CN104363654A - Wireless sensor network three-dimensional node positioning method based on tunneling method - Google Patents

Abstract

The invention provides a wireless sensor network three-dimensional node positioning method based on a tunneling method. The method includes the steps of 1, initializing a wireless sensor network, for each node, acquiring a distance between one-hop neighbor nodes, including the former node, and acquiring an anchor node coordinate matrix C; 2, calculating absolute coordinate matrixes Xi and Xj of the one-hop neighbor nodes; 3, calculating a target function Sigma(Xj) at the absolute coordinate matrix Xj; 4, if the former node is an unknown one, acquiring coordinates of the former node by means of a centroid algorithm to form an anchor node, and transmitting the coordinates to all one-hop neighbor nodes; 5, repeating the steps from 1 to 4 to finish positioning till all nodes turn into anchor nodes. The method has the advantages that the problem of the existing positioning methods that error accumulation occurs due to a computation process complicated by increase in dimensionality of a three-dimensional space can be solved, positioning error is small, and positioning precision is high.

Description

Based on the wireless sensor network tri-dimensional node positioning method of Tunneling method

Technical field

The present invention relates to wireless sensor network field, be specifically related to the wireless sensor network tri-dimensional node positioning method (being called for short TMDS method) based on Tunneling method.

Background technology

Wireless sensor network (Wireless Sensor Network, WSN) node locating technique is one of main support technology of wireless sensor network, the process of node locating is the node utilizing a few locations known, determines the position of unknown node according to certain algorithm or certain mechanism.Current two dimensional wireless sensor network nodes location technology has been tending towards ripe, but the research of aspect, regarding three-dimensional space nodes location is but relatively little.In actual applications, due to landform restriction (as aloft, ocean, forest, the complex-terrain such as mountain area) or environmental limitations (as being positioned at aerial differing heights or the different depth of ocean), wireless senser is made often spatially to become three-dimensional distribution, instead of plane distribution, so be only that to carry out two-dimensional localization to transducer on two dimensional surface be far from being enough, need Position Research to expand to three dimensions.Three dimensions is because the increase of dimension, and calculating process is complicated, there will be the accumulation of error, even if the error of node self poisoning is very little, and also can be clearly after three-dimensional computing.In addition, after wireless sensor network system completes self poisoning, also will in conjunction with the accurate location of node self coordinate realization to external object, therefore the location algorithm of node self needs higher positioning accuracy.In recent years, wireless sensor network three-dimensional nodes orientation problem has been had to thought and the solution of many novelties.What proposed by Shang etc. the earliest comes from the location technology that psychometry various dimensions calibrate (Multidimensional scaling, MDS), for node locating provides a kind of new thinking.MDS is a kind of data analysis technique, is obtained carrying out computing based on similarity matrix (distance matrix as being made up of Euclidean distance between node) by the point in hyperspace.MDS provides multiple method to solve orientation problem, if internodal distance is all known, then utilizes the method for singular value decomposition directly to obtain the coordinate of node; If internodal distance only has part known, then the method for repeated optimization can only be utilized to solve, and algorithm in this paper belongs to the latter.Compared with other location algorithm, the location algorithm based on MDS can make full use of all internodal related informations in network and locate multiple node simultaneously, also can obtain the relative position figure of node when not having anchor node; When needs absolute position, the anchor node number that budgetary estimate needs is minimum, does not also limit the deployment of anchor node; And MDS for solve node locating problem can when there is error in limited range information and distance value still can after obtain relatively accurate coordinate.The algorithm of more existing MDS at present, most is representational MDS-MAP, MDS-MAP (P) and MDS-MAP (P, R) algorithm.MDS-MAP is a kind of centralized location algorithm based on MDS, and first MDS-MAP algorithm utilizes multidimensional scaling technology to set up the local map of adjacent node in a series of three dimensions, then realizes the whole network location through Coordinate Conversion.MDS-MAP algorithm make use of the advantage that MDS itself has, avoid the error introduced with the approximate internodal actual distance of shortest path distance simultaneously, therefore its positioning precision improves, but maximum shortcoming needs centralized calculating, is not suitable for network large-scale, pockety.MDS-MAP (P) algorithm and MDS-MAP (P, R) algorithm is the distributed improvement of MDS-MAP algorithm, by whole network is divided into subnet, for each subnet independent operating MDS-MAP algorithm, obtain local coordinate system, then conversion and fusion calculation result realize the whole network and locate.The complexity that this conversion and fusion will increase algorithm greatly, and can transmission error be introduced in the process changed and merge, and cause the accumulation of error, and also network size is larger, and this accumulation of error is more obvious, and computation complexity also becomes geometry multiple to increase.

Summary of the invention

Technical problem to be solved by this invention is to provide the wireless sensor network tri-dimensional node positioning method based on Tunneling method, can solve in current localization method because the increase of three dimensions dimension causes calculating process complicated, there will be the problem of the accumulation of error, and position error is little, positioning precision is high.

For solving above-mentioned existing technical problem, the present invention adopts following scheme: based on the wireless sensor network tri-dimensional node positioning method of Tunneling method, comprise the following steps:

Step one: wireless sensor network initialization, for each node, obtain the distance comprised between its single-hop neighbor node, and judge which node be unknown node which be anchor node, obtain anchor node coordinates matrix C, when there is unknown node and anchor node number is more than or equal to 3, perform step 2; If there is no unknown node, algorithm stops; If there is unknown node but anchor node number is less than 3 time suspend computing, recover to perform step 2 until meet after anchor node number is more than or equal to 3;

Step 2: the absolute coordinate matrix calculating single-hop neighbor node:

ε＝ε _max,Z＝X ₀；

for(i＝1:i _max)

{ execution algorithm TMDS Tunneling method obtains unknown node coordinates matrix X _i

Z＝X _i；

Reduce the value of wucha_p;

}

Execution algorithm TMDS Tunneling method, obtains unknown node coordinates matrix X _j;

Step 3: calculate at X _jtarget function σ (the X at place _j), then judge whether inequality is below set up,

|σ(X _j)-σ(X)|<wucha_p

If set up, send to corresponding neighbor node calculating the coordinate figure obtained, otherwise directly abandon coordinate figure, wherein wucha_p is the error threshold preset;

Step 4: if self be unknown node and receive other node calculate coordinate figure out, so utilize centroid algorithm to obtain the coordinate of self, thus become an anchor node, then the coordinate figure of self is sent to all single-hop neighbor nodes;

Step 5: repeat step one to step 4, until all nodes are all anchor node, complete location.

As preferably, in described step one, the initialized concrete steps of radio sensing network are: first anchor node is to its each neighbor node broadcast own location information, and utilize classical tolerance MDS general principle to adopt the mode of Matrix Solving to solve to obtain anchor node coordinates matrix, classical tolerance MDS general principle is as described below:

Use matrix X _{n × 3}to represent in 3 dimension spaces the coordinate of n point, to any two points l, h, for the Euclidean distance between them square, available following formula represents:

${d_{\mathrm{lh}}}^2\left(X\right)={d_{\mathrm{lh}}}^2=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{(x_{\mathrm{la}}-x_{\mathrm{ha}})}^2=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}({x_{\mathrm{la}}}^2+{x_{\mathrm{ha}}}^2-{2x}_{\mathrm{la}}{x}_{\mathrm{ha}})---\left(1\right)$

To the point of 3 in three dimensions, corresponding matrix $X=\left[\begin{array}{ccc}{x}_{11}& x_{12}& x_{13}\\ x_{21}& x_{22}& x_{23}\\ x_{31}& x_{32}& x_{33}\end{array}\right],$ Use D ²(X) matrix of square distance is represented, then D ²(X) can be expressed as:

$\begin{array}{c}{D}^2\left(X\right)=\left[\begin{array}{ccc}0& {d_{12}}^2& {d_{13}}^2\\ {d_{21}}^2& 0& {d_{23}}^2\\ {d_{31}}^2& {d_{32}}^2& 0\end{array}\right]=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x_{1a}}^2& {x_{1a}}^2& {x_{1a}}^2\\ {x_{2a}}^2& {x_{2a}}^2& {x_{2a}}^2\\ {x_{3a}}^2& {x_{3a}}^2& {x_{3a}}^2\end{array}\right]+\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\\ {x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\\ {x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\end{array}\right]\\ -2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x}_{1a}{x}_{1a}& x_{1a}{x}_{2a}& x_{1a}{x}_{3a}\\ x_{2a}{x}_{1a}& x_{2a}{x}_{2a}& x_{2a}{x}_{3a}\\ x_{3a}{x}_{1a}& x_{3a}{x}_{2a}& x_{3a}{x}_{3a}\end{array}\right]\\ =\left[\begin{array}{c}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{1a}}^2\\ \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{2a}}^2\\ \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{3a}}^2\end{array}\right]\left[\begin{array}{ccc}1& 1& 1\end{array}\right]+\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\left[\begin{array}{ccc}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{1a}}^2& \begin{array}{}\end{array}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{2a}}^2\begin{array}{c}\end{array}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{3a}}^2& \end{array}\right]-2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_a{X_a}^T\\ ={\mathrm{Ce}}^T+{\mathrm{eC}}^T-2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_a{X_a}^T\end{array}---\left(2\right)$

Wherein X _abe a row of matrix X, to be element be C column vector, vectorial e to be element be all 1 column matrix.

As preferably, in described step 2, the Tunneling method concrete steps of execution algorithm TMDS are: the repeated optimization computational process utilizing Tunneling Method to be improved is:

Tunneling Method is used to target function σ (X), the function τ (X) that burrows of the MDS optimized algorithm based on Tunneling Method algorithm is defined as follows:

τ(X)＝σ(X)-σ(X ^*) (3)

Wherein X ^*for the local minizing point of σ (X),

In formula (3), τ (X) can do following distortion and obtain τ ₁(X)

τ(X)＝|σ(X)-σ(X ^*)|

τ(X)＝|σ(X)-σ(X ^*)|/P(X)

Wherein $P\left(X\right)={\left|\right|D\left(X^{*}\right)-D\left(X\right)\left|\right|}_w^2=\underset{i<j}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_{\mathrm{ij}}{(d_{\mathrm{ij}}\left(X^{*}\right)-d_{\mathrm{ij}}\left(X\right))}^2,$

τ(X)＝|σ(X)-σ(X ^*)| ^λ/P(X)

Wherein λ (the 0< λ <1) intensity parameters that is the function that burrows,

τ(X)＝|σ(X)-σ(X ^*)| ^λ(1+1/P(X))

τ(X)＝|σ(X)-σ(X ^*)| ^λ(1+ω/P(X))

Wherein ω (ω >1) Width Function that is the function that burrows,

${\mathrm{\&tau;}}_1\left(X\right)={|\mathrm{\&sigma;}\left(X\right)-\mathrm{\&sigma;}\left(X^{*}\right)|}^{\mathrm{\&lambda;}}{\mathrm{\&Pi;}}_{k=1}^r{(1+\mathrm{\&omega;}/P_k\left(X\right))}^{1/r}---\left(4\right)$

Wherein r is r alternative X,

Above-mentioned τ ₁(X) all conditions that function needs possess that burrows is met as follows:

A. τ ₁(X) do not change the zero point of being multiplied by after the X of a circulation, the function that burrows only also with τ ₁(X) identical;

B. by regulating the intensity parameters λ of limit can change the impact of function pole value on the function that burrows that burrow, due to level off to 1, to τ ₁(X) the configuration quantity that minimizes reduces gradually, can also avoid leveling off to horizontal line 0;

C. by selecting different limit width parameter ω, limit can be regulated to affect the size of its territory, and burrow function τ ₁(X) two ratios based on X function can be seen as, such τ ₁(X) minimize optimization problem and can regard a batch ticket problem as, for ease of mark, supposes P (X) >0, by τ ₁(X) be labeled as

${\mathrm{\&tau;}}_1\left(X\right)=\frac{M\left(X\right)}{P\left(X\right)}---\left(5\right)$

Wherein M (X)=N (X) (ω+P (X)), such τ ₁(X) can pass through N (X) (ω+P (X))/P (X) and N (X)=| σ (X)-σ (X ^*) | ^λobtain a limit determined, suppose to find a Y, following formula is set up

${\mathrm{\&tau;}}_1\left(X\right)=\frac{M\left(X\right)}{P\left(X\right)}\&le;\frac{M\left(Y\right)}{P\left(Y\right)}={\mathrm{\&tau;}}_1\left(Y\right)---\left(6\right)$

P (X) is multiplied by both sides, uses P (X) >0, then can obtain

$M\left(X\right)-\frac{M\left(Y\right)}{P\left(Y\right)}P\left(X\right)\&le;0---\left(7\right)$

Or F (q, X)=M (X)-qP (X)≤0 (8)

Like this, as long as an X can be found to make F (q, X) <0, then τ ₁(X) < τ ₁(Y) just set up, therefore, using iteration optimization algorithms to F (q, X), is namely realize τ ₁(X) minimize optimization;

have and τ ₁(X) identical zero point and stationary point, but more easily construct its Optimization Framework, so right enforcement minimizes interative computation, and for each Optimization Steps and majorized function, only provide the function about X and step, calculation step is as follows:

1) as formula (5), (6), (7), (8), the mode of batch ticket is used to obtain F (q, X);

2) optimize F (q, X), be namely

$M\left(X\right)=\sqrt{N\left(X\right)}\sqrt{\left(\underset{k=1}{\overset{r}{\mathrm{\&Pi;}}}{(P_k\left(X\right)+\mathrm{\&omega;})}^{\frac{1}{r}}\right)}---\left(9\right)$ With $-\sqrt{\left(\underset{k=1}{\overset{r}{\mathrm{\&Pi;}}}{P}_k{\left(X\right)}^{\frac{1}{r}}\right)}---\left(10\right)$

3) with the product of two functions, namely N (X) and iteration optimization is carried out to M (X):

A. to N (X)=| σ (X)-σ (X ^*) | ^λbe optimized, by a nonnegative function | σ (X)-σ (X ^*) | the optimization of root realize;

B. there is σ (X) > σ (X in imagination ^*), then | σ (X)-σ (X ^*) |=σ (X)-σ (X ^*), and all verify with the more new data of this imagination to interative computation each time.If this is envisioned for negative, i.e. σ (X)≤σ (X ^*), then the step that burrows stops, because found an X ^*, reach the object optimizing computing;

4) right be optimized, by P _k(X) output is optimized to realize:

A. according to formula (1), (2), (3), (4), d is used _ij(X _k) replace δ _ij, be namely to P _k(X) be optimized;

5) right be optimized, by function P _k(X) and the optimization of output valve realizes:

A. according to formula (1), (2), (3), (4), d is used _ij(X _k) replace δ _ij, be namely to P _k(X) be optimized;

B. according to Cauchy-Schwarz inequality, right being optimized, is namely to d _ijand-d (X) _ij(X) optimization;

C. use double optimization method to d _ij(X) being optimized, is namely right be optimized, described double optimization method is exactly the point with some distribution disorders of conic fitting;

D. according to Holder inequality pair optimization, be namely to the optimization of formula (1) based on the quadratic function of X;

E. according to the p-d of Holder inequality _ij(X) namely optimization be to the optimization of formula (1) based on the linear function of X.

As preferably, from as unknown node in described step 4, receive the position coordinates that other node sends over, the computational process utilizing centroid algorithm to obtain self coordinate is:

Suppose that 3 anchor node coordinates are respectively (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x ₃, y ₃, z ₃), unknown node (x _j, y _j, z _j) be respectively d to the Euclidean distance of three anchor nodes ₁, d ₂, d ₃, then unknown node coordinate is:

$x_j=\frac{\frac{x_1}{d_1+d_2}+\frac{x_2}{d_2+d_3}+\frac{x_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}$

$y_j=\frac{\frac{y_1}{d_1+d_2}+\frac{y_2}{d_2+d_3}+\frac{y_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}$

$z_j=\frac{\frac{z_1}{d_1+d_2}+\frac{z_2}{d_2+d_3}+\frac{z_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}.$

Beneficial effect:

The present invention adopts technique scheme to provide wireless sensor network tri-dimensional node positioning method based on Tunneling method, can solve in current localization method because the increase of three dimensions dimension causes calculating process complicated, there will be the problem of the accumulation of error, and position error is little, positioning precision is high.

Accompanying drawing explanation

Fig. 1 is unknown node and anchor node random distribution figure in the present invention;

Fig. 2 is the impact of node communication radius on performance of the present invention;

Fig. 3 is the impact of network node on performance of the present invention;

Fig. 4 is the impact of anchor node ratio on performance of the present invention.

Embodiment

Based on the wireless sensor network tri-dimensional node positioning method of Tunneling method, comprise the following steps:

Step one: wireless sensor network initialization, for each node, obtain the distance comprised between its single-hop neighbor node, and judge which node be unknown node which be anchor node, obtain anchor node coordinates matrix C, when there is unknown node and anchor node number is more than or equal to 3, perform step 2; If there is no unknown node, algorithm stops; If there is unknown node but anchor node number is less than 3 time suspend computing, recover to perform step 2 until meet after anchor node number is more than or equal to 3;

Step 2: the absolute coordinate matrix calculating single-hop neighbor node:

ε＝ε _max,Z＝X ₀；

for(i＝1:i _max)

{ execution algorithm TMDS Tunneling method obtains unknown node coordinates matrix X _i

Z＝X _i；

Reduce the value of wucha_p;

}

Execution algorithm TMDS Tunneling method, obtains unknown node coordinates matrix X _j;

Step 3: calculate at X _jtarget function σ (the X at place _j), then judge whether inequality is below set up,

|σ(X _j)-σ(X)|<wucha_p

If set up, send to corresponding neighbor node calculating the coordinate figure obtained, otherwise directly abandon coordinate figure, wherein wucha_p is the error threshold preset;

Step 4: if self be unknown node and receive other node calculate coordinate figure out, so utilize centroid algorithm to obtain the coordinate of self, thus become an anchor node, then the coordinate figure of self is sent to all single-hop neighbor nodes;

Step 5: repeat step one to step 4, until all nodes are all anchor node, complete location.In described step one, the initialized concrete steps of radio sensing network are: first anchor node is to its each neighbor node broadcast own location information, and utilize classical tolerance MDS general principle to adopt the mode of Matrix Solving to solve to obtain anchor node coordinates matrix, classical tolerance MDS general principle is as described below:

Use matrix X _{n × 3}to represent in 3 dimension spaces the coordinate of n point, to any two points l, h, for the Euclidean distance between them square, available following formula represents:

${d_{\mathrm{lh}}}^2\left(X\right)={d_{\mathrm{lh}}}^2=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{(x_{\mathrm{la}}-x_{\mathrm{ha}})}^2=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}({x_{\mathrm{la}}}^2+{x_{\mathrm{ha}}}^2-{2x}_{\mathrm{la}}{x}_{\mathrm{ha}})---\left(1\right)$

To the point of 3 in three dimensions, corresponding matrix $X=\left[\begin{array}{ccc}{x}_{11}& x_{12}& x_{13}\\ x_{21}& x_{22}& x_{23}\\ x_{31}& x_{32}& x_{33}\end{array}\right],$ Use D ²(X) matrix of square distance is represented, then D ²(X) can be expressed as:

$\begin{array}{c}{D}^2\left(X\right)=\left[\begin{array}{ccc}0& {d_{12}}^2& {d_{13}}^2\\ {d_{21}}^2& 0& {d_{23}}^2\\ {d_{31}}^2& {d_{32}}^2& 0\end{array}\right]=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x_{1a}}^2& {x_{1a}}^2& {x_{1a}}^2\\ {x_{2a}}^2& {x_{2a}}^2& {x_{2a}}^2\\ {x_{3a}}^2& {x_{3a}}^2& {x_{3a}}^2\end{array}\right]+\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\\ {x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\\ {x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\end{array}\right]\\ -2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x}_{1a}{x}_{1a}& x_{1a}{x}_{2a}& x_{1a}{x}_{3a}\\ x_{2a}{x}_{1a}& x_{2a}{x}_{2a}& x_{2a}{x}_{3a}\\ x_{3a}{x}_{1a}& x_{3a}{x}_{2a}& x_{3a}{x}_{3a}\end{array}\right]\\ =\left[\begin{array}{c}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{1a}}^2\\ \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{2a}}^2\\ \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{3a}}^2\end{array}\right]\left[\begin{array}{ccc}1& 1& 1\end{array}\right]+\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]\left[\begin{array}{ccc}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{1a}}^2& \begin{array}{}\end{array}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{2a}}^2\begin{array}{}\end{array}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{3a}}^2& \end{array}\right]-2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_a{X_a}^T\\ ={\mathrm{Ce}}^T+{\mathrm{eC}}^T-2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_a{X_a}^T\end{array}---\left(2\right)$

Wherein X _abe a row of matrix X, to be element be C column vector, vectorial e to be element be all 1 column matrix.

In described step 2, the Tunneling method concrete steps of execution algorithm TMDS are: the repeated optimization computational process utilizing TunnelingMethod to be improved is:

Tunneling Method is used to target function σ (X), the function τ (X) that burrows of the MDS optimized algorithm based on Tunneling Method algorithm is defined as follows:

τ(X)＝σ(X)-σ(X ^*) (3)

Wherein X ^*for the local minizing point of σ (X),

In formula (3), τ (X) can do following distortion and obtain τ ₁(X)

τ(X)＝|σ(X)-σ(X ^*)|

τ(X)＝|σ(X)-σ(X ^*)|/P(X)

Wherein $P\left(X\right)={\left|\right|D\left(X^{*}\right)-D\left(X\right)\left|\right|}_w^2=\underset{i<j}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_{\mathrm{ij}}{(d_{\mathrm{ij}}\left(X^{*}\right)-d_{\mathrm{ij}}\left(X\right))}^2,$

τ(X)＝|σ(X)-σ(X ^*)| ^λ/P(X)

Wherein λ (the 0< λ <1) intensity parameters that is the function that burrows,

τ(X)＝|σ(X)-σ(X ^*)| ^λ(1+1/P(X))

τ(X)＝|σ(X)-σ(X ^*)| ^λ(1+ω/P(X))

Wherein ω (ω >1) Width Function that is the function that burrows,

${\mathrm{\&tau;}}_1\left(X\right)={|\mathrm{\&sigma;}\left(X\right)-\mathrm{\&sigma;}\left(X^{*}\right)|}^{\mathrm{\&lambda;}}{\mathrm{\&Pi;}}_{k=1}^r{(1+\mathrm{\&omega;}/P_k\left(X\right))}^{1/r}---\left(4\right)$

Wherein r is r alternative X,

Above-mentioned τ ₁(X) all conditions that function needs possess that burrows is met as follows:

A. τ ₁(X) do not change the zero point of being multiplied by after the X of a circulation, the function that burrows only also with τ ₁(X) identical;

B. by regulating the intensity parameters λ of limit can change the impact of function pole value on the function that burrows that burrow, due to level off to 1, to τ ₁(X) the configuration quantity that minimizes reduces gradually, can also avoid leveling off to horizontal line 0;

C. by selecting different limit width parameter ω, limit can be regulated to affect the size of its territory, and burrow function τ ₁(X) two ratios based on X function can be seen as, such τ ₁(X) minimize optimization problem and can regard a batch ticket problem as, for ease of mark, supposes P (X) >0, by τ ₁(X) be labeled as

${\mathrm{\&tau;}}_1\left(X\right)=\frac{M\left(X\right)}{P\left(X\right)}---\left(5\right)$

Wherein M (X)=N (X) (ω+P (X)), such τ ₁(X) can pass through N (X) (ω+P (X))/P (X) and N (X)=| σ (X)-σ (X ^*) | ^λobtain a limit determined, suppose to find a Y, following formula is set up

${\mathrm{\&tau;}}_1\left(X\right)=\frac{M\left(X\right)}{P\left(X\right)}\&le;\frac{M\left(Y\right)}{P\left(Y\right)}={\mathrm{\&tau;}}_1\left(Y\right)---\left(6\right)$

P (X) is multiplied by both sides, uses P (X) >0, then can obtain

$M\left(X\right)-\frac{M\left(Y\right)}{P\left(Y\right)}P\left(X\right)\&le;0---\left(7\right)$

Or F (q, X)=M (X)-qP (X)≤0 (8)

Like this, as long as an X can be found to make F (q, X) <0, then τ ₁(X) < τ ₁(Y) just set up, therefore, using iteration optimization algorithms to F (q, X), is namely realize τ ₁(X) minimize optimization;

have and τ ₁(X) identical zero point and stationary point, but more easily construct its Optimization Framework, so right enforcement minimizes interative computation, and for each Optimization Steps and majorized function, only provide the function about X and step, calculation step is as follows:

1) as formula (5), (6), (7), (8), the mode of batch ticket is used to obtain F (q, X);

2) optimize F (q, X), be namely

$M\left(X\right)=\sqrt{N\left(X\right)}\sqrt{\left(\underset{k=1}{\overset{r}{\mathrm{\&Pi;}}}{(P_k\left(X\right)+\mathrm{\&omega;})}^{\frac{1}{r}}\right)}---\left(9\right)$ With $-\sqrt{\left(\underset{k=1}{\overset{r}{\mathrm{\&Pi;}}}{P}_k{\left(X\right)}^{\frac{1}{r}}\right)}---\left(10\right)$

3) with the product of two functions, namely N (X) and iteration optimization is carried out to M (X):

A. to N (X)=| σ (X)-σ (X ^*) | ^λbe optimized, by a nonnegative function | σ (X)-σ (X ^*) | the optimization of root realize;

B. there is σ (X) > σ (X in imagination ^*), then | σ (X)-σ (X ^*) |=σ (X)-σ (X ^*), and all verify with the more new data of this imagination to interative computation each time.If this is envisioned for negative, i.e. σ (X)≤σ (X ^*), then the step that burrows stops, because found an X ^*, reach the object optimizing computing;

4) right be optimized, by P _k(X) output is optimized to realize:

A. according to formula (1), (2), (3), (4), d is used _ij(X _k) replace δ _ij, be namely to P _k(X) be optimized;

5) right be optimized, by function P _k(X) and the optimization of output valve realizes:

A. according to formula (1), (2), (3), (4), d is used _ij(X _k) replace δ _ij, be namely to P _k(X) be optimized;

B. according to Cauchy-Schwarz inequality, right being optimized, is namely to d _ijand-d (X) _ij(X) optimization;

C. use double optimization method to d _ij(X) being optimized, is namely right be optimized, described double optimization method is exactly the point with some distribution disorders of conic fitting;

D. according to Holder inequality pair optimization, be namely to the optimization of formula (1) based on the quadratic function of X;

E. according to the p-d of Holder inequality _ij(X) namely optimization be to the optimization of formula (1) based on the linear function of X.

Certainly as unknown node in described step 4, receive the position coordinates that other node sends over, the computational process utilizing centroid algorithm to obtain self coordinate is:

Suppose that 3 anchor node coordinates are respectively (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x ₃, y ₃, z ₃), unknown node (x _j, y _j, z _j) be respectively d to the Euclidean distance of three anchor nodes ₁, d ₂, d ₃, then unknown node coordinate is:

$x_j=\frac{\frac{x_1}{d_1+d_2}+\frac{x_2}{d_2+d_3}+\frac{x_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}$

$y_j=\frac{\frac{y_1}{d_1+d_2}+\frac{y_2}{d_2+d_3}+\frac{y_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}$

$z_j=\frac{\frac{z_1}{d_1+d_2}+\frac{z_2}{d_2+d_3}+\frac{z_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}.$

For verifying validity of the present invention, Matlab7.8.0 (R2009a) (64) are adopted to realize emulation testing experiment to the present invention's (being called for short TMDS method) and MDS algorithm.Tunneling method can be translated as the method for burrowing.TMDS method carries out performance evaluation from node communication radius, number of network node, anchor node ratio tripartite in the face of TMDS algorithm.Experiment simulation environment is as described below: the square geometrical model adopting 10m*10m*10m, carries out the layout of node location, as shown in Figure 1 in this model space.It is as follows that common simulated environment is set: during same interative computation rule, node communication radius is identical; Repeated optimization algorithm iteration number of times is iterative_time=60 time, and interative computation error threshold is absolute_error_value=0.0001; Node locating error threshold wucha_p=0.05m, and definition is as unknown node position error error≤wucha_p, this location node is as the criterion true location node.

Table 1, table 2 represent that MDS algorithm and TMDS method are run 10 times continuously under identical simulated environment respectively, the result data of unknown node average localization error, accurately location node number, node accurately location rate and program runtime.Identical simulated environment arranges as follows: anchor node number M=8, is distributed in 8 vertex positions of square model respectively; All nodes have same communication radius R=8.

Table 1 MDS algorithm

Table 2 TMDS method

Can draw from the data of table 1, table 2, from the accuracy of algorithm location, TMDS algorithm 10 continuous operations, have the accurate location that can realize all unknown node for 9 times, and accurate location rate is 1; For once node accurately locates number is 49, and accurate location rate is 0.98, is namely the accurate location that TMDS algorithm can realize node substantially.Compare MDS algorithm, 10 continuous operations have the accurate location realizing 50 nodes for 4 times, and accurately location rate is lower wherein 2 minor nodes, is respectively: 0.08 and 0.1, are namely the accurate location not realizing node for this twice.From the running time of algorithm, generally speaking TMDS algorithm and MDS algorithm can complete algorithm computing within a short period of time.The MDS algorithm time is more stable, substantially between 13s ~ 14s, completes algorithm computing, and TMDS algorithm is because will carry out the interative computation of repeated optimization, so the time is slightly long; Again because 50 distributions of unknown node in the model space have randomness, choosing of repeated optimization algorithm iteration computing first local minimum has randomness, searching global optimum needs the number of times of interative computation different, so the positioning time completing whole node can be variant.In sum, the local minimum problem applying to Tunneling Method solve repeated optimization algorithm achieves good effect on wireless sensor node location.

Figure 2 shows that the impact of node communication radius on TMDS algorithm performance, now simulated environment is as follows: unknown node number N=50, is randomly distributed in the square model space of 10m*10m*10m; Anchor node number M=8, is distributed in 8 vertex positions of square model respectively; Analyzing communication node radius is carried out on the impact of algorithm performance by concept transfer communication radius size.From Fig. 2 (a), curve can draw, along with the increase of node communication radius, unknown node accurately locates number to be increased gradually, and the accurate localization ratio of node increases gradually.Wherein when communication radius R is increased to 8m, the number of accurate location node reaches 50, and continues to increase node communication radius, and unknown node accurately location rate remains 1 always.From Fig. 2 (b), curve can draw, along with the increase of node communication radius, the mean error of accurate location node location reduces gradually.Wherein when communication radius R is increased to from 8m from 4m, mean error downward trend is very fast; Continue to increase communication radius R, in 8m to the 12m stage, error change tends towards stability.When communication radius is less, network-in-dialing degree is low, can with the unknown node decreased number of node communication, during TMDS test, the node communication radius less (during for 8m) needed can reach higher node accurately location rate and lower node locating error, along with the increase of node communication radius, locating effect is stablized.

When Figure 3 shows that node communication radius is R=8, network node is on the impact of TMDS algorithm performance.According to the analysis to Fig. 2, when the communication radius R of node is 8m, be easier to the impact of other factors on algorithm performance of analysis node, so when analyzing anchor node ratio and affecting algorithm performance, arranging common simulated environment is: anchor node number M=8, is distributed in 8 vertex positions of square model respectively; Node has same communication radius, is R=8m; Change anchor node ratio by the number changing unknown node, analyze network node to the impact of algorithm performance.Curve from Fig. 3 (a) and Fig. 3 (b) can draw, along with number of network node increases to 78 from 38, namely unknown node number is 30 increase to 70, and the accurate location rate of unknown node is 1 always.When number of network node be 83 be namely unknown node number is 75, accurate location rate starts to decline.Namely in the environment that TMDS algorithm is less at anchor node number, number of network node is more, unknown node accurately location rate can continue to remain 1, demonstrate TMDS algorithm to have and accurately can locate unknown node in the few environment of anchor node number, and locating effect is stablized.

Figure 4 shows that the impact of anchor node ratio on TMDS algorithm performance, now simulated environment is as follows: unknown node number N=100, is randomly distributed in the model space; Anchor node wherein 8 are distributed in 8 vertex positions of square model respectively, and all the other anchor nodes are randomly distributed in the model space; All nodes have same communication radius, are R=8; By changing the quantity of anchor node, analyze anchor node ratio to the impact of algorithm performance.Can draw from the curve Fig. 4 (a), along with the increase of anchor node ratio, unknown node accurately locates quantity to be increased.When wherein anchor node ratio is 0.1, it is 40 that unknown node accurately locates number, anchor node ratio is that accurately to locate number be 100 to 0.15 unknown node when increasing to 0.5 always, and when illustrating that anchor node ratio is more than or equal to 0.15, TMDS algorithm accurately can be located all unknown node.Can draw from the curve Fig. 4 (b), along with the increase of anchor node ratio, unknown node position error reduces gradually, and wherein anchor node ratio was 0.1 to 0.16 stage, and unknown node average localization error declines rapidly.Increased to for 0.5 stage in anchor node ratio 0.16, average localization error has comparatively minor swing, but all in the accurate position error threshold range of unknown node, can realize the accurate location of node, and the accurate locating effect of unknown node is stablized.

The advantage of TMDS method:

(1) TMDS method is a kind of wireless sensor network distribution node location algorithm based on anchor node multidimensional scaling technology, this location algorithm is the absolute fix utilizing anchor node position and internodal Euclidean distance information directly to realize unknown node, do not need Coordinate Conversion and network integration computing, avoid the error accumulation of this process;

(2) core of TMDS method is a kind of repeated optimization method based on anchor node newly, the method derives on the basis of STRESS algorithm, and utilize the method (Tunneling Method) that burrows to solve repeated optimization method local minimum problem, improve the accuracy of optimum results;

(3) TMDS method is a kind of innovatory algorithm based on MDS, utilization be internodal otherness, result of calculation is stablized, and node locating effect also has higher stability.

Anchor node calibration MDS technology is utilized directly to obtain the absolute coordinate of unknown node, thus do not need complicated Local coordinate system to merge and relative coordinate to the conversion of absolute coordinate, take into account local minimum problem in MDS optimization simultaneously, while can degree of precision being reached, also there is higher stability.The method of burrowing in the method is deterministic type Global Optimization Method, global minimum can be searched out in minimization problem search procedure, jump out local minizing point, obtain the minimum point that a functional value is less, repeat this process and try to achieve globally optimal solution, thus improve the convergence rate of method, enhancing the ability of its global optimizing, in 3-D wireless sensor network node location, providing a kind of brand-new method and thinking for solving repeated optimization algorithm.Experimental result shows repeated optimization algorithm to be applied in 3-D wireless sensor network node location algorithm in conjunction with global optimization theory, improve the number that unknown node is accurately located, reduce unknown node position error, and ensure that node is randomly dispersed in the stability of the accurate locating effect of environment interior joint of 3-D wireless sensor network.

Specific embodiment described herein is only to the explanation for example of the present invention's spirit.Those skilled in the art can make various amendment or supplement or adopt similar mode to substitute to described specific embodiment, but can't depart from spirit of the present invention or surmount the scope that appended claims defines.

Claims (4)

1., based on the wireless sensor network tri-dimensional node positioning method of Tunneling method, it is characterized in that:

Comprise the following steps:

Step one: wireless sensor network initialization, for each node, obtain the distance comprised between its single-hop neighbor node, and judge which node be unknown node which be anchor node, obtain anchor node coordinates matrix C, when there is unknown node and anchor node number is more than or equal to 3, perform step 2; If there is no unknown node, algorithm stops; If there is unknown node but anchor node number is less than 3 time suspend computing, recover to perform step 2 until meet after anchor node number is more than or equal to 3;

Step 2: the absolute coordinate matrix calculating single-hop neighbor node:

ε＝ε _max,Z＝X ₀；

for(i＝1:i _max)

{ execution algorithm TMDSTunneling method obtains unknown node coordinates matrix X _iz=X _i;

Reduce the value of wucha_p;

}

Execution algorithm TMDSTunneling method, obtains unknown node coordinates matrix X _j;

Step 3: calculate at X _jtarget function σ (the X at place _j), then judge whether inequality is below set up,

|σ(X _j)-σ(X)|<wucha_p

If set up, send to corresponding neighbor node calculating the coordinate figure obtained, no

Then directly abandon coordinate figure, wherein wucha_p is the error threshold preset;

Step 4: if self be unknown node and receive other node calculate coordinate figure out, so utilize centroid algorithm to obtain the coordinate of self, thus become an anchor node, then the coordinate figure of self is sent to all single-hop neighbor nodes;

Step 5: repeat step one to step 4, until all nodes are all anchor node, complete location.

2. the wireless sensor network tri-dimensional node positioning method based on Tunneling method according to claim 1, it is characterized in that: in described step one, the initialized concrete steps of radio sensing network are: first anchor node is to its each neighbor node broadcast own location information, and utilize classical tolerance MDS general principle to adopt the mode of Matrix Solving to solve to obtain anchor node coordinates matrix, classical tolerance MDS general principle is as described below:

Use matrix X _{n × 3}to represent in 3 dimension spaces the coordinate of n point, to any two points l, h, for the Euclidean distance between them square, available following formula represents:

${d_{\mathrm{lh}}}^2\left(X\right)={d_{\mathrm{lh}}}^2=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{(x_{\mathrm{la}}-x_{\mathrm{ha}})}^2=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}({x_{\mathrm{la}}}^2+{x_{\mathrm{ha}}}^2-2x_{\mathrm{la}}{x}_{\mathrm{ha}})---\left(1\right)$

To the point of 3 in three dimensions, corresponding matrix $X=\left[\begin{array}{ccc}{x}_{11}& x_{12}& x_{13}\\ x_{21}& x_{22}& x_{23}\\ x_{31}& x_{32}& x_{33}\end{array}\right],$ Use D ²(X) matrix of square distance is represented, then D ²(X) can be expressed as:

$\begin{array}{c}{D}^2\left(X\right)=\left[\begin{array}{ccc}0& {d_{12}}^2& {d_{13}}^2\\ {d_{21}}^2& 0& {d_{23}}^2\\ {d_{31}}^2& {d_{32}}^2& 0\end{array}\right]=\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x_{1a}}^2& {x_{1a}}^2& {x_{1a}}^2\\ {x_{2a}}^2& {x_{2a}}^2& {x_{2a}}^2\\ {x_{3a}}^2& {x_{3a}}^2& {x_{3a}}^2\end{array}\right]+\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\\ {x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\\ {x_{1a}}^2& {x_{2a}}^2& {x_{3a}}^2\end{array}\right]\\ -2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}\left[\begin{array}{ccc}{x}_{1a}{x}_{1a}& x_{1a}{x}_{2a}& x_{1a}{x}_{3a}\\ x_{2a}{x}_{1a}& x_{2a}{x}_{2a}& x_{2a}{x}_{3a}\\ x_{3a}{x}_{1a}& x_{3a}{x}_{2a}& x_{3a}{x}_{3a}\end{array}\right]\\ =\left[\begin{array}{c}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{1a}}^2\\ \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{2a}}^2\\ \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{3a}}^2\end{array}\right]\left[\begin{array}{ccc}1& 1& 1\end{array}\right]\left[\begin{array}{ccc}\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{1a}}^2& \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{2a}}^2& \underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{x_{3a}}^2\end{array}\right]-2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_a{X_a}^T\\ ={\mathrm{Ce}}^T+e{C}^T-2\underset{a=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_a{X_a}^T\end{array}---\left(2\right)$

Wherein X _abe a row of matrix X, to be element be C column vector, vectorial e to be element be all 1 column matrix.

3. the wireless sensor network tri-dimensional node positioning method based on Tunneling method according to claim 2, is characterized in that: in described step 2, the Tunneling method concrete steps of execution algorithm TMDS are: the repeated optimization computational process utilizing Tunneling Method to be improved is:

Tunneling Method is used to target function σ (X), the function τ (X) that burrows of the MDS optimized algorithm based on Tunneling Method algorithm is defined as follows:

τ(X)＝σ(X)-σ(X ^*) (3)

Wherein X ^*for the local minizing point of σ (X),

In formula (3), τ (X) can do following distortion and obtain τ ₁(X)

τ(X)＝|σ(X)-σ(X ^*)|

τ(X)＝|σ(X)-σ(X ^*)|/P(X)

Wherein $P\left(X\right)={\left|\right|D\left(X^{*}\right)-D\left(X\right)\left|\right|}_w^2=\underset{i<j}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_{\mathrm{ij}}{(d_{\mathrm{ij}}\left(X^{*}\right)-d_{\mathrm{ij}}\left(X\right))}^2,$

τ(X)＝|σ(X)-σ(X ^*)| ^λ/P(X)

Wherein λ (the 0< λ <1) intensity parameters that is the function that burrows,

τ(X)＝|σ(X)-σ(X ^*)| ^λ(1+1/P(X))

τ(X)＝|σ(X)-σ(X ^*)| ^λ(1+ω/P(X))

Wherein ω (ω >1) Width Function that is the function that burrows,

${\mathrm{\&tau;}}_1\left(X\right)={|\mathrm{\&sigma;}\left(X\right)-\mathrm{\&sigma;}\left(X^{*}\right)|}^{\mathrm{\&lambda;}}{\mathrm{\&Pi;}}_{k=1}^r{(1+\mathrm{\&omega;}/P_k\left(X\right))}^{1/r}---\left(4\right)$

Wherein r is r alternative X,

Above-mentioned τ ₁(X) all conditions that function needs possess that burrows is met as follows:

A. τ ₁(X) do not change the zero point of being multiplied by after the X of a circulation, the function that burrows only also with τ ₁(X) identical;

B. by regulating the intensity parameters λ of limit can change the impact of function pole value on the function that burrows that burrow, due to level off to 1, to τ ₁(X) the configuration quantity that minimizes reduces gradually, can also avoid leveling off to horizontal line 0;

C. by selecting different limit width parameter ω, limit can be regulated to affect the size of its territory, and burrow function τ ₁(X) two ratios based on X function can be seen as, such τ ₁(X) minimize optimization problem and can regard a batch ticket problem as, for ease of mark, supposes P (X) >0, by τ ₁(X) be labeled as

${\mathrm{\&tau;}}_1\left(X\right)=\frac{M\left(X\right)}{P\left(X\right)}---\left(5\right)$

Wherein M (X)=N (X) (ω+P (X)), such τ ₁(X) can pass through N (X) (ω+P (X))/P (X) and N (X)=| σ (X)-σ (X ^*) | ^λobtain a limit determined, suppose to find a Y, following formula is set up

${\mathrm{\&tau;}}_1\left(X\right)=\frac{M\left(X\right)}{P\left(X\right)}\&le;\frac{M\left(Y\right)}{P\left(Y\right)}={\mathrm{\&tau;}}_1\left(Y\right)---\left(6\right)$

P (X) is multiplied by both sides, uses P (X) >0, then can obtain

$M\left(X\right)-\frac{M\left(Y\right)}{P\left(Y\right)}P\left(X\right)\&le;0---\left(7\right)$

Or F (q, X)=M (X)-qP (X)≤0 (8)

Like this, as long as an X can be found to make F (q, X) <0, then τ ₁(X) < τ ₁(Y) just set up, therefore, using iteration optimization algorithms to F (q, X), is namely realize τ ₁(X) minimize optimization;

have and τ ₁(X) identical zero point and stationary point, but more easily construct its Optimization Framework, so right enforcement minimizes interative computation, and for each Optimization Steps and majorized function, only provide the function about X and step, calculation step is as follows:

1) as formula (5), (6), (7), (8), the mode of batch ticket is used to obtain F (q, X);

2) optimize F (q, X), be namely

$M\left(X\right)=\sqrt{N\left(X\right)}\sqrt{\left(\underset{k=1}{\overset{r}{\mathrm{\&Pi;}}}{(P_k\left(X\right)+\mathrm{\&omega;})}^{\frac{1}{r}}\right)}---\left(9\right)$

With $-\sqrt{\left(\underset{k=1}{\overset{r}{\mathrm{\&Pi;}}}{P}_k{\left(X\right)}^{\frac{1}{r}}\right)}---\left(10\right)$

3) with the product of two functions, namely N (X) and iteration optimization is carried out to M (X):

A. to N (X)=| σ (X)-σ (X ^*) | ^λbe optimized, by a nonnegative function | σ (X)-σ (X ^*) | the optimization of root realize;

B. there is σ (X) > σ (X in imagination ^*), then | σ (X)-σ (X ^*) |=σ (X)-σ (X ^*), and all verify with the more new data of this imagination to interative computation each time.If this is envisioned for negative, i.e. σ (X)≤σ (X ^*), then the step that burrows stops, because found an X ^*, reach the object optimizing computing;

4) right be optimized, by P _k(X) output is optimized to realize:

A. according to formula (1), (2), (3), (4), d is used _ij(X _k) replace δ _ij, be namely to P _k(X) be optimized;

5) right be optimized, by function P _k(X) and the optimization of output valve realizes:

A. according to formula (1), (2), (3), (4), d is used _ij(X _k) replace δ _ij, be namely to P _k(X) be optimized;

B. according to Cauchy-Schwarz inequality, right being optimized, is namely to d _ijand-d (X) _ij(X) optimization;

C. use double optimization method to d _ij(X) being optimized, is namely to d _ij ²(X) be optimized, described double optimization method is exactly the point with some distribution disorders of conic fitting;

D. according to Holder inequality to d _ij ²(X) namely optimization be to the optimization of formula (1) based on the quadratic function of X;

E. according to the p-d of Holder inequality _ij(X) namely optimization be to the optimization of formula (1) based on the linear function of X.

4. the wireless sensor network tri-dimensional node positioning method based on Tunneling method according to claim 3, it is characterized in that: certainly as unknown node in described step 4, receive the position coordinates that other node sends over, the computational process utilizing centroid algorithm to obtain self coordinate is:

Suppose that 3 anchor node coordinates are respectively (x ₁, y ₁, z ₁), (x ₂, y ₂, z ₂), (x ₃, y ₃, z ₃), unknown node (x _j, y _j, z _j) be respectively d to the Euclidean distance of three anchor nodes ₁, d ₂, d ₃, then unknown node coordinate is:

$x_j=\frac{\frac{x_1}{d_1+d_2}+\frac{x_2}{d_2+d_3}+\frac{x_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}$

$y_j=\frac{\frac{y_1}{d_1+d_2}+\frac{y_2}{d_2+d_3}+\frac{y_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}$

$z_j=\frac{\frac{z_1}{d_1+d_2}+\frac{z_2}{d_2+d_3}+\frac{z_3}{d_1+d_3}}{\frac{1}{d_1+d_2}+\frac{1}{d_2+d_3}+\frac{1}{d_1+d_3}}.$