following steps:
step 51: setting an evaluative fitness function, wherein the establishment of the fitness function is specifically as follows:
step 511: taking the anchor node parameter combination as a particle, and constructing a proper fitness function by using the absolute coordinates and the relative coordinates of the anchor nodes:
wherein (x) 1 ,x 2 ) Is the anchor node relative coordinates, (y) 1 ,y 2 ) As absolute coordinates of anchor node, deltax 1 ,Δx 2 For translation vector, alpha is rotation angle, t is turnover parameter;
step 512: setting an error function f (Deltax 1 ,Δx 2 α, t) to measure the degree of difference between the actual coordinates (X, Y) of the anchor node and the estimated absolute coordinates (X, Y), the formula is:
wherein N is the number of anchor nodes, A= [ (x) i cosα-ty i sinα)+Δx 1 -X i ] 2 ，B＝[(x i sinα+ty i cosα)+Δx 2 -Y i ] 2 ，f(Δx 1 ,Δx 2 The smaller the α, t), the better the parameter optimization effect, the smaller the positioning error, the error function f (Δx) 1 ,Δx 2 Alpha, t) is used as an fitness function of a particle swarm optimization algorithm to search for the population optimum P g ；
Step 52: calculating the speed by using a new particle motion formula, generating a new guide vector by using arithmetic crossover, differential evolution crossover and selection operation, substituting the new guide vector into the particle motion formula by adopting a guide vector substitution strategy, wherein the particle motion formula specifically comprises:
in the search space in D-dimension, one particle i has two vectors, one is the velocity vector V i ＝(v i1 ,v i2 ,…v id ,…v iD ) The other is the position vector X i ＝(x i1 ,x i2 ,…x id ,…x iD ) The position and speed vectors of each particle are randomly initialized according to the space to be searched, and then the two parameters are iteratively searched and updated by using an updating formula of the position and the speed, wherein the updating formula is as follows:
v id ＝wv id +cr d (GV id -x id )
wherein w is an inertia factor with positive value, c is an acceleration factor, r d Is uniformly distributed in [0,1 ]]Random number, GV between i Then called the pilot vector, the variable t represents the number of iterations, d represents one of the dimensions, d e 1,2]Vector GV is guided i The construction method comprises the following steps:
step 521: arithmetic crossover
Let two particles P i And P j Crossover is performed to generate a new velocity vector V id ：
V id ＝r 1 P i +(1-r 1 )P j
Before the crossover operation is performed, the historical optimum position (P 1 ,P 2 ,…,P N ) Performing random permutation to optimize P for the group g Performing more detailed local search around;
step 522: differential evolution crossover
Differential evolutionary cross-action on velocity vector V i And a target vector T i Generating a new vector U i ：
Wherein CR is a crossover factor;
step 523: selection operation
Evaluating a newly generated vector U by means of an fitness function i And taking the evaluation result as a guide vector:
step 524: alternative strategies
Selecting the guiding vector with the best adaptability to replace the current guiding vector, and changing the position and the speed of the particles to get out of local optimum;
step 53: calculating a new fitness function according to the new guide vector generated in the step 52, and judging the fitness of the particles by using the sum of the distance differences between the real coordinates and the estimated coordinates of all anchor nodes as the new fitness function;
step 54: judging whether the preset precision or the maximum iteration times are reached, if so, converting the relative coordinates of all unknown nodes into absolute coordinates through the optimized coordinate conversion parameters; if not, repeating step 52 and step 53 in sequence.
2. The improved particle swarm-based multi-dimensional scale node positioning method of claim 1, wherein:
in the step 1, initializing the wireless sensor network by taking into account a shadow model of environmental factor changes:
wherein P is R (m) represents the signal power received by the receiving end, P T Representing the signal power at the transmitting end, PL (m 0 ) Represents the distance m from the transmitting end 0 Path loss atConsumption, m represents the distance between the transmitting end and the receiving end, m 0 Represents the reference distance, eta represents the channel attenuation factor, the value range is 2-4, X δ ＝N(0,δ 2 ) Is a random variable of the debilitating component of RSSI to obtain a distance matrix [ m ] of neighboring nodes ij ]。
3. The improved particle swarm-based multi-dimensional scale node positioning method of claim 1, wherein:
in the step 2: the clustering stage adopts a rapid clustering method to perform clustering and inspect the public nodes, and comprises the following steps:
step 21: node k randomly generates a timer t k ＝rand(0,t max ) And empty the cluster head list MyHeader to which the user belongs at the moment
Step 22: when the timer of the node ends, the node broadcasts a message to announce that the node becomes a cluster head, and the message contains a type identifier msgtype=header and a node identification ID;
step 23: if node k receives message msgtype=leader before timer is finished, stopping timing, adding node identification ID of the leader node to own myleader list, and then broadcasting a connection request message by node k, wherein the connection request message contains type identifier msgtype=join and node identification ID;
step 24: if only the cluster head uses the MSGTYPE=join response message, the cluster head checks a MyHeader list of the connection request message, and if the list contains an ID of the cluster head, the cluster head stores the message; the Cluster head stores the connection request message into a self Cluster-reactant list, wherein the connection request message comprises a node identification ID and a MyHeader list, and then the Cluster head broadcasts and confirms the message, and the Cluster head comprises a type identifier MYGTYPE=ack, a Cluster head ID and a Cluster-reactant list;
step 25: when node k receives message msgtype=ack, checking the Cluster head ID of the Cluster where itself is located, if the ID is in the Cluster head list, it will store the message and update the Cluster-remmber list;
step 26: the cluster head checks whether the cluster has enough public nodes with the adjacent clusters, if not, the two-hop adjacent nodes are cached to serve as member nodes of the cluster, and the sufficient public nodes are ensured to be fused among the clusters.
4. The improved particle swarm-based multi-dimensional scale node positioning method of claim 1, wherein:
in the step 3: distance matrix [ m ] between nodes in relative positioning stage of nodes in cluster ij ]Using the square of the P-dimensional space as input and decomposing the relative map between the output nodes by using the singular values to make the P-dimensional space have n nodes X i I=1, …, n, the square of the euclidean distance between adjacent nodes is D 2 ＝m ij 2 Matrix B represents the node inner product and the uniqueness of the solution is achieved by classical multidimensional scaling algorithm (MDS) by transferring the node center coordinates to the origin of coordinates, D 2 Double-decentering is performed, and both sides are multiplied by a centering matrix H, wherein H=E-n -1 1, E represents an n-order identity matrix, the inner product B is represented by a p-dimensional coordinate matrix X form, the rank of the matrix B represents the coordinate dimension p, then singular value decomposition is carried out on the matrix B, the eigenvalues are arranged according to the order of magnitude, and the first p maximum eigenvalues lambda are taken 1 λ 2 ,…,λ p Then, a diagonal matrix Λ is formed, and the corresponding eigenvector e is formed 1 ,e 2 ,…e p And forming an N multiplied by P dimensional matrix V, and finally representing the coordinates of all nodes as follows by an MDS algorithm:
X＝V·Λ 1/2 。
5. the improved particle swarm-based multi-dimensional scale node positioning method of claim 1, wherein:
in the step 4: in the inter-cluster fusion stage, one cluster A with more public nodes is selected to be fused with an adjacent cluster B, a least square method-based inter-cluster coordinate registration method is adopted to perform coordinate registration on each cluster to achieve fusion, the steps are repeated until all nodes in a network are contained, n public nodes are shared in the cluster A and the cluster B, a rotation matrix of coordinates of the public nodes in local maps of the cluster A and the cluster B is represented by Q, the rotation matrix Q is solved by a least square method, then the cluster B is fused to the cluster A, and a formula for fusing the cluster B to the cluster A is as follows:
X A ＝s×Q(X B )+x 0
where s is a scaling factor, x 0 Is a translation vector.
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