CN104902565A - Distributed wireless sensor network three-dimensional multi-dimensional scaling (MDS) location method - Google Patents

Abstract

The invention relates to the field of wireless sensor networks, more particularly to a distributed wireless sensor network three-dimensional multi-dimensional scaling (MDS) location method. According to the method, firstly, a configured and optimized anchor node is used as a cluster head so as to cluster nodes in the whole network; then a relative coordinate graph of a cluster is established through MDS in each cluster; next, relative coordinates of all clusters are fused according to weight size among all clusters, so as to form a relative coordinate graph of the whole network; and finally, according to the relative coordinate graph of the whole network, an absolute coordinate graph of the whole network is obtained through a coordinate normalization method. The method has high data accuracy and good stability, furthermore, the method needs a small quantity of anchor nodes, thereby saving cost effectively.

Description

The three-dimensional MDS localization method of a kind of distributed wireless sensor network

Technical field

The present invention relates to wireless sensor network field, be specifically related to the three-dimensional MDS localization method of a kind of distributed wireless sensor network.

Background technology

Positional information is people or the natural quality of object in physical world, and the life activity of people is all relevant with position.In the various application of wireless sensor network, the location technology of node is one of extremely important support technology.Only know the particular location of sensor node, the data that node perceived obtains just have actual using value.

Multidimensional Scaling (Multi-Dimensional Scaling, MDS) is a kind of multi-variate statistical analysis technology in modern statistics, is widely used in the every field such as market survey, political realms, medical domain.The essence of MDS algorithm is that the diversity (similitude) of some target analysis information objects is measured, and is mapped to the space of low-dimensional from a hyperspace, draws each relative coordinate in lower dimensional space.The general principle of wireless sensor network MDS location technology is: using the jumping figure relation in network between destination node or distance relation as diversity (similitude) information between node, by MDS technology, these information are presented in the mode of two dimension or three-dimensional coordinate quantitatively, again by reducing the method for dimension, in lower dimensional space, calculate the coordinate of node, ensure that distance between these destination nodes is farthest close to the diversity (similitude) between original node.

Classical MDS algorithm needs to carry out when network full-mesh, is a kind of centralized localization method, is not suitable for large-scale network.

Summary of the invention

The present invention is directed to the deficiency of classical MDS location algorithm, propose the three-dimensional MDS localization method of a kind of distributed wireless sensor network.

The present invention is formed primarily of following step: 1, carry out sub-clustering based on anchor node to whole network; 2, the calculating of bunch interior nodes local coordinate; 3, bunch the fusion of local coordinate between; 4, overall relative coordinate is to the conversion of overall absolute coordinate.

The concrete steps of the inventive method are:

Step 1: sub-clustering is carried out to whole network based on anchor node

Anchor node in network sends broadcast packet in inundation mode to all unknown node, self nearest anchor node of each unknown node recording distance, and to add with this anchor node be in the sub-clustering of bunch head.

Step 2: the calculating of bunch interior nodes local coordinate

By nodes all in network based on after anchor node sub-clustering, calculate the local coordinate of single bunch of interior nodes.Specifically, first Dissimilarity matrix to be set up according to all internodal phase mutual edge distances in each bunch or hop count information.Then by classical MDS algorithm, the relative coordinate of all nodes in this bunch is obtained.

Step 3: the fusion of local coordinate between bunch

Two aspects of the key that between bunch, the fusion of local coordinate will be considered: the fusion sequence of coordinate system and three-dimensional coordinate blending algorithm.

(1) fusion sequence of coordinate system: coordinate fusion sequence is from two coordinate systems that weight is maximum, and weighted value here represents the quantity of common node in two coordinate systems; Two coordinates that following weight is maximum are found, until all coordinate systems merge become a coordinate system after each fusion.

(2) three-dimensional coordinate blending algorithm: three-dimensional coordinate blending algorithm adopts the Unitary coordinate method based on common node.If two need the three-dimensional system of coordinate of bunch A and bunch B merged to be respectively O _ax _ay _az _aand O _bx _by _bz _bif will realize the splicing of coordinate points in two coordinate systems, then the coordinate transform formula between two coordinate systems is such as formula shown in lower:

$\left[\begin{array}{c}{x}_A\\ y_A\\ z_A\\ 1\end{array}\right]=M_{\mathrm{BA}}\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]=\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]=\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]$

Can be expressed as:

$\left[\begin{array}{c}{x}_A\\ y_A\\ z_A\\ 1\end{array}\right]=\left[\begin{array}{cccc}{R}_1& R_2& R_3& T_x\\ R_4& R_5& R_6& T_y\\ R_7& R_8& R_9& T_z\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]$

In above formula, M _bAfor the nodal coordinate system O of bunch A _ax _ay _az _ato the node coordinate O of bunch B _bx _by _bz _bcoordinate conversion matrix, have 12 variablees, which provide a determination the spin matrix R between two coordinate systems and origin of coordinates O _ato O _btranslation variable T _x, T _y, T _z.Wherein, spin matrix $R=\left[\begin{array}{ccc}{R}_1& R_2& R_3\\ R_4& R_5& R_6\\ R_7& R_8& R_9\end{array}\right]$ The orthogonality condition that must meet is shown below:

$\left\{\begin{array}{c}{R}_1^2+R_4^2+R_7^2=1\\ R_2^2+R_5^2+R_8^2=1\\ R_3^2+R_6^2+R_9^2=1\\ R_1{R}_2+R_4{R}_5+R_7{R}_8=0\\ R_1{R}_3+R_4{R}_6+R_7{R}_9=0\\ R_2{R}_3+R_5{R}_6+R_8{R}_9=0\end{array}\right.$

Step 4: overall relative coordinate is to the conversion of overall absolute coordinate

After all unknown node and anchor node are all fused into an overall relative coordinate, anchor node is relied on to complete fusion as the common node of two coordinate systems, the overall absolute coordinate of anchor node refers to the coordinate obtained by GPS, using the common node of anchor node as Coordinate Conversion, convert overall relative coordinate to overall absolute coordinate by following formula.

$\left[\begin{array}{c}{x}_{\mathrm{Ai}}\\ y_{\mathrm{Ai}}\\ z_{\mathrm{Ai}}\\ 1\end{array}\right]=M_{\mathrm{BA}}\left[\begin{array}{c}{x}_{\mathrm{Bi}}\\ y_{\mathrm{Bi}}\\ z_{\mathrm{Bi}}\\ 1\end{array}\right]=R_{\mathrm{BA}}\left[\begin{array}{c}{x}_{\mathrm{Bi}}\\ y_{\mathrm{Bi}}\\ z_{\mathrm{Bi}}\end{array}\right]+T_{\mathrm{BA}},i=\mathrm{1,2},\·\·\·,n$

In above formula, coordinate system O _ax _ay _az _aand O _bx _by _bz _bbe respectively overall absolute coordinate system and overall relative coordinate system, R _bAfor spin matrix, T _bAfor overall absolute coordinate system origin of coordinates O _ato overall relative coordinate system origin of coordinates O _btranslation variable.

The invention has the beneficial effects as follows:

(1), precision of the present invention is high, good stability;

(2), the present invention is distributed, can be applicable to large-scale network node location;

(3), the present invention is low to anchor node quantitative requirement, effectively saved cost.

Accompanying drawing explanation

Fig. 1 is for implementing scene schematic diagram;

Fig. 2 is algorithm flow chart of the present invention;

Fig. 3 is Nodes Three-dimensional deployment diagram;

Position error comparison diagram during anchor node number change in Fig. 4 embodiment;

Position error comparison diagram during the change of network-in-dialing degree in Fig. 5 embodiment;

Time consumption comparison diagram during unknown node number change in Fig. 6 embodiment.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

The three-dimensional MDS location algorithm of this distributed wireless sensor network comprises following steps:

Step 1: sub-clustering is carried out to whole network based on anchor node

With reference to Fig. 1, the anchor node in network sends broadcast packet in inundation mode to all unknown node, self nearest anchor node of each unknown node recording distance, and to add with this anchor node be in the sub-clustering of bunch head.

Step 2: the calculating of bunch interior nodes local coordinate

By nodes all in network based on after anchor node sub-clustering, calculate the local coordinate of single bunch of interior nodes.Specifically, first Dissimilarity matrix to be set up according to internodal phase mutual edge distances all in each sub-clustering or hop count information.Then by classical MDS algorithm, the relative coordinate of all nodes in this bunch is obtained.

Step 3: the fusion of local coordinate between bunch

Two aspects of the key that between bunch, the fusion of local coordinate will be considered: the fusion sequence of coordinate system and three-dimensional coordinate blending algorithm.

(1) fusion sequence of coordinate system: coordinate fusion sequence is from two coordinate systems that weight is maximum from two coordinate systems that weight is maximum for coordinate fusion sequence, and weighted value here represents the quantity of common node in two coordinate systems.Two coordinates that following weight is maximum are found, until all coordinate systems merge become a coordinate system after each fusion.

(2) three-dimensional coordinate blending algorithm: three-dimensional coordinate blending algorithm adopts the Unitary coordinate method based on common node.If two need the three-dimensional system of coordinate of bunch A and bunch B merged to be respectively O _ax _ay _az _aand O _bx _by _bz _bif will realize the splicing of coordinate points in two coordinate systems, then the coordinate transform formula between two coordinate systems is as follows:

$\left[\begin{array}{c}{x}_A\\ y_A\\ z_A\\ 1\end{array}\right]=M_{\mathrm{BA}}\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]=\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]=\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]$

Can be expressed as:

$\left[\begin{array}{c}{x}_A\\ y_A\\ z_A\\ 1\end{array}\right]=\left[\begin{array}{cccc}{R}_1& R_2& R_3& T_x\\ R_4& R_5& R_6& T_y\\ R_7& R_8& R_9& T_z\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]$

In above formula, M _bAfor the nodal coordinate system O of bunch A _ax _ay _az _ato the node coordinate O of bunch B _bx _by _bz _bcoordinate conversion matrix, have 12 variablees, which provide a determination the spin matrix R between two coordinate systems and origin of coordinates O _ato O _btranslation variable T _x, T _y, T _z.Wherein, spin matrix $R=\left[\begin{array}{ccc}{R}_1& R_2& R_3\\ R_4& R_5& R_6\\ R_7& R_8& R_9\end{array}\right]$ The orthogonality condition that must meet is shown below:

$\left\{\begin{array}{c}{R}_1^2+R_4^2+R_7^2=1\\ R_2^2+R_5^2+R_8^2=1\\ R_3^2+R_6^2+R_9^2=1\\ R_1{R}_2+R_4{R}_5+R_7{R}_8=0\\ R_1{R}_3+R_4{R}_6+R_7{R}_9=0\\ R_2{R}_3+R_5{R}_6+R_8{R}_9=0\end{array}\right.$

Step 4: overall relative coordinate is to the conversion of overall absolute coordinate

After all unknown node and anchor node are all fused into an overall relative coordinate, beaconing nodes is relied on to complete fusion as the common node of two coordinate systems, the overall absolute coordinate of anchor node refers to the coordinate obtained by GPS, using the common node of anchor node as Coordinate Conversion, convert overall relative coordinate to overall absolute coordinate by following formula.

$\left[\begin{array}{c}{x}_{\mathrm{Ai}}\\ y_{\mathrm{Ai}}\\ z_{\mathrm{Ai}}\\ 1\end{array}\right]=M_{\mathrm{BA}}\left[\begin{array}{c}{x}_{\mathrm{Bi}}\\ y_{\mathrm{Bi}}\\ z_{\mathrm{Bi}}\\ 1\end{array}\right]=R_{\mathrm{BA}}\left[\begin{array}{c}{x}_{\mathrm{Bi}}\\ y_{\mathrm{Bi}}\\ z_{\mathrm{Bi}}\end{array}\right]+T_{\mathrm{BA}},i=\mathrm{1,2},\·\·\·,n$

In above formula, coordinate system O _ax _ay _az _aand O _bx _by _bz _bbe respectively overall absolute coordinate system and overall relative coordinate system, R _bAfor spin matrix, T _bAfor overall absolute coordinate system origin of coordinates O _ato overall relative coordinate system origin of coordinates O _btranslation variable.

The overall flow of each step is with reference to Fig. 2 above.

In order to assess availability of the present invention and validity, this algorithm is emulated.With reference to shown in Fig. 3, experiment condition be 300*300*300 cubic meter three-dimensional square region in the unknown node of random distribution some and the beaconing nodes through distributing rationally, between node, communication adopts energy attenuation propagation model.In order to simulate condition heterogeneous, the cube communication blind district of a 160*300*220 cubic meter is set in the middle of square region.

Fig. 4, Fig. 5, Fig. 6 are result analogous diagram.Fig. 4 shows the positioning precision emulation using three kinds of different location algorithms to obtain under different anchor node number condition.Fig. 5 shows the positioning precision that different location algorithm obtains in heterogeneous networks degree of communication situation and compares.Fig. 6 show unknown node quantity different time the different time comparison diagram that expends.Known with reference to the simulation result in above figure, D3D-MDS algorithm has higher positioning precision and lower time complexity compared to traditional MDS-MAP algorithm and DV-HOP algorithm.

Claims (1)

1. the three-dimensional MDS localization method of distributed wireless sensor network, is characterized in that the method comprises the following steps:

Step 1: sub-clustering is carried out to whole network based on anchor node

Anchor node in network sends broadcast packet in inundation mode to all unknown node, self nearest anchor node of each unknown node recording distance, and to add with this anchor node be in the sub-clustering of bunch head;

Step 2: the calculating of bunch interior nodes local coordinate

By nodes all in network based on after anchor node sub-clustering, calculate the local coordinate of single bunch of interior nodes; Specifically, first Dissimilarity matrix to be set up according to all internodal phase mutual edge distances in each bunch or hop count information; Then by classical MDS algorithm, the relative coordinate of all nodes in this bunch is obtained;

Step 3: the fusion of local coordinate between bunch

Two aspects of the key that between bunch, the fusion of local coordinate will be considered: the fusion sequence of coordinate system and three-dimensional coordinate blending algorithm;

(1) fusion sequence of coordinate system: coordinate fusion sequence is from two coordinate systems that weight is maximum, and weighted value here represents the quantity of common node in two coordinate systems; Two coordinates that following weight is maximum are found, until all coordinate systems merge become a coordinate system after each fusion;

(2) three-dimensional coordinate blending algorithm: three-dimensional coordinate blending algorithm adopts the Unitary coordinate method based on common node; If two need the three-dimensional system of coordinate of bunch A and bunch B merged to be respectively O _ax _ay _az _aand O _bx _by _bz _bif will realize the splicing of coordinate points in two coordinate systems, then the coordinate transform formula between two coordinate systems is such as formula shown in lower:

$\left[\begin{array}{c}{x}_A\\ y_A\\ z_A\\ 1\end{array}\right]=M_{\mathrm{BA}}\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]=\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]$

Can be expressed as:

$\left[\begin{array}{c}{x}_A\\ y_A\\ z_A\\ 1\end{array}\right]=\left[\begin{array}{cccc}{R}_1& R_2& R_3& T_x\\ R_4& R_5& R_6& T_y\\ R_7& R_8& R_9& T_z\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_B\\ y_B\\ z_B\\ 1\end{array}\right]$

In above formula, M _bAfor the nodal coordinate system O of bunch A _ax _ay _az _ato the node coordinate O of bunch B _bx _by _bz _bcoordinate conversion matrix, have 12 variablees, which provide a determination the spin matrix R between two coordinate systems and origin of coordinates O _ato O _btranslation variable T _x, T _y, T _z; Wherein, spin matrix $R=\left[\begin{array}{ccc}{R}_1& R_2& R_3\\ R_4& R_5& R_6\\ R_7& R_8& R_9\end{array}\right]$ The orthogonality condition that must meet is shown below:

$\left\{\begin{array}{c}{R}_1^2+R_4^2+R_7^2=1\\ R_2^2+R_5^2+R_8^2=1\\ R_3^2+R_6^2+R_9^2=1\\ R_1{R}_2+R_4{R}_5+R_7{R}_8=0\\ R_1{R}_3+R_4{R}_6+R_7{R}_9=0\\ R_2{R}_3+R_5{R}_6+R_8{R}_9=0\end{array}\right.$

Step 4: overall relative coordinate is to the conversion of overall absolute coordinate

After all unknown node and anchor node are all fused into an overall relative coordinate, anchor node is relied on to complete fusion as the common node of two coordinate systems, the overall absolute coordinate of anchor node refers to the coordinate obtained by GPS, using the common node of anchor node as Coordinate Conversion, convert overall relative coordinate to overall absolute coordinate by following formula;

$\left[\begin{array}{c}{x}_{\mathrm{Ai}}\\ y_{\mathrm{Ai}}\\ z_{\mathrm{Ai}}\\ 1\end{array}\right]=M_{\mathrm{BA}}\left[\begin{array}{c}{x}_{\mathrm{Bi}}\\ y_{\mathrm{Bi}}\\ z_{\mathrm{Bi}}\\ 1\end{array}\right]=R_{\mathrm{BA}}\left[\begin{array}{c}{x}_{\mathrm{Bi}}\\ y_{\mathrm{Bi}}\\ z_{\mathrm{Bi}}\end{array}\right]+T_{\mathrm{BA}},i=\mathrm{1,2},...,n$

In above formula, coordinate system O _ax _ay _az _aand O _bx _by _bz _bbe respectively overall absolute coordinate system and overall relative coordinate system, R _bAfor spin matrix, T _bAfor overall absolute coordinate system origin of coordinates O _ato overall relative coordinate system origin of coordinates O _btranslation variable.