CN102938875B - 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 form in the mode of self-organizing and multi-hop, its objective is that perception collaboratively, collection, processing and transmission network cover the monitoring information of perceptive object in geographic area, and report to 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, is mainly that the physical distance based between anchor node and unknown node is measured, and determines the position of laying other nodes in district according to certain location mechanism.In numerous distance-finding methods, received signal strength indicator (RSSI) model range finding is not only without adding additional hardware equipment, and can be 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 node.Because signal signal strength signal intensity in communication process can reduce, the signal strength signal intensity of receiving according to acceptance point, just can estimate the distance of launch point and acceptance point, and 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 formula, d _irepresent the actual range between acceptance point and i launch point, d ₀represent known reference distance, n is 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 that represents 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, RSSI location mainly contains least square, maximum likelihood is estimated and 3 kinds of algorithms of region barycenter.

Least-squares estimation thinks that each anchor node positioning precision is equal to, and the node of available error sum of squares minimum, as its estimation point, makes this algorithm have the advantage that amount of calculation is little.But in fact each anchor node in the air standard deviation sigma _idifference, causes its positioning precision not to be equal to, thereby makes the comprehensive positioning precision of least square not high.King builds firm grade and estimates that at < < weighted least-squares the application > > in wireless sensor network positioning progressively improves node weights by iteration refinement, has improved the positioning precision of least-squares estimation.Region barycenter location algorithm is mainly triangle barycenter location algorithm, because traditional barycenter is that how much barycenter are difficult to improve positioning precision.Tie Qiu < < A localization strategy based on n-times trilateralcentriod with weight > >, the a collection of scholars such as radio sensing network correction weighted mass center location algorithm > > of the outstanding < < of Liu Yun based on RSSI introduces triangle barycenter location algorithm by weights, by different weights choosing methods, improved certainty of measurement, improving in varying degrees positioning precision thus.Maximum likelihood is estimated the estimation point using overlapping region Probability maximum value point as unknown node, can on probability, approach the true coordinate of unknown node most.Maximum likelihood estimates to have very high positioning precision about 0.3m, Koichi Miyauchi, consider that at the 2010 < < Performance Improvement of Location Estimation UsingDeviation on Received Signal In Wireless Sensor Networks > > that deliver thereby the RSSI value under certain dominance level has improved the authenticity that receives RSSI value, has improved positioning precision under low measurement number of times.

Summary of the invention

In view of this, technical problem to be solved by this invention is to provide 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, comprises the following steps:

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

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

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

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

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

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

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

In 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 i anchor node signal communication process, d ' _ithe measured distance that represents unknown node and i anchor node, n represents anchor node number;

S42: using 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 formula, represent that i anchor node is at the barycenter of overlapping region, Φ () represents the probable value of standardized normal distribution, d ₁, d ₂the distance that represents integral domain, θ ₁, θ ₂the angular range that shows integral domain, c ₁be illustrated in standardized normal distribution mathematical expectation of probability on interval, c ₂be illustrated in standardized normal distribution mathematical expectation of probability on 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 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,

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

Accompanying drawing explanation

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

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

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

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

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

The affect schematic diagram of the standard deviation that Fig. 5 provides for the embodiment of the present invention on positioning precision;

The anchor node that Fig. 6 provides for the embodiment of the present invention is measured the affect schematic diagram of number of times on positioning precision.

Embodiment

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

Embodiment 1

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

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

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

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

S4: drawn the overlapping region of the location circle ring area under default significance level by the location circle ring area of each anchor node, and obtain each anchor node at the probability barycenter in this region 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, anchor node coordinate is (x _i, y _i), i=1 wherein ... n represents the number of anchor node, and unknown node coordinate is (x, y), d _irepresent the distance between anchor node and unknown node.Distance between described anchor node and 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,

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 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 i anchor node signal communication process, d ' _ithe measured distance that represents unknown node and i anchor node, n represents anchor node number;

S42: using 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 formula, represent that i anchor node is at the barycenter of overlapping region, Φ () represents the probable value of standardized normal distribution, d ₁, d ₂the distance that represents integral domain, θ ₁, θ ₂the angular range that shows integral domain, c ₁be illustrated in standardized normal distribution mathematical expectation of probability on interval, c ₂be illustrated in standardized normal distribution mathematical expectation of probability on 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 method for positioning mass center first, with probability barycenter, as the estimation of unknown node, realize radio sensing network node location and estimate to compare the positioning precision with same magnitude with maximum likelihood, amount of calculation has but reduced by 95% left and right, more simple in realization.In calculating, with the locating ring overlapping region under certain significance level, replace radio sensing network distributed areas, can avoid unnecessary calculating.

Embodiment 2

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

In order to overcome the impact of received signal strength measurement error on 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 anchor node coordinate is (x _i, y _i), i=1 wherein ... n, unknown node coordinate is (x, y).According to the distance relation between 2 o'clock, set up following equation group again

(x-x _i) ²+(y-y _i) ²＝d _i ²，i＝1…n；

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

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

The probability density function that obtains needing to derive behind overlapping region overlapping region, can be obtained by 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 formula, P _i(d _i') represent the signal strength signal intensity that acceptance point receives, d _ithe distance that ' expression transmitting-receiving node records.Because P _i(d _i')=P _i(d _i), connection solution formula (1) can obtain 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.

$f\left(d_i\right)=\frac{10n}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_i{d}_i\ln 10}{e}^{-\frac{{\left(10\mathrm{nlg}(d_i/d_i^{\&prime;})\right)}^2}{2{{\mathrm{\&sigma;}}_i}^2}}---\left(4\right)$

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

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

$={\&Integral;}_0^{\sqrt{{(x-x_1)}^2+{(y-y_1)}^2}}f\left(d_1\right)d_{d_1}\&times;{\&Integral;}_0^{\sqrt{{(x-x_2)}^2+{(y-y_2)}^2}}f\left(d_2\right)d_{d_2}...\&times;{\&Integral;}_0^{\sqrt{{\left({x-x}_n\right)}^2+{(y-y_n)}^2}}f\left(d_n\right)d_{d_n}---\left(5\right)$

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

$f(x,y)=\underset{\underset{k\&NotEqual;i}{k=1}}{\overset{n}{\mathrm{\&Pi;}}}P\left(d_k\right)\frac{10n}{\sqrt{2\mathrm{\&pi;}}{\mathrm{\&sigma;}}_i\ln 10\sqrt{{\left({x-x}_i\right)}^2+{\left({y-y}_i\right)}^2}}{e}^{-\frac{{\left(10\mathrm{nlg}(\sqrt{{\left({x-x}_i\right)}^2+{(y-y_i)}^2}/d_i^{\&prime;})\right)}^2}{2{{\mathrm{\&sigma;}}_i}^2}}---\left(6\right)$

By formula (6), can obtain the center-of-mass coordinate of each anchor node in overlapping region is

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

${\stackrel{\&OverBar;}{y}}_i=\frac{{d_2}^2(-{\cos \mathrm{\&theta;}}_2+{\cos \mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_1)-{d_1}^2({-\cos \mathrm{\&theta;}}_2+\cos {\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-{0.5c}_2)}{d_2({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_2}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_1)-d_1({\mathrm{\&theta;}}_2-{\mathrm{\&theta;}}_1)(\mathrm{\&Phi;}\left(\frac{10\mathrm{nlg}\frac{d_1}{d_i^{\&prime;}}}{{\mathrm{\&sigma;}}_i}\right)-c_2)}+y_i---\left(7\right)$

In formula (7), Φ () represents the probable value of standardized normal distribution, d ₁, d ₂the distance that represents integral domain, θ ₁, θ ₂the angular range that shows integral domain, c ₁be illustrated in standardized normal distribution mathematical expectation of probability on interval, c ₂be illustrated in n the center-of-mass coordinate that standardized normal distribution mathematical expectation of probability on 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 positioning precision of 20 unknown node checking the present invention and the triangle centroid algorithm based on RSSI, the probability centroid algorithm positioning precision 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 is got average to the RSSI of same anchor node after receiving this information, obtains unknown node to the measured distance of anchor node;

By RF range finding model inference, go out unknown node to the probability distribution of anchor node distance, the d that to obtain in the level of signifiance be 0.1 _ispan;

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

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

Using the density function of probability density function as overlapping region, derive each anchor node in the probability barycenter expression formula of overlapping region, the probability center-of-mass coordinate set of obtaining is removed after maximum and minimum value, and the probability barycenter that obtains overlapping region is 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 precision that improved with the triangle barycenter location algorithm based on RSSI.Due to the mathematic(al) representation of the probability barycenter of having derived, the present invention has low to hardware requirement and realizes simple feature, so the present invention can be for multiple wireless sensor network positioning occasion.

Be located in the square area of 10m * 10m, 7 anchor nodes are randomly dispersed in distributed areas, choose: P in experiment _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, σ when different _i=[1,1.3,1.5,2,2.1,2.5,3], σ value 3～10 when identical.Use respectively the triangle centroid algorithm based on RSSI and carry out emulation based on RSSI probability centroid algorithm, simulation result is as Fig. 3, Fig. 4, Fig. 5, Fig. 6 in accompanying drawing.Fig. 3 is that the present invention locates schematic diagram, comprises overlapping region corresponding to the probability barycenter of each anchor node and final estimated coordinates in figure.Fig. 4 is the positioning precision contrast of 20 nodes of two kinds of algorithm random measurements.Fig. 5 probes into the impact of σ on two kinds of algorithm positioning precisioies when σ value is identical, and along with the increase positioning precision decline of σ, the present invention changes comparatively mild.Fig. 6 has probed into anchor node and has measured the impact of number of times on two kinds of algorithm positioning precisioies, and anchor node is measured number of times increase can improve positioning precision, gets 8～11 times for good in reality.It is better that the present invention compares the performance of the triangle barycenter location algorithm based on RSSI, 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 good targeting scheme.

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

Claims (5)

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

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

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

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

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

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:

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

In 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 i anchor node signal communication process, d _i' representing the measured distance of unknown node and i anchor node, n represents anchor node number;

S42: using 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 formula, represent that i anchor node is at the barycenter of overlapping region, Φ () represents the probable value of standardized normal distribution, d ₁, d ₂the distance that represents integral domain, θ ₁, θ ₂the angular range that shows integral domain, c ₁be illustrated in standardized normal distribution mathematical expectation of probability on interval, c ₂be illustrated in standardized normal distribution mathematical expectation of probability on interval;

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

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

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

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

5. the wireless sensor network positioning method based on RSSI probability barycenter according to claim 4, is characterized in that: the described default level of signifiance is taken as at 0.1 o'clock,