CN103945532A - Three-dimensional weighted centroid positioning method based on mass-spring model - Google Patents

Abstract

The invention relates to the technical field of node positioning in wireless sensor networks, in particular to a three-dimensional weighted centroid positioning method based on a mass-spring model. The positioning method includes the steps: in an initial phase, amending a weight of the three-dimensional weighted centroid positioning method, and estimating the initial positions of unknown nodes by the weighted centroid positioning method with the amended weight; in an optimizing phase, amending the measuring distance by the aid of error factors, adjusting the unknown nodes to the best positions by the method of the mass-spring model. The positioning method is applicable to positioning geometric peripheral nodes comprising anchor nodes and has the advantages of high positioning accuracy and strong robustness.

Description

A kind of three-dimensional weighted mass center localization method based on Mass-spring Model

Technical field

The present invention relates to node locating technique field in wireless sensor network, more specifically, relate to a kind of three-dimensional weighted mass center localization method based on Mass-spring Model.

Background technology

In wireless sensor network, node locating is prerequisite and the basis that wireless sensor network is applied to the neighborhood such as target monitoring and tracking.Because sensing node has the easily feature such as affected by environment of limited energy, communication conventionally, after obtaining the correct location of anchor node self, the how quickly and accurately position of localizing objects node, it is very important that high-precision localization method seems.

According to estimation mechanism to node location, generally localization method is divided into localization method based on range finding and non-ranging localization method.The conventional measuring technique of localization method based on range finding mainly contains RSSI, TDOA, TOA, AOA, and node obtains after distance or angle information, can position by trilateration or Maximum Likelihood Estimation Method.Non-ranging localization method is mainly to estimate node location by internodal communication information, and its advantage is that hardware requirement is lower, but positioning precision is limited.Typical non-ranging localization method has method for positioning mass center, DV-Hop, APIT and MDS-MAP method etc.

Weighted mass center localization method is a kind of method based on range finding, although weighted mass center localization method provides a kind of simple and effective localization method, the positioning precision of the method has much room for improvement and is not suitable for the node of locating the polygon periphery being made up of anchor node.In recent years, a lot of relevant documents improve for two-dimentional WCL method.But these positioning precisioies of improving one's methods mainly depend on the setting of weights.In actual environment, unknown node may be positioned at the polygon periphery being made up of anchor node, now only adopts the method for weighting to fail to reach good locating effect.

Summary of the invention

The object of the invention is to overcome the weak point of existing localization method, a kind of three-dimensional weighted mass center localization method based on Mass-spring Model is provided, effectively solve the problem that existing weighted mass center localization method exists, improved positioning precision, and strengthened robustness.

To achieve these goals, the method concrete steps that the present invention proposes are as follows:

Step 1: unknown node is calculated the measuring distance of unknown node to anchor node according to RSSI information;

Step 2: select minimum measuring distance from all measuring distances, according to the weights of minimum measuring distance correction weighted mass center localization method;

Step 3: by revising the initial position of the three-dimensional weighted mass center localization method calculating unknown node after weights;

Step 4: the error of calculation factor, according to the measuring distance of error factor correction unknown node and each anchor node;

Step 5: adopt three-dimensional mass spring optimization (MSO) method to carry out iteration optimization processing to unknown node position, when until stop iteration while meeting stopping criterion for iteration, thereby determine unknown node position.

In above-mentioned localization method, in described step 1, measuring distance adopts logarithm-normal distribution model to calculate.Measuring distance acquires according to following formula:

$\mathrm{RSSI}=P_{\mathrm{send}}+P_{\mathrm{amplify}}-\mathrm{PL}\left(d_0\right)-10\mathrm{\ηlg}\left(\frac{d}{d_0}\right)-X_{\mathrm{\σ}}$

Wherein d is measuring distance, PL (d ₀) be signal propagation distance d ₀path loss, η is signal propagation path fading coefficients, X _σbe 0 for meeting average, variance is σ ²gaussian random variable, σ gets 4～10, P _sendfor transmitting power; P _amplifyfor antenna gain.

In above-mentioned localization method, in described step 2, weights are to calculate according to following formula:

$w_i={\left(\frac{1}{d_i\·d_{\min }}\right)}^{d_i/4.34}$

Wherein d _iunknown node p and anchor node B _imeasuring distance, d _minit is minimum measuring distance.

In described step 3, calculate according to the following formula the initial position of unknown node

$p(\hat{x},\hat{y},\hat{z})=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[{\left(\frac{1}{d_i\·d_{\min }}\right)}^{d_i/4.34}\·B_i(x_i,y_i,z_i)]}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\left(\frac{1}{d_i\·d_{\min }}\right)}^{d_i/4.34}}=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_i\·B_i(x_i,y_i,z_i)]}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_i}$

Wherein m is anchor node number, B _i(x _i, y _i, z _i) expression anchor node B _icoordinate.

In above-mentioned localization method, described in described step 4, in step 4, error factor refers to the mean value of the correction factor drawing according to the difference of the calculating distance between anchor node and measuring distance;

As anchor node B _iwith anchor node B _jcan intercom mutually, obtain anchor node B according to following formula _iwith anchor node B _jbetween correction factor a _ij:

$a_{\mathrm{ij}}=\frac{L_{\mathrm{ij}}-{\hat{L}}_{\mathrm{ij}}}{{\hat{L}}_{\mathrm{ij}}},i,j\∈\{\mathrm{1,2},...,m\},j>i$

Wherein for anchor node B _iwith anchor node B _jmeasuring distance, L _ijfor anchor node B _iwith anchor node B _jcalculating distance, x _i, y _i, z _irefer to respectively anchor node B _icoordinate figure, x _j, y _j, z _jrefer to respectively anchor node B _jcoordinate figure, calculate all correction factors by above formula, correction factor is averaged to filtering processing, obtain error factor and be:

$a=\underset{i=1,j>i}{\overset{g}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}$

Wherein g is correction factor a _ijnumber;

If all can not communicate by letter between anchor node, error factor is set as a=0;

Unknown node p and anchor node B _imeasuring distance be modified to d _i=d _i(1+a),, if revised distance is greater than maximum communication distance, so this time do not carry out correction.

In described step 5 unknown node p iteration more new formula be:

$p(k+1)=p\left(k\right)+\stackrel{\→}{F}\left(k\right)/\left(2m\right)$

Wherein k is the iterations of three-dimensional mass spring optimization method, for the spring that unknown node p is subject to is made a concerted effort, the positional value of unknown node after the k time iteration of p (k+1) expression.

Above-mentioned be defined as:

$\stackrel{\→}{F}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\stackrel{\→}{F}}_i$

Unknown node p makes a concerted effort to adjust according to spring.Wherein for unknown node p is to anchor node B _ispring force, be defined as:

${\stackrel{\→}{F}}_i={\stackrel{\→}{v}}_i({\hat{d}}_i-d_i)$

Wherein for estimated distance, ${\hat{d}}_i=\sqrt{{(\hat{x}-x_i)}^2+{\left(\widehat{y-y_i}\right)}^2+{\left(\widehat{z-z_i}\right)}^2},$ for unknown node p is to anchor node B _iunit vector, ${\stackrel{\→}{v}}_i=((x_i-\hat{x})/d_i,(y_i-\hat{y})/d_i,(z_i-\hat{z})/d_i).$

Compared with prior art, the beneficial effect of localization method of the present invention is: (1) localization method of the present invention is applicable to locate the node of the solid periphery being made up of anchor node; (2) weights of revising are dynamic value, have improved the positioning precision of weighting localization method; (3), in the situation that measurement exists certain error, mass spring optimization method can make node be adjusted to optimum position.

Brief description of the drawings

Fig. 1 is unknown node location exemplary plot.

Fig. 2 is unknown node optimizing process exemplary plot.

Embodiment

Describe implementation process in detail below in conjunction with accompanying drawing, so that the technical characterictic to the inventive method and advantage are interpretated more in-depth.The high-precision localization method of one provided by the invention, concrete implementation step is as follows:

1. measuring distance

As shown in Figure 1, establish unknown node p (x, y, z) and can receive m anchor node B (x _i, y _i, z _i) coordinate information,

Each anchor node has unique ID and the known coordinate value of oneself, and all anchor nodes have identical communication range.Unknown node towards periphery anchor node sends request signal, and the anchor node that receives this request signal sends to the ID of self and positional information the unknown node of appointment.Unknown node is according to receiving RSSI value, adopt the measuring distance between logarithm-normal distribution model computing node, and filtering measuring distance exceedes the exceptional value of communication radius length (because the factors such as environment have influence on RSSI value, the measuring distance calculating may be greater than the communication radius of sensing node, obviously these numerical value are undesirable, are considered as exceptional value.Therefore need filtering it, to reach minimizing error.)。If now unknown node only receives four anchor node information, exceptional value is made as to the value of communication radius.Measuring distance calculates by following formula:

$\mathrm{RSSI}=P_{\mathrm{send}}+P_{\mathrm{amplify}}-\mathrm{PL}\left(d_0\right)-10\mathrm{\ηlg}\left(\frac{d}{d_0}\right)-X_{\mathrm{\σ}}$

Wherein d is measuring distance, PL (d ₀) for signal propagation distance be d ₀path loss, d ₀normal value is 1m; η is signal propagation path fading coefficients, and the value of η increases along with increasing of barrier, conventionally gets between 2～5; X _σbe 0 for meeting average, variance is σ ²gaussian random variable, σ often gets 4～10; P _sendfor transmitting power; P _amplifyfor antenna gain.

2. calculate the initial position of unknown node

From all measuring distances, obtain minimum distance, the weights computing formula of the three-dimensional weighted mass center localization method of correction is as follows:

$w_i={\left(\frac{1}{d_i\·d_{\min }}\right)}^{d_i/4.34}$

Wherein d _iunknown node p and anchor node B _imeasuring distance, d _minit is minimum measuring distance.The initial position of unknown node calculates according to following formula:

$p(\hat{x},\hat{y},\hat{z})=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[{\left(\frac{1}{d_i\·d_{\min }}\right)}^{d_i/4.34}\·B_i(x_i,y_i,z_i)]}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\left(\frac{1}{d_i\·d_{\min }}\right)}^{d_i/4.34}}=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_i\·B_i(x_i,y_i,z_i)]}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_i}$

3. revise measuring distance

The positional information of the peripherad anchor node broadcast of anchor node self, if anchor node B _iwith anchor node B _jcan intercom mutually, the correction factor obtaining calculates according to following formula:

$a_{\mathrm{ij}}=\frac{L_{\mathrm{ij}}-{\hat{L}}_{\mathrm{ij}}}{{\hat{L}}_{\mathrm{ij}}},i,j\∈\{\mathrm{1,2},...,m\},j>i$

Wherein for anchor node B _iwith anchor node B _jmeasuring distance, L _ijfor anchor node B _iwith anchor node B _jcalculating distance, calculate all correction factors by above formula, correction factor averaged to filtering processing, obtain error factor and be:

$a=\underset{i=1,j>i}{\overset{g}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}$

Wherein g is correction factor a _ijnumber, if all can not communicate by letter between anchor node, error factor is set as a=0, unknown node p and anchor node B _imeasuring distance be modified to d _i=d _i(1+a),, if revised distance is greater than maximum communication distance, so this time do not carry out correction.

4. optimize unknown node position

As shown in Figure 1, when unknown node may appear at different positions, adopt the method for Mass-spring Model can overcome the correctly node of network for location 1 (b) of weighting localization method.As shown in Fig. 2 (a), the difference of two internodal measuring distances and estimated distance is considered as to the spring force of physics spring model.If current estimated distance is greater than measuring distance, spring force is pulling force.On the contrary, if estimated distance is less than measuring distance, spring force is thrust.Unknown node p carries out MSO method and is optimized processing, and its iteration more new formula is:

$p(k+1)=p\left(k\right)+\stackrel{\→}{F}\left(k\right)/\left(2m\right)$

Wherein k is the iterations (being set as 50) of MSO method, for the spring that unknown node p is subject to is made a concerted effort, be defined as:

$\stackrel{\→}{F}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\stackrel{\→}{F}}_i$

As shown in Fig. 2 (c), unknown node p makes a concerted effort to adjust according to spring.Wherein for unknown node p is to the spring force of anchor node Bi, as shown in Fig. 2 (b), be defined as:

Wherein for estimated distance, ${\hat{d}}_i=\sqrt{{(\hat{x}-x_i)}^2+{\left(\widehat{y-y_i}\right)}^2+{\left(\widehat{z-z_i}\right)}^2},$ for unknown node p is to anchor node B _iunit vector, ${\stackrel{\→}{v}}_i=((x_i-\hat{x})/d_i,(y_i-\hat{y})/d_i,(z_i-\hat{z})/d_i).$

Above-described embodiments of the present invention, do not form limiting the scope of the present invention.Any amendment of having done within spiritual principles of the present invention, be equal to and replace and improvement etc., within all should being included in claim protection range of the present invention.

Claims (5)

1. the three-dimensional weighted mass center localization method based on Mass-spring Model, is applicable to the unknown node of the solid periphery that is made up of anchor node, location, it is characterized in that, comprises the steps:

Step 1: unknown node is calculated the measuring distance of unknown node to anchor node according to RSSI information;

Step 2: select minimum measuring distance from all measuring distances, according to the weight w of minimum measuring distance correction weighted mass center localization method _i;

$w_i={\left(\frac{1}{d_i\·d_{\min }}\right)}^{d_i/4.34}$

Wherein d _iunknown node p and anchor node B _imeasuring distance, d _minit is minimum measuring distance;

Step 3: by revising the initial position of the three-dimensional weighted mass center localization method calculating unknown node after weights

$p(\hat{x},\hat{y},\hat{z})=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}[w_i\·B_i(x_i,y_i,z_i)}{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{w}_i}$

Wherein m represents the total number of anchor node, B _i(x _i, y _i, z _i) expression anchor node B _icoordinate;

Step 4: the error of calculation factor, according to the measuring distance of error factor correction unknown node and each anchor node;

Step 5: adopt three-dimensional mass spring optimization method to carry out iteration optimization processing to unknown node position, stop iteration in the time meeting stopping criterion for iteration, thereby determine unknown node position.

2. the three-dimensional weighted mass center localization method based on Mass-spring Model according to claim 1, is characterized in that, in described step 1, measuring distance adopts logarithm-normal distribution model to calculate.

3. the three-dimensional weighted mass center localization method based on Mass-spring Model according to claim 2, is characterized in that, measuring distance acquires according to following formula:

$\mathrm{RSSI}=P_{\mathrm{send}}+P_{\mathrm{amplify}}-\mathrm{PL}\left(d_0\right)-10\mathrm{\ηlg}\left(\frac{d}{d_0}\right)-X_{\mathrm{\σ}}$

Wherein d is measuring distance, PL (d ₀) be signal propagation distance d ₀path loss, η is signal propagation path fading coefficients, X _σbe 0 for meeting average, variance is σ ²gaussian random variable, σ gets 4～10, P _sendfor transmitting power; P _amplifyfor antenna gain.

4. the three-dimensional weighted mass center localization method based on Mass-spring Model according to claim 3, it is characterized in that, in described step 4, error factor refers to the mean value of the correction factor drawing according to the difference of the calculating distance between anchor node and measuring distance;

As anchor node B _iwith anchor node B _jcan intercom mutually, obtain anchor node B according to following formula _iwith anchor node B _jbetween correction factor a _ij:

$a_{\mathrm{ij}}=\frac{L_{\mathrm{ij}}-{\hat{L}}_{\mathrm{ij}}}{{\hat{L}}_{\mathrm{ij}}},i,j\∈\{\mathrm{1,2},...,m\},j>i$

Wherein for anchor node B _iwith anchor node B _jmeasuring distance, L _ijfor anchor node B _iwith anchor node B _jcalculating distance, x _i, y _i, z _irefer to respectively anchor node B _icoordinate figure, x _j, y _j, z _jrefer to respectively anchor node B _jcoordinate figure, calculate all correction factors by above formula, correction factor is averaged to filtering processing, obtain error factor and be:

$a=\underset{i=1,j>i}{\overset{g}{\mathrm{\Σ}}}{a}_{\mathrm{ij}}$

Wherein g is correction factor a _ijnumber;

If all can not communicate by letter between anchor node, error factor is set as a=0;

Unknown node p and anchor node B _imeasuring distance be modified to d _i=d _i(1+a),, if revised distance is greater than maximum communication distance, so this time do not carry out correction.

5. the three-dimensional weighted mass center localization method based on Mass-spring Model according to claim 4, is characterized in that, in described step 5 unknown node p iteration more new formula be:

$p(k+1)=p\left(k\right)+\stackrel{\→}{F}\left(k\right)/\left(2m\right)$

Wherein k is the iterations of three-dimensional mass spring optimization method, for the spring that unknown node p is subject to is made a concerted effort, the positional value of unknown node after the k time iteration of p (k+1) expression.