CN110493717A - A kind of non-ranging node fusion and positioning method suitable for concave domain - Google Patents
A kind of non-ranging node fusion and positioning method suitable for concave domain Download PDFInfo
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Abstract
The invention proposes a kind of non-ranging node fusion and positioning methods suitable for concave domain, to solve the problems, such as that existing localization method position error when concave domain is used alone is larger.Step of the present invention are as follows: the location information of all node broadcasts itself of each anchor node into whole network in sensor network obtains the minimum hop count between whole network interior joint；By comparing between node most short jumping figure value and shortest path hop count filtering by concave edge effect anchor node information；Euclidean distance between node pair matrix is constructed by the distance between filtered any two node of single-hop correction value, the estimated location of all unknown nodes is calculated using MDS-MAP location algorithm；Objective function is established, is optimized using unknown node estimated location of the simulated annealing location algorithm to step 3.The present invention can obtain more accurate positioning result under equivalent network environment, improve positioning accuracy, have stronger practicability in the network distribution of some complexity.
Description
Technical field
The present invention relates to the technical fields more particularly to a kind of suitable for the non-of concave domain of wireless sensor node positioning
Ranging node fusion and positioning method.
Background technique
In recent years, many scholars set out with application from different perspectives and are unfolded to study to node locating, and achieve abundant
Research achievement.According to whether the distance between physical measurement neighbor node or angle information, node locating is divided into based on survey
Away from node positioning method and non-ranging node positioning method.It is needed based on ranging node positioning method through certain physical distance measurement skill
Art (such as angle of arrival AOA, arrival time TOA, utilize time difference TDOA and received signal strength indicator RSSI) measures neighbour
Occupy the distance between node or angle.Ideal environment is generally required based on ranging node locating algorithm or is pacified for node
Fill additional firmware, however the signal propagation in actual environment is easy to be reflected, multipath transmisstion, non line of sight, antenna gain etc. because
Element influences, and adds precise distance measurement equipment for node installation and increases network cost and node energy consumption again.Therefore it is based on ranging
Node positioning method is not suitable for the wireless sensor network of large-scale low-cost.And non-ranging node positioning method only utilizes biography
Communication information between sensor node carries out position calculating, it is only necessary to network-in-dialing, the nothing suitable for large-scale low-cost
Line sensor network has important research significance.
The application of wireless sensor network is closely coupled with actual environment, therefore its correlative study should fully consider reality
The influence that environment studies wireless sensor network.For node locating problem, the influence of environmental factor is equally existed, if
The influence of environmental factor is not accounted in research process, the positioning result obtained is often incredible.In practical application,
Since wireless sensor network node deployment has, randomness, there are signals of communication between larger barrier, node in monitoring region
The factors such as unstable cause node deployment region to form concave domain.Sensor node communication capacity is limited, between node often
It is to be communicated by way of multi-hop.By concave domain drop centre type edge effect, the sensor section communicated by multi-hop
Shortest path between point is likely to much away from straight line, to cause biggish shortest path error between them.And
Shortest path between sensor node is the premise for carrying out nodal exactness positioning, only when the shortest path between node is close
When true path, it is likely to obtain the accurate positioning of node.Therefore, how under concave domain with non-ranging node positioning method
The accurate positioning result for obtaining unknown node has important practical value, is worth being furtherd investigate.
Ranging node positioning method is node location to be estimated using the distance or angle information between node and node, rather than survey
Away from the connectivity that node positioning method is using sensor node.Compared to ranging localization algorithm, non-ranging node positioning method
It is more suitable for the wireless sensor network of large-scale low-cost.The non-ranging node locating algorithm studied in recent years has:
1. improved APIT algorithm: the algorithm (is calculated in original APIT based on the positioning for putting method of testing in best triangle
Method) it joined period refinement on the basis of algorithm, and one group of adaptive weight and threshold value are given, it solves around anchor node
The problem of field cannot be positioned less than 3.Although the algorithm positioning accuracy is higher, communication overhead is larger, the density of anchor node
It is required that it is relatively high, it is not suitable for concave domain.
2.CATL algorithm: CATL (the multipoint iterative location algorithm for avoiding concave point) algorithm is suitable for two-dimentional three-dimensional space net
Network only restores original network topology by link information, does not depend on network boundary without anchor node.Its key idea is discovery
Recess node, wherein shortest path bending and the distance based on hop count start to deviate significantly from real Euclidean distance.
And a kind of iteration agreement is developed, which positions network using a kind of more delay mechanisms for avoiding trap.Although the algorithm
Positioning result is more accurate, and expense is moderate, but realizes that difficulty is larger, will receive limitation under complex environment.
3.DRAL algorithm: the algorithm is the positioning in order to reduce concentric anchor beacon (CAB) algorithm in wireless sensor network
Error proposes a kind of node locating algorithm based on double restricted areas (DRAL).Basic thought is each pair of anchor node of connection
All perpendicular bisectors of line are used to obtain the alternatively possible band of position of unknown node.Based on new possible position area
Domain, can obtain less effective crosspoint, and using average value the estimating as unknown node in all these effective crosspoints
Count position.The algorithm has many advantages, such as that computational efficiency is high, communication overhead is small.But require anchor node quantity more, for evil summary
Adaptive capacity to environment is poor.
Algorithm above has the limitation respectively used.DV-HOP (location algorithm based on node hop count) location algorithm is
Niculescu et al. routes (Distance vector routing) and the proposition of GPS principle according to distance vector, is non-survey
Away from the most widely used algorithm in distributed location method series.It is to participate in node locating using multi-hop anchor node, fixed
Position coverage rate is larger, similar to traditional distance vector routing mechanism.The core concept of the algorithm is all first in network
Anchor node is broadcasted to the whole network, if the number for the anchor node that unknown node is subject to is greater than 3, can be carried out in next step, if small
In 3, then can not be positioned.The most jete that the node that can communicate passes through the available anchor node of broadcast to unknown node
Number；Then average distance, that is, single-hop correction value of anchor node is calculated, the product with single-hop corrected value and minimum hop count is as unknown
The estimated distance of node and anchor node；The coordinate of estimation node is finally calculated with trilateration or maximum-likelihood method.DV-hop
The basic procedure of location algorithm is as shown in Figure 1.In the existing location algorithm without ranging DV-HOP location algorithm have it is low at
The characteristics of this is easily realized.DV-HOP location algorithm to the estimation of the shortest distance be by minimum hop count multiplied by single-hop corrected value come
It arrives, then obtains the estimated coordinates of unknown node with maximum-likelihood method.When anchor node is evenly distributed, the error of node is smaller, but
It is when Node distribution is uneven, especially in concave domain, node error is larger.
What foreign countries proposed, the position the MDS-MAP algorithm based on MDS multi-dimension analysis technology is Columbia Univ USA
A kind of centralized location algorithm that Yi Shang et al. is proposed.MDS (multidimensional scaling) algorithm is a kind of exploratory data analysis skill
Art is a kind of dimensionality reduction technology in essence.There are two purposes for MDS algorithm: reducing data volume first is that passing through in order to make data
It more easily handles and is more of practical significance；Second is that the concealed structure relationship between identification data.Between Main Analysis things
The data of similitude, either the data of actual range, are also possible to the subjective judgement data to similitude.MDS algorithm can
To find out the structural relation hidden between respondent, and by the large scale data compression containing multiple variables to a low-dimensional sky
Between, by one group of intuitive spatial perception figure the information in data be depicted come.The principle of MDS algorithm is exactly to pass through input one
Degree of similarity matrix between group objects, finds opposite position coordinates in lower dimensional space.By this technical application to wirelessly
It is exactly using all sensor nodes as object, the distance between node is as similar in sensor network nodes positioning
Property degree matrix, finally calculates the position coordinates of node.As shown in Fig. 2, MDS-MAP location algorithm is by three phases group
At:
(1) network topology connected graph is generated from global angle first, and assigns distance value for each edge.When neighbor node it
Between distance when can measure or can be obtained by distance estimating algorithm, which is exactly the distance between node.
(2) to euclidean distance between node pair matrix D2Using opposite between all nodes in standard MDS algorithm estimation whole network
Position.Its core is singular value decomposition, generates the two-dimensional phase of whole network to coordinate system, each section in relative coordinate system
Point has location information.
(3) after the relative position for obtaining all nodes, the relative coordinate of anchor node can also be obtained therefrom.When anchor section
When point number is met certain condition (two dimension needs at least three anchor node, three-dimensional at least four anchor node), according to known anchor node
True coordinate, calculate by translation, rotation and map etc. transform methods convert absolute seat for anchor node relative coordinate system
Mark corresponding parameter.These transformation parameters are applied in the relative coordinate of unknown node, so that it may by the phase of unknown node
Absolute coordinate is converted into coordinate, absolute coordinate is exactly the estimated location of node.
MDS-MAP location algorithm can be smaller in network connectivity, and positioning meter is completed in the small numbers of situation of anchor node
It calculates.When distance can be with precise measurement between node, positioning accuracy is higher；When the distance between node is unable to measure, node
The distance between replaced with hop count, position error is larger, and is not suitable for concave domain.MDS-MAP location algorithm is benefit
With the shortest distance between node carry out unknown node position calculate, if obtain node between the accurate shortest distance it
Afterwards, can obtain accurate node location, but cannot obtain the distance between node, especially concave domain lower node it
Between the shortest distance much deviateed straight line by concave edge effect in the case where, position error is larger.
Summary of the invention
For existing localization method, when concave domain is used alone, there are the technical problem that position error is larger, this hairs
It is bright to propose a kind of non-ranging node fusion and positioning method suitable for concave domain, either in concave domain still in convex area
There is very strong usability in domain, and the density requirements of node are not also high, small power consumption, and it is strong to be disturbed ability, before having application well
Scape.
In order to achieve the above object, the technical scheme of the present invention is realized as follows: it is a kind of suitable for the non-of concave domain
Ranging node fusion and positioning method, its step are as follows:
Step 1: the position letter of all node broadcasts itself of each node into whole network in sensor network
Breath, to obtain the minimum hop count between whole network interior joint；
Step 2: the coordinate of the anchor node obtained using step 1 is calculated the distance between anchor node and obtains most short hop count
Value, by comparing between anchor node most short jumping figure value and shortest path hop count filtering by concave edge effect nodal information；
Step 3: node is constructed by the distance between filtered any two node of single-hop correction value step 2
Between distance matrix, the estimated location of all unknown nodes is calculated using MDS-MAP location algorithm；
Step 4: objective function is established using anchor node, the estimated location of unknown node and single-hop corrected value, utilizes simulation
Annealing location algorithm optimizes the estimated location of step 3, and the optimal solution that loop iteration obtains is exactly the final of unknown node
Estimated coordinates.
Each anchor node broadcasts the location information of itself, position letter to whole network in sensor network in the step 1
Breath includes ID, coordinate (x, y) and the hop count of anchor node, and the initial value of hop count is zero；Each unknown node is broadcasted to whole network
The location information of itself, location information include the ID and hop count of unknown node, and the initial value of hop count is zero；Receive broadcast message
Hop count is simultaneously added one by the relevant information of sensor node record node, is transmitted to other nodes, all nodes in sensor network
Position and the minimum hop count of each anchor node are all had recorded, there are also the minimum hop counts for arriving other nodes；What if node received
Hop count adds a minimum hop count not less than the anchor node recorded in the location information of anchor node, then gives up this information；Institute
Stating the minimum hop count between whole network interior joint is the most jete to other each nodes that each sensor node obtains
Number, including the minimum hop count between anchor node and anchor node, minimum hop count between anchor node and unknown node, unknown node and
Minimum hop count between unknown node.
The implementation method of the step 2 is: being propagated and is obtained between anchor node most by the information that step 1 broadcast is realized
Short path hop count SP compares the shortest path hop count SP between anchor node and most short jumping figure value AD/R, if the value of the two
It is approximately equal, i.e., | SP-AD/R | < 0.2, illustrate not influenced by concave boundary；If the value difference of the two is farther out, illustrate this
The shortest distance is filtered out the anchor node by concave edge effect by concave edge effect between two anchor nodes；The most short jump
Numerical value AD/R be the distance between the anchor node AD that is calculated using the coordinate of anchor node divided by communication radius R obtain correctly most
Short jumping figure value.
The method that euclidean distance between node pair matrix is constructed in the step 3 is:
A, filtered remaining not by anchor node coordinate and the step 1 calculating of concave edge effect using step 2
Shortest path hop count between anchor node calculates single-hop corrected value hopsize:
Here i and j is not by the anchor node of concave edge effect, SPijIt is most short between anchor node i and anchor node j
Route jumping figure；
B, be multiplied by shortest path hop count between single-hop corrected value hopsize and node obtain any two node it
Between shortest path:
dks=hopsize*SPks (2)
Wherein, dksIt is the estimated distance between any two node k and node s, SPksBe between node k and node s most
Short path hop count；I, j, k, s refer to the number of sensor node；
C, according to the shortest distance d between the calculated any two node of formula (2)ks, section needed for establishing MDS algorithm
Distance matrix D between point2:
Wherein, d12 d13...d1N, d21 d23...d2N, dN2 dN2 dN3... it respectively indicates between two sensor nodes
Distance；N representative sensor node total number, N=n+m, n are unknown node numbers, and m is anchor node number；d12Refer to the 1st sensing
The distance between device node and the 2nd sensor node, d2NRefer to the 2nd between sensor node and n-th sensor node
Distance.
The method that MDS-MAP location algorithm calculates the estimated location of all unknown nodes in the step 2 is:
To euclidean distance between node pair matrix D2The phase in entire sensor network between all nodes is estimated using standard MDS algorithm
To position: according to Distance matrix D2Structural matrix B:
Wherein, E is n rank unit matrix, and I is n rank all 1's matrix, and matrix J is in being calculated by matrix E and matrix I
Heart matrix；
Singular value decomposition is carried out to matrix B, and calculates a matrix X:
[V S T]=svd (B) (6)
X=T*sqrt (S) (7)
Wherein, V and T is two unitary matrice obtained by singular value decomposition svd function；Matrix S is by singular value point
The diagonal matrix with matrix B with size that solution svd function obtains；Sqrt is extraction of square root function in matlab；
The preceding two-dimensional data of matrix X is taken to obtain the relative coordinate of all nodes；According to the relative coordinate of the anchor node of calculating
With the true coordinate of known anchor node, absolute coordinate pair is converted for anchor node relative coordinate system by translation, rotation and mapping
The transformation parameter answered；These transformation parameters are applied in the relative coordinate of unknown node, by the relative coordinate of unknown node
It is converted into absolute coordinate, obtains the coordinate of the estimated location of unknown node.
Objective function in the step 4 are as follows: avoid using non-neighbor node, the distance between neighbor node passes through list
Jump the objective function that corrected value hopsize is obtained, therefore designed are as follows:
Wherein, n indicates unknown node number, and m indicates anchor node number, naijIt indicates between unknown node i and anchor node j
Neighborhood, nuikIndicate the neighborhood between unknown node i and unknown node k, if it is neighbor node, then its value is
1；If not neighbor node, then its value is 0；Indicate the estimated distance between unknown node i and anchor node j, and
Represent the estimated distance between unknown node i and unknown node k；The estimated coordinates of unknown node i are represented,Generation
The estimated coordinates of table unknown node k, (xj,yj) represent the coordinate of anchor node j；Objective function S is all unknown nodes to comprising anchor
The quadratic sum of the difference of distance between node and the actual distance and estimated coordinates of all neighbor nodes of other unknown nodes.
It is using method for solving of the simulated annealing location algorithm to objective function S:
1, initial temperature T is set0, the cycle-index L at each temperature is set, step 3 is calculated to one group obtained not
Know node estimated coordinates as initial solution m0, and with the value S0 of formula (8) calculating target function；
2, the initial value that cycle counter is arranged is b=1, b=1,2,3 ... L；
3, by initial solution m0As parameter, according to last estimated location m0Caused node actual range and estimation position
The ratio of distance is set multiplied by the coordinate difference between neighbor node, so that the distance between node actual range between node is close
Principle, calculate the new estimated coordinates m1 of one group of unknown node with formula (9):
M1=inv (V1+V2) * ((B1X+B2X) * m0+ (V3-B3X) * AU) (9)
Wherein, inv is matrix inversion matrix function；The diagonal line storage of n rank matrix V 1 is that unknown node neighbours are unknown
The number of node is -1 if two nodes are neighbor nodes on off-diagonal, is otherwise 0；Size is the matrix V 2 of n × m
Diagonal line on store be unknown node neighbours' anchor node number, remaining element be 0；The matrix V 3 that size is n × m stores
Be exactly neighborhood matrix between unknown node and anchor node, if two nodes are neighbor nodes, corresponding value is
1, it is otherwise 0；The diagonal positions of n rank matrix B 1X are and the actual range of all unknown nodes of unknown node i neighbours and estimate
Count the sum of the ratio of distance, off-diagonal position, if two nodes are neighbor nodes, for the negative value of ratio, if not
Neighbor node is then 0；The diagonal positions of n rank matrix B 2X be with the actual range of all anchor nodes of unknown node i neighbours and
The sum of ratio of estimated distance, off-diagonal position are 0；Size be n × m matrix B 3X store be and unknown node neighbours
All anchor nodes actual range and estimated distance ratio；Size be m × 2 matrix A U store be anchor node seat
Mark；
According to the new estimated coordinates m1 calculating target function S1 of the unknown node of calculating, then the increment of objective function be Δ=
S1-S0；
4, the increment calculated according to Metropolis criterion and step 3, it is determined whether receive new solution m1:
Wherein, P is the probability value calculated, T0It is current temperature；
Be randomly generated one [0,1) random number R in section if the value of probability value P is greater than random number R receives new produce
Raw solution m1 is as current optimal solution, that is, assignment m0=m1 again, and corresponding target function value S0=S1 goes to step 5；It is no
Do not receive newly generated solution m1 then, continues using m0 as current optimal solution, corresponding target function value S0 is constant, goes to step 6；
If 5, cycle count number b, which is less than, terminates iterative steps L, b=b+1, step 3 is turned to, step is otherwise turned to
6；
If 6, temperature T0Greater than cooling temperature, initial temperature T is reset0, enable T0=T0* α turns to step
2；If temperature is less than cooling temperature, exporting current optimal solution is optimal solution, and end loop iteration；Wherein, α is cooling
Coefficient, and range is 0~1.
Beneficial effects of the present invention: the single-hop corrected value calculated first with DV-HOP algorithm is found out between node most
Short distance；Then the shortest distance found out is applied in MDS-MAP algorithm, finds out the estimated location of one group of unknown node；Most
Afterwards in order to make the algorithm obtain more accurate positioning result in concave domain, unknown is asked to previous step with simulated annealing
Node estimated location optimizes, and further decreases position error.Simulation result shows present invention energy under equivalent network environment
More accurate positioning result is enough obtained, there is very high application value；It has a clear superiority on improving positioning accuracy, one
There is stronger practicability in the case of a little complicated network distributions.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is the flow chart of DV-hop algorithm.
Fig. 2 is the flow chart of MDS-MAP algorithm.
Fig. 3 is flow chart of the invention.
Fig. 4 is the algorithm flow chart that simulated annealing optimizes initial parameter m0 in Fig. 3.
Fig. 5 is irregular area node distribution map, wherein (a) is c-type region, (b) is hollow region.
Fig. 6 is concave domain shortest path figure.
Fig. 7 is Node distribution analogous diagram.
Fig. 8 is anchor node number-position error schematic diagram of the present invention with existing algorithm.
Fig. 9 is communication radius-position error schematic diagram of the present invention with existing algorithm.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other under that premise of not paying creative labor
Embodiment shall fall within the protection scope of the present invention.
As shown in figure 3, a kind of non-ranging node fusion and positioning method suitable for concave domain, is directed in complicated ring
Border lower sensor Node distribution forms concave domain, and anchor node is unevenly distributed, as shown in Figure 5.In order to be suitable for concave domain,
Influence of the concave boundary to node shortest distance is reduced, positioning accuracy is improved, thought of the invention is divided into four steps:
The first step, the position letter of all node broadcasts itself of each node into whole network in sensor network
Breath, to obtain the minimum hop count between whole network interior joint；
Second step calculates the distance between anchor node using the coordinate of anchor node and obtains most short jumping figure value, by comparing anchor
Most short jumping figure value and shortest path hop count between node filter the anchor node information by concave edge effect；
Third step constructs node by the distance between filtered any two node of single-hop correction value step 2
Between distance matrix, the estimated location of all unknown nodes is calculated using MDS-MAP location algorithm；
4th step, due in concave domain, two non-neighbor nodes, especially between farther away non-neighbor node
The shortest distance is easy to be influenced by concave boundary, therefore is calculated by MDS-MAP location algorithm and obtain unknown node estimation seat
Mark has certain position error.Therefore the present invention carries out third step calculating acquisition result with simulated annealing location algorithm excellent
Change, choose suitable objective function S and generate next group of solution, uses one group of estimated coordinates of third step calculating as initial shape
State is optimized by simulated annealing intelligent optimization algorithm.
It is influenced by concave boundary, will cause when calculating shortest path of the edge anchor node to anchor node in concave domain
Biggish error.As shown in fig. 6, node j to node i actual range be dotted line, but location estimation distance be it is shown in solid,
It can be seen that location estimation distance is far longer than actual range.And the location estimation of Fig. 6 drop centre type regional nodes s to node k
Distance and actual range just differ very little.For this problem, the present invention will be by the anchor node information filtering of concave edge effect
Fall, carry out estimation neighbor node apart from when, only use and do not calculated by the anchor node information of concave edge effect.
Detailed step of the present invention is as follows:
Step 1: the position letter of all node broadcasts itself of each node into whole network in sensor network
Breath, to obtain the minimum hop count between whole network interior joint.
It include the position letter that each anchor node broadcasts itself to whole network in sensor network in the location information of broadcast
Breath, location information includes the ID of anchor node, coordinate (x, y) and hop count, and the initial value of hop count is zero；Each unknown node is to entire
The location information of Web broadcast itself, location information include the ID and hop count of unknown node, and the initial value of hop count is zero.It receives wide
Broadcast information sensor node record node relevant information (wherein anchor node be anchor node ID, coordinate (x, y) and hop count,
Unknown node is the ID and hop count of unknown node) and hop count is added one, it is transmitted to other nodes, all nodes in sensor network
Position and the minimum hop count of each anchor node are all had recorded, there are also the minimum hop counts for arriving other nodes.
Give up invalid anchor node information, if hop count adds one to be not less than in the location information for the anchor node that node receives
The minimum hop count of the anchor node of record, then give up this information.After a while, each sensor node is ok
The minimum hop count of other each nodes is acquired, here includes minimum hop count between anchor node and anchor node, anchor node and not
Know the minimum hop count between node, the minimum hop count between unknown node and unknown node.
Step 2: the distance between anchor node is calculated using the coordinate of anchor node and obtains most short jumping figure value, by comparing anchor
Most short jumping figure value and shortest path hop count between node filter the anchor node information by concave edge effect.
The distance between anchor node AD (Anchor distance) is calculated using the coordinate of anchor node, between them
Distance AD obtains a correct most short jumping figure value AD/R divided by communication radius R.By step 1, can be propagated by information
The minimum hop count between node is obtained, certainly also comprising the shortest path hop count SP between anchor node.
According to the shortest path hop count SP between anchor node and most short jumping figure value AD/R comparing result, the value approximation phase of the two
Deng if, Rule of judgment of the present invention is | SP-AD/R | < 0.2, and illustrate not influenced by concave boundary, just as the node s in Fig. 5
With node k.Two values differ farther out, such as node i and j in Fig. 4, need to filter out these by the anchor of concave edge effect
Node.The number filtered out is related with actual network environment, is to provide the condition of a filtering here.
Step 3: pass through the distance between the filtered any two node of single-hop correction value step 2 structure node
Between distance matrix, the estimated location of all unknown nodes is calculated using MDS-MAP location algorithm.
According to step 2, the anchor node by concave edge effect is filtered out, with remaining not by the anchor of concave edge effect
The shortest path hop count SP between anchor node that node coordinate and step 1 calculate calculates a single-hop corrected value hopsize:
Here i and j refers to not by the anchor node of concave edge effect, SPijRefer between anchor node i and anchor node j
Shortest path hop count, hopsize are exactly single-hop corrected value.Pass through the shortest path between single-hop corrected value hopsize and node
Hop count multiplication is obtained with the shortest path between any two node:
dks=hopsize*SPks (2)
Wherein, dksIt is the estimated distance between any two node k and node s, SPksBe two node k and node s it
Between shortest path hop count, hopsize be according to formula (1) calculate single-hop corrected value.Here i, j, k, s refers to sensor section
The number of point, i-th of sensor node, j-th of sensor node, k-th of sensor node, s-th of sensor node, sensing
A total of n+m sensor node in device network.
The shortest distance between any two node can be calculated according to formula (2), so as to form MDS algorithm is established
Required euclidean distance between node pair matrix D2:
Wherein, d12,d13...d1N, d21, d23...d2N, dN2,dN2,dN3... it respectively indicates between two sensor nodes
Distance is all to calculate to obtain by formula (2).Here N is representative sensor node total number, and N=n+m, n are unknown nodes
Number, m are anchor node numbers；d12Refer to the distance between the 1st sensor node and the 2nd sensor node, d2NRefer to
The distance between 2 sensor nodes and n-th sensor node.
To euclidean distance between node pair matrix D2The phase in entire sensor network between all nodes is estimated using standard MDS algorithm
To position.Its core is singular value decomposition, generates the two-dimensional phase of entire sensor network to coordinate system, in relative coordinate system
Each node has location information.Circular is according to Distance matrix D2Construct center matrix B:
Wherein, E is n rank unit matrix, and I is n rank all 1's matrix, and matrix J is in being calculated by matrix E and matrix I
Heart matrix；Singular value decomposition is carried out to center matrix B, and calculates a matrix X:
[V S T]=svd (B) (6)
X=T*sqrt (S) (7)
Wherein, V and T is two unitary matrice obtained by singular value decomposition svd function；Matrix S is by singular value point
The diagonal matrix with matrix B with size that solution svd function obtains；Sqrt is extraction of square root function in matlab.
Take matrix X preceding two-dimensional data be exactly all nodes relative coordinate, be exactly singular value decomposition obtain node between
Relative coordinate, be exactly that the opposite seat between the available node of singular value decomposition is passed through according to the distance between node matrix
Mark, also contains the relative coordinate of anchor node here, according to the true coordinate of known anchor node, calculate by translation, rotation and
Anchor node relative coordinate system is converted the corresponding transformation parameter of absolute coordinate by the transform methods such as mapping.By these transformation parameters
It is applied in the relative coordinate of unknown node, so that it may the relative coordinate of unknown node is converted into absolute coordinate, this seat
Mark is exactly the estimated location of unknown node.
Step 4: objective function is established using anchor node, the estimated location of nodes of locations and single-hop corrected value, utilizes simulation
Annealing location algorithm optimizes the estimated location of step 3, and the optimal solution that loop iteration obtains is exactly the position of nodes of locations
Coordinate.
Choose objective function.Objective function is used to judge the superiority and inferiority of one group of solution, because in concave domain, non-neighbor node
Between the shortest distance be likely to be influenced by concave boundary, therefore the design of objective function is avoided using non-neighbor node.It is adjacent
The objective function that the distance between node is occupied in step 3, can be obtained by single-hop corrected value hopsize, therefore is designed
Are as follows:
Wherein, n indicates unknown node number, and m indicates anchor node number, naijIt indicates between unknown node i and anchor node j
Neighborhood, nuikIndicate the neighborhood between unknown node i and unknown node k, if it is neighbor node, then its value is
1；If not neighbor node, then its value is 0.Indicate the estimated distance between unknown node i and anchor node j, and
Represent the estimated distance between unknown node i and unknown node k.The estimated coordinates of unknown node i are represented,Generation
The estimated coordinates of table unknown node k, (xj,yj) represent the coordinate of anchor node j.Objective function S expression means all unknown sections
Difference of the point to distance between the actual distance and estimated coordinates of its all neighbor node (including anchor node and other unknown nodes)
The quadratic sum of value.The corresponding objective function S value of one group of estimated coordinates is smaller, is considered as this group of estimated coordinates closer to actual bit
Set
As shown in figure 4, being using method for solving of the simulated annealing location algorithm to objective function S:
1, initial temperature T is set0, the present invention is set as T0=100, an initial temperature is set, and every iteration is primary, T0
It will and then reduce once, the cycle-index L at each temperature is set, L=1000 is arranged in the present invention, and step 3 is calculated and is obtained
One group of unknown node estimated coordinates as initial solution m0, and with the value S0 of formula (8) calculating target function；
2, the initial value that cycle counter is arranged is b=1, b=1,2,3 ... L；
3, using initial solution m0 as parameter, the new explanation m1 of one group of unknown node estimated coordinates is calculated with formula (9).Principle is root
According to node actual range caused by last estimated location m0 and the ratio of estimated location distance multiplied by between neighbor node
Coordinate difference, so that the distance between node actual range between node is close.
M1=inv (V1+V2) * ((B1X+B2X) * m0+ (V3-B3X) * AU) (9)
Wherein, inv is the function of the matrix inversion matrix in matlab.V1 is n rank matrix, and n refers to unknown node number,
The diagonal line storage of matrix V 1 be unknown node neighbours' unknown node number, if two nodes are neighbours on off-diagonal
Node is then -1, is otherwise 0.V2 is n × m matrix, and n refers to unknown node number, and m is anchor node number, is stored on diagonal line
Be unknown node neighbours' anchor node number, remaining element be 0.V3 is n × m matrix, and n refers to unknown node number, and m is anchor
Node number；What is stored is exactly the neighborhood matrix between unknown node and anchor node, if two nodes are neighbor nodes,
Then corresponding value is 1, is otherwise 0.B1X is n rank matrix, and n refers to unknown node number.Diagonal positions are and unknown node i
The sum of actual range and the ratio of estimated distance of all unknown nodes of neighbours, off-diagonal position, if two nodes are
Neighbor node is then the negative value of ratio, is then 0 if not neighbor node.B2X is n rank matrix, and n refers to unknown node number,
Diagonal positions are the non-diagonal the sum of with the actual range of all anchor nodes of unknown node i neighbours and the ratio of estimated distance
Line position is 0.B3X is n × m matrix, and n refers to unknown node number, and m is anchor node number, and storage is and unknown node neighbour
The actual range of all anchor nodes occupied and the ratio of estimated distance.AU is the matrix of m × 2, and m is anchor node number, and storage is
The coordinate of anchor node.
The new estimated coordinates m1 calculating target function S1 of unknown node calculated according to formula (9), the then increment of objective function
For Δ=S1-S0；
4, the value calculated according to Metropolis criterion and step 3, it is determined whether receive new solution m1:
Wherein, P is the probability value calculated, T0It is Current Temperatures, Δ is the difference that step 3 is calculated.With
Machine generate one [0,1) random number R in section if the value of probability value P is greater than random number R receives newly generated solution m1 work
For current optimal solution, that is, assignment m0=m1 again, corresponding target function value S0=S1 goes to step 5；Otherwise do not receive new
The solution m1 of generation continues using m0 as current optimal solution, and corresponding target function value S0 is constant, goes to step 6.
If 5, cycle count number b, which is less than, terminates iterative steps L, b=b+1, step 3 is turned to；Otherwise step is turned to
6。
If 6, temperature T0Greater than cooling temperature (it is 0.01 that cooling temperature, which is arranged, in the present invention), initial temperature T is reset,
Enable T0=T0* α turns to step 2；If temperature is less than cooling temperature 0.01, exporting current optimal solution is optimal solution, and is tied
Beam loop iteration.Wherein, α is coefficient of temperature drop, and range is 0~1, and the present invention is set as 0.85.
Position error can be greatly reduced in order to embody the present invention, it will be in MDS-MAP algorithm, DV-HOP algorithm and the present invention
MDS-MAP-SA algorithm compares.Experiment is emulated on MATLAB platform, is had chosen 100 nodes and is randomly distributed in
It is tested in the region of 100*100.Initial temperature T, α and cycle-index L in experimentation, such as in simulated annealing are
Oneself setting, on the one hand consider the algorithm time, is on the other hand exactly by largely testing the value taken.Wherein, * indicates anchor section
Point, O indicate unknown node.As shown in fig. 7, distribution map of the node in concave domain.
The position error of DV-MDS-SA algorithm, DV-hop algorithm and MDS-MAP algorithm is compared first, such as Fig. 8
It is shown.As shown in Figure 8, same amount of anchor node, for other conditions also in identical situation, position error of the invention is obviously low
In other two kinds of algorithms.As the quantity of anchor node increases, location information increases between node, and error also can reduce therewith, DV-
The position error of MDS-SA algorithm is also below other two kinds.
Then communication radius in network is compared with position error, as shown in Figure 9.Other conditions are constant, by anchor section
The number of point is fixed as 20.When communication radius R increases, the position error of these three algorithms can also reduce therewith.Here
The reason of be that with the increase of communication radius, the degree of communication of network increases.Degree of communication indicate be in one network, can
With the mean number for the node that a node is directly communicated.As shown in Figure 8, under the same terms, DV-MDS- of the invention
SA algorithm becomes apparent from than other two kinds of algorithm downward trends.Under same communication radius, DV-MDS-SA algorithm of the invention is determined
Position error is minimum, can effectively save node energy energy consumption.
The simulation experiment result of two above shows other conditions all under the same conditions, and the quantity for changing anchor node increases
More or node communication radius increases, and the position error of node can be gradually reduced.It is contemplated that communication power consumption, anchor node
Number and communication radius cannot infinitely increase.
Wireless sensor node location technology is all a full of challenges research topic all the time.The present invention is in concave
In the non-ranging situation in region can greatly less node position error, first by the most short jumping figure value AD/R of Rule of judgment and most
Whether short path hop count SP is close, whether obtain egress is influenced by or not boundary；The node by edge effect is excluded, for not by side
The node that boundary influences, acquires a single-hop corrected value, single-hop corrected value and the product of the hop count of anchor node to unknown node are
The shortest distance obtains estimated coordinates then by the processing of shortest distance application MDS algorithm；The mesh of last design simulation annealing algorithm
Scalar functions optimize estimated coordinates.The present invention has a clear superiority on improving positioning accuracy, in the network of some complexity
Under distribution situation, improved algorithm has stronger practicability.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all in essence of the invention
Within mind and principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (7)
1. a kind of non-ranging node fusion and positioning method suitable for concave domain, which is characterized in that its step are as follows:
Step 1: the location information of all node broadcasts itself of each node into whole network in sensor network, from
And obtain the minimum hop count between whole network interior joint；
Step 2: the coordinate of the anchor node obtained using step 1 is calculated the distance between anchor node and obtains most short jumping figure value, is led to
It crosses and compares most short jumping figure value between anchor node and the filtering of shortest path hop count by the nodal information of concave edge effect；
Step 3: node spacing is constructed by the distance between filtered any two node of single-hop correction value step 2
From matrix, the estimated location of all unknown nodes is calculated using MDS-MAP location algorithm；
Step 4: objective function is established using anchor node, the estimated location of unknown node and single-hop corrected value, utilizes simulated annealing
Location algorithm optimizes the estimated location of step 3, and the optimal solution that loop iteration obtains is exactly the final estimation of unknown node
Coordinate.
2. the non-ranging node fusion and positioning method according to claim 1 suitable for concave domain, which is characterized in that institute
State in step 1 that each anchor node broadcasts the location information of itself to whole network in sensor network, location information includes anchor section
ID, coordinate (x, y) and the hop count of point, the initial value of hop count is zero；Each unknown node broadcasts the position of itself to whole network
Information, location information include the ID and hop count of unknown node, and the initial value of hop count is zero；Receive the sensor node of broadcast message
Hop count is simultaneously added one by the relevant information for recording node, is transmitted to other nodes, and all nodes all have recorded often in sensor network
The position of a anchor node and minimum hop count, there are also the minimum hop counts for arriving other nodes；If the position for the anchor node that node receives
Hop count adds a minimum hop count not less than the anchor node recorded in confidence breath, then gives up this information；The whole network
Minimum hop count between interior joint is the minimum hop count to other each nodes that each sensor node obtains, including anchor section
Minimum hop count between point and anchor node, the minimum hop count between anchor node and unknown node, unknown node and unknown node it
Between minimum hop count.
3. the non-ranging node fusion and positioning method according to claim 1 or 2 suitable for concave domain, feature exist
In the implementation method of the step 2 is: propagating the shortest path obtained between anchor node by the information that step 1 broadcast is realized
Diameter hop count SP compares the shortest path hop count SP between anchor node and most short jumping figure value AD/R, if the value of the two is approximate
It is equal, i.e., | SP-AD/R | < 0.2, illustrate not influenced by concave boundary；If the value difference of the two is farther out, illustrate the two
The shortest distance is filtered out the anchor node by concave edge effect by concave edge effect between anchor node；The most short jumping figure value
AD/R is the correct most short jump that the distance between the anchor node calculated using the coordinate of anchor node AD is obtained divided by communication radius R
Numerical value.
4. the non-ranging node fusion and positioning method according to claim 3 suitable for concave domain, which is characterized in that institute
Stating the method that euclidean distance between node pair matrix is constructed in step 3 is:
A, the filtered remaining anchor section not calculated by the anchor node coordinate and step 1 of concave edge effect of step 2 is utilized
Shortest path hop count between point calculates single-hop corrected value hopsize:
Here i and j is not by the anchor node of concave edge effect, SPijIt is the shortest path between anchor node i and anchor node j
Hop count；
B, it is multiplied and is obtained between any two node by the shortest path hop count between single-hop corrected value hopsize and node
Shortest path:
dks=hopsize*SPks (2)
Wherein, dksIt is the estimated distance between any two node k and node s, SPksIt is shortest path between node k and node s
Hop count；I, j, k, s refer to the number of sensor node；
C, according to the shortest distance d between the calculated any two node of formula (2)ks, between node needed for establishing MDS algorithm
Distance matrix D2:
Wherein, d12 d13...d1N, d21 d23...d2N, dN2 dN2 dN3... respectively indicate the distance between two sensor nodes；
N representative sensor node total number, N=n+m, n are unknown node numbers, and m is anchor node number；d12Refer to the 1st sensor section
The distance between point and the 2nd sensor node, d2NRefer to the 2nd between sensor node and n-th sensor node away from
From.
5. the non-ranging node fusion and positioning method according to claim 4 suitable for concave domain, which is characterized in that institute
The method for stating the estimated location that MDS-MAP location algorithm calculates all unknown nodes in step 2 is:
To euclidean distance between node pair matrix D2The opposite position in entire sensor network between all nodes is estimated using standard MDS algorithm
It sets: according to Distance matrix D2Structural matrix B:
Wherein, E is n rank unit matrix, and I is n rank all 1's matrix, and matrix J is the central moment being calculated by matrix E and matrix I
Battle array；
Singular value decomposition is carried out to matrix B, and calculates a matrix X:
[V S T]=svd (B) (6)
X=T*sqrt (S) (7)
Wherein, V and T is two unitary matrice obtained by singular value decomposition svd function；Matrix S is by singular value decomposition svd
The diagonal matrix with matrix B with size that function obtains；Sqrt is extraction of square root function in matlab；
The preceding two-dimensional data of matrix X is taken to obtain the relative coordinate of all nodes；According to the relative coordinate of the anchor node of calculating and
It is corresponding by anchor node relative coordinate system to convert absolute coordinate by translation, rotation and mapping for the true coordinate for knowing anchor node
Transformation parameter；These transformation parameters are applied in the relative coordinate of unknown node, the relative coordinate of unknown node is converted
At absolute coordinate, the coordinate of the estimated location of unknown node is obtained.
6. being suitable for the non-ranging node fusion and positioning method of concave domain according to claim 1 or 5, feature exists
In objective function in the step 4 are as follows: avoid using non-neighbor node, the distance between neighbor node passes through single-hop and corrects
Value hopsize is obtained, therefore the objective function designed are as follows:
Wherein, n indicates unknown node number, and m indicates anchor node number, naijIndicate the neighbour between unknown node i and anchor node j
Occupy relationship, nuikIndicate the neighborhood between unknown node i and unknown node k, if it is neighbor node, then its value is 1；Such as
Fruit is not neighbor node, then its value is 0；Indicate the estimated distance between unknown node i and anchor node j, andIt represents
Estimated distance between unknown node i and unknown node k；The estimated coordinates of unknown node i are represented,It represents not
Know the estimated coordinates of node k, (xj,yj) represent the coordinate of anchor node j；Objective function S is all unknown nodes to comprising anchor node
The quadratic sum of the difference of distance between the actual distance and estimated coordinates of all neighbor nodes of other unknown nodes.
7. the non-ranging node fusion and positioning method according to claim 6 suitable for concave domain, which is characterized in that benefit
It is with method for solving of the simulated annealing location algorithm to objective function S:
1, initial temperature T is set0, the cycle-index L at each temperature is set, step 3 is calculated to the one group of unknown section obtained
Point estimation coordinate is as initial solution m0, and with the value S0 of formula (8) calculating target function；
2, the initial value that cycle counter is arranged is b=1, b=1,2,3 ... L；
3, by initial solution m0As parameter, according to last estimated location m0Caused node actual range and estimated location away from
From ratio multiplied by the coordinate difference between neighbor node so that the original that the distance between node actual range between node is close
Reason calculates the new estimated coordinates m1 of one group of unknown node with formula (9):
M1=inv (V1+V2) * ((B1X+B2X) * m0+ (V3-B3X) * AU) (9)
Wherein, inv is matrix inversion matrix function；The diagonal line storage of n rank matrix V 1 is unknown node neighbours' unknown node
Number, be -1 if two nodes are neighbor nodes on off-diagonal, be otherwise 0；Size is pair of the matrix V 2 of n × m
What is stored on linea angulata is the number of unknown node neighbours' anchor node, remaining element is 0；The storage of matrix V 3 that size is n × m is just
It is the neighborhood matrix between unknown node and anchor node, if two nodes are neighbor nodes, corresponding value is 1, no
It is then 0；The diagonal positions of n rank matrix B 1X be with the actual range of all unknown nodes of unknown node i neighbours and estimation away from
From the sum of ratio, off-diagonal position, if two nodes are neighbor nodes, for the negative value of ratio, if not neighbours
Node is then 0；The diagonal positions of n rank matrix B 2X are and the actual range of all anchor nodes of unknown node i neighbours and estimation
The sum of ratio of distance, off-diagonal position are 0；What size stored for the matrix B 3X of n × m is institute with unknown node neighbours
There are the actual range of anchor node and the ratio of estimated distance；Size be m × 2 matrix A U store be anchor node coordinate；
According to the new estimated coordinates m1 calculating target function S1 of the unknown node of calculating, then the increment of objective function is Δ=S1-
S0；
4, the increment calculated according to Metropolis criterion and step 3, it is determined whether receive new solution m1:
Wherein, P is the probability value calculated, T0It is current temperature；
Be randomly generated one [0,1) random number R in section receives newly generated if the value of probability value P is greater than random number R
M1 is solved as current optimal solution, that is, assignment m0=m1 again, corresponding target function value S0=S1 go to step 5；Otherwise not
Receive newly generated solution m1, continues using m0 as current optimal solution, corresponding target function value S0 is constant, goes to step 6；
If 5, cycle count number b, which is less than, terminates iterative steps L, b=b+1, step 3 is turned to, step 6 is otherwise turned to；
If 6, temperature T0Greater than cooling temperature, initial temperature T is reset0, enable T0=T0* α turns to step 2；If
Temperature is less than cooling temperature, and exporting current optimal solution is optimal solution, and end loop iteration；Wherein, α is coefficient of temperature drop,
And range is 0~1.
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