CN105223549A - The full mobile node positioning method of a kind of wireless sensor network based on RSSI - Google Patents

Abstract

The present invention relates to the full mobile node positioning method of a kind of wireless sensor network based on RSSI.Current ranging localization algorithm is used for static node location, or part of nodes moves, the situation that part of nodes is static, have no and RSSI location algorithm is applied to anchor node and unknown node and is all in node locating under mobile status, and algorithm cannot solve the node locating when anchor node quantity is less than 3 at present.The object of the invention is to the above-mentioned deficiency overcoming prior art, provide a kind of wireless sensor network based on RSSI full mobile node positioning method.The present invention can unknown node and four, three, two and an anchor node communication time, adopt different algorithms to draw the position of unknown node.

Description

The full mobile node positioning method of a kind of wireless sensor network based on RSSI

Technical field

What the present invention relates to is network node locating method, is specifically related to the full mobile node positioning method of wireless sensor network based on RSSI.

Background technology

Wireless sensor network (wirelesssensornetworks, WSN) form by being deployed in cheap microsensor nodes a large amount of in monitored area, the network system of the self-organization of the multi-hop formed by communication, its objective is the information of perceptive object in perception collaboratively, acquisition and processing network's coverage area, and send to observer.

In sensor network, the monitoring of positional information to sensor network is most important, and the node location of the position that event occurs or obtaining information is the important information comprised in sensor node supervisory messages.Therefore, determining the position that event occurs or obtaining the node location of message is one of the most basic function of sensor network, plays a part key to the validity of sensor network application.

In sensor network nodes location technology, according to node self position whether known, sensor node is divided into anchor node and unknown node.The shared within network nodes ratio of anchor node is very little, can obtain the exact position of self by carrying the means such as GPS positioning equipment.Anchor node is the reference point of unknown node location, and unknown node calculates self position according to certain location algorithm by the positional information of anchor node.Distance according to whether between measured node, can be divided into location algorithm based on the location algorithm of range finding and the location algorithm without the need to range finding.Location algorithm without the need to range finding positions mainly through the information such as hop count, network connectivty.Location algorithm based on range finding passes through the distance between ranging technology measured node, and recycling measures the coordinate that the range information obtained calculates unknown node.Based on range finding location technology because needs calculate internodal distance, so its positioning precision is higher than range-free localization algorithm.Wherein, the location technology of finding range based on signal receiving strength (receivedsignalstrengthindicator, RSSI) is a more representational implementation.Signal intensity when principle of work based on RSSI range finding is the transmitting of known transmitting node, receiving node, according to the intensity receiving signal, utilizes signal propagation model that is theoretical or experience that signal intensity is converted into distance, thus calculates the position of node.Because RSSI algorithm has that location algorithm is simple, cost is low, power consumption is little, is widely used without the need to advantages such as time synchronized and extra hardware.Such as, but this algorithm is due to the interference easily by environment, and the uncertainty such as multi-path jamming, diffraction, barrier, non-line-of-sight in radio signal propagation process all can affect wireless signal strength, the precision based on RSSI range finding and location is affected.RSSI is introduced centroid localization algorithm, the advantage of both utilizations, the positioning precision improving wireless sensor network is one of main direction of studying of current location technology.Current ranging localization algorithm is used for static node location, or part of nodes moves, the situation that part of nodes is static, have no and RSSI location algorithm is applied to anchor node and unknown node and is all in node locating under mobile status, and algorithm cannot solve the node locating when anchor node quantity is less than 3 at present.

Summary of the invention

The object of the invention is to the above-mentioned deficiency overcoming prior art, provide a kind of wireless sensor network based on RSSI full mobile node positioning method.Concrete steps are as follows:

1. the determination of range finding model

Generally, the average power of Received signal strength presents Decay Rate along with the increase of distance, and the theoretical model generally adopted in wireless transmission is shadowing model, as shown in formula (1):

$P_r=P_r\left(d_0\right)-10n\lg \left(\frac{d}{d_0}\right)+X---\left(1\right)$

In formula, P _rrepresent the received power (dBm) of wireless signal; P _r(d ₀) expression reference distance is d ₀wireless signal in the received power (dBm) of receiving end, d represents the distance (m) between Transmit-Receive Unit, d ₀be reference distance (m), n represents the path dissipation index with environmental correclation, X to be average be 0 Gaussian random variable (dBm).Reference distance d ₀normal value 1m, institute with the formula (1) can approximate representation be:

P _r＝A-10nlg(d)(2)

In formula, A be signal transmission distance 1m far away time Received signal strength power (dBm), n is the path loss coefficient relevant with environment, and d is signal transmission distance.

Least square method can be adopted to determine A and n value in formula (2), under identical experimental situation, measure one group of distance d _iwith the value P of received signal power intensity _ri, make y=P _rwith x=lg (d), then formula (2) can be expressed as:

y＝A-10nx(3)

If approximate matched curve is sum of square of deviations is:

In formula for x _ibring the formula about coefficient a after matched curve into, y _ifor x _ithe data measured under corresponding experimental situation.According to the principle matched curve making sum of square of deviations minimum.

Each point is to the distance sum of matched curve, and namely sum of square of deviations can be expressed as:

$R^2=\underset{i=1}{\overset{n}{\Σ}}{\[y_i-(a_0+a_{1}x+\mathrm{...}+a_k{x}^k)\]}^2---\left(5\right)$

A is asked on the right of (5) formula _ilocal derviation, and be expressed as matrix form:

[a can be solved by (6) formula ₀a ₁a _k], and then can matched curve be determined, then by matched curve contrast with the curve of reality, can A and n be determined, finally can obtain the distance of shadowing model and the formula of received signal strength.

2. concrete position fixing process

(1) when anchor node and unknown node are all random movement, in the k moment, when unknown node X can communicate with 4 and above anchor node, choose wherein 4 RSSI value maximum anchor node A, B, C, D to locate this unknown node, RSSI is larger, and just to represent anchor node distance unknown node nearer.The signal intensity from anchor node A, B, C, D that unknown node receives is respectively RSSI _a, RSSI _b, RSSI _c, RSSI _d, utilize distance transformation model, the distance of X to anchor node A, B, C, D can be calculated, be expressed as d _a, d _b, d _c, d _d.In two dimensional surface location, locate a unknown node and need three anchor nodes that can communicate with it, therefore, from these four anchor nodes, select arbitrarily three to locate unknown node, then same unknown node altogether can by location 4 times, and each elements of a fix are respectively (x ₁, y ₁), (x ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄).Suppose first with B, C, D for anchor node location unknown node X, respectively with anchor node B, C, D for round dot, d _b, d _c, d _dfor three circles of radius intersect at an X, then this point is the position of unknown node, and computing formula is as (7):

$\left\{\begin{array}{c}\sqrt{{(x_1-x_B)}^2+{(y_1-y_B)}^2}=d_B\\ \sqrt{{(x_1-x_C)}^2+{(y_1-y_C)}^2}=d_C\\ \sqrt{{(x_1-x_D)}^2+{(y_1-y_D)}^2}=d_D\end{array}\right.---\left(7\right)$

(x in formula _b, y _b), (x _c, y _c), (x _d, y _d) be respectively the coordinate of anchor node B, C, D, (x ₁, y ₁) coordinate of unknown node X for being located by anchor node B, C, D, d _b, d _c, d _dbe respectively anchor node B, C, D distance to unknown node X, as shown in Figure 2.

Through type (7) can try to achieve the coordinate of unknown node X.

$\left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]={\left[\begin{array}{cc}2(x_B-x_D)& 2(y_B-y_D)\\ 2(x_C-x_D)& 2(y_C-y_D)\end{array}\right]}^{-1}\left[\begin{array}{c}{x}_B^2-x_D^2+y_B^2-y_D^2+d_D^2-d_B^2\\ x_C^2-x_D^2+y_C^2-y_D^2+d_D^2-d_C^2\end{array}\right]---\left(8\right)$

Utilize said method, can obtain with anchor node A, C, D respectively, A, B, D, the unknown node coordinate (x of A, B, C location ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄).

Use the coordinate of barycenter weighting location algorithm determination unknown node:

Distance value d is less, and the precision of corresponding location is also higher, and any three anchor nodes are less to the distance altogether of unknown node, and location result precision is out higher, so the weights of such coordinate should be larger.(x ₁, y ₁), (x ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄) weights M ₁, M ₂, M ₃, M ₄be respectively:

$\left\{\begin{array}{c}{M}_1=\frac{\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_2=\frac{\frac{1}{d_A}+\frac{1}{d_C}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_3=\frac{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_4=\frac{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\end{array}\right.---\left(9\right)$

In formula denominator represent four anchor nodes divide be clipped to unknown node inverse distance and, molecule be corresponding three anchor nodes participating in location to unknown node inverse distance with.

Calculate thus, the coordinate of unknown node is (x', y')

$\left\{\begin{array}{c}{x}^{\′}=\frac{(M_1{x}_1+M_2{x}_2+M_3{x}_3+M_4{x}_4)}{4}\\ y^{\′}=\frac{(M_1{y}_1+M_2{y}_2+M_3{y}_3+M_4{y}_4)}{4}\end{array}\right.---\left(10\right)$

When anchor node and unknown node are all random movement, in the k moment, when unknown node X can communicate with 4 and above anchor node, coordinate (the x' of unknown node is calculated according to formula (10), y') after, in order to improve the positioning precision of mobile node further, location coordinate is out revised;

Environmentally situation, a given distance value σ and σ > 0, when distance between two nodes is less than σ, then think that two Nodes are in same environment, the error caused due to environment when so locating this two nodes is approximate the same, in 4 anchor nodes, they are respectively d to the distance of unknown node X _a, d _b, d _c, d _d, pick out the distance value being less than σ, then think that these anchor nodes and unknown node are in identical environment;

1) as only having the distance d of anchor node A distance unknown node in A, B, C, D tetra-anchor nodes _a< σ, then use anchor node B, C, D to carry out positioning anchor node A, and the coordinate of the A calculated point is (x' _a, y' _a), positioning error is (e _x, e _y) be expressed as:

$\left\{\begin{array}{c}{e}_x=x_A-x_A^{\&prime;}\\ e_y=y_A-y_A^{\&prime;}\end{array}\right.---\left(11\right)$

The positioning error that this error representative unknown node environment causes;

2) if there is multiple value to meet d > σ in the distance value of unknown node and anchor node, then the method adopting weighting to be averaging carrys out the error of calculation, if anchor node A, B, C, D are to the distance value d of unknown node X _a, d _b, d _c, d _dall be less than σ, then respectively with wherein three anchor nodes for beaconing nodes locates an other anchor node, be again respectively A (x' by the anchor node coordinate of locating _a, y' _a) B (x' _b, y' _b) C (x' _c, y' _c) D (x' _d, y' _d), obtaining positioning error is respectively, as formula (12)

$\left\{\begin{array}{c}{e}_{Ax}=x_A-x_A^{\&prime;}\\ e_{Ay}=y_A-y_A^{\&prime;}\\ e_{Bx}=x_B-x_B^{\&prime;}\\ e_{By}=y_B-y_B^{\&prime;}\\ e_{Cx}=x_C-x_C^{\&prime;}\\ e_{Cy}=y_C-y_C^{\&prime;}\\ e_{Dx}=x_D-x_D^{\&prime;}\\ e_{Dy}=y_D-y_D^{\&prime;}\end{array}\right.---\left(12\right)$

(e _ax, e _ay), (e _ax, e _ay), (e _ax, e _ay), (e _ax, e _ay) weights be respectively W _a, W _b, W _c, W _d, as formula (13)

$\left\{\begin{array}{c}{W}_A=\frac{\frac{1}{d_A}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_B=\frac{\frac{1}{d_B}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_C=\frac{\frac{1}{d_C}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_D=\frac{\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\end{array}\right.---\left(13\right)$

The denominator of weights are each anchor nodes to unknown node inverse distance and, molecule is wherein by the anchor node of the locating inverse to unknown node distance, distance value is less, represent that the distance of anchor node distance unknown node is nearer, the error produced when so locating this anchor node more can represent the error during unknown node of location, so weights are larger;

Final error is (e _x, e _y) can be expressed as

$\left\{\begin{array}{c}{e}_x=\frac{W_A{e}_{Ax}+W_B{e}_{Bx}+W_C{e}_{Cx}+W_D{e}_{Dx}}{4}\\ e_y=\frac{W_A{e}_{Ay}+W_B{e}_{By}+W_C{e}_{Cy}+W_D{e}_{Dy}}{4}\end{array}\right.---\left(14\right)$

The coordinate (x, y) of revised unknown node is

$\{\begin{array}{c}x=x^{\&prime;}+e_x\\ y=y^{\&prime;}+e_y\end{array}---\left(15\right)$

(2) when anchor node and unknown node are all random movement, in the kth moment, in time only having 3 anchor nodes can communicate with unknown node, suppose that anchor node is respectively A, B, C, the signal intensity that unknown node receives is respectively RSSI _a, RSSI _b, RSSI _c, utilize distance transformation model, the distance that its point is clipped to unknown node is d _a, d _b, d _c, then respectively with anchor node A, B, C for the center of circle, respectively with d _a, d _b, d _cfor radius draws circle, intersect at unknown node X, trilateration can be adopted to locate unknown node X.Computing formula is:

$\left\{\begin{array}{c}\sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\\ \sqrt{{(x-x_B)}^2+{(y-y_B)}^2}=d_B\\ \sqrt{{(x-x_C)}^2+{(y-y_C)}^2}=d_C\end{array}\right.---\left(16\right)$

Just the coordinate (x, y) of unknown node X can be tried to achieve thus.

$\left[\begin{array}{c}x\\ y\end{array}\right]={\left[\begin{array}{cc}2(x_A-x_C)& 2(y_A-y_C)\\ 2(x_B-x_C)& 2(y_B-y_C)\end{array}\right]}^{-1}\left[\begin{array}{c}{x}_A^2-x_C^2+y_A^2-y_C^2+d_C^2-d_A^2\\ x_B^2-x_C^2+y_B^2-y_C^2+d_C^2-d_B^2\end{array}\right]---\left(17\right)$

(3) when anchor node and unknown node are all random movement, in the k moment, when unknown node X can only communicate with 2 anchor node A with B, if the translational speed of unknown node is v, it is (x that unknown node locates successfully its coordinate in the k-1 moment _k-1, y _k-1).K moment anchor node A with B communicates with unknown node X, and anchor node is respectively d to the distance of unknown node X _a, d _b, respectively with anchor node A and B for the center of circle, with d _a, d _bfor radius draws circle, then the point that two circles intersect is respectively X ₁and X ₂, the coordinate X of intersection point is obtained according to formula (18) ₁(x ₁, y ₁), X ₂(x ₂, y ₂), as shown in Figure 3.

$\left\{\begin{array}{c}\sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\\ \sqrt{{(x-x_B)}^2+{(y-y_B)}^2}=d_B\end{array}\right.---\left(18\right)$

Then the position of k-1 moment unknown node X is calculated to X ₁and X ₂distance value be respectively d ₁, d ₂, by d ₁, d ₂compare in speed, the position with corresponding to speed v distance value relatively, is the position in unknown node k moment.Even | d ₁-v| < | d ₂-v|, then x ₁for unknown node X is in the position in k moment; If | d ₂-v| < | d ₁-v|, then x ₂for unknown node X is in the position in k moment.

(4) when anchor node and unknown node are all when random mobile, in the k moment, when only have 1 anchor node A can with unknown node X communication time, the translational speed of unknown node is v, k-n to the k-1 moment, and unknown node is located successfully.The coordinate pitch angle sequence of front n moment location is respectively θ _i=(θ _k-n, θ _k-n+1..., θ _k-1), wherein deduct last item with latter one and obtain adjacent differential seat angle sequence Δ θ _i=(Δ θ ₁, Δ θ ₂..., Δ θ _n-1).Utilize this n-1 differential seat angle to predict the n-th differential seat angle, and then calculate the pitch angle of k moment unknown node relative to true origin.The method of prediction is grey prediction, using differential seat angle sequence as original series, makes Δ θ _i=x ⁽⁰⁾(m), wherein m=i=1 ... n-1 detailed process is as follows:

Original series is:

x ⁽⁰⁾(m)＝(x ⁽⁰⁾(1),x ⁽⁰⁾(2),…,x ⁽⁰⁾(n-1))(19)

1) single order Accumulating generation sequence is done:

$x^{\left(1\right)}\left(k\right)=\underset{m=1}{\overset{k}{\&Sigma;}}{x}^{\left(0\right)}\left(m\right),k=1,\mathrm{...},n-1---\left(20\right)$

2) background value of GM (1,1) is constructed:

$z^{\left(1\right)}(k+1)=\frac{1}{2}\&lsqb;x^{\left(1\right)}\left(k\right)+x^{\left(1\right)}(k+1)\&rsqb;,k=1,2,\mathrm{...},n-2---\left(21\right)$

3) x is set up ⁽¹⁾(k), (k=1,2 ..., n-1) first-order linear albinism differential equation:

$\frac{{\mathrm{dx}}^{\left(1\right)}\left(k\right)}{dt}+{\mathrm{ax}}^{\left(1\right)}\left(k\right)=u---\left(22\right)$

Wherein a, u are undetermined coefficient, and the white function formula of equation (22) is:

$x^{\left(1\right)}\left(k\right)=\left(x^{\left(0\right)}\right(1)-\frac{u}{a})e^{-a(k-1)}+\frac{u}{a},k=1,2,\mathrm{...},n-1---\left(23\right)$

4) according to principle of least square method estimated parameter a, u

${\&lsqb;\hat{a},\hat{u}\&rsqb;}^T={\left(B^{T}B\right)}^{-1}{B}^T{Y}_n---\left(24\right)$

Wherein, data matrix B and Y _nfor:

$B=\left[\begin{array}{cc}-\frac{1}{2}{Z}^{\left(1\right)}\left(2\right)& 1\\ -\frac{1}{2}{Z}^{\left(1\right)}\left(3\right)& 1\\ .& .\\ .& .\\ .& .\\ -\frac{1}{2}{Z}^{\left(1\right)}(n-1)& 1\end{array}\right]---\left(25\right)$

$Y_n=\left[\begin{array}{c}{x}^{\left(0\right)}\left(2\right)\\ x^{\left(0\right)}\left(3\right)\\ .\\ .\\ .\\ x^{\left(0\right)}(n-1)\end{array}\right]---\left(26\right)$

5) by the estimated value of a, u substitution formula (23), obtains predictive equation

6) original data sequence model is set up:

${\hat{x}}^{\left(0\right)}\left(1\right)=x^{\left(0\right)}\left(1\right)---\left(27\right)$

${\hat{x}}^{\left(0\right)}\left(k\right)={\hat{x}}^{\left(1\right)}\left(k\right)-{\hat{x}}^{\left(1\right)}(k-1)=(1-e^{\hat{a}})\left({\hat{x}}^{\left(0\right)}\right(1)-\frac{\hat{u}}{\hat{a}})e^{-\hat{a}(k+1)},k=2,3...---\left(28\right)$

In formula, for original data sequence x ⁽⁰⁾(k), (k=1,2 ..., n-1)) match value; for original data sequence x ⁽⁰⁾(k), (k=1,2 ..., n-1) predicted value.

Dope Δ θ _nafter, the position calculating k moment unknown node relative to the pitch angle of true origin is:

θ _k＝θ _k-1+Δθ _n(29)

The k-1 moment, with the position of unknown node X for the center of circle, speed v be the circle of radius and k moment with anchor node A position for the center of circle, d _afor the circle of radius intersects at X ₁and X ₂two points, have a point to be the position of k moment unknown node X in these two points.Owing to having estimated the pitch angle of k moment unknown node and initial point line L, by judging X ₁and X ₂distance to straight line L can determine which point is correct position, and namely the point of close together is the position that k moment unknown node moves to, as shown in Figure 4, and X ₂for the position of k moment unknown node.

The coordinate of k-1 moment unknown node X is (x _k-1, y _k-1), the coordinate of k moment anchor node A is (x _a, y _a), X ₁and X ₂computing formula is:

$\left\{\begin{array}{c}\sqrt{{(x-x_{k-1})}^2+{(y-y_{k-1})}^2}=v\\ \sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\end{array}\right.---\left(30\right)$

Accompanying drawing explanation

The present invention is described in detail below in conjunction with the drawings and specific embodiments;

Fig. 1 is system flowchart of the present invention;

Fig. 2 is trilateration of the present invention;

The situation that Fig. 3 is anchor node number that the present invention can communicate with unknown node when being 2;

The situation that Fig. 4 is anchor node number that the present invention can communicate with unknown node when being 1.

Embodiment

The technological means realized for making the present invention, creation characteristic, reaching object and effect is easy to understand, below in conjunction with embodiment, setting forth the present invention further.

With reference to Fig. 1-4, this embodiment by the following technical solutions: the present invention proposes a kind of based on RSSI weighted mass center mobile node location algorithm, by the wireless sensor network of RSSI weighted mass center algorithm application in the movement entirely of anchor node and unknown node.In conjunction with the speed of unknown node and the change at not pitch angle in the same time, solve the problem cannot located when anchor node is less than 3 time in RSSI location algorithm.

1. the determination of range finding model

Generally, the average power of Received signal strength presents Decay Rate along with the increase of distance, and the theoretical model generally adopted in wireless transmission is shadowing model, as shown in formula (1):

$P_r=P_r\left(d_0\right)-10n\lg \left(\frac{d}{d_0}\right)+X---\left(1\right)$

In formula, P _rrepresent the received power (dBm) of wireless signal; P _r(d ₀) expression reference distance is d ₀wireless signal in the received power (dBm) of receiving end, d represents the distance (m) between Transmit-Receive Unit, d ₀be reference distance (m), n represents the path dissipation index with environmental correclation, X to be average be 0 Gaussian random variable (dBm).Reference distance d ₀normal value 1m, institute with the formula (1) can approximate representation be:

P _r＝A-10nlg(d)(2)

In formula, A be signal transmission distance 1m far away time Received signal strength power (dBm), n is the path loss coefficient relevant with environment, and d is signal transmission distance.

Least square method can be adopted to determine A and n value in formula (2), under identical experimental situation, measure one group of distance d _iwith the value P of received signal power intensity _ri, make y=P _rwith x=lg (d), then formula (2) can be expressed as:

y＝A-10nx(3)

If approximate matched curve is sum of square of deviations is:

In formula for x _ibring the formula about coefficient a after matched curve into, y _ifor x _ithe data measured under corresponding experimental situation.According to the principle matched curve making sum of square of deviations minimum.

Each point is to the distance sum of matched curve, and namely sum of square of deviations can be expressed as:

$R^2=\underset{i=1}{\overset{n}{\&Sigma;}}{\&lsqb;y_i-(a_0+a_{1}x+\mathrm{...}+a_k{x}^k)\&rsqb;}^2---\left(5\right)$

A is asked on the right of (5) formula _ilocal derviation, and be expressed as matrix form:

[a can be solved by (6) formula ₀a ₁a _k], and then can matched curve be determined, then by matched curve contrast with the curve of reality, can A and n be determined, finally can obtain the distance of shadowing model and the formula of received signal strength.

2. concrete position fixing process

(1) when anchor node and unknown node are all random movement, in the k moment, when unknown node X can communicate with 4 and above anchor node, choose wherein 4 RSSI value maximum anchor node A, B, C, D to locate this unknown node, RSSI is larger, and just to represent anchor node distance unknown node nearer.The signal intensity from anchor node A, B, C, D that unknown node receives is respectively RSSI _a, RSSI _b, RSSI _c, RSSI _d, utilize distance transformation model, the distance of X to anchor node A, B, C, D can be calculated, be expressed as d _a, d _b, d _c, d _d.In two dimensional surface location, locate a unknown node and need three anchor nodes that can communicate with it, therefore, from these four anchor nodes, select arbitrarily three to locate unknown node, then same unknown node altogether can by location 4 times, and each elements of a fix are respectively (x ₁, y ₁), (x ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄).Suppose first with B, C, D for anchor node location unknown node X, respectively with anchor node B, C, D for round dot, d _b, d _c, d _dfor three circles of radius intersect at an X, then this point is the position of unknown node, and computing formula is as (7):

$\left\{\begin{array}{c}\sqrt{{(x_1-x_B)}^2+{(y_1-y_B)}^2}=d_B\\ \sqrt{{(x_1-x_C)}^2+{(y_1-y_C)}^2}=d_C\\ \sqrt{{(x_1-x_D)}^2+{(y_1-y_D)}^2}=d_D\end{array}\right.---\left(7\right)$

(x in formula _b, y _b), (x _c, y _c), (x _d, y _d) be respectively the coordinate of anchor node B, C, D, (x ₁, y ₁) coordinate of unknown node X for being located by anchor node B, C, D, d _b, d _c, d _dbe respectively anchor node B, C, D distance to unknown node X, as shown in Figure 2.

Through type (7) can try to achieve the coordinate of unknown node X.

$\left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]={\left[\begin{array}{cc}2(x_B-x_D)& 2(y_B-y_D)\\ 2(x_C-x_D)& 2(y_C-y_D)\end{array}\right]}^{-1}\left[\begin{array}{c}{x}_B^2-x_D^2+y_B^2-y_D^2+d_D^2-d_B^2\\ x_C^2-x_D^2+y_C^2-y_D^2+d_D^2-d_C^2\end{array}\right]---\left(8\right)$

Utilize said method, can obtain with anchor node A, C, D respectively, A, B, D, the unknown node coordinate (x of A, B, C location ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄).

Use the coordinate of barycenter weighting location algorithm determination unknown node:

Distance value d is less, and the precision of corresponding location is also higher, and any three anchor nodes are less to the distance altogether of unknown node, and location result precision is out higher, so the weights of such coordinate should be larger.(x ₁, y ₁), (x ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄) weights M ₁, M ₂, M ₃, M ₄be respectively:

$\left\{\begin{array}{c}{M}_1=\frac{\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_2=\frac{\frac{1}{d_A}+\frac{1}{d_C}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_3=\frac{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_4=\frac{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\end{array}\right.---\left(9\right)$

In formula denominator represent four anchor nodes divide be clipped to unknown node inverse distance and, molecule be corresponding three anchor nodes participating in location to unknown node inverse distance with.

Calculate thus, the coordinate of unknown node is (x', y')

$\left\{\begin{array}{c}{x}^{\&prime;}=\frac{(M_1{x}_1+M_2{x}_2+M_3{x}_3+M_4{x}_4)}{4}\\ y^{\&prime;}=\frac{(M_1{y}_1+M_2{y}_2+M_3{y}_3+M_4{y}_4)}{4}\end{array}\right.---\left(10\right)$

On this basis, in order to improve the positioning precision of mobile node further, now location coordinate is out revised.

Environmentally situation, a given distance value σ and σ > 0, when distance between two nodes is less than σ, then think that two Nodes are in same environment, the error caused due to environment when so locating this two nodes is approximate the same.In 4 anchor nodes, they are respectively d to the distance of unknown node X _a, d _b, d _c, d _d, pick out the distance value being less than σ, then think that these anchor nodes and unknown node are in identical environment.

1) as only having the distance d of anchor node A distance unknown node in A, B, C, D tetra-anchor nodes _a< σ, then use anchor node B, C, D to carry out positioning anchor node A, and the coordinate of the A calculated point is (x' _a, y' _a), positioning error is (e _x, e _y) be expressed as:

$\left\{\begin{array}{c}{e}_x=x_A-x_A^{\&prime;}\\ e_y=y_A-y_A^{\&prime;}\end{array}\right.---\left(11\right)$

The positioning error that this error representative unknown node environment causes.

2) if there is multiple value to meet d > σ in the distance value of unknown node and anchor node, then the method adopting weighting to be averaging carrys out the error of calculation.If anchor node A, B, C, D are to the distance value d of unknown node X _a, d _b, d _c, d _dall be less than σ, then respectively with wherein three anchor nodes for beaconing nodes locates an other anchor node, be again respectively A (x' by the anchor node coordinate of locating _a, y' _a) B (x' _b, y' _b) C (x' _c, y' _c) D (x' _d, y' _d), obtaining positioning error is respectively, as formula (12)

$\left\{\begin{array}{c}{e}_{Ax}=x_A-x_A^{\&prime;}\\ e_{Ay}=y_A-y_A^{\&prime;}\\ e_{Bx}=x_B-x_B^{\&prime;}\\ e_{By}=y_B-y_B^{\&prime;}\\ e_{Cx}=x_C-x_C^{\&prime;}\\ e_{Cy}=y_C-y_C^{\&prime;}\\ e_{Dx}=x_D-x_D^{\&prime;}\\ e_{Dy}=y_D-y_D^{\&prime;}\end{array}\right.---\left(12\right)$

(e _ax, e _ay), (e _ax, e _ay), (e _ax, e _ay), (e _ax, e _ay) weights be respectively W _a, W _b, W _c, W _d, as formula (13)

$\left\{\begin{array}{c}{W}_A=\frac{\frac{1}{d_A}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_B=\frac{\frac{1}{d_B}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_C=\frac{\frac{1}{d_C}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_D=\frac{\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\end{array}\right.---\left(13\right)$

The denominator of weights are each anchor nodes to unknown node inverse distance and, molecule is wherein by the anchor node of the locating inverse to unknown node distance, distance value is less, represent that the distance of anchor node distance unknown node is nearer, the error produced when so locating this anchor node more can represent the error during unknown node of location, so weights are larger.

Final error is (e _x, e _y) can be expressed as

$\left\{\begin{array}{c}{e}_x=\frac{W_A{e}_{Ax}+W_B{e}_{Bx}+W_C{e}_{Cx}+W_D{e}_{Dx}}{4}\\ e_y=\frac{W_A{e}_{Ay}+W_B{e}_{By}+W_C{e}_{Cy}+W_D{e}_{Dy}}{4}\end{array}\right.---\left(14\right)$

The coordinate (x, y) of revised unknown node is

$\{\begin{array}{c}x=x^{\&prime;}+e_x\\ y=y^{\&prime;}+e_y\end{array}---\left(15\right)$

3) if be all greater than given σ in the distance of 4 anchor node middle distance unknown node, then do not position the correction of precision, then the coordinate of unknown node is (x', y')

(2) when anchor node and unknown node are all random movement, in the kth moment, in time only having 3 anchor nodes can communicate with unknown node, suppose that anchor node is respectively A, B, C, the signal intensity that unknown node receives is respectively RSSI _a, RSSI _b, RSSI _c, utilize distance transformation model, the distance that its point is clipped to unknown node is d _a, d _b, d _c, then respectively with anchor node A, B, C for the center of circle, respectively with d _a, d _b, d _cfor radius draws circle, intersect at unknown node X, trilateration can be adopted to locate unknown node X.Computing formula is:

$\left\{\begin{array}{c}\sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\\ \sqrt{{(x-x_B)}^2+{(y-y_B)}^2}=d_B\\ \sqrt{{(x-x_C)}^2+{(y-y_C)}^2}=d_C\end{array}\right.---\left(16\right)$

Just the coordinate (x, y) of unknown node X can be tried to achieve thus.

$\left[\begin{array}{c}x\\ y\end{array}\right]={\left[\begin{array}{cc}2(x_A-x_C)& 2(y_A-y_C)\\ 2(x_B-x_C)& 2(y_B-y_C)\end{array}\right]}^{-1}\left[\begin{array}{c}{x}_A^2-x_C^2+y_A^2-y_C^2+d_C^2-d_A^2\\ x_B^2-x_C^2+y_B^2-y_C^2+d_C^2-d_B^2\end{array}\right]---\left(17\right)$

When anchor node and unknown node are all random movement, in the k moment, when unknown node X can only communicate with 2 anchor node A with B, if the translational speed of unknown node is v, it is (x that unknown node locates successfully its coordinate in the k-1 moment _k-1, y _k-1).K moment anchor node A with B communicates with unknown node X, and anchor node is respectively d to the distance of unknown node X _a, d _b, respectively with anchor node A and B for the center of circle, with d _a, d _bfor radius draws circle, then the point that two circles intersect is respectively X ₁and X ₂, the coordinate X of intersection point is obtained according to formula (18) ₁(x ₁, y ₁), X ₂(x ₂, y ₂), as shown in Figure 3.

$\left\{\begin{array}{c}\sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\\ \sqrt{{(x-x_B)}^2+{(y-y_B)}^2}=d_B\end{array}\right.---\left(18\right)$

Then the position of k-1 moment unknown node X is calculated to X ₁and X ₂distance value be respectively d ₁, d ₂, by d ₁, d ₂compare in speed, the position with corresponding to speed v distance value relatively, is the position in unknown node k moment.Even | d ₁-v| < | d ₂-v|, then x ₁for unknown node X is in the position in k moment; If | d ₂-v| < | d ₁-v|, then x ₂for unknown node X is in the position in k moment.

(4) when anchor node and unknown node are all when random mobile, in the k moment, when only have 1 anchor node A can with unknown node X communication time, the translational speed of unknown node is v, k-n to the k-1 moment, and unknown node is located successfully.The coordinate pitch angle sequence of front n moment location is respectively θ _i=(θ _k-n, θ _k-n+1..., θ _k-1), wherein deduct last item with latter one and obtain adjacent differential seat angle sequence Δ θ _i=(Δ θ ₁, Δ θ ₂..., Δ θ _n-1).Utilize this n-1 differential seat angle to predict the n-th differential seat angle, and then calculate the pitch angle of k moment unknown node relative to true origin.The method of prediction is grey prediction, using differential seat angle sequence as original series, makes Δ θ _i=x ⁽⁰⁾(m), wherein m=i=1 ... n-1 detailed process is as follows:

Original series is:

x ⁽⁰⁾(m)＝(x ⁽⁰⁾(1),x ⁽⁰⁾(2),…,x ⁽⁰⁾(n-1))(19)

1) single order Accumulating generation sequence is done:

$x^{\left(1\right)}\left(k\right)=\underset{m=1}{\overset{k}{\&Sigma;}}{x}^{\left(0\right)}\left(m\right),k=1,\mathrm{...},n-1---\left(20\right)$

2) background value of GM (1,1) is constructed:

$z^{\left(1\right)}(k+1)=\frac{1}{2}\&lsqb;x^{\left(1\right)}\left(k\right)+x^{\left(1\right)}(k+1)\&rsqb;,k=1,2,\mathrm{...},n-2---\left(21\right)$

3) x is set up ⁽¹⁾(k), (k=1,2 ..., n-1) first-order linear albinism differential equation:

$\frac{{\mathrm{dx}}^{\left(1\right)}\left(k\right)}{dt}+{\mathrm{ax}}^{\left(1\right)}\left(k\right)=u---\left(22\right)$

Wherein a, u are undetermined coefficient, and the white function formula of equation (22) is:

$x^{\left(1\right)}\left(k\right)=\left(x^{\left(0\right)}\right(1)-\frac{u}{a})e^{-a(k-1)}+\frac{u}{a},k=1,2,\mathrm{...},n-1---\left(23\right)$

4) according to principle of least square method estimated parameter a, u

${\&lsqb;\hat{a},\hat{u}\&rsqb;}^T={\left(B^{T}B\right)}^{-1}{B}^T{Y}_n---\left(24\right)$

Wherein, data matrix B and Y _nfor:

$B=\left[\begin{array}{cc}-\frac{1}{2}{Z}^{\left(1\right)}\left(2\right)& 1\\ -\frac{1}{2}{Z}^{\left(1\right)}\left(3\right)& 1\\ .& .\\ .& .\\ .& .\\ -\frac{1}{2}{Z}^{\left(1\right)}(n-1)& 1\end{array}\right]---\left(25\right)$

$Y_n=\left[\begin{array}{c}{x}^{\left(0\right)}\left(2\right)\\ x^{\left(0\right)}\left(3\right)\\ .\\ .\\ .\\ x^{\left(0\right)}(n-1)\end{array}\right]---\left(26\right)$

5) by the estimated value of a, u substitution formula (23), obtains predictive equation

6) original data sequence model is set up:

${\hat{x}}^{\left(0\right)}\left(1\right)=x^{\left(0\right)}\left(1\right)---\left(27\right)$

${\hat{x}}^{\left(0\right)}\left(k\right)={\hat{x}}^{\left(1\right)}\left(k\right)-{\hat{x}}^{\left(1\right)}(k-1)=(1-e^{\hat{a}})\left({\hat{x}}^{\left(0\right)}\right(1)-\frac{\hat{u}}{\hat{a}})e^{-\hat{a}(k+1)},k=2,3...---\left(28\right)$

In formula, for original data sequence x ⁽⁰⁾(k), (k=1,2 ..., n-1)) match value; for original data sequence x ⁽⁰⁾(k), (k=1,2 ..., n-1) predicted value.

Dope Δ θ _nafter, the position calculating k moment unknown node relative to the pitch angle of true origin is:

θ _k＝θ _k-1+Δθ _n(29)

The k-1 moment, with the position of unknown node X for the center of circle, speed v be the circle of radius and k moment with anchor node A position for the center of circle, d _afor the circle of radius intersects at X ₁and X ₂two points, have a point to be the position of k moment unknown node X in these two points.Owing to having estimated the pitch angle of k moment unknown node and initial point line L, by judging X ₁and X ₂distance to straight line L can determine which point is correct position, and namely the point of close together is the position that k moment unknown node moves to, as shown in Figure 4, and X ₂for the position of k moment unknown node.

The coordinate of k-1 moment unknown node X is (x _k-1, y _k-1), the coordinate of k moment anchor node A is (x _a, y _a), X ₁and X ₂computing formula is:

$\left\{\begin{array}{c}\sqrt{{(x-x_{k-1})}^2+{(y-y_{k-1})}^2}=v\\ \sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\end{array}\right.---\left(30\right)$

More than show and describe ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; what describe in above-described embodiment and instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.Application claims protection domain is defined by appending claims and equivalent thereof.

Claims (6)

1., based on the full mobile node positioning method of wireless sensor network of RSSI, it is characterized in that, when unknown node can with four, three, two and the communication of anchor node time, all can draw the position of unknown node, and can be revised positioning precision by error.

2. the full mobile node positioning method of a kind of wireless sensor network based on RSSI according to claim 1, it is characterized in that, when anchor node and unknown node are all random movement, in the k moment, when unknown node X can communicate with 4 and above anchor node, choose wherein 4 RSSI value maximum anchor node A, B, C, D to locate this unknown node, RSSI is larger, and just to represent anchor node distance unknown node nearer, and the signal intensity from anchor node A, B, C, D that unknown node receives is respectively RSSI _a, RSSI _b, RSSI _c, RSSI _d, utilize distance transformation model, the distance of X to anchor node A, B, C, D can be calculated, be expressed as d _a, d _b, d _c, d _d, in two dimensional surface location, locate a unknown node and need three anchor nodes that can communicate with it, therefore, from these four anchor nodes, select arbitrarily three to locate unknown node, then same unknown node altogether can by location 4 times, and each elements of a fix are respectively (x ₁, y ₁), (x ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄), suppose first with B, C, D for anchor node location unknown node X, respectively with anchor node B, C, D for round dot, d _b, d _c, d _dfor three circles of radius intersect at an X, then this point is the position of unknown node, and computing formula is as (7):

$\left\{\begin{array}{c}\sqrt{{(x_1-x_B)}^2+{(y_1-y_B)}^2}=d_B\\ \sqrt{{(x_1-x_C)}^2+{(y_1-y_C)}^2}=d_C\\ \sqrt{{(x_1-x_D)}^2+{(y_1-y_D)}^2}=d_D\end{array}\right.---\left(7\right)$

(x in formula _b, y _b), (x _c, y _c), (x _d, y _d) be respectively the coordinate of anchor node B, C, D, (x ₁, y ₁) coordinate of unknown node X for being located by anchor node B, C, D, d _b, d _c, d _dbe respectively anchor node B, C, D distance to unknown node X, as shown in Figure 2;

Through type (7) can try to achieve the coordinate of unknown node X:

$\left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]={\left[\begin{array}{cc}2(x_B-x_D)& 2(y_B-y_D)\\ 2(x_C-x_D)& 2(y_C-y_D)\end{array}\right]}^{-1}\left[\begin{array}{c}{x}_B^2-x_D^2+y_B^2-y_D^2+d_D^2-d_B^2\\ x_C^2-x_D^2+y_C^2-y_D^2+d_D^2-d_C^2\end{array}\right]---\left(8\right)$

Utilize said method, can obtain with anchor node A, C, D respectively, A, B, D, the unknown node coordinate (x of A, B, C location ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄)

Use the coordinate of barycenter weighting location algorithm determination unknown node:

Distance value d is less, and the precision of corresponding location is also higher, and any three anchor nodes are less to the distance altogether of unknown node, and location result precision is out higher, so the weights of such coordinate should be comparatively large, and (x ₁, y ₁), (x ₂, y ₂), (x ₃, y ₃), (x ₄, y ₄) weights M ₁, M ₂, M ₃, M ₄be respectively:

$\left\{\begin{array}{c}{M}_1=\frac{\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_2=\frac{\frac{1}{d_A}+\frac{1}{d_C}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_3=\frac{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ M_4=\frac{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\end{array}\right.---\left(9\right)$

In formula denominator represent four anchor nodes divide be clipped to unknown node inverse distance and, molecule be corresponding three anchor nodes participating in location to unknown node inverse distance with;

Calculate thus, the coordinate of unknown node is (x', y')

$\left\{\begin{array}{c}{x}^{\&prime;}=\frac{(M_1{x}_1+M_2{x}_2+M_3{x}_3+M_4{x}_4)}{4}\\ y^{\&prime;}=\frac{(M_1{y}_1+M_2{y}_2+M_3{y}_3+M_4{y}_4)}{4}\end{array}\right..---\left(10\right)$

3. the full mobile node positioning method of a kind of wireless sensor network based on RSSI according to claim 1, it is characterized in that, when anchor node and unknown node are all random movement, in the kth moment, in time only having 3 anchor nodes can communicate with unknown node, suppose that anchor node is respectively A, B, C, the signal intensity that unknown node receives is respectively RSSI _a, RSSI _b, RSSI _c, utilize distance transformation model, the distance that its point is clipped to unknown node is d _a, d _b, d _c, then respectively with anchor node A, B, C for the center of circle, respectively with d _a, d _b, d _cfor radius draws circle, intersect at unknown node X, trilateration can be adopted to locate unknown node X, and computing formula is:

$\left\{\begin{array}{c}\sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\\ \sqrt{{(x-x_B)}^2+{(y-y_B)}^2}=d_B\\ \sqrt{{(x-x_C)}^2+{(y-y_C)}^2}=d_C\end{array}\right.---\left(16\right)$

Just the coordinate (x, y) of unknown node X can be tried to achieve thus

$\left[\begin{array}{c}x\\ y\end{array}\right]={\left[\begin{array}{cc}2(x_A-x_C)& 2(y_A-y_C)\\ 2(x_B-x_C)& 2(y_B-y_C)\end{array}\right]}^{-1}\left[\begin{array}{c}{x}_A^2-x_C^2+y_A^2-y_C^2+d_C^2-d_A^2\\ x_B^2-x_C^2+y_B^2-y_C^2+d_C^2-d_B^2\end{array}\right].---\left(17\right)$

4. the full mobile node positioning method of a kind of wireless sensor network based on RSSI according to claim 1, it is characterized in that, when anchor node and unknown node are all random movement, in the k moment, when unknown node X can only communicate with 2 anchor node A with B, if the translational speed of unknown node is v, it is (x that unknown node locates successfully its coordinate in the k-1 moment _k-1, y _k-1), k moment anchor node A with B communicates with unknown node X, and anchor node is respectively d to the distance of unknown node X _a, d _b, respectively with anchor node A and B for the center of circle, with d _a, d _bfor radius draws circle, then the point that two circles intersect is respectively X ₁and X ₂, the coordinate X of intersection point is obtained according to formula (18) ₁(x ₁, y ₁), X ₂(x ₂, y ₂), as shown in Figure 3;

$\left\{\begin{array}{c}\sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\\ \sqrt{{(x-x_B)}^2+{(y-y_B)}^2}=d_B\end{array}\right.---\left(18\right)$

Then the position of k-1 moment unknown node X is calculated to X ₁and X ₂distance value be respectively d ₁, d ₂, by d ₁, d ₂compare in speed, the position with corresponding to speed v distance value relatively, is the position in unknown node k moment, even | and d ₁-v| < | d ₂-v|, then x ₁for unknown node X is in the position in k moment; If | d ₂-v| < | d ₁-v|, then x ₂for unknown node X is in the position in k moment.

5. the full mobile node positioning method of a kind of wireless sensor network based on RSSI according to claim 1, it is characterized in that, when anchor node and unknown node are all random movement, in the k moment, when only have 1 anchor node A can with unknown node X communication time, the translational speed of unknown node is v, k-n to the k-1 moment, unknown node is located successfully, and the coordinate pitch angle sequence of front n moment location is respectively θ _i=(θ _k-n, θ _k-n+1..., θ _k-1), wherein deduct last item with latter one and obtain adjacent differential seat angle sequence Δ θ _i=(Δ θ ₁, Δ θ ₂..., Δ θ _n-1), utilize this n-1 differential seat angle to predict the n-th differential seat angle, and then calculate the pitch angle of k moment unknown node relative to true origin, the method for prediction is grey prediction, using differential seat angle sequence as original series, makes Δ θ _i=x ⁽⁰⁾(m), wherein m=i=1 ... n-1 detailed process is as follows:

Original series is:

x ⁽⁰⁾(m)＝(x ⁽⁰⁾(1),x ⁽⁰⁾(2),…,x ⁽⁰⁾(n-1))(19)

1) single order Accumulating generation sequence is done:

$x^{\left(1\right)}\left(k\right)=\underset{m=1}{\overset{k}{\&Sigma;}}{x}^{\left(0\right)}\left(m\right),k=1,\mathrm{...},n-1---\left(20\right)$

2) background value of GM (1,1) is constructed:

$z^{\left(1\right)}(k+1)=\frac{1}{2}\&lsqb;x^{\left(1\right)}\left(k\right)+x^{\left(1\right)}(k+1)\&rsqb;,k=1,2,\mathrm{...},n-2---\left(21\right)$

3) x is set up ⁽¹⁾(k), (k=1,2 ..., n-1) first-order linear albinism differential equation:

$\frac{{\mathrm{dx}}^{\left(1\right)}\left(k\right)}{dt}+{\mathrm{ax}}^{\left(1\right)}\left(k\right)=u---\left(22\right)$

Wherein a, u are undetermined coefficient, and the white function formula of equation (22) is:

$x^{\left(1\right)}\left(k\right)=\left(x^{\left(0\right)}\right(1)-\frac{u}{a})e^{-a(k-1)}+\frac{u}{a},k=1,2,\mathrm{...},n-1---\left(23\right)$

4) according to principle of least square method estimated parameter a, u

${\&lsqb;\hat{a},\hat{u}\&rsqb;}^T={\left(B^{T}B\right)}^{-1}{B}^T{Y}_n---\left(24\right)$

Wherein, data matrix B and Y _nfor:

$B=\left[\begin{array}{cc}-\frac{1}{2}{Z}^{\left(1\right)}\left(2\right)& 1\\ -\frac{1}{2}{Z}^{\left(1\right)}\left(3\right)& 1\\ .& .\\ .& .\\ .& .\\ -\frac{1}{2}{Z}^{\left(1\right)}(n-1)& 1\end{array}\right]---\left(25\right)$

$Y_n=\left[\begin{array}{c}{x}^{\left(0\right)}\left(2\right)\\ x^{\left(0\right)}\left(3\right)\\ .\\ .\\ .\\ x^{\left(0\right)}(n-1)\end{array}\right]---\left(26\right)$

5) by the estimated value of a, u substitution formula (23), obtains predictive equation

6) original data sequence model is set up:

In formula, for original data sequence x ⁽⁰⁾(k), (k=1,2 ..., n-1)) match value; for original data sequence x ⁽⁰⁾(k), (k=1,2 ..., n-1) predicted value;

Dope Δ θ _nafter, the position calculating k moment unknown node relative to the pitch angle of true origin is:

θ _k＝θ _k-1+Δθ _n(29)

The k-1 moment, with the position of unknown node X for the center of circle, speed v be the circle of radius and k moment with anchor node A position for the center of circle, d _afor the circle of radius intersects at X ₁and X ₂two points, have a point to be the position of k moment unknown node X in these two points, owing to having estimated the pitch angle of k moment unknown node and initial point line L, by judging X ₁and X ₂distance to straight line L can determine which point is correct position, and namely the point of close together is the position that k moment unknown node moves to, as shown in Figure 4, and X ₂for the position of k moment unknown node;

The coordinate of k-1 moment unknown node X is (x _k-1, y _k-1), the coordinate of k moment anchor node A is (x _a, y _a), X ₁and X ₂computing formula is:

$\left\{\begin{array}{c}\sqrt{{(x-x_{k-1})}^2+{(y-y_{k-1})}^2}=v\\ \sqrt{{(x-x_A)}^2+{(y-y_A)}^2}=d_A\end{array}\right..---\left(30\right)$

6. the full mobile node positioning method of a kind of wireless sensor network based on RSSI according to claim 1, it is characterized in that, when anchor node and unknown node are all random movement, in the k moment, when unknown node X can communicate with 4 and above anchor node, calculate the coordinate (x', y') of unknown node according to formula (10) after, in order to improve the positioning precision of mobile node further, location coordinate is out revised;

Environmentally situation, a given distance value σ and σ > 0, when distance between two nodes is less than σ, then think that two Nodes are in same environment, the error caused due to environment when so locating this two nodes is approximate the same, in 4 anchor nodes, they are respectively d to the distance of unknown node X _a, d _b, d _c, d _d, pick out the distance value being less than σ, then think that these anchor nodes and unknown node are in identical environment;

1) as only having the distance d of anchor node A distance unknown node in A, B, C, D tetra-anchor nodes _a< σ, then use anchor node B, C, D to carry out positioning anchor node A, and the coordinate of the A calculated point is (x' _a, y' _a), positioning error is (e _x, e _y) be expressed as:

$\{\begin{array}{c}{e}_x=x_A-x_A^{\&prime;}\\ e_y=y_A-y_A^{\&prime;}\end{array}---\left(11\right)$

The positioning error that this error representative unknown node environment causes;

2) if there is multiple value to meet d > σ in the distance value of unknown node and anchor node, then the method adopting weighting to be averaging carrys out the error of calculation, if anchor node A, B, C, D are to the distance value d of unknown node X _a, d _b, d _c, d _dall be less than σ, then respectively with wherein three anchor nodes for beaconing nodes locates an other anchor node, be again respectively A (x' by the anchor node coordinate of locating _a, y' _a) B (x' _b, y' _b) C (x' _c, y' _c) D (x' _d, y' _d), obtaining positioning error is respectively, as formula (12)

$\left\{\begin{array}{c}{e}_{Ax}=x_A-x_A^{\&prime;}\\ e_{Ay}=y_A-y_A^{\&prime;}\\ e_{Bx}=x_B-x_B^{\&prime;}\\ e_{By}=y_B-y_B^{\&prime;}\\ e_{Cx}=x_C-x_C^{\&prime;}\\ e_{Cy}=y_C-y_C^{\&prime;}\\ e_{Dx}=x_D-x_D^{\&prime;}\\ e_{Dy}=y_D-y_D^{\&prime;}\end{array}\right.---\left(12\right)$

(e _ax, e _ay), (e _ax, e _ay), (e _ax, e _ay), (e _ax, e _ay) weights be respectively W _a, W _b, W _c, W _d, as formula (13)

$\left\{\begin{array}{c}{W}_A=\frac{\frac{1}{d_A}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_B=\frac{\frac{1}{d_B}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_C=\frac{\frac{1}{d_C}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\\ W_D=\frac{\frac{1}{d_D}}{\frac{1}{d_A}+\frac{1}{d_B}+\frac{1}{d_C}+\frac{1}{d_D}}\end{array}\right.---\left(13\right)$

The denominator of weights are each anchor nodes to unknown node inverse distance and, molecule is wherein by the anchor node of the locating inverse to unknown node distance, distance value is less, represent that the distance of anchor node distance unknown node is nearer, the error produced when so locating this anchor node more can represent the error during unknown node of location, so weights are larger;

Final error is (e _x, e _y) can be expressed as

$\left\{\begin{array}{c}{e}_x=\frac{W_A{e}_{Ax}+W_B{e}_{Bx}+W_C{e}_{Cx}+W_D{e}_{Dx}}{4}\\ e_y=\frac{W_A{e}_{Ay}+W_B{e}_{By}+W_C{e}_{Cy}+W_D{e}_{Dy}}{4}\end{array}\right.---\left(14\right)$

The coordinate (x, y) of revised unknown node is

$\{\begin{array}{c}x=x^{\&prime;}+e_x\\ y=y^{\&prime;}+e_y\end{array}.---\left(15\right)$