CN102938875A - RSSI (Received Signal Strength Indicator)-based probability-centroid positioning method for wireless sensor network - Google Patents

Abstract

The invention discloses an RSSI (Received Signal Strength Indication)-based probability-centroid positioning method for a wireless sensor network. The method comprises the following steps: (1) n anchor nodes broadcast information around periodically, the information comprises the IDs (identifiers) and coordinates of the nodes, and the RSSI mean value of the same anchor node is obtained after the information is received by an unknown node; (2) through an RF (Radio Frequency) ranging model, the probability distribution of the distances between the anchor nodes and the unknown node is obtained, and n circular rings of a certain level of significance and the probability density function of each node are then obtained; (3) a ring overlap region is obtained according to the circular rings in the step (2), and the probability centroid of each anchor node in the overlap region is obtained according to the probability density function; and (4) the n centroids are fused so as to obtain the probability centroid of the overlap region, i.e. the estimation point of the unknown node. According to the method, the probability density function is taken as the density function of the overlap region, and the concept of the density function is introduced based on the existing centroid positioning method, so that the positioning accuracy is increased by about 40% compared with that of an RSSI-based triangle centroid positioning algorithm.

Description

Wireless sensor network positioning method based on RSSI probability barycenter

Technical field

The present invention relates to a kind of wireless sensor network positioning method, particularly a kind of localization method based on RSSI for radio sensing network.

Background technology

Wireless sensor network (WSN) wireless network that to be a large amount of static or mobile transducers consist of in the mode of self-organizing and multi-hop, its objective is that collaboratively perception, collection, processing and transmission network cover the monitoring information of perceptive object in the geographic area, and report to the user.It has a wide range of applications at military, civilian, industrial and other some commercial fields.Wireless sensor network node is located as one of key technology of radio sensing network, and the physical distance that mainly is based between anchor node and unknown node is measured, and determines to lay the position of other nodes in the district according to certain location mechanism.In numerous distance-finding methods, the range finding of received signal strength indicator (RSSI) model not only need not to add additional hardware equipment, and can be used for multiple electromagnetic wave.Therefore its convenience, low cost and versatility have excited people's research interest.RSSI by signal decay in the air to estimate the distance between the node.Because signal signal strength signal intensity in communication process can reduce, and according to the signal strength signal intensity that acceptance point is received, just can estimate the distance of launch point and acceptance point, its Mathematical Modeling is

$P_i\left(d_i\right)=P_T-P\left(d_0\right)-10\mathrm{nlg}\left(\frac{d_i}{d_0}\right)+X_{{\mathrm{\σ}}_i}---\left(1\right)$

In the formula, d _iActual range between expression acceptance point and i the launch point, d ₀Represent known reference distance, n is the fading channel index, generally gets 2～4,

Be that average is zero, standard deviation is σ _iGaussian random variable represent the measure error of anchor node, P _TThe signal strength signal intensity of expression launch point, P (d ₀) expression range transmission point d ₀The signal strength signal intensity at place, P _i(d _i) expression range transmission point d _iThe signal strength signal intensity at place.At present, the RSSI location mainly contains least square, maximum likelihood is estimated and 3 kinds of algorithms of regional barycenter.

Least-squares estimation thinks that each anchor node positioning accuracy is equal to, and the node of available error sum of squares minimum is as its estimation point, so that this algorithm has the little advantage of amount of calculation.But in fact each anchor node in the air

Standard deviation sigma _iDifference causes its positioning accuracy not to be equal to, thereby so that the comprehensive positioning accuracy of least square is not high.The king builds firm grade and progressively improves the node weights at " weighted least-squares is estimated the application in wireless sensor network positioning " by the iteration refinement, has improved the positioning accuracy of least-squares estimation.Zone barycenter location algorithm mainly is triangle barycenter location algorithm, is difficult to improve positioning accuracy because traditional barycenter is how much barycenter.The a collection of scholars such as Tie Qiu " A localization strategy based on n-times trilateralcentriod with weight ", Liu Yunjie " based on the radio sensing network correction weighted mass center location algorithm of RSSI " introduce triangle barycenter location algorithm with weights, improve certainty of measurement by different weights choosing methods, improved in varying degrees positioning accuracy thus.Maximum likelihood estimates the estimation point of overlapping region Probability maximum value point as unknown node, can be on probability near the true coordinate of unknown node.Maximum likelihood estimates to have very high positioning accuracy about 0.3m, Koichi Miyauchi, at 2010 " the Performance Improvement of Location Estimation UsingDeviation on Received Signal In Wireless Sensor Networks " that deliver consider that thus the RSSI value under certain dominance level has improved the authenticity that receives RSSI value, improved positioning accuracy hanging down under the measurement number of times.

Summary of the invention

In view of this, technical problem to be solved by this invention provides a kind of wireless sensor network positioning method based on RSSI probability barycenter, and the method can be located fast to radio sensing network node.

The object of the present invention is achieved like this:

A kind of wireless sensor network positioning algorithm based on RSSI probability barycenter provided by the invention may further comprise the steps:

S1: determine wireless sensor network positioning zone, anchor node coordinate and be randomly dispersed in the interior unknown node of this locating area;

S2: by anchor node broadcast message periodically towards periphery, unknown node receives that the RSSI to same anchor node gets average after this information, obtains unknown node to the measured distance of anchor node;

S3: by RF range finding model try to achieve anchor node and unknown node distance probability distribution, preset location circle ring area under the significance level and the probability density function of each node;

S4: drawn the overlapping region of the location circle ring area under the default significance level by the location circle ring area of each anchor node, and obtain each anchor node at this regional probability barycenter by probability density function;

S5: get average as the estimation point coordinate of unknown node after removing the maximum of probability center-of-mass coordinate and minimum value.

Further, described locating ring overlapping region is determined by following formula:

$\left\{\begin{array}{c}\max (x_i-d_i)\≤x\≤\min (x_i+d_i)\\ \max (y_i-d_i)\≤y\≤\min (y_i+d_i)\end{array};\right.$

Wherein, the anchor node coordinate is (x _i, y _i), i=1 wherein ... n represents the number of anchor node, and the unknown node coordinate is (x, y), d _iDistance between expression anchor node and the unknown node.

Further, the probability barycenter of the overlapping region of described location circle ring area is determined by following steps:

S41: each anchor node at the probability density function of the overlapping region of location circle ring area is:

$f(x,y)=\underset{\underset{k\&NotEqual;i}{k=1}}{\overset{n}{\mathrm{\&Pi;}}}P\left(d_k\right)\frac{10\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">n</figure-callout>}}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_i\ln 10\sqrt{{\left({x-x}_i\right)}^2+{\left({y-y}_i\right)}^2}}{e}^{-\frac{{\left(10\mathrm{nlg}(\sqrt{{\left({x-x}_i\right)}^2+{(y-y_i)}^2}/d_i^{\&prime;})\right)}^2}{2{{\mathrm{\&sigma;}}_i}^2}};$

In the formula, k represents k anchor node, P (d _k) represent that unknown node and k anchor node are at a distance of d _kProbability, σ _iRepresent the standard deviation in the i anchor node signal communication process, d ' _iThe measured distance of expression unknown node and i anchor node, n represents the anchor node number;

S42: with probability density function as the density function of the overlapping region of location circle ring area and by calculating each anchor node to get off in the probability center-of-mass coordinate of overlapping region:

${\stackrel{\&OverBar;}{x}}_i=\frac{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2({\sin \mathrm{\&theta;}}_2-{\sin \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^2({\sin \mathrm{\&theta;}}_2-\sin {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+x_i$

${\stackrel{\&OverBar;}{y}}_i=\frac{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2(-{\cos \mathrm{\&theta;}}_2+{\cos \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_1)-{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^2({-\cos \mathrm{\&theta;}}_2+\cos {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+y_i;$

In the formula,

Represent i anchor node at the barycenter of overlapping region, the probable value of Φ () expression standardized normal distribution, d ₁, d ₂The distance of expression integral domain, θ ₁, θ ₂The angular range that shows integral domain, c ₁Be illustrated in Standardized normal distribution mathematical expectation of probability on the interval, c ₂Be illustrated in

Standardized normal distribution mathematical expectation of probability on the interval.

Further, the estimation point coordinate of described unknown node calculates by following formula:

$(\hat{x},\hat{y})=\frac{1}{n-2}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{x}}_i-\max \left({\stackrel{\&OverBar;}{x}}_i\right)-\min \left({\stackrel{\&OverBar;}{x}}_i\right),\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{y}}_i-\max \left({\stackrel{\&OverBar;}{y}}_i\right)-\min \left({\stackrel{\&OverBar;}{y}}_i\right)).$

Further, the distance between described anchor node and the unknown node is by measured distance d _i' and the default level of signifiance is definite.

Further, the described default level of signifiance is taken as at 0.1 o'clock, then

The invention has the advantages that: the present invention asks for the probability barycenter with probability density function as the density function of overlapping region, can reach in theory with maximum likelihood to estimate identical positioning accuracy.The concept of introducing density function in the locating ring overlapping region improves the positioning accuracy of barycenter location, is equal to a series of weighted mass center location algorithms and considers that there is difference in essence in the overlapping region.The method positioning accuracy is higher.To hardware requirement low and realize simple, so the present invention can be used for multiple wireless sensor network positioning occasion.

Description of drawings

In order to make the purpose, technical solutions and advantages of the present invention clearer, the present invention is described in further detail below in conjunction with accompanying drawing, wherein:

The RSSI probability barycenter wireless sensor network positioning algorithm flow chart that Fig. 1 provides for the embodiment of the invention;

The locating ring overlapping region schematic diagram that Fig. 2 provides for the embodiment of the invention;

The positioning result schematic diagram to a θ (5,3) that Fig. 3 provides for the embodiment of the invention;

Fig. 4 contrasts schematic diagram for the result of two kinds of location algorithms that the embodiment of the invention provides;

The standard deviation that Fig. 5 provides for the embodiment of the invention is on the schematic diagram that affects of positioning accuracy;

The anchor node that Fig. 6 provides for the embodiment of the invention is measured number of times to the schematic diagram that affects of positioning accuracy.

Embodiment

Below with reference to accompanying drawing, the preferred embodiments of the present invention are described in detail; Should be appreciated that preferred embodiment only for the present invention is described, rather than in order to limit protection scope of the present invention.

Embodiment 1

The RSSI probability barycenter wireless sensor network positioning algorithm flow chart that Fig. 1 provides for the embodiment of the invention, the locating ring overlapping region schematic diagram that Fig. 2 provides for the embodiment of the invention, as shown in the figure: a kind of wireless sensor network positioning algorithm based on RSSI probability barycenter provided by the invention may further comprise the steps:

S1: determine wireless sensor network positioning zone, anchor node coordinate and be randomly dispersed in the interior unknown node of this locating area;

S2: by anchor node broadcast message periodically towards periphery, unknown node receives that the RSSI to same anchor node gets average after this information, obtains unknown node to the measured distance of anchor node;

S3: by RF range finding model try to achieve anchor node and unknown node distance probability distribution, preset location circle ring area under the significance level and the probability density function of each node;

S4: drawn the overlapping region of the location circle ring area under the default significance level by the location circle ring area of each anchor node, and obtain each anchor node at this regional probability barycenter by probability density function;

S5: get average as the estimation point coordinate of unknown node after removing the maximum of probability center-of-mass coordinate and minimum value.

Described locating ring overlapping region is determined by following formula:

$\left\{\begin{array}{c}\max (x_i-d_i)\&le;x\&le;\min (x_i+d_i)\\ \max (y_i-d_i)\&le;y\&le;\min (y_i+d_i)\end{array};\right.$

Wherein, the anchor node coordinate is (x _i, y _i), i=1 wherein ... n represents the number of anchor node, and the unknown node coordinate is (x, y), d _iDistance between expression anchor node and the unknown node.Distance between described anchor node and the unknown node is by measured distance d _i' and the default level of signifiance is definite.The described default level of signifiance is taken as at 0.1 o'clock, then

The probability barycenter of the overlapping region of described location circle ring area is determined by following steps:

S41: each anchor node at the probability density function of the overlapping region of location circle ring area is:

$f(x,y)=\underset{\underset{k\&NotEqual;i}{k=1}}{\overset{n}{\mathrm{\&Pi;}}}P\left(d_k\right)\frac{10\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">n</figure-callout>}}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_i\ln 10\sqrt{{\left({x-x}_i\right)}^2+{\left({y-y}_i\right)}^2}}{e}^{-\frac{{\left(10\mathrm{nlg}(\sqrt{{\left({x-x}_i\right)}^2+{(y-y_i)}^2}/d_i^{\&prime;})\right)}^2}{2{{\mathrm{\&sigma;}}_i}^2}};$

In the formula, k represents k anchor node, P (d _k) represent that unknown node and k anchor node are at a distance of d _kProbability, σ _iRepresent the standard deviation in the i anchor node signal communication process, d ' _iThe measured distance of expression unknown node and i anchor node, n represents the anchor node number;

S42: with probability density function as the density function of the overlapping region of location circle ring area and by calculating each anchor node to get off in the probability center-of-mass coordinate of overlapping region:

${\stackrel{\&OverBar;}{x}}_i=\frac{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2({\sin \mathrm{\&theta;}}_2-{\sin \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^2({\sin \mathrm{\&theta;}}_2-\sin {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+x_i$

${\stackrel{\&OverBar;}{y}}_i=\frac{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2(-{\cos \mathrm{\&theta;}}_2+{\cos \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_1)-{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^2({-\cos \mathrm{\&theta;}}_2+\cos {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+y_i;$

In the formula,

Represent i anchor node at the barycenter of overlapping region, the probable value of Φ () expression standardized normal distribution, d ₁, d ₂The distance of expression integral domain, θ ₁, θ ₂The angular range that shows integral domain, c ₁Be illustrated in

Standardized normal distribution mathematical expectation of probability on the interval, c ₂Be illustrated in

Standardized normal distribution mathematical expectation of probability on the interval.

The estimation point coordinate of described unknown node calculates by following formula:

$(\hat{x},\hat{y})=\frac{1}{n-2}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{x}}_i-\max \left({\stackrel{\&OverBar;}{x}}_i\right)-\min \left({\stackrel{\&OverBar;}{x}}_i\right),\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{y}}_i-\max \left({\stackrel{\&OverBar;}{y}}_i\right)-\min \left({\stackrel{\&OverBar;}{y}}_i\right)).$

The location algorithm that the present embodiment provides is introduced the concept of density function in the method for positioning mass center first, estimate compare the positioning accuracy that have with magnitude as the estimation realization radio sensing network node location of unknown node with maximum likelihood with the probability barycenter, amount of calculation has but reduced about 95%, and is more simple in the realization.In calculating, replace the radio sensing network distributed areas with the locating ring overlapping region under certain significance level, can avoid unnecessary calculating.

Embodiment 2

Below in detail statement based on the process of the wireless sensor network positioning method of RSSI probability barycenter:

In order to overcome the received signal strength measurement error to the impact of wireless sensor network node location, embodiment provided by the invention obtains unknown node corresponding to the distance range of anchor node under 0.1 the level of signifiance.

$d_i^{\&prime;}{10}^{-1.65{\mathrm{\&sigma;}}_i/10n}\&le;d_i\&le;d_i^{\&prime;}{10}^{1.65{\mathrm{\&sigma;}}_i/10n},$

If the anchor node coordinate is (x _i, y _i), i=1 wherein ... n, unknown node coordinate are (x, y).Set up following equation group according to the distance relation between 2 o'clock again

(x-x _i) ²+(y-y _i) ²＝d _i ²，i＝1…n；

In order to simplify calculating, can be by the approximate anchor node locating ring overlapping region that replaces, the dashed rectangle zone of three annulus intersection regions among Fig. 2, x then, the scope of y is.

$\left\{\begin{array}{c}\max (x_i-d_i)\&le;x\&le;\min (x_i+d_i)\\ \max (y_i-d_i)\&le;y\&le;\min (y_i+d_i)\end{array},\right.$

Obtain to derive behind the overlapping region probability density function of overlapping region, can be got by the range finding model

$P_i\left(d_i^{\&prime;}\right)=P_T-P\left(d_0\right)-10\mathrm{nlg}\left(\frac{d_i^{\&prime;}}{d_0}\right)---\left(2\right)$

In the formula, P _i(d _i') signal strength signal intensity that receives of expression acceptance point, d _iThe distance that ' expression transmitting-receiving node records.Because P _i(d _i')=P _i(d _i), connection solution formula (1) can get with formula (2).

$P\left(d_i\right)=P\{D_i\&le;d_i\}=P\{d_i^{\&prime;}{10}^{\frac{X_{\mathrm{\&sigma;i}}}{10n}}\&le;d_i\}=P\{X\&le;10\mathrm{nlg}\frac{d_i}{d_i^{\&prime;}}\}=\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_i}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)---\left(3\right)$

Can draw d thus _iProbability density function be.

$f\left(d_i\right)=\frac{10\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">n</figure-callout>}}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_i{d}_i\ln 10}{e}^{-\frac{{\left(10\mathrm{nlg}(d_i/d_i^{\&prime;})\right)}^2}{2{{\mathrm{\&sigma;}}_i}^2}}---\left(4\right)$

Because the measurement model of each anchor node is separate, then the probability distribution of overlapping region arbitrary node is.

$P=P\left(d_1\right)P\left(d_2\right)...P\left(d_n\right)$

$={\&Integral;}_0^{\sqrt{{(x-x_1)}^2+{(y-y_1)}^2}}f\left(d_1\right){\mathrm{<figure-callout\; id="1"\; label="d\; d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_{d_{}}\&times;{\&Integral;}_0^{\sqrt{{(x-x_2)}^2+{(y-y_2)}^2}}f\left(d_2\right){\mathrm{<figure-callout\; id="2"\; label="d\; d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_{d_{}}...\&times;{\&Integral;}_0^{\sqrt{{\left({x-x}_n\right)}^2+{(y-y_n)}^2}}f\left(d_n\right)d_{d_n}---\left(5\right)$

To d in the formula (5) ₁D _nAsk respectively local derviation, can obtain each anchor node at the probability density function of overlapping region:

$f(x,y)=\underset{\underset{k\&NotEqual;i}{k=1}}{\overset{n}{\mathrm{\&Pi;}}}P\left(d_k\right)\frac{10\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">n</figure-callout>}}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_i\ln 10\sqrt{{\left({x-x}_i\right)}^2+{\left({y-y}_i\right)}^2}}{e}^{-\frac{{\left(10\mathrm{nlg}(\sqrt{{\left({x-x}_i\right)}^2+{(y-y_i)}^2}/d_i^{\&prime;})\right)}^2}{2{{\mathrm{\&sigma;}}_i}^2}}---\left(6\right)$

Can obtain the center-of-mass coordinate of each anchor node in the overlapping region by formula (6) is

${\stackrel{\&OverBar;}{x}}_i=\frac{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2({\sin \mathrm{\&theta;}}_2-{\sin \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^2({\sin \mathrm{\&theta;}}_2-\sin {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+x_i$

${\stackrel{\&OverBar;}{y}}_i=\frac{{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}^2(-{\cos \mathrm{\&theta;}}_2+{\cos \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_1)-{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA00002458270600031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1}^2({-\cos \mathrm{\&theta;}}_2+\cos {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+y_i---\left(7\right)$

In formula (7), the probable value of Φ () expression standardized normal distribution, d ₁, d ₂The distance of expression integral domain, θ ₁, θ ₂The angular range that shows integral domain, c ₁Be illustrated in Standardized normal distribution mathematical expectation of probability on the interval, c ₂Be illustrated in

N the center-of-mass coordinate that standardized normal distribution mathematical expectation of probability on the interval obtains through type (7), substitution formula (8) is obtained the estimated value of position coordinates

$(\hat{x},\hat{y})=\frac{1}{n-2}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{x}}_i-\max \left({\stackrel{\&OverBar;}{x}}_i\right)-\min \left({\stackrel{\&OverBar;}{x}}_i\right),\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{y}}_i-\max \left({\stackrel{\&OverBar;}{y}}_i\right)-\min \left({\stackrel{\&OverBar;}{y}}_i\right))---\left(8\right)$

As shown in Figure 3, choose at random the checking the present invention of 20 unknown node and based on the positioning accuracy of the triangle centroid algorithm of RSSI, the probability centroid algorithm positioning accuracy based on RSSI is higher as can be seen from Figure.

Wireless sensor network positioning algorithm based on RSSI probability barycenter of the present invention is comprised of following steps:

Anchor node is broadcast message periodically towards periphery, and ordinary node receives that the RSSI to same anchor node gets average after this information, obtains unknown node to the measured distance of anchor node;

Go out unknown node to the probability distribution of anchor node distance by RF range finding model inference, obtaining in the level of signifiance is 0.1 d _iSpan;

By d _iObtain the locating ring overlapping region of each anchor node;

Each anchor node is measured separate, can obtain each anchor node at the probability density function of overlapping region by the probability distribution in (2);

With the density function of probability density function as the overlapping region, derive each anchor node in the probability barycenter expression formula of overlapping region, after maximum and minimum value were removed in set to the probability center-of-mass coordinate obtained, the probability barycenter that obtains the overlapping region was the unknown node coordinate.

The present invention obtains the probability barycenter of overlapping region by the probability density function of overlapping region, be equivalent in theory Probability maximum value point, compares the obvious positioning accuracy that improved with the triangle barycenter location algorithm based on RSSI.The mathematic(al) representation of probability barycenter owing to having derived, the present invention has low to hardware requirement and realizes simple characteristics, so the present invention can be used for multiple wireless sensor network positioning occasion.

Be located in the square area of 10m * 10m, 7 anchor nodes are randomly dispersed in the distributed areas, choose in the experiment: P _T=4dB, P (d ₀)=55dB, d ₀=1m, n=3, the deviation of 7 anchor nodes is chosen minute identical and different two kinds of situations, not σ simultaneously _i=[1,1.3,1.5,2,2.1,2.5,3], σ value 3～10 when identical.Use respectively based on the triangle centroid algorithm of RSSI with based on RSSI probability centroid algorithm and carry out emulation, Fig. 3, Fig. 4, Fig. 5, Fig. 6 in simulation result such as the accompanying drawing.Fig. 3 is that the present invention locates schematic diagram, comprises the overlapping region among the figure corresponding to the probability barycenter of each anchor node and final estimated coordinates.Fig. 4 is the positioning accuracy contrast of 20 nodes of two kinds of algorithm random measurements.Fig. 5 probes into σ to the impact of two kinds of algorithm positioning accuracies when the σ value is identical, along with the increase positioning accuracy decline of σ, the present invention changes comparatively mild.Fig. 6 has probed into anchor node and has measured number of times to the impact of two kinds of algorithm positioning accuracies, and anchor node is measured the number of times increase can improve positioning accuracy, gets 8～11 times in the reality for good.The present invention compares based on the performance of the triangle barycenter location algorithm of RSSI better, and algorithm of the present invention is low to hardware requirement, can adapt to preferably the requirement of WSN low cost and low-power consumption, is a kind of preferably targeting scheme.

The above is the preferred embodiments of the present invention only, is not limited to the present invention, and obviously, those skilled in the art can carry out various changes and modification and not break away from the spirit and scope of the present invention the present invention.Like this, if of the present invention these are revised and modification belongs within the scope of claim of the present invention and equivalent technologies thereof, then the present invention also is intended to comprise these changes and modification interior.

Claims (6)

1. based on the wireless sensor network positioning method of RSSI probability barycenter, it is characterized in that: may further comprise the steps:

S1: determine wireless sensor network positioning zone, anchor node coordinate and be randomly dispersed in the interior unknown node of this locating area;

S2: by anchor node broadcast message periodically towards periphery, unknown node receives that the RSSI to same anchor node gets average after this information, obtains unknown node to the measured distance of anchor node;

S3: by RF range finding model try to achieve anchor node and unknown node distance probability distribution, preset location circle ring area under the significance level and the probability density function of each node;

S4: drawn the overlapping region of the location circle ring area under the default significance level by the location circle ring area of each anchor node, and obtain each anchor node at this regional probability barycenter by probability density function;

S5: get average as the estimation point coordinate of unknown node after removing the maximum of probability center-of-mass coordinate and minimum value.

2. the wireless sensor network positioning method based on RSSI probability barycenter according to claim 1, it is characterized in that: described locating ring overlapping region is determined by following formula:

$\left\{\begin{array}{c}\max (x_i-d_i)\&le;x\&le;\min (x_i+d_i)\\ \max (y_i-d_i)\&le;y\&le;\min (y_i+d_i)\end{array};\right.$

Wherein, the anchor node coordinate is (x _i, y _i), i=1 wherein ... n represents the anchor node number, and the unknown node coordinate is (x, y), and di represents the distance between anchor node and the unknown node.

3. the wireless sensor network positioning method based on RSSI probability barycenter according to claim 1, it is characterized in that: the probability barycenter of the overlapping region of described location circle ring area is determined by following steps:

S41: each anchor node at the probability density function of the overlapping region of location circle ring area is:

$f(x,y)=\underset{\underset{k\&NotEqual;i}{k=1}}{\overset{n}{\mathrm{\&Pi;}}}P\left(d_k\right)\frac{10n}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_i\ln 10\sqrt{{\left({x-x}_i\right)}^2+{\left({y-y}_i\right)}^2}}{e}^{-\frac{{\left(10\mathrm{nlg}(\sqrt{{\left({x-x}_i\right)}^2+{(y-y_i)}^2}/d_i^{\&prime;})\right)}^2}{2{{\mathrm{\&sigma;}}_i}^2};}$

In the formula, k represents k anchor node, P (d _k) represent that unknown node and k anchor node are at a distance of d _kProbability, σ _iRepresent the standard deviation in the i anchor node signal communication process, d ' _iThe measured distance of expression unknown node and i anchor node, n represents the anchor node number;

S42: with probability density function as the density function of the overlapping region of location circle ring area and by calculating each anchor node to get off in the probability center-of-mass coordinate of overlapping region:

${\stackrel{\&OverBar;}{x}}_i=\frac{{d_2}^2({\sin \mathrm{\&theta;}}_2-{\sin \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-{d_1}^2({\sin \mathrm{\&theta;}}_2-\sin {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+x_i$

${\stackrel{\&OverBar;}{y}}_i=\frac{{d_2}^2(-{\cos \mathrm{\&theta;}}_2+{\cos \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_1)-{d_1}^2({-\cos \mathrm{\&theta;}}_2+\cos {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+y_i;$

In the formula,

Represent i anchor node at the barycenter of overlapping region, the probable value of Φ () expression standardized normal distribution, d ₁, d ₂The distance of expression integral domain, θ ₁, θ ₂The angular range that shows integral domain, c ₁Be illustrated in

Standardized normal distribution mathematical expectation of probability on the interval, c ₂Be illustrated in Standardized normal distribution mathematical expectation of probability on the interval.

4. the wireless sensor network positioning method based on RSSI probability barycenter according to claim 1, it is characterized in that: the estimation point coordinate of described unknown node calculates by following formula:

$(\hat{x},\hat{y})=\frac{1}{n-2}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{x}}_i-\max \left({\stackrel{\&OverBar;}{x}}_i\right)-\min \left({\stackrel{\&OverBar;}{x}}_i\right),\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{y}}_i-\max \left({\stackrel{\&OverBar;}{y}}_i\right)-\min \left({\stackrel{\&OverBar;}{y}}_i\right)).$

5. the wireless sensor network positioning method based on RSSI probability barycenter according to claim 2, it is characterized in that: the distance between described anchor node and the unknown node is by measured distance d _i' and the default level of signifiance is definite.

6. the wireless sensor network positioning method based on RSSI probability barycenter according to claim 5, it is characterized in that: the described default level of signifiance is taken as at 0.1 o'clock, then

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