CN105792357B - A kind of node positioning method of the Distributed Wireless Sensor Networks based on hybrid measurement - Google Patents
A kind of node positioning method of the Distributed Wireless Sensor Networks based on hybrid measurement Download PDFInfo
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Abstract
The invention discloses a kind of node positioning methods of Distributed Wireless Sensor Networks based on hybrid measurement, it provides a unified solution to problem for the orientation problem under hybrid measurement, each node can possess different measurement capabilities, including distance, angle and relative position measurement；In this case, distributed algorithm of the present invention makes each unknown node be estimated that the unknown of oneself, each node unify the direction of local coordinate system without being equipped with the equipment of similar compass, the flexibility of positioning increased in rugged environment；Furthermore inventive algorithm has the property of exponential convergence, fast convergence rate, and estimated value can will not be made to fall into local optimum with global convergence, algorithm.
Description
Technical field
The invention belongs to technology of wireless sensing network fields, and in particular to a kind of distributed wireless biography based on hybrid measurement
Feel the node positioning method of network.
Background technique
In application of higher wireless sensor network, orientation problem is a basic problem, and sensor node localization problem is in military affairs
It is of great significance in the application such as search, target following.The target of orientation problem is to determine sensor node in some coordinate system
Under physical location.
It in massive wireless sensor, is limited by factors such as sensor node volume, costs, cannot be all
Node is equipped with Global localization device such as GPS.In wireless sensor network, there are huge number of sensor nodes, so often
A sensor node cannot obtain the information of all the sensors node, so needing distributed location algorithm.I.e. each sensing
Device node only need to be measured and be communicated with neighbouring sensor node, so that it may the position of oneself is estimated by distributed algorithm
Information.In large-scale sensor network, sensor node probably possesses different measurement capabilities.Two in sensor network
A most common metrical information is range information and reaches angle information, so sensor node may be there are three types of measurement capability: away from
From measurement capability, angle of arrival measurement capability, relative position measurement ability (with a distance from having both and arrival angular measurement).
Chinese patent application " the wireless sensor network based on distributed optimal strategy of Publication No. CN101730224A
Node positioning method " in disclose a kind of wireless sensor network node locating method, but this method requires each node
The relative distance and relative angle of capable measurement neighbor node, however in massive wireless sensor, it is likely that it is every
A node only has a kind of measurement capability, distance or angle, without having the measurement capability of the two.
The orientation problem that existing technology is rarely hybrid measurement provides the solution framework of a system, based on optimization
Location algorithm is easily ensnared into locally optimal solution and can not finally position.Meanwhile when using arrival angle information, the prior art is big
Assume that node is equipped with compass to which local coordinate axis has common direction, this is when having price limit and energy limit
It is unpractical.
Summary of the invention
For above-mentioned technical problem present in the prior art, the present invention provides a kind of distributions based on hybrid measurement
The node positioning method of wireless sensor network, this method provide unification for the sensor node localization problem under hybrid measurement
Analytical framework, and algorithm is completed under each sensor node local coordinate system, does not need to be equipped with compass.
A kind of node positioning method of the Distributed Wireless Sensor Networks based on hybrid measurement, includes the following steps:
(1) for not installing any node i of GPS in network, its neighbor node set N is determinedi；
(2) it is saved according to relatively each neighbours of the interactive information calculate node i of the metrical information of node i itself and its neighbor node
The barycentric coodinates of point；
(3) for node i, following iterative equation is based on according to the barycentric coodinates of its relatively each neighbor node and solves egress
The position coordinates of i itself:
Wherein: pi(t) and pi(t+1) be respectively the t times iteration and the t+1 times iteration node i position coordinates, pj(t) it is
The position coordinates of the t times iteration node j, node j are that neighbor node, that is, node j of node i belongs to neighbor node set Ni, AijFor
The barycentric coodinates of node i counterpart node j, γ is weight coefficient and γ ∈ (0,1), t are the number of iterations.
Neighbor node set N is determined in the step (1)iMethod are as follows: broadcast all nodes in network, if
Node i receives the broadcast data packet of node j, it is determined that node i and node j neighbor node each other；All neighbours of node i are saved
Point composition neighbor node set Ni。
The barycentric coodinates of relatively each neighbor node of calculate node i in the step (2), detailed process is as follows:
2.1 for neighbor node set NiIn any node j, from neighbor node set NiIn find out all about node j
3 neighbours combination, described 3 neighbours combination comprising node j and other two belong to neighbor node set NiIn
Node, these three nodes neighbor node and node i is located in the delta-shaped region that these three nodes are surrounded each other；
2.2 combine any 3 neighbours about node j, which includes node j, node l and node k；Root
According to the measurement capability type of these three nodes, the local gravity center coordinate of node i counterpart node j, node l and node k are calculated；
2.3 combine according to 3 neighbours that step 2.2 traverses all about node j, obtain N number of about the opposite section of node i
The local gravity center coordinate a of point jij, and then the barycentric coodinates A of node i counterpart node j is calculated according to the following formulaij:
Wherein: the kind number that 3 neighbours that N is all about node j combine,For in 3 neighbours' combinations of n
The local gravity center coordinate of node i counterpart node j.
If node i has distance measurement capability or angle of arrival measurement capability, node j, node l in the step 2.2
There is relative position measurement ability and assume that the node is node j at least there is node in node k, then passes through following public affairs
The local gravity center coordinate a of formula calculate node i counterpart node j, node l and node kij、ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node
J, the directed area of node i and the surrounded delta-shaped region of node l, SjkiTo be surrounded triangle by node j, node k and node i
The directed area in shape region, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l,WithPosition coordinates under node j coordinate system of respectively node j, node l, node k and node i and
If node i has distance measurement capability in the step 2.2, at least have two in node j, node l and node k
A node also has distance measurement capability and assumes that the two nodes are respectively node j and node l, then is calculated by the following formula
The local gravity center coordinate a of node i counterpart node j, node l and node kij、ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node
J, the directed area of node i and the surrounded delta-shaped region of node l, SjkiTo be surrounded triangle by node j, node k and node i
The directed area in shape region, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l, dij=dji
And indicate distance of the node j to node i, dik=dkiAnd indicate distance of the node k to node i, dil=dliAnd indicate section
Distance of the point l to node i, dkj=djkAnd indicate distance of the node j to node k, dkl=dlkAnd indicate node l to node k
Distance, djl=dljAnd indicate the distance of node l to node j.
If node i has distance measurement capability in the step 2.2, at least have two in node j, node l and node k
A node has angle of arrival measurement capability and assumes that the two nodes are respectively node j and node l, then passes through following procedure meter
The local gravity center coordinate a of operator node i counterpart node j, node l and node kij、ailAnd aik:
Firstly, determining position coordinates of the node i under node j coordinate systemAnd node j is sat in node j
Position coordinates under mark systemWherein: dijFor the distance of node j to node i,Extremely for node j coordinate system lower node i
The angle of arrival of node j；
Then, position coordinates of the calculate node l under node j coordinate system according to the following formula
Wherein: dilFor the distance of node l to node i,For the angle of arrival of node j coordinate system lower node i to node l,Angle of arrival for node l coordinate system lower node i to node l, αljFor the rotation of node j coordinate system counterpart node l coordinate system
Angle, δjlForArgument in node j coordinate system, δljForArgument in node l coordinate system,For node j coordinate
It is angle of arrival of the lower node l to node j,For the angle of arrival of node l coordinate system lower node j to node l；
In turn, by solving position coordinates of the following equation calculate node k under node j coordinate system
Wherein:For the angle of arrival of node j coordinate system lower node k to node l,For node j coordinate system lower node k
To the angle of arrival of node j,For the angle of arrival of node l coordinate system lower node k to node l,TIndicate transposition；
Finally, being calculated by the following formula the local gravity center coordinate a of node i counterpart node j, node l and node kij、
ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node
J, the directed area of node i and the surrounded delta-shaped region of node l, SjkiTo be surrounded triangle by node j, node k and node i
The directed area in shape region, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l.
If node i has angle of arrival measurement capability in the step 2.2, at least deposited in node j, node l and node k
Also there is angle of arrival measurement capability in a node and assume that the node is node j, then pass through following procedure calculate node i phase
To the local gravity center coordinate a of node j, node l and node kij、ailAnd aik:
Firstly, determining the mapping position vector q of node iiThe mapping position vector of=0 and node j For
Node i coordinate system lower node j to node i angle of arrival；
Then, pass through the mapping position vector q of solution following equation calculate node ll:
αji=δij-δji+π
Wherein:For the angle of arrival of node i coordinate system lower node l to node j,For node i coordinate system lower node l
To the angle of arrival of node i,For the angle of arrival of node j coordinate system lower node l to node j,TIndicate transposition, αjiFor node i
The rotation angle of coordinate system counterpart node j coordinate system, δijForArgument in node i coordinate system, δjiForIt is sat in node j
Argument in mark system,For the angle of arrival of node i coordinate system lower node j to node i,For node j coordinate system lower node i
To the angle of arrival of node j；
In turn, pass through the mapping position vector q of solution following equation calculate node kk:
Wherein:For the angle of arrival of node i coordinate system lower node k to node j,For node i coordinate system lower node k
To the angle of arrival of node i,For the angle of arrival of node j coordinate system lower node k to node j；
Finally, being calculated by the following formula the local gravity center coordinate a of node i counterpart node j, node l and node kij、
ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node
J, the directed area of node i and the surrounded delta-shaped region of node l, SjkiTo be surrounded triangle by node j, node k and node i
The directed area in shape region, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l.
If node i has angle of arrival measurement capability in the step 2.2, at least deposited in node j, node l and node k
There is distance measurement capability in two nodes and assume that the two nodes are respectively node j and node l, then pass through following procedure meter
The local gravity center coordinate a of operator node i counterpart node j, node l and node kij、ailAnd aik:
Firstly, determining position coordinates of the node j under node i coordinate systemNode l is in node i coordinate system
Under position coordinatesAnd position coordinates of the node i under node i coordinate systemWherein: dijFor node
Distance of the j to node i, dilFor the distance of node l to node i,For the angle of arrival of node i coordinate system lower node j to node i
Degree,For the angle of arrival of node i coordinate system lower node l to node i；
Then, by solving position coordinates of the following equation calculate node k under node i coordinate system
Wherein:Angle of arrival for node i coordinate system lower node k to node i, djkFor node k to the distance of node j,
dlkFor node k to the distance of node l,TIndicate transposition；
Finally, being calculated by the following formula the local gravity center coordinate a of node i counterpart node j, node l and node kij、
ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node
J, the directed area of node i and the surrounded delta-shaped region of node l, SjkiTo be surrounded triangle by node j, node k and node i
The directed area in shape region, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l.
If node i has relative position measurement ability in the step 2.2, it is calculated by the following formula node i phase
To the local gravity center coordinate a of node j, node l and node kij、ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node
J, the directed area of node i and the surrounded delta-shaped region of node l, SjkiTo be surrounded triangle by node j, node k and node i
The directed area in shape region, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l,WithRespectively position coordinates under node i coordinate system of node j, node l, node k and node i and
The present invention provides a unified solution to problem for the orientation problem under hybrid measurement, and each node can
To possess different measurement capabilities, including distance, angle and relative position measurement；In this case, the present invention is distributed calculates
Method makes each unknown node be estimated that the unknown of oneself, each node are unified without being equipped with the equipment of similar compass
The direction of local coordinate system increases the flexibility of positioning in rugged environment；Furthermore inventive algorithm has exponential convergence
Property, fast convergence rate, and estimated value can will not be made to fall into local optimum with global convergence, algorithm.
Detailed description of the invention
Fig. 1 is the step flow diagram of the method for the present invention.
Fig. 2 is the schematic diagram of wireless sensor network；Wherein rectangular node belongs to B class, and circular node belongs to R class, and three
Angular node belongs to D class.
Fig. 3 is the communication measurement topology schematic diagram of distributed sensor meshed network.
Fig. 4 is that unknown node is shown from initial position estimation value to the track of final position estimated value under location algorithm of the present invention
It is intended to.
Fig. 5 is unknown node estimated result under location algorithm of the present invention about normalization error-algorithm iteration number pass
It is curve graph.
Specific embodiment
In order to more specifically describe the present invention, with reference to the accompanying drawing and specific embodiment is to technical solution of the present invention
It is described in detail.
As shown in Figure 1, the present invention is based on the node positioning method of the Distributed Wireless Sensor Networks of hybrid measurement include with
Lower step:
Step 1, the present embodiment is distributed 9 sensor nodes in 90 × 90 simulating area, as shown in Figure 2.Wherein, it imitates
The transverse direction in true region is X-axis, and longitudinal is Y-axis, and anchor node is chosen for A={ 1,2,3 }, unknown node be chosen for S=4,5,6,7,
8,9}；Unknown node is divided into three classes, i.e. D class (representing has distance measurement capability), and (representing, there is B class angle of arrival to measure energy
Power), R class (representing has relative position measurement ability).
Step 2, all the sensors node is broadcasted, if unknown node i can receive the broadcast of sensor node l transmission
Data packet, then it is assumed that neighbor node, neighbor node can be anchor node and be also possible to sensor node l each other with unknown node i
Unknown node；Unknown node i establishes the neighboring node list N of oneself as a result,i.Fig. 3 is the emulation zone of present embodiment 90 × 90
The communication measurement topology of each node in domain.
Step 3, barycentric coodinates of some unknown node i relative to neighbor node are calculated:
Step 3-1, arbitrarily from Ni3 neighbor nodes of middle selection, if they each other neighbor node and unknown node from
Body is located in their convex closure, carries out in next step.
Step 3-2 has following three kinds of situations if i belongs to D class:
At least there is a neighbor node and belong to R class, be denoted as node j in step 3-2 (a).Then node i can be by logical
It is obtained at believer in a certain religion jWithWhereinpiPosition of the node i under global coordinate system is represented to sit
Mark, subscript j represent the numerical value under node j local coordinate system.Barycentric coodinates { aij,ail,aikIt is calculated as follows:
Wherein the calculation formula of directed area is as follows:
Step 3-2 (b), at least two neighbor nodes belong to D class, are denoted as j and l.Barycentric coodinates { aij,ail,aikAs the following formula
It calculates:
Wherein directed area calculation formula is as follows:
Wherein d represents the distance measured between node.
Step 3-2 (c), at least two neighbor nodes belong to B class, are denoted as j and l.Then node i can measure dij、dikWith
dil, angle measurement can be obtained from node jWithWherein:
It can be obtained from node lWithUse δjlIt indicatesWith the local coordinate system Σ of node jjX-axis it
Between angle.It calculates:
αlj=δjl-δlj+π
And it calculates:
Wherein R (αlj) it is with angle [alpha]ljFor the spin matrix of parameter.Then it can calculateWithAndIt can be solved from following equation:
Then barycentric coodinates { aij,ail,aikCan be calculated according to the formula in step 3-2 (a).
Step 3-3 has following three kinds of situations if node i belongs to B class:
At least there is a neighbor node and belong to R class, be denoted as node j and step 3-2 (a) calculation in step 3-3 (a)
Equally.
At least there is a neighbor node and belong to B class, be denoted as node j in step 3-3 (b)；Node i can measureWithAngle measurement can be obtained from node jWithIt calculates:
Enable qi=0 andQ is solved from following equationsl:
And q is solved from following equationk:
Then barycentric coodinates { aij,ail,aikCan be calculated according to the formula in step 3-2 (a).
Step 3-3 (c), at least two neighbor nodes belong to D class, are denoted as j and l.Then node i can measure
WithAnd it can communicate from j and l and obtain djk、dji、djl、dliAnd dlk；It calculates:
It is solved from following equation
Then barycentric coodinates { aij,ail,aikCan be calculated according to the formula in step 3-2 (a).
Step 3-4, if node i belongs to R class, barycentric coodinates { aij,ail,aikCan be according in step 3-2 (a)
Formula calculate.
Step 3-5 calculates each group of combination selected in step 3-1 according to above-mentioned stepsWithWherein n
Possible combination is represented, angle weight of the neighbor node j with respect to unknown node i is finally calculated as follows:
Wherein N is the number of all possible combinations.
Step 4, all sensor nodes are by oneself current position estimation value pi(t) all neighbor nodes are sent to.
For anchor node, current GPS result is as sent.It is iterated to calculate if first time, each unknown node arbitrarily selects one
Initial value is as initial estimate.After each unknown node receives the position estimation value of neighbor node transmission.Iteration updates certainly
Oneself position estimation value, more new formula are as follows
Wherein, pj(t) be the t times iteration of node j estimated result；γ ∈ (0,1) is a constant；AijFor unknown node
Barycentric coodinates of the i relative to neighbor node j；T+1 is the number that current iteration calculates.
Fig. 4 be execute iterative algorithm when, unknown node from position initial estimate to final position coordinate estimated value
Track.The coordinate of three anchor nodes is p1=(0,0), p2=(40,80), p3=(80,0), six unknown node accurate coordinate p4
=(62,20), p5=(30,40), p6=(40,60), p7=(50,45), p8=(20,20), p9=(40,6).Constant parameter takes
Value γ=0.5.As seen from Figure 4, each unknown node can be (in figure hollow from arbitrary initial position to the estimated value of own coordinate
Circle represents initial position) converge to actual coordinate value.
Fig. 5 indicates normalization error-the number of iterations relation curve when running this iterative algorithm, and normalization error is each
The error of secondary obtained positioning result divided by initial estimate error.From fig. 5, it can be seen that there are measurement error the case where
Under, the normalization error extension of algorithm positioning converges near 0, fast convergence rate.
This hair can be understood and applied the above description of the embodiments is intended to facilitate those skilled in the art
It is bright.Person skilled in the art obviously easily can make various modifications to above-described embodiment, and described herein
General Principle is applied in other embodiments without having to go through creative labor.Therefore, the present invention is not limited to the above embodiments,
Those skilled in the art's announcement according to the present invention, the improvement made for the present invention and modification all should be in protections of the invention
Within the scope of.
Claims (2)
1. a kind of node positioning method of the Distributed Wireless Sensor Networks based on hybrid measurement, includes the following steps:
(1) for not installing any node i of GPS in network, its neighbor node set N is determinedi；
(2) according to relatively each neighbor node of interactive information calculate node i of the metrical information of node i itself and its neighbor node
Barycentric coodinates, detailed process is as follows:
2.1 for neighbor node set NiIn any node j, from neighbor node set NiIn find out the three of all about node j
Point neighbours' combination, 3 neighbours combination includes node j and other two belongs to neighbor node set NiIn node,
These three nodes neighbor node and node i is located in the delta-shaped region that these three nodes are surrounded each other；
2.2 combine any 3 neighbours about node j, which includes node j, node l and node k；According to this
The measurement capability type of three nodes calculates the local gravity center coordinate of node i counterpart node j, node l and node k；Its
In:
1. at least existing in node j, node l and node k if node i has distance measurement capability or angle of arrival measurement capability
One node has relative position measurement ability and assumes that the node is node j, then is calculated by the following formula the opposite section of node i
The local gravity center coordinate a of point j, node l and node kij、ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node j, section
The directed area of the surrounded delta-shaped region of point i and node l, SjkiTo be surrounded delta by node j, node k and node i
The directed area in domain, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l,
WithPosition coordinates under node j coordinate system of respectively node j, node l, node k and node i and
2. at least there are two nodes in node j, node l and node k also has distance if node i has distance measurement capability
Measurement capability and assume that the two nodes are respectively node j and node l, then be calculated by the following formula node i counterpart node j,
The local gravity center coordinate a of node l and node kij、ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node j, section
The directed area of the surrounded delta-shaped region of point i and node l, SjkiTo be surrounded delta by node j, node k and node i
The directed area in domain, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l, dij=djiAnd
Indicate distance of the node j to node i, dik=dkiAnd indicate distance of the node k to node i, dil=dliAnd indicate node l
To the distance of node i, dkj=djkAnd indicate distance of the node j to node k, dkl=dlkAnd indicate node l to node k's
Distance, djl=dljAnd indicate the distance of node l to node j；
3. at least there are two nodes in node j, node l and node k has angle of arrival if node i has distance measurement capability
It spends measurement capability and assumes that the two nodes are respectively node j and node l, then pass through following procedure calculate node i counterpart node
J, the local gravity center coordinate a of node l and node kij、ailAnd aik:
Firstly, determining position coordinates of the node i under node j coordinate systemAnd node j is under node j coordinate system
Position coordinatesWherein: dijFor the distance of node j to node i,It is node j coordinate system lower node i to node j's
Angle of arrival；
Then, position coordinates of the calculate node l under node j coordinate system according to the following formula
Wherein: dilFor the distance of node l to node i,For the angle of arrival of node j coordinate system lower node i to node l,For
Angle of arrival of the node l coordinate system lower node i to node l, αljFor the rotation angle of node j coordinate system counterpart node l coordinate system,
δjlForArgument in node j coordinate system, δljForArgument in node l coordinate system,For under node j coordinate system
The angle of arrival of node l to node j,For the angle of arrival of node l coordinate system lower node j to node l；
In turn, by solving position coordinates of the following equation calculate node k under node j coordinate system
Wherein:For the angle of arrival of node j coordinate system lower node k to node l,For node j coordinate system lower node k to section
The angle of arrival of point j,For the angle of arrival of node l coordinate system lower node k to node l, T indicates transposition；
Finally, being calculated by the following formula the local gravity center coordinate a of node i counterpart node j, node l and node kij、ailWith
aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node j, section
The directed area of the surrounded delta-shaped region of point i and node l, SjkiTo be surrounded delta by node j, node k and node i
The directed area in domain, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l；
4. at least there is a node in node j, node l and node k also has if node i has angle of arrival measurement capability
Angle of arrival measurement capability and assume the node be node j, then by following procedure calculate node i counterpart node j, node l with
And the local gravity center coordinate a of node kij、ailAnd aik:
Firstly, determining the mapping position vector q of node iiThe mapping position vector of=0 and node j For node i
Coordinate system lower node j to node i angle of arrival；
Then, pass through the mapping position vector q of solution following equation calculate node ll:
αji=δij-δji+π
Wherein:For the angle of arrival of node i coordinate system lower node l to node j,For node i coordinate system lower node l to section
The angle of arrival of point i,For the angle of arrival of node j coordinate system lower node l to node j, T indicates transposition, αjiFor node i seat
The rotation angle of mark system counterpart node j coordinate system, δijForArgument in node i coordinate system, δjiForIn node j coordinate
Argument in system,For the angle of arrival of node i coordinate system lower node j to node i,Extremely for node j coordinate system lower node i
The angle of arrival of node j；
In turn, pass through the mapping position vector q of solution following equation calculate node kk:
Wherein:For the angle of arrival of node i coordinate system lower node k to node j,For node i coordinate system lower node k to section
The angle of arrival of point i,For the angle of arrival of node j coordinate system lower node k to node j；
Finally, being calculated by the following formula the local gravity center coordinate a of node i counterpart node j, node l and node kij、ailWith
aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node j, section
The directed area of the surrounded delta-shaped region of point i and node l, SjkiTo be surrounded delta by node j, node k and node i
The directed area in domain, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l；
5. at least exist if node i has angle of arrival measurement capability, in node j, node l and node k two nodes have away from
From measurement capability and assume that the two nodes are respectively node j and node l, then passes through following procedure calculate node i counterpart node
J, the local gravity center coordinate a of node l and node kij、ailAnd aik:
Firstly, determining position coordinates of the node j under node i coordinate systemNode l is under node i coordinate system
Position coordinatesAnd position coordinates of the node i under node i coordinate systemWherein: dijExtremely for node j
The distance of node i, dilFor the distance of node l to node i,For the angle of arrival of node i coordinate system lower node j to node i,For the angle of arrival of node i coordinate system lower node l to node i；
Then, by solving position coordinates of the following equation calculate node k under node i coordinate system
Wherein:Angle of arrival for node i coordinate system lower node k to node i, djkFor node k to the distance of node j, dlkFor
The distance of node k to node l, T indicate transposition；
Finally, being calculated by the following formula the local gravity center coordinate a of node i counterpart node j, node l and node kij、ailWith
aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node j, section
The directed area of the surrounded delta-shaped region of point i and node l, SjkiTo be surrounded delta by node j, node k and node i
The directed area in domain, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l；
6. if node i have relative position measurement ability, be calculated by the following formula node i counterpart node j, node l and
The local gravity center coordinate a of node kij、ailAnd aik:
Wherein: SiklFor by the directed area of node i, the surrounded delta-shaped region of node k and node l, SjilFor by node j, section
The directed area of the surrounded delta-shaped region of point i and node l, SjkiTo be surrounded delta by node j, node k and node i
The directed area in domain, SjklFor by the directed area of node j, the surrounded delta-shaped region of node k and node l,
WithRespectively position coordinates under node i coordinate system of node j, node l, node k and node i and
2.3 combine according to 3 neighbours that step 2.2 traverses all about node j, obtain N number of about node i counterpart node j's
Local gravity center coordinate aij, and then the barycentric coodinates A of node i counterpart node j is calculated according to the following formulaij:
Wherein: the kind number that 3 neighbours that N is all about node j combine,To combine interior joint i in 3 neighbours of n
The local gravity center coordinate of counterpart node j；
(3) for node i, following iterative equation is based on according to the barycentric coodinates of its relatively each neighbor node and solves node i certainly
The position coordinates of body:
Wherein: pi(t) and pi(t+1) be respectively the t times iteration and the t+1 times iteration node i position coordinates, pjIt (t) is t
The position coordinates of secondary iteration node j, node j are that neighbor node, that is, node j of node i belongs to neighbor node set Ni, AijFor section
The barycentric coodinates of point i counterpart node j, γ is weight coefficient and γ ∈ (0,1), t are the number of iterations.
2. node positioning method according to claim 1, it is characterised in that: determine neighbor node set N in step (1)i's
Method are as follows: broadcast all nodes in network, if node i receives the broadcast data packet of node j, it is determined that node i and section
Point j neighbor node each other；All neighbor nodes of node i are formed into neighbor node set Ni。
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| A Barycentric Coordinate Based Distributed Localization Algorithm for Sensor Networks;Yingfei Diao et.al.;《IEEE》;20140716;摘要、正文第2、3节 |
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