CN104144499A - Wireless sensor network positioning method based on RSSI vector similarity degree and generalized inverse - Google Patents

Abstract

The invention discloses a wireless sensor network positioning method based on the RSSI vector similarity degree and generalized inverse. Gauss curve fitting is carried out on the probability of a specific RSSI value occurring at different distances, piecewise linear interpolation is carried out on an RSSI-d (relation between intensity and distances) curve, and a positioning algorithm that a quadrangle serves as a positioning unit, internal positioning of the positioning unit and external positioning of the positioning unit are carried out, and areas where nodes are likely to exist are rapidly locked is designed; meanwhile, by compassion of the similarity degree between RSSI vectors of unknown nodes and RSSI vectors of reference nodes, the reference anchor node nearest to the unknown nodes is continuously updated and determined, and the area where the unknown nodes are located is narrowed; for the situation that the distance measurement error is random and can not be controlled due to randomness of RSSI measurement errors, the generalized inverse method is introduced as the supplement of the positioning algorithm, the whole positioning algorithm is perfected, and the actual feasibility of the algorithm is improved.

Description

Based on RSSI vector phase recency and generalized inverse wireless sensor network locating method

Technical field

The present invention relates to wireless sensor network location technology, specifically a kind of based on RSSI vector phase recency and generalized inverse wireless sensor network locating method.

Background technology

At wireless sensor network (WSN, Wireless Sensor Network) every application in, only have the information that sensor node is caught and gathered to combine with node self-position, just can accurately illustrate " locale ", could reflect faithfully Target monitoring area.Obviously, the positional information of node is the prerequisite of sensor node perception and image data, only has the perception data of node, and there is no the positional information in perception data source, and this is to lack practical significance.Therefore, in wireless sensor network, node locating seems particularly important, and location technology also just must become an indispensable function and a crucial support technology of wireless sensor network.The positional information of node, for network data acquisition and event monitoring, is very important.Wireless sensor network Position Research has very important meaning for tracking, the monitoring in remote sensing field, contributes to comparison route, optimize communicate task, synthetic routing table.Once learn the position that event occurs, can calculate rapidly best route in order to send information to management node, for balancing network energy load and communication load, the best route of each node is conventionally not identical.

At present, there is the multiple research about Wireless Sensor Network Located Algorithm.Document (Rashedur R M, Barker K, Alhajj R.Replica Placement in Data Grid:Considering Utility and Risk[C] .Proceedings of IEEE International Conference on Coding and Computing, 2005:354-359) be coordinate position by three limit positioning modes estimation unknown node, locating effect is good.Document (Shi Qinqin, Huo Hong. use steepest descent algorithm to improve the node locating precision [J] of maximum likelihood estimation algorithm. computer application research, 2008,25 (7): 2038-2040) use steepest descent algorithm to optimize the node locating value of maximum likelihood estimation algorithm gained, it is the improvement to maximal possibility estimation positioning mode, can obtain with less calculation cost the raising of positioning precision, successful.Document (Wang XB, Fu MY, Zhang HS.Target tracking in wireless sensor networks based on the combination of KF and MLE using distance measurements[J] .IEEE Trans.on Mobile Computing, 2012,11 (4): 567-576) having merged maximum likelihood estimates and Kalman filtering, obtain the double effects of node precalculated position and node tracking, and there is higher positioning precision.

Centroid algorithm because of its convenient operation and the less feature of error rather well received in many localization methods of wireless sensor network, sequence location (the SBL that the people such as K Yedavalli propose, Sequence-Based Localization) algorithm, it is all the instantiation of barycenter positioning mode that the people such as Liu Zhihua have proposed the sequence location new algorithm that sequence location algorithm and 3 orthocenter methods combine, also obtained good positioning precision, but in boundary node location or imperfect environmental positioning, also need to improve.

The people such as Liu Shaofei have proposed a kind of based on average DV-Hop improvement algorithm of jumping apart from estimation and position correction, estimate that in order to solve by single anchor node the network Average hop distance of gained cannot reflect the deficiency of real network Average hop distance, obtains good positioning precision.But the scope of the positioning precision of this algorithm is to be based upon on the circulation correction algorithm of position, if position correction iteration mistake, positioning result is still influenced.

Summary of the invention

For above deficiency of the prior art, the object of the present invention is to provide and a kind ofly avoided the fluctuation of RSSI on the impact of positioning precision, accurate easy wireless sensor network locating method, technical scheme of the present invention is as follows: a kind of based on RSSI vector phase recency and generalized inverse wireless sensor network locating method, it comprises the following steps:

101, obtain received signal strength indicator (Received Signal Strength Indicator) the RSSI value between node to be positioned, and obtain probability density RSSI-d (intensity and distance relation) curve by carrying out gaussian curve approximation at the probability of the RSSI of different distance place value appearance;

102, in probability density curve RSSI-d (intensity and distance relation) curve matching in step 101 being obtained, the RSSI probability density of each distance is found peak value f (RSSI _i) _max, by this peak value f (RSSI _i) _maxcorresponding apart from d as the estimated distance between transmitting-receiving node, d=f (RSSI _i) _max* k+b, parameter k and b are the variation tendency of probability density with distance, the model of trying to achieve probability density curve RSSI-d is:

$d=\max (f_0+a*e^{\frac{-2{({\mathrm{RSSI}}_i-\stackrel{\‾}{\mathrm{RSSI}})}^2}{{\mathrm{\σ}}^2}})*k+b,{\mathrm{\σ}}^2=\frac{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{({\mathrm{RSSI}}_i-\mathrm{\μ})}^2}{n-1}$

Parameter f ₀represent the RSSI probability density in somewhere, can be determined by the substitution of two groups of specific RSSI values for example RSSI=117dBm and RSSI=61dBm.μ represents the RSSI population mean of measuring.

103, probability density curve RSSI-d (intensity and distance relation) model is adopted to piecewise linear interpolation method;

104, to the RSSI-d after step 103 piecewise linear interpolation (intensity and distance relation) curve, adopt taking quadrangle as positioning unit, treat according to the outside positioning mode of positioning unit positioned internal method and positioning unit the region that location node exists and position;

105, the comparison of close degree between the RSSI vector of the RSSI vector sum reference node by node to be positioned, constantly updates and determines the reference anchor node nearest apart from unknown node, determines node to be positioned region.

Further, described RSSI adopts respectively 117dBm or 89dBm or 61dBm or 25dBm,

Further, the method that in step 101, gaussian curve approximation adopts is least square method.Utilize least square method can try to achieve easily unknown data, be applicable to linear relationship, and make the quadratic sum of error between these data of trying to achieve and real data for minimum.

Further, the Gauss curve fitting function prototype of described Gaussian curve is:

$f\left(x\right)=a*e^{\frac{-2{(x-\mathrm{\μ})}^2}{{\mathrm{\ω}}^2}}---\left(1\right)$

Wherein n represents the total number of numerical value of measuring.μ represents the RSSI population mean of measuring. $a=\frac{1}{\mathrm{\σ}\sqrt{2\mathrm{\π}}}$

Further, in the time of RSSI=117dBm, gained Gaussian curve equation is:

$f\left(x\right)=0.463*e^{{\left(\frac{x-117}{1.214}\right)}^2}.$

Further, in step 103, establishing RSSI-d (intensity and distance relation) curve has RSSI ₁and RSSI ₂, its corresponding function is respectively f _1maxand f _2max, so for want to try to achieve corresponding f _imax∈ (f _1max, f _2max), will meet relation:

$\mathrm{\β}=\frac{f_{i\max }-f_{1\max }}{{\mathrm{RSSI}}_i-{\mathrm{RSSI}}_1}=\frac{f_{2\max }-f_{i\max }}{{\mathrm{RSSI}}_2-{\mathrm{RSSI}}_i}$

In formula, if β is called interpolation coefficient. β <1, can carry out interpolation; If β is >1, can carry out extrapolation.

Further, after step 106, also comprise range error at random when uncontrollable, introduce Generalized Inverse Method as the supplementary step in location.

Advantage of the present invention and beneficial effect are as follows:

First the present invention has adopted distance-finding method and the gaussian curve approximation based on RSSI, by analyzing and process experimental data, draws the totally conclusion of approximate Normal Distribution of RSSI, the negative effect that is intended to reject small probability, the large RSSI value of disturbing.

Secondly, the RSSI-d curve of adjacent node is adopted to the method for piecewise linear interpolation, according to the RSSI value of minority and the relation of its distance, calculate distance corresponding to any RSSI value.

In addition, the core of location algorithm of the present invention, designed the location algorithm based on RSSI vector phase recency, first find the reference anchor node nearest apart from unknown node, then judge that unknown node is inner or outside at the quadrangle forming apart from its four nearest anchor nodes, take a little two kinds of different location mechanisms inside and outside figure.

Especially, for the film micro area at quick lock in unknown node place, propose the concept of vectorial phase recency, constantly find the reference anchor node nearest apart from unknown node, thereby determine the region at unknown node place; Meanwhile, introduce generalized inverse, estimate the coordinate position of unknown node, perfect localization method, improves location feasibility, has verified the positional accuracy of algorithm.

Brief description of the drawings

In Fig. 1, a, b, c, d are respectively 4 groups of different RSSI value probability density curves of the present invention;

Fig. 2 is RSSI experiment value of the present invention and RSSI matched curve tendency chart;

Fig. 3 is that unknown node of the present invention positioning unit in the time that figure is inner is divided and sample point is determined schematic diagram;

Fig. 4 is that unknown node of the present invention is located schematic diagram in the time that figure is outside;

Fig. 5 is that the present invention utilizes generalized inverse location algorithm;

Fig. 6 is the flow chart of the preferred embodiment of the present invention;

Fig. 7 is the flow chart of outside location;

Fig. 8 is the flow chart of positioned internal.

Embodiment

The invention will be further elaborated to provide an infinite embodiment below in conjunction with accompanying drawing.But should be appreciated that, these describe example just, and do not really want to limit the scope of the invention.In addition, in the following description, omitted the description to known features and technology, to avoid unnecessarily obscuring concept of the present invention.

The present invention designs a kind of based on RSSI vector phase recency and generalized inverse wireless sensor network locating method.The method comprises the steps.

1, based on RSSI distance-finding method

In order to analyze the regularity of distribution of RSSI, the present invention carries out confluence analysis to many groups RSSI data, has drawn RSSI and be respectively 4 groups of probability density curves of 117dBm, 89dBm, 61dBm, 25dBm, as Fig. 1.Fig. 6 is the flow chart of the preferred embodiment of the present invention;

Fig. 7 is the flow chart of outside location; Fig. 8 is the flow chart of positioned internal.

Can be found out by above-mentioned 4 groups of RSSI probability density curves, it is a probability distribution that the RSSI value of actual measurement distributes, and the probability density curve of experiment RSSI data has following features:

Centrality: the peak (being the position at mean place) of curve is positioned at central authorities substantially.

Basic symmetry: curve centered by mean, left and right almost symmetry, curve two ends approach transverse axis.

Mobility gradually: curve is started by mean place place, the alteration trend of the left and right sides is gradually and declines.

Some scholars are studied the distribution pattern of RSSI, think that RSSI is totally similar to Normal Distribution.Can find out from experimental data and probability density curve, the RSSI probability density curve of actual measurement and truly having of the probability density curve of normal distribution are agreed with part.So the present invention has totally carried out Gauss curve fitting to experiment RSSI, rejects misdata and the invalid data of small probability, finds out probability peak, extract and the immediate estimated distance of actual distance, for nodal exactness location provides experiment basis.In order to improve RSSI range accuracy, adopt least square method to do Gauss curve fitting to RSSI probability density curve.

Gauss curve fitting function prototype is:

$f\left(x\right)=a*e^{\frac{-2{(x-\mathrm{\&mu;})}^2}{{\mathrm{\&omega;}}^2}}---\left(1\right)$

Wherein $\mathrm{\&mu;}=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{RSSI}}_i}{n},\mathrm{\&omega;}=\sqrt{\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{({\mathrm{RSSI}}_i-\mathrm{\&mu;})}^2}{n-1}}.$

The probability density curve at matching RSSI=117dBm place, gained Gaussian curve equation is:

$f\left(x\right)=0.4643*e^{{\left(\frac{x-117}{1.214}\right)}^2}---\left(2\right)$

As seen from the figure, in original probability density curve, the value of maximum probability is RSSI=117dBm, and in the probability density curve of the Gaussian Profile that matching obtains, the value of maximum probability is μ=117dBm, matching income effect and former data consistent.

Fig. 2 has shown respectively the relation between RSSI-d experiment value and RSSI-d matched curve, and as seen from the figure, the experimental data of matching acquired results and RSSI-d occurs deviation in indivedual distances, but all presents exponential damping trend generally.Because transmitting signal is in closely decay fast, and attenuation law is obvious; When remote, decay comparatively slow, and error increases.Also can be found out by lab diagram, 6m is with interior matched curve, and effect is better, and error of fitting is less; Along with the increase of distance, fitting effect has certain deviation, and error of fitting increases.So 10m approaches linear relationship with the RSSI value at interior neighbor distance place, can try to achieve the RSSI value that there is no the distance of measuring by interpolation.

According to upper joint analysis, the RSSI value of known actual measurement approaches Gaussian Profile at different distance place, the distance between the just most possible thing receiving node in place and transmitting node that RSSI distribution density is larger.To the RSSI probability density peak-seeking of each distance,, there is relation: d=f (RSSI in the estimated distance using corresponding this peak value distance between transmitting-receiving node between probability density peak value and distance _i) _max* k+b, parameter k and b are the variation tendency of probability density with distance, can try to achieve by substitution data.The model of RSSI-d is:

$d=\max (f_0+a*e^{\frac{-2{({\mathrm{RSSI}}_i-\stackrel{\&OverBar;}{\mathrm{RSSI}})}^2}{{\mathrm{\&sigma;}}^2}})*k+d---\left(3\right)$

If known RSSI ₁and RSSI ₂the function at place is respectively f _1maxand f _2max, so for want to try to achieve corresponding f _imax∈ (f _1max, f _2max), will meet relation:

$\mathrm{\&beta;}=\frac{f_{i\max }-f_{1\max }}{{\mathrm{RSSI}}_i-{\mathrm{RSSI}}_1}=\frac{f_{2\max }-f_{i\max }}{{\mathrm{RSSI}}_2-{\mathrm{RSSI}}_i}---\left(4\right)$

In formula (3), if β is called interpolation coefficient. β <1, can carry out interpolation; If β is >1, can carry out extrapolation.

If known RSSI _i, can pass through f _imax=(1-β) * f _1max+ β * f _2maxask for corresponding normal state peak value f _imax, according to above-mentioned model, can try to achieve the most possible corresponding distance d of this RSSI _i.

Between 0-25m, can carry out interpolation to the RSSI-d model in different RSSI interval, for this RSSI-d interpolation model is extrapolated to larger RSSI interval, carry out remote distance estimations, make it to have more actual availability, we spread to 56 (respective distances 1～10m) by RSSI from 117.Finally, averaging of income range error and the average range error of Shadowing model are to such as table 1.

Table 1 RSSI-d model and the contrast of Shadowing model range error

As can be seen from Table 1, Shadowing model and RSSI-d model can be inferred and try to achieve corresponding distance according to RSSI value, reach range finding effect.But can be found out by range error, the average range error of RSSI-d interpolation model is less than the average range error of Shadowing model, and this has benefited from linear interpolation between short distance.

2, the WSN location algorithm based on RSSI vector phase recency

The existing location algorithm using leg-of-mutton center of gravity, barycenter etc. as finish node estimated coordinates, obtain considerable positioning precision although can progressively dwindle locating area by different division methods, but in these localization methods, the prerequisite that some location algorithm is carried out is that unknown node is in positioning unit inside, it is inner or outside at positioning unit that some does not distinguish node, do not discuss node in the time that positioning unit is outside because error is excessive, and overall positioning precision is caused to the situation of negative effect; As FTLM location model and SBL algorithm.The present invention chooses apart from 4 nearest nodes of node to be measured, and as with reference to anchor node, and the quadrangle that these 4 anchor nodes are formed is as the locating area of unknown node, determines that by area-constrained relation unknown node to be positioned is inner or outside at quadrangle.This section has solved following problem: if in quadrangle inside, how to choose reference sample point; If in quadrangle outside, how in the situation that position error is as far as possible little, to determine unknown node coordinate position.

As Fig. 3, according to quadrangle area restriction relation formula, known some P is in quadrangle ABCD inside.By triangle area restriction relation formula, known some P is in △ DAO.Unknown node is at the location mechanism of figure inside, and step is as follows:

Step 1: △ DAO has 6 reference sample point D, A, O, E, F, G;

Step 2: the phase recency between the RSSI vector of above-mentioned 6 the reference sample points of RSSI vector sum of comparison point P;

Step 3: find the reference sample point that close degree is the highest, apart from its nearest some E, D, G.

In like manner, in △ EGD, be H, I, J apart from the nearest reference sample point of P.Equally △ HIJ is done to aforesaid operations, known some P is in △ LIM.So far, no longer dwindle micro-Delta Region, △ LIM is final positioning unit, gets the coordinate of this leg-of-mutton barycenter as node P to be positioned.

Unknown node is as follows at the location mechanism of figure outside: as Fig. 4, P is unknown node to be positioned, A, B, C, D be apart from nearest 4 of P with reference to anchor node, AC and BD are two diagonal of quadrangle ABCD, O is two diagonal intersection points (coordinate can be tried to achieve), is regarded as new reference sample point.

According to quadrangle area restriction relation formula, equation is false, and known some P is in quadrangle ABCD outside.Unknown node P receives four RSSI values with reference to anchor node: { RSSI _d, RSSI _a, RSSI _b, RSSI _c, some D, A, P composition △ PAD.Here due to the RSSI value that can record between every 2, by signal attenuation model, can try to achieve the distance (Atria limit) between every 2, and the coordinate of anchor node A and D is known, can try to achieve unknown node coordinate by following equation group:

$\left\{\begin{array}{c}L=d_{\mathrm{AD}}+d_{\mathrm{DP}}+d_{\mathrm{PA}}\\ S_{\mathrm{\&Delta;PAD}}=\sqrt{\frac{L}{2}*(\frac{L}{2}-d_{\mathrm{AD}})*(\frac{L}{2}-d_{\mathrm{DP}})*(\frac{L}{2}-d_{\mathrm{PA}})}\\ S_{\mathrm{\&Delta;PAD}}==\frac{1}{2}{d}_{\mathrm{AD}}*d_{\mathrm{PO}1}\\ d_{\mathrm{PO}1}=\frac{A*x+B*y+C}{\sqrt{A^2+B^2}}\end{array}\right\}---\left(8\right)$

Wherein L is triangle girth, and S is triangle area, and d is the triangle length of side, A*x+B*y+C=0 is the linear equation of AD place straight line, solving equations (8) can be tried to achieve two groups of coordinate P (X, Y) and the P1 (X1, Y1) of unknown node.

In like manner, choose that RSSI value in RSSI vector ranks first place and the 3rd some D and some B, they form △ PBD together with P point self, also can try to achieve two groups of unknown node coordinate P (X, and P1 (X2, Y2) Y). comprehensive two leg-of-mutton two groups solutions, can try to achieve two leg-of-mutton public vertex P, can obtain the coordinate P (X, Y) of unknown node.(1) unknown node is at the location mechanism of positioning unit inside

As Fig. 3, P is unknown node to be positioned, A, B, C, D be apart from nearest 4 of P with reference to anchor node, A, B, C, the quadrangle that D surrounds is positioning unit.AC and BD are two diagonal of quadrangle ABCD, and O is two diagonal intersection points (coordinate can be tried to achieve), are regarded as new reference sample point.By following area-constrained relation, can determine that unknown node is inner or outside at quadrangle ABCD.

$S_{\mathrm{ABCD}}=S_{\mathrm{\&Delta;ABP}}+S_{\mathrm{\&Delta;BCP}}+S_{\mathrm{\&Delta;CDP}}+S_{\mathrm{\&Delta;DAP}}\&DoubleRightArrow;$ Point P is in quadrangle ABCD inside;

$S_{\mathrm{\&Delta;DAO}}=S_{\mathrm{\&Delta;DPA}}+S_{\mathrm{\&Delta;APO}}+S_{\mathrm{\&Delta;OPD}}\&DoubleRightArrow;$ Point P is in △ DAO inside.

If unknown node, in ABCD inside, as Fig. 3, is taked following operation, dwindle positioning unit:

Step 1: judging point P is at △ ABO, and △ BCO, in △ CDO or △ DAO.

Step 2: in some in these four triangles of fruit dot P, by getting the mode of every limit mid point of this triangle, obtain 3 new reference sample points, i.e. 3 mid points.

Step 3: again the RSSI vector (6 RSSI vectors) of the original triangular apex of RSSI vector sum of unknown node P and 3 reference sample points newly obtaining is done to the comparison of phase recency totally, find out the reference sample point that phase recency is the highest, be 3 nearest reference sample points of distance P, obtain E herein, G, D.

By that analogy, constantly repeat above-mentioned steps, the mode of the mid point on the limit by the new cocked hat of continuous searching, obtains the reference sample point nearest apart from unknown node P, and then constantly dwindling micro-Delta Region at unknown node place, Fig. 3 mid point P is finally locked in △ LIM.

(2) unknown node is at the location mechanism of positioning unit outside

If unknown node is in outside, as Fig. 4.Be total to summit triangle by two and determine unknown node coordinate.

Main operation is as follows:

Step 1: find rank forefront two D, A point of RSSI vector (by strong to the weak) meta of unknown node P, they form △ PAD. with P self

Step 2: find and rank first place in the RSSI vector of unknown node P and the 3rd D, B point, they form △ PBD with P self.

Step 3: because each Atria length of side is known, triangle area can be asked; Two apex coordinates are known, relend and help area formula can try to achieve the height of a P to opposite side.

Respectively △ PAD and △ PBD are done the operation of above-mentioned steps 3, can try to achieve the coordinate of two concurrent triangle public vertex P.

Although this method is feasible, but in ranging process, the rssi measurement error span of all directions may be also inconsistent, and the change of distance on correspondence direction just increases and decreases inconsistent, at this moment said method just can not be tried to achieve two leg-of-mutton public vertex, and the equation group of simultaneous is without public solution.

As Fig. 5, due to the existence of RSSI random meausrement error, the final P obtaining that calculates ₁' (x' ₁, y' ₁) and P' ₂(x' ₂, y' ₂) do not overlap, the equation group of institute's simultaneous does not have public solution.For this reason, we introduce Generalized Inverse Method and carry out calculating location coordinate.

Known A ∈ C ^{m × n}with b ∈ C ^m, ask the vectorial X ∈ C of system of linear equations AX=b ^m

If above formula has solution, be referred to as compatibility condition group; If above formula, without solution, is referred to as incompatible equations group.For incompatible equations group, there is not the general solution under ordinary meaning, this trifle is intended to utilize generalized inverse to try to achieve best fit approximation solution to inconsistent without solving equations.We by shape as:

$X=\underset{X\&Element;C^m}{\min }\left|\right|\mathrm{AX}-b\left|\right|---\left(9\right)$

Solution be called the least square solution of incompatible equations group, wherein, || || represent European norm.

Definition 1: if incompatible system of linear equations AX=b meets wherein, be the least squares generalized inverse of A, exist so meet claim be the least square solution of this equation group, separate than other, the error sum of squares causing minimum.

If G is a matrix, a least square solution of incompatible equations, || AGb-b|| ₂minimum, so just has: || A (Gb+ (I-GA) Z)-b|| ₂=|| AGb-b|| ₂

with it is all a least square solution of this incompatible system of linear equations.

While calculating unknown node coordinate according to anchor node A, B, D, group can establish an equation:

$\left\{\begin{array}{c}|k_{\mathrm{AD}}*x-y|+b_1-h_{\mathrm{AD}\&perp;}*\sqrt{k_{\mathrm{AD}}^2+1}=0\\ |k_{\mathrm{AD}}*x-y|+b_2-h_{\mathrm{BD}\&perp;}*\sqrt{k_{\mathrm{BD}}^2+1}=0\\ 2(x_A-x_D)x+2(y_A-y_D)y=d_{\mathrm{PA}}^2-d_{\mathrm{PD}}^2+x_{\mathrm{PD}}^2-x_{\mathrm{PA}}^2+y_{\mathrm{PD}}^2-y_{\mathrm{PA}}^2\\ 2(x_B-x_D)x+2(y_B-y_D)y=d_{\mathrm{PB}}^2-d_{\mathrm{PD}}^2+x_{\mathrm{PD}}^2-x_{\mathrm{PB}}^2+y_{\mathrm{PD}}^2-y_{\mathrm{PB}}^2\end{array}\right\}---\left(10\right)$

Turned into shape as the system of linear equations of AX=b, wherein coefficient matrices A and vectorial b are respectively:

$A=\left[\begin{array}{cc}{k}_{\mathrm{AD}}& -1\\ k_{\mathrm{BD}}& -1\\ 2(x_A-x_D)& 2(y_A-y_D)\\ 2(x_B-x_D)& 2(y_B-y_D)\end{array}\right]b=\left[\begin{array}{c}{h}_{\mathrm{AD}\&perp;}*\sqrt{k_{\mathrm{AD}}^2+1}-b_1\\ h_{\mathrm{BD}\&perp;}*\sqrt{k_{\mathrm{BD}}^2+1}-b_2\\ d_{\mathrm{PA}}^2-d_{\mathrm{PD}}^2+x_{\mathrm{PD}}^2-x_{\mathrm{PA}}^2+y_{\mathrm{PD}}^2-y_{\mathrm{PA}}^2\\ d_{\mathrm{PB}}^2-d_{\mathrm{PD}}^2+x_{\mathrm{PD}}^2-x_{\mathrm{PB}}^2+y_{\mathrm{PD}}^2-y_{\mathrm{PB}}^2\end{array}\right]$

Because this equation group without public solution, is incompatible system of linear equations, the least squares generalized inverse of this equation group is:

$A_i^{-}={\left(A^{T}A\right)}^{-1}{A}^T---\left(10\right)$

So the least square solution of this incompatible system of linear equations is:

$\begin{array}{c}\tilde{X}=A_i^{-}b\\ =A_i^{-}\left[\begin{array}{c}{h}_{\mathrm{AD}\&perp;}*\sqrt{k_{\mathrm{AD}}^2+1}-b_1\\ h_{\mathrm{BD}\&perp;}*\sqrt{k_{\mathrm{BD}}^2+1}-b_2\\ d_{\mathrm{PA}}^2-d_{\mathrm{PD}}^2+x_{\mathrm{PD}}^2-x_{\mathrm{PA}}^2+y_{\mathrm{PD}}^2-y_{\mathrm{PA}}^2\\ d_{\mathrm{PB}}^2-d_{\mathrm{PD}}^2+x_{\mathrm{PD}}^2-x_{\mathrm{PB}}^2+y_{\mathrm{PD}}^2-y_{\mathrm{PB}}^2\end{array},\right]\end{array}---\left(11\right)$

Can try to achieve like this $\tilde{X}=\left[\begin{array}{c}\tilde{x}\\ \tilde{y}\end{array}\right],$ Unknown node estimated coordinates is

To sum up, unknown node is in the time that figure is inner, and four anchor nodes formation quadrangle positioning units that utilization is nearest apart from unknown node, in new positioning unit, constantly find apart from its nearest reference sample point, thereby constantly dwindles the region at unknown node place; Unknown node, in the time that figure is outside, adopts mathematical method how much, introduces generalized inverse, tries to achieve unknown node coordinate.

For the similarity degree between the RSSI vector of the RSSI vector sum reference sample point of properer description node to be positioned, find exactly near the reference sample point of " recently " unknown node, we have designed new index-vectorial phase recency.

Definition 2: if node can receive the broadcast singal of n anchor node, so, the intensity level RSSI of a received n signal can form vectorial set:

Ψ＝{RSSI ₁,RSSI ₂,…,RSSI _i}(i＝1,2,…,n) (12)

Wherein, RSSI _irepresent that receiving node receives the RSSI value of i anchor node.

RSSI in subtend duration set Ψ sorts from big to small, is gathered

Ψ'＝{X(R ₁),X(R ₂),…X(R _j)}(j＝1,2,…,n) (13)

We will gather the key value collection that Ψ ' is called RSSI, wherein, and X (R _j) represent the RSSI value of the rank j position that this node receives,, apart from the near anchor node of unknown node j, we are referred to as RSSI key value.

M reference sample point receive n anchor node RSSI vector table be denoted as:

RSSI in vector table is sorted from big to small, gathered

Wherein, X (R _kj) represent the RSSI value of the rank j position that k reference sample point receive, apart from the near anchor node of unknown node j.

Definition 3: by keyword set Ψ '={ X (R independently ₁), X (R ₂) ... X (R _j) (j=1,2 ..., n) form two different vector: R' _t={ X (R _t1), X (R _t2) ..., X (R _tj) ... X (R _tn), R' _k={ X (R _k1), X (R _k2) ..., X (R _kq) ... X (R _kn),

Keyword X (R between two vectors _tp) irrelevance be:

d(p)＝|X(R _Tp)-X(R _kq)|,if R _Tp＝R _kq (16)

Definition 4:RSSI vector R _t={ RSSI _t1, RSSI _t2..., RSSI _tjrSSI _tn, R _k={ RSSI _k1, RSSI _k2..., RSSI _kqrSSI _knto RSSI vector R _tdo normalized:

$\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{rssi}}_{\mathrm{Tp}}=1,(p=\mathrm{1,2},...,n)---\left(17\right)$

So, RSSI vector R _twith RSSI vector R _kbetween phase recency ρ (k) be:

$\mathrm{\&rho;}\left(k\right)=\mathrm{\&rho;}(R_T,R_k)=\underset{p=1}{\overset{n}{\mathrm{\&Sigma;}}}d\left(p\right)*{\mathrm{rssi}}_{\mathrm{Tp}},(k=\mathrm{1,2},...,m)(p=\mathrm{1,2},...,n)R_k\&Element;R---\left(18\right)$

Wherein, d (p) is keyword X (R _tp) irrelevance, rssi _tprepresent _tpthe significance level of the RSSI of place.

From definition 4, vector similarity meets following relation:

1) ρ (R _t, R _k)>=0, and if only if irrelevance X (R _tp) (p=1,2 ..., n) be establishment in 0 o'clock.

2) ρ (R _t, R _k) less, vectorial R is described _twith R _kbetween difference less, close degree is higher; Otherwise, illustrating that between vector, difference is larger, close degree is lower.

To ρ (k) (k=1,2 ..., m) row ascending order, so, in vector table R with vector

R _T＝{RSSI _T1,RSSI _T2,…,RSSI _Tj…RSSI _Tn} (19)

N the vector that close degree is the highest meet ρ (k) (k=1,2 ... N, N<m) <min (ρ (k) is (k>N))

In the present invention, by phase recency defined above, constantly find the top n reference sample point the highest with unknown node similarity degree, thereby constantly dwindle the region at unknown node place; For several times, finally choose the region that reference sample point surrounds that phase recency ρ (k) occupies front N is unknown node estimation region to iteration like this.For the close degree of accurate description unknown node and each reference sample point, and then accurately estimating unknown node coordinate, the present invention, according to close degree, does weighting processing to each reference sample point, and final estimated coordinates using the barycenter in this region as unknown node, computing formula is as follows:

$(x,y)=(\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{x}_k*{\mathrm{rssi}}_{\mathrm{Tk}},\frac{1}{N}\underset{k=1}{\overset{N}{\mathrm{\&Sigma;}}}{y}_k*{\mathrm{rssi}}_{\mathrm{Tk}})$

These embodiment are interpreted as being only not used in and limiting the scope of the invention for the present invention is described above.After having read the content of record of the present invention, technical staff can make various changes or modifications the present invention, and these equivalences change and modification falls into the inventive method claim limited range equally.

Claims (7)

1. based on RSSI vector phase recency and a generalized inverse wireless sensor network locating method, it is characterized in that, comprise the following steps:

101, obtain the received signal strength indicator RSSI value between the node of node to be positioned, and the probability occurring in the RSSI of different distance place value is carried out to gaussian curve approximation and obtains the relation curve of probability density RSSI-d intensity and distance;

102, in probability density curve RSSI-d intensity matching in step 101 being obtained and distance relation curve, the RSSI probability density of each distance is found peak value f (RSSI _i) _max, by this peak value f (RSSI _i) _maxcorresponding apart from d as the estimated distance between transmitting-receiving node, d=f (RSSI _i) _max* k+b, parameter k and b are the variation tendency of probability density with distance, the model of trying to achieve probability density curve RSSI-d is:

parameter f ₀represent the RSSI probability density in somewhere, can be determined by the substitution of two groups of specific RSSI values,

103, probability density curve RSSI-d intensity and distance relation model are adopted to piecewise linear interpolation method;

104, to the RSSI-d intensity after step 103 piecewise linear interpolation and distance relation curve, adopt taking quadrangle as positioning unit, treat according to the outside positioning mode of positioning unit positioned internal method and positioning unit the region that location node exists and position;

105, the comparison of close degree between the RSSI vector of the RSSI vector sum reference node by node to be positioned, constantly updates and determines the reference anchor node nearest apart from unknown node, determines node to be positioned region.

2. according to claim 1 based on RSSI vector phase recency and generalized inverse wireless sensor network locating method, it is characterized in that: described RSSI adopts respectively 117dBm or 89dBm or 61dBm or 25dBm.

3. according to claim 1 based on RSSI vector phase recency and generalized inverse wireless sensor network locating method, it is characterized in that: the method that in step 101, gaussian curve approximation adopts is least square method.

According to described in claim 1 or 3 based on RSSI vector phase recency and generalized inverse wireless sensor network locating method, it is characterized in that: the Gauss curve fitting function prototype of described Gaussian curve is:

Wherein n represents the total number of numerical value of measuring, and μ represents the RSSI population mean of measuring,

5. according to claim 4 based on RSSI vector phase recency and generalized inverse wireless sensor network locating method, it is characterized in that: in the time of RSSI=117dBm, gained Gaussian curve equation is:

。

6. according to claim 1 based on RSSI vector phase recency and generalized inverse wireless sensor network locating method, it is characterized in that: in step 103, establish RSSI-d intensity and distance relation curve has RSSI ₁and RSSI ₂, its corresponding function is respectively f _1maxand f _2max, so for want to try to achieve corresponding f _imax∈ (f _1max, f _2max), will meet relation:

In formula, if β is called interpolation coefficient. β <1, can carry out interpolation; If β is >1, can carry out extrapolation.

7. according to claim 1 based on RSSI vector phase recency and generalized inverse wireless sensor network locating method, it is characterized in that: after step 106, also comprise range error at random when uncontrollable, introduce Generalized Inverse Method as the supplementary step in location.