CN104898089A - Device-free localization method based on space migration compressive sensing - Google Patents

Abstract

The invention discloses a device-free localization method based on space migration compressive sensing, and belongs to the field of device-free localization. The method comprises the following steps: deploying sensor nodes; collecting matrixes at reference positions in a sample area and a to-be-monitored area to obtain a migration function; migrating the sensing matrix in the sample area and a measurement vector in the to-be-monitored area according to the migration function to obtain a migrated sensing matrix and a migrated measurement vector; and recovering the position of a target by adopting the theory of compressive sensing according to the migrated sensing matrix and the migrated measurement vector. According to the invention, the sensing matrix in the sample area and the measurement vector in the to-be-monitored area are migrated, and the position information of the target in the monitored area is determined by a compressive sensing localization method. Therefore, human consumption and communication cost brought by sensing matrix rebuilding for the to-be-monitored area are avoided, and the feasibility of realizing localization of different areas through compressive sensing is improved.

Description

A kind of passive type localization method based on spatial migration compressed sensing

Technical field

The present invention relates to passive positioning field, particularly a kind of passive type localization method based on spatial migration compressed sensing.

Background technology

In recent years, passive type location (Device Free Localization, be called for short DFL) feature that technology does not need user to wear any wireless device and do not require user's active participate position fixing process with it, receive the huge concern of academia and industrial community.The passive type localization method of main flow utilizes target to be positioned to position the disturbance of wireless signal in monitored area, generally there are two steps: in the training stage, location model (priori storehouse) is set up with " position of target " relation based on " received signal strength " (Received Signal Strength is called for short RSS); At positioning stage, by real-time RSS value being mated with priori storehouse, determine the position of target.

But existing DFL method all has a common prerequisite, namely training obtains priori storehouse is all obtain for given region.When locating area size once change, the linkage length that node deployment is formed will change, corresponding target also can change the disturbance of wireless signal, therefore need to carry out to new region the priori storehouse that re-training obtains new region, each position of this scanning guarded region that requires a great deal of time, so high with the large energy consumption of data volume and that manpower consumption is huge problem.And in the application of real world, because the region monitored in different application is also different, so the acquisition all carrying out priori to all guarded regions is obviously unrealistic and infeasible.

Existing many passive type localization methods all do not consider this problem, and they are divided into following 3 classes substantially:

The first kind: wait the location of the passive type based on study for representative with a top.By being that adjacent equilateral triangle forms multiple hexagon by node deployment, and carry out the pattern that communicates with intermediate node and hexagon summit node, utilize target to be in the interference of different grid position places to signal and set up priori storehouse.But because the method needs the node disposing comparatively dense to obtain higher cost, and need when monitored area changes to re-establish priori storehouse, therefore these class methods do not solve the problem that the large energy consumption of data volume is high and manpower consumption is huge.

Equations of The Second Kind: with Joseph Wilson etc. for the tomography passive type of representative is located.By node being evenly deployed in the surrounding of monitored area, communicate between two between all nodes, set up tomography knowledge base at diverse location to the interference that communication node causes between two according to target, the position of method to target in conjunction with tomographic map shows, thus realizes location.But these class methods are owing to needing communication between two between node, and need to set up tomography knowledge base for different monitored area, therefore do not solve the problem that the large energy consumption of data volume is high and manpower consumption is huge.

3rd class: the passive type location based on compressed sensing (Compressive Sensing is called for short CS) taking Fang Dingyi as representative.Dispose the node of same number in the both sides of locating area, the node only having label identical communicates.Build perception matrix by the RSS value of all links when each grid place of record object before location, during location, all links collect one group of RSS value, by these group data and perception matrix, accurately obtain the position of target.The method owing to not needing to communicate between two between all nodes and to dispose node less, thus greatly reduces data volume, reduces energy consumption.But when monitored area changes, also need to build perception matrix to different regions, therefore can not solve the large problem of manpower consumption.

In sum, this three classes localization method does not all consider the problem that monitored area changes, and the location model namely set up a given area can not be used for the new region varied in size.And it is very unpractical for setting up a corresponding location model for all regions varied in size in reality.Therefore, the passive type location of carrying out practical application in the face of many monitored areas needs new technology.

Summary of the invention

In order to solve the problem of prior art, the invention provides a kind of passive type localization method based on spatial migration compressed sensing, the described passive type localization method based on spatial migration compressed sensing comprises:

Step one, disposes sensor node respectively in sample areas and region to be monitored;

Step 2, by the RSS matrix of reference position in described sensor node collecting sample region and region to be monitored;

Step 3, according to the described RSS matrix in described sample areas and region to be monitored, obtains moving function;

Step 4, by the sample RSS value in described sensor node collecting sample region, is combined as perception matrix by described sample RSS value;

Step 5, gathers the location RSS value in region to be monitored by described sensor node, described location RSS value be combined as and measure vector;

Step 6, according to described migration function, moves the measurement vector in the perception matrix of described sample areas and described region to be monitored, obtains the measurement vector after the perception matrix after moving and migration;

Step 7, when the area of described sample areas is less than the area in described region to be monitored, carries out gridding interpolation process to the perception matrix after migration, obtains the high resolving power perception matrix after moving;

Step 8, according to the measurement vector after the perception matrix after migration and migration, utilizes compressive sensing theory to recover the position of target.

Optionally, the described passive type localization method based on spatial migration compressed sensing, also comprises:

When the area of described sample areas is not less than the area in described region to be monitored, after completing steps six, directly carry out step 8.

Optionally, describedly dispose sensor node respectively in sample areas and region to be monitored, comprising:

If the size l × a of sample areas, the size in region to be monitored is u × b, the wireless link length formed at the node of sample areas deployment is l, the wireless link length that the node of regional deployment to be monitored is formed is u, and l ≠ u, the link number of sample areas and regional deployment to be monitored is M.

Optionally, the described RSS matrix by reference position in described sensor node collecting sample region and region to be monitored, comprising:

First sample areas and region to be monitored are all divided into N number of square net, then choose identical reference position point respectively in sample areas and region to be monitored, use 1,2 respectively ... n and 1 ', 2 ' ... n ' expression, n=n '≤N.

Then allow target stand in grid place selected in sample areas and region to be monitored respectively successively, record the RSS matrix s of sample areas ^lwith the RSS matrix s in region to be monitored ^u, wherein;

$s^l=(s_{11}^l,\·\·\·,s_{M1}^l,\·\·\·,s_{1j}^l,\·\·\·,s_{\mathrm{Mj}}^l,\·\·\·,s_{1n}^l,\·\·\·,s_{\mathrm{Mn}}^l),$

$s^u=(s_{11\′}^u,\·\·\·,s_{M1\′}^u,\·\·\·,s_{1j\′}^u,\·\·\·,s_{\mathrm{Mj}\′}^u,\·\·\·,s_{1n\′}^u,\·\·\·,s_{\mathrm{Mn}\′}^u),$

And s _ij={ s _ij(1) ..., s _ij(q) ..., s _ij(Q) } ^tq continuous print RSS value of i-th link when representing that target is in jth grid.

Optionally, according to the described RSS matrix in described sample areas and region to be monitored, obtain moving function, comprising:

According to the described RSS matrix s of described sample areas ^lwith the described RSS matrix s in region to be monitored ^u, by s ^land s ^lproject respectively, obtain y ^l=Ws ^l, y ^u=Ws ^u, make x=(x ^l, x ^u), y=(y ^l, y ^u), constructor y=Wx, makes y ^land y ^ube distributed on projector space similar as far as possible, namely

Described F (W) is for measuring y ^ldistribution p _l(y) and y ^udistribution p _uthe majorized function of the spacing of (y);

By projective distribution range observation function D _w(p _l|| p _u) substitute into formula (1), obtain

Be migration function.

Optionally, described by the sample RSS value in described sensor node collecting sample region, described sample RSS value is combined as perception matrix, comprises:

Allow target stand in all grid places of sample areas successively, the RSS value measuring each grid place obtains perception matrix

Wherein, s _ij={ s _ij(1) ..., s _ij(q) ..., s _ij(Q) } ^t.

Optionally, gathered the location RSS value in region to be monitored by described sensor node, described location RSS value be combined as and measure vector, comprising:

When record object is in region to be monitored, the RSS value of every bar link, obtains measuring vectorial R _{m × 1 × Q}=[r ₁..., r _i..., r _m] ^t, wherein, r _i={ r _i(1) ..., r _i(q) ..., r _i(Q) } ^t.

Optionally, described according to described migration function, the measurement vector in the perception matrix of described sample areas and described region to be monitored is moved, obtains the measurement vector after the perception matrix after moving and migration, comprising:

Perception matrix is multiplied with migration function W respectively with measurement vector, obtains the perception matrix after moving $S_{M\×N\×Q}^{\′}=\left(W{s}_{\mathrm{ij}}^l\right),i\∈[1,M],j\∈[1,M]$ With the measurement vector after migration $R_{M\×1\×Q}^{\′}=\left(W{r}_i^u\right),i\∈[1,M];$

Dimension-reduction treatment is carried out to the perception matrix after described migration and the measurement vector after described migration, obtains the perception matrix after dimensionality reduction and measure vector.

Optionally, when the described area when described sample areas is less than the area in described region to be monitored, gridding interpolation process is carried out to described sample areas, obtains the high resolving power perception matrix after moving, comprising:

First, when the area l × a of described sample areas is less than the area u × b in described region to be monitored, when number of grid is N, the grid length of side of sample areas is ω _l, the grid length of side in region to be monitored is ω _u;

Secondly, each grid in described region to be monitored is divided into individual sub-grid, the length of side of described each sub-grid is the quantity of described sub-grid is

Finally, choose the grid at sub-grid i' place and 8 adjacent mesh nearest with this grid distance, totally 9 grids form adjacent grid, are obtained the RSS value of sub-grid i' by interpolation, and then obtain the high resolving power perception matrix after moving.

Optionally, according to the measurement vector after the perception matrix after migration and migration, utilize compressive sensing theory to recover the position of target, comprising:

By utilize compressed sensing reconstruction algorithm ( algorithm) can position vector θ be obtained:

Wherein, be pseudoinverse operator, c>0 is a constant, and δ is also a constant but can not be tending towards 1, obtains the location that namely θ completes region to be monitored internal object, and

θ＝[θ ₁,…,θ _j,…θ _N] ^T，

Wherein, θ _j∈ { 0,1}, the θ when a jth grid there being target _j=1, otherwise be 0.

The beneficial effect that technical scheme provided by the invention is brought is:

By the perception matrix of sample areas and the measurement vector of monitored area are moved, and utilize the localization method of compressed sensing, avoid and treat monitored area and carry out perception matrix and rebuild the manpower consumption and communication overhead that bring, improve the feasibility utilizing compressed sensing to realize zones of different location.

Accompanying drawing explanation

In order to be illustrated more clearly in technical scheme of the present invention, below the accompanying drawing used required in describing embodiment is briefly described, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is a kind of passive type localization method process flow diagram based on spatial migration compressed sensing provided by the invention;

Fig. 2 is the concrete deployment schematic diagram of sensor node provided by the invention;

Fig. 3 is the distribution plan under different linkage length provided by the invention before RSS migration and after migration;

Fig. 4 is migration scheme provided by the invention;

Fig. 5 is the geometric figure of Bregman Divergence provided by the invention;

Fig. 6 is gridding interpolation schematic diagram provided by the invention;

Fig. 7 is after linkage length provided by the invention moves to 12m from 4m, positioning error accumulated probability distribution (CDF) figure of several method;

Fig. 8 is the time overhead under three kinds of migration situation provided by the invention;

Fig. 9 is that after linkage length provided by the invention moves to 12m from 4m, the energy ezpenditure of several method compares.

Embodiment

For making structure of the present invention and advantage clearly, below in conjunction with accompanying drawing, structure of the present invention is further described.

Embodiment one

The invention provides a kind of passive type localization method based on spatial migration compressed sensing, as shown in Figure 1, the described passive type localization method based on spatial migration compressed sensing comprises:

Step one, disposes sensor node respectively in sample areas and region to be monitored;

Step 2, by the RSS matrix of reference position in described sensor node collecting sample region and region to be monitored;

Step 3, according to the described RSS matrix in described sample areas and region to be monitored, obtains moving function;

Step 4, by the sample RSS value in described sensor node collecting sample region, is combined as perception matrix by described sample RSS value;

Step 5, gathers the location RSS value in region to be monitored by described sensor node, described location RSS value be combined as and measure vector;

Step 6, according to described migration function, moves the measurement vector in the perception matrix of described sample areas and described region to be monitored, obtains the measurement vector after the perception matrix after moving and migration;

Step 7, when the area of described sample areas is less than the area in described region to be monitored, carries out gridding interpolation process to the perception matrix after migration, obtains the high resolving power perception matrix after moving;

Step 8, according to the measurement vector after the perception matrix after migration and migration, utilizes compressive sensing theory to recover the position of target.

In force, the present invention, on the basis of the DFL method based on CS, proposes a kind of DFL method (TCL) based on spatial migration CS.Numerous based in the DFL method of CS, TCL has the advantage of CS theory thus can solve the problem of high energy consumption and a large amount of manpower consumption.The present invention concentrates the high energy consumption problem and a large amount of manpower consumption's problem that solve and carry out causing based on the DFL of CS in different monitored areas.

First collect the RSS value of raw monitored region and a small amount of reference position in new monitored area, then utilize the RSS value of acquisition to obtain migration function.The perception matrix in the raw monitored region obtained in advance just can move by TCL, then again reuses in different monitored areas.So just, the object reducing energy ezpenditure and the manpower consumption brought at new monitored area reconstruct perception matrix can be reached.The migration part of TCL also can use in other DFL method, and it can not only use and application can use in other location in the location of zones of different.Such as different object type, along with the location of time variations, in these location, the migration part of TCL is applicable equally.

Based on above-mentioned theory, the present invention proposes a kind of passive type localization method based on spatial migration compressed sensing, choose obtain perception matrix region as sample areas, and need to determine that the region of target location is as region to be monitored, all sensor node is disposed in two regions, as shown in Figure 2, sample areas is different with region area to be monitored for the concrete deployment way of sensor node, therefore disposes the wireless communication link length difference that node is formed.Obtain the RSS value of sample areas and a small amount of reference position in region to be monitored respectively, obtain the migration function making sample areas and region RSS to be monitored distribute identical, be i.e. the different corresponding identical RSS distribution of linkage length, as shown in Figure 3.The RSS value of positions all in sample areas is formed perception matrix, and the measurement vector that the RSS value corresponding when being in region to be monitored of target is formed, according to migration function, perception matrix is carried out migration cycle to identical space respectively with measurement vector, perception matrix after measurement vector sum migration after utilizing compressive sensing theory to combine migration recovers the positional information of target, thus reaches the effect that the target treated in monitored area positions.

The method is relative to passive type localization method of the prior art, by this migration function, the perception matrix obtained in advance can move in mapping space by we, and the perception matrix after an identical migration can be shared in monitored areas (linkage lengths different in other words) different like this.So do, in different monitored areas, greatly reduce the manpower consumption rebuilding perception matrix and bring.

Optionally, the described passive type localization method based on spatial migration compressed sensing, also comprises:

When the area of described sample areas is greater than the area in described region to be monitored, after completing steps six, directly carry out step 8.

In force, propose in step 7 when the area of sample areas is less than the area in region to be monitored, need the perception matrix after to migration to carry out gridding interpolation process, obtain the high resolving power perception matrix after moving.

The perception matrix after to migration why is needed to carry out gridding interpolation process, because the measurement vector in the perception matrix in sample areas and region to be monitored carries out migrating in mapping space going by one of important step of this programme exactly, thus the target location in region to be monitored can be drawn by the measurement vector calculation after the perception matrix after migration and migration, because sample areas and area grid to be monitored vary in size, and sizing grid is exactly the lowest resolution of positioning result, the problem whether precision declines therefore can be there is after migration terminates.

If the area of sample areas is greater than the area in region to be monitored, when namely the size of mesh opening of sample areas is greater than area grid size to be monitored, the positioning resolution in region to be monitored increases, and therefore positioning precision can not reduce; If the area of sample areas is less than the area in region to be monitored, namely when the size of mesh opening of sample areas is less than area grid size to be monitored, after perception matrix is moved, the size of the corresponding grid position of each matrix element data can increase, make the packing density in region to be monitored too low, positioning resolution declines, and causes positioning precision to decline.Therefore, when the area of sample areas is less than the area in region to be monitored, the perception matrix after to the migration of sample areas correspondence is needed to carry out gridding interpolation process; And when the area of sample areas is not less than the area in region to be monitored, can ensure that the positioning precision of perception matrix in region to be monitored after moving can not decline, therefore after completing steps six, do not need to carry out gridding interpolation process, directly carry out the positioning action in step 8, reach the effect that saving resource consumes.

Optionally, dispose sensor node respectively in sample areas and region to be monitored, comprising:

Sensor node is disposed respectively, as shown in Figure 2 in the both sides in sample areas and region to be monitored.If the size l × a of sample areas, the size in region to be monitored is u × b, the wireless link length formed at the node of sample areas deployment is l, the wireless link length that the node of regional deployment to be monitored is formed is u, and l ≠ u, the number of nodes of sample areas and regional deployment to be monitored is respectively 2M, forms relation one to one and constructs M bar link ({ TX _i, RX _i, i ∈ [1, M]), as shown in Figure 4.

Optionally, by the RSS matrix of reference position in described sensor node collecting sample region and region to be monitored, comprising:

First sample areas and region to be monitored are all divided into N number of square net, then the ratio of sample areas and area grid size to be monitored is l/u.Then choose identical reference position point (grid) respectively in sample areas and region to be monitored, use 1,2 respectively ... n and 1 ', 2 ' ... n ' expression, n=n '≤N, as shown in Figure 2.

Then allow target stand in grid place selected in sample areas and region to be monitored respectively successively, record the RSS matrix of sample areas and the RSS matrix in region to be monitored, wherein;

$s^l=(s_{11}^l,\·\·\·,s_{M1}^l,\·\·\·,s_{1j}^l,\·\·\·,s_{\mathrm{Mj}}^l,\·\·\·,s_{1n}^l,\·\·\·,s_{\mathrm{Mn}}^l),$

$s^u=(s_{11\′}^u,\·\·\·,s_{M1\′}^u,\·\·\·,s_{1j\′}^u,\·\·\·,s_{\mathrm{Mj}\′}^u,\·\·\·,s_{1n\′}^u,\·\·\·,s_{\mathrm{Mn}\′}^u),$

And s _ij={ s _ij(1) ..., s _ij(q) ..., s _ij(Q) } ^tq continuous print RSS value of i-th link when representing that target is in jth grid.

Optionally, according to the described RSS matrix in described sample areas and region to be monitored, obtain moving function, comprising:

According to the described RSS matrix s of described sample areas ^lwith the described RSS matrix s in region to be monitored ^u, by s ^land s ^uproject respectively, obtain y ^l=Ws ^l, y ^u=Ws ^l.Make x=(x ^l, x ^u), y=(y ^l, y ^u), constructor y=Wx, makes y ^land y ^ube distributed on projector space similar as far as possible, namely

Described F (W) is for measuring y ^ldistribution p _l(y) and y ^udistribution p _uthe majorized function of the spacing of (y);

By projective distribution range observation function D _w(p _l|| p _u) substitute into formula (1), obtain

Be migration function.

In force, in order to the target utilizing the perception matrix of sample areas to treat in monitored area positions, needing perception matrix to move, in order to obtain moving function, also needing to carry out following steps:

For the original expression that the matrix W described in formula (1) is exactly migration function in fact, for different sample areas and region to be monitored, the actual migration function obtained also is not quite similar.

In order to make the RSS matrix s of sample areas ^lwith the RSS matrix s in region to be monitored ^uidentical by moving rear distribution, calculate p by the graceful difference of Donald Bragg (Bregman Divergence) _l(y) and p _udistance between (y).If y ^land y ^uhigher-dimension Gaussian distribution identical, then corresponding one dimension Gaussian distribution is also identical, and namely sample areas is also identical with the RSS distribution of the corresponding same position in region to be monitored.So problem is converted into solve make p _l(y) and p _uy majorized function that the distance between () is minimum.Wherein, D _w(p _l|| p _u) be measure p at projector space _l(y) and p _uthe Bregman Divergence function of (y) distribution distance.

Next, for based on the theoretical optimizing process to migration function of Bregman Divergence:

In Bregman Divergence, provide

D _w(f,g)＝∫d(ξ(f),ξ(g))

d(ξ(f),ξ(g))＝Φ(ξ(g))-f{(ξ(g))-ξ(f)}-Φ(ξ(f))

Wherein, dv=dv (y) is Lebesgue measure, d (ξ (f), ξ (g)) difference of value that to be function phi put at ξ (g) and f (ξ (g)-ξ (f))+Φ (ξ (f)), wherein f (ξ (g)-ξ (f))+Φ (ξ (f)) is for function phi is at (ξ (f), Φ (ξ (f))) value put at ξ (g) of the tangent line put, as shown in Figure 5.Make g=p _u(y), f=p _l(y), then p _l(y) and p _uy () can be expressed as based on the distance of Bregman Divergence

D _W(p _l||p _u) _＝∫{Φ(ξ(p _u(y)))-Φ(ξ(p _l(y)))}

-f{ξ(p _u(y))-ξ(p _l(y))}dv(y)

RSS value s can be made according to above formula ^land s ^lmove to a mapping space, concrete mode is by minimizing y ^land y ^lbetween distance obtain.

In order to easier obtain D _w(p _l|| p _u) solution, we have selected function phi (y)=y ², this function is substituted in above formula, then corresponding Bregman Divergence can be expressed as the form of quadratic form:

$D_w\left(p_l\right|\left|p_u\right)={\∫(p_l\left(y\right)-p_u\left(y\right))}^2\mathrm{dy}=\∫p_l^2\left(y\right)-2p_l\left(y\right)p_u\left(y\right)+p_u^2\left(y\right)\mathrm{dy}.---\left(2\right)$

Consider single sample noise, simultaneously in order to slow down the sample changed caused by environment as far as possible, we utilize Density Estimator (Kernel Density Estimation, being called for short KDE) method carries out the calculating of probability density, by probability density being expressed as the weighted sum of the core between independent variable and other samples.Then probability density function p _l(y) and p _u(y) be

$p_l\left(y\right)=\frac{1}{\mathrm{Mn}\·{\mathrm{\σ}}_l}\underset{i=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}{G}_{{\mathrm{\Σ}}_u}\left(\frac{y-y_i}{{\mathrm{\σ}}_l}\right),---\left(3\right)$

$p_u\left(y\right)=\frac{1}{\mathrm{Mn}\·{\mathrm{\σ}}_u}\underset{i^{\′}=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}{G}_{{\mathrm{\Σ}}_u}\left(\frac{y-y_{i^{\′}}}{{\mathrm{\σ}}_u}\right).---\left(4\right)$

Formula (3) and (4) are updated in formula (2), p _l(y) and p _uy the Bregman Divergence between () distribution becomes

$\begin{array}{c}{D}_W\left(p_1\right|\left|p_u\right)={\∫\left(\frac{1}{\mathrm{Mn}{\mathrm{\σ}}_l}\underset{i=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}{G}_{{\mathrm{\Σ}}_l}\left(\frac{y_i-y_i}{{\mathrm{\σ}}_l}\right)\right)}^2\mathrm{dy}\\ +\∫{\left(\frac{1}{\mathrm{Mn}{\mathrm{\σ}}_u}\underset{i^{\′}=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}{G}_{{\mathrm{\Σ}}_l}\left(\frac{y_i-y_{i^{\′}}}{{\mathrm{\σ}}_u}\right)\right)}^2\mathrm{dy}\\ -\frac{2}{M^2{n}^2{\mathrm{\σ}}_u{\mathrm{\σ}}_l}{\mathrm{\Σ}}_{i=1}^{\mathrm{Mn}}{\mathrm{\Σ}}_{i^{\′}=1}^{\mathrm{Mn}}{G}_{{\mathrm{\Σ}}_l}\left(\frac{y_i-y_i}{{\mathrm{\σ}}_l}\right)G_{{\mathrm{\Σ}}_u}\left(\frac{y-y_{i^{\′}}}{{\mathrm{\σ}}_u}\right)\mathrm{dy}\end{array}.$

And for Gaussian kernel, there is following equation

${\∫G}_{{\mathrm{\Σ}}_l}\left(\frac{y-y_i}{{\mathrm{\σ}}_l}\right)G_{{\mathrm{\Σ}}_u}\left(\frac{y-y_{i^{\′}}}{{\mathrm{\σ}}_u}\right)\mathrm{dy}=G_{{\mathrm{\σ}}_l^2{\mathrm{\Σ}}_l+{\mathrm{\σ}}_u^2{\mathrm{\Σ}}_u}(y-y_{i^{\′}})$

Therefore, comprehensive above-mentioned formula, finally has

$\begin{array}{c}{D}_W\left(p_l\right|\left|p_u\right)=\frac{1}{M^2{n}^2{{\mathrm{\σ}}_l}^2}{\mathrm{\Σ}}_{i=1}^{\mathrm{Mn}}{\mathrm{\Σ}}_{i^{\′}=1}^{\mathrm{Mn}}{G}_{2{\mathrm{\σ}}_{\mathrm{l\Σl}}^2}(y_i-y_{i^{\′}})\\ +\frac{1}{M^2{n}^2{{\mathrm{\σ}}_u}^2}{\mathrm{\Σ}}_{i=1}^{\mathrm{Mn}}{\mathrm{\Σ}}_{i^{\′}=1}^{\mathrm{Mn}}{G}_{2{\mathrm{\σ}}_{\mathrm{u\Σu}}^2}(y_i-y_{i^{\′}})\\ -\frac{1}{M^2{n}^2{\mathrm{\σ}}_u{\mathrm{\σ}}_l}{\mathrm{\Σ}}_{i=1}^{\mathrm{Mn}}{\mathrm{\Σ}}_{i^{\′}=1}^{\mathrm{Mn}}{G}_{{\mathrm{\σ}}_{\mathrm{l\Σl}}^2+{\mathrm{\σ}}_{\mathrm{u\Σu}}^2}(y_i-y_{i^{\′}})\end{array}-.---\left(5\right)$

Formula (5) is substituted into formula in, just can obtain the migration function W of actual needs.

Further, obtaining moving in the process of function W, main thought goes to improve the solution of genetic algorithm generation by gradient descent algorithm thus obtains minimum iterative value.Consider that gradient descent algorithm can obtain the Local Minimum iterative value the most close with initial guess, genetic algorithm can provide a good solution in addition, but may local minimum be missed, therefore we need the advantages of two schemes to get up, and go to deal with problems by the method for a mixing, this scheme is exactly go to improve the solution generated by genetic algorithm with gradient descent algorithm.

The first step, generates initial solution by genetic algorithm;

Genetic algorithm is that evolution laws that a class uses for reference organic sphere develops and the randomization searching method that comes at first, biological is undertaken hybridizing by the algebraically of quantification and variation is evolved.The solution of this algorithm comprises W, σ _u, σ _l, the adaptability of each solution is by calculating represent.Be described to solve W below:

1) estimate: retain the solution with 10% of the highest fitness;

2) select: the solution of random generation 10%;

3) intersect: select two solutions from parent randomly, and produce the solution of 60% by following linear combination:

W ^new＝τ·W ^old(d)+(1-τ)·W ^old(2),τ∈(0,1)；

4) make a variation: select a solution from parent randomly, increase randomly or reduce the value produced by exponential distribution, produce the solution of 20%.

σ _u, σ _lprocessing procedure be the same with W.The process of genetic algorithm is stopped when the solution of five generations successively is not improved time.Because genetic algorithm finds the process of optimum solution by the time a large amount of for cost, in order to reduce time overhead, we set σ _u, σ _linitial value in the noise range of RSS value, reduce the space of search thus the speed of convergence speedup with this.

Second step, utilizes gradient descent algorithm to improve the solution of genetic algorithm generation;

The process utilizing gradient descent algorithm to obtain optimum W iteratively can be expressed as:

$W_{k+1}=W_k-{\mathrm{\η}}_k\left({\∂}_W{D}_W\left(p_l\right|\left|p_u\right)\right),$

η _kbe the learning rate of the kth time iteration controlling gradient step, we make η _k=η ₀/ k, represent the gradient of W, when we know D _w(p _l|| p _u) derivative time we just can obtain the optimum solution of W.For formula (5):

$\frac{\∂}{\∂y_i}{G}_{{\mathrm{\Σ}}_l+{\mathrm{\Σ}}_u}(y_i-y_{i^{\′}})=(y_{i^{\′}}-y_i){({\mathrm{\Σ}}_l+{\mathrm{\Σ}}_u)}^{-1}{G}_{{\mathrm{\Σ}}_l+{\mathrm{\Σ}}_u}(y_i-y_{i^{\′}}),$

Then D _w(p _l|| p _u) derivative be

$\begin{array}{c}\frac{{\∂D}_W\left(p_l\right|\left|p_u\right)}{\∂W}=\frac{\∂D_W\left(p_l\right|\left|p_u\right)}{\∂y}\·\frac{\∂y}{\∂W}\\ =\underset{i=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}\frac{\∂D_W\left(p_l\right|\left|p_u\right)}{\∂y_i}\·\frac{\∂y_i}{\∂W}+\underset{i^{\′}=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}\frac{\∂D_W\left(p_l\right|\left|p_u\right)}{\∂y_{i^{\′}}}\·\frac{\∂y_{i^{\′}}}{\∂W}\\ =\underset{i=1}{\overset{\mathrm{MN}}{\mathrm{\Σ}}}\frac{\∂D_W\left(p_l\right|\left|p_u\right)}{\∂y_i}\·{\mathrm{\χ}}_i+\underset{i=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}\frac{\∂D_W\left(p_l\right|\left|p_u\right)}{\∂y_{i^{\′}}}\·{\mathrm{\χ}}_{i^{\′}}\end{array}$

Wherein

$\begin{array}{c}\frac{\∂D_W\left(p_l\right|\left|p_u\right)}{\∂y_i}=\frac{{\left({\mathrm{\Σ}}_l\right)}^{-1}}{M^2{n}^2{\mathrm{\σ}}_l^4}\underset{i^{\′}=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}(y_{i^{\′}}-y_i)G_{2{\mathrm{\σ}}_{l{\mathrm{\Σ}}_l}^2}(y_i-y_{i^{\′}})\\ -\frac{2{({\mathrm{\σ}}_l^2{\mathrm{\Σ}}_l+{\mathrm{\σ}}_u^2{\mathrm{\Σ}}_u)}^{-1}}{M^2{n}^2{\mathrm{\σ}}_l{\mathrm{\σ}}_u{{}^{}}_{}}\underset{i\′=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}(y_{i^{\′}}-y_i)G_{{\mathrm{\σ}}_{l{\mathrm{\Σ}}_l}^2+{\mathrm{\σ}}_{u{\mathrm{\Σ}}_u}^2}(y_i-y_{i^{\′}}),\\ \frac{\∂D_W\left(p_l\right|\left|p_u\right)}{\∂y_{i^{\′}}}=\frac{{\left({\mathrm{\Σ}}_l\right)}^{-1}}{M^2{n}^2{\mathrm{\σ}}_u^4}\underset{i=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}(y_{i^{\′}}-y_i)G_{2{\mathrm{\σ}}_{u{\mathrm{\Σ}}_u}^2}(y_i-y_{i^{\′}})\\ -\frac{2{({\mathrm{\σ}}_l^2{\mathrm{\Σ}}_l+{\mathrm{\σ}}_u^2{\mathrm{\Σ}}_u)}^{-1}}{M^2{n}^2{\mathrm{\σ}}_l{\mathrm{\σ}}_u}\underset{i=1}{\overset{\mathrm{Mn}}{\mathrm{\Σ}}}(y_{i^{\′}}-y_i)G_{{\mathrm{\σ}}_{l{\mathrm{\Σ}}_l}^2+{\mathrm{\σ}}_{u{\mathrm{\Σ}}_u}^2}(y_i-y_{i^{\′}}).\end{array}$

So far, optimum migration function W can be obtained by continuous iteration.

Optionally, by the sample RSS value in described sensor node collecting sample region, by described sample

RSS value is combined as perception matrix, comprising:

In force, allow target stand in all grid places of sample areas successively, the RSS value measuring each grid place obtains perception matrix

Wherein, s _ij={ s _ij(1) ..., s _ij(q) ..., s _ij(Q) } ^trepresent Q the continuous print RSS value of the corresponding grid j of link i.

Optionally, gathered the location RSS value in region to be monitored by described sensor node, described location RSS value be combined as and measure vector, comprising:

In force, when record object is in region to be monitored, the RSS value of every bar link, obtains measuring vectorial R _{m × 1 × Q}=[r ₁..., r _i..., r _m] ^t, wherein, r _i={ r _i(1) ..., r _i(1) ..., r _i(Q) } ^t.

Optionally, according to described migration function, the measurement vector in the perception matrix of described sample areas and described territory to be monitored is moved, obtains the measurement vector after the perception matrix after moving and migration, comprising:

In force, perception matrix is multiplied with migration function W respectively with measurement vector, obtains the perception matrix after moving

$S_{M\×N\×Q}^{\′}=\left(W{s}_{\mathrm{ij}}^l\right),i\∈[1,M],j\∈[1,M]---\left(6\right)$

With the measurement vector after migration

$R_{M\×1\×Q}^{\′}=\left(W{r}_i^u\right),i\∈[1,M].---\left(7\right)$

Adopt the method for maximum probability value to carry out dimensionality reduction operation to the two-dimensional measurement vector shown in the three-dimensional perception matrix shown in formula (6) and formula (7) respectively, concrete operations utilize formula below to carry out:

$s_{\mathrm{ij}}=\arg \underset{1\≤q\≤Q}{\max }p\left(s_{\mathrm{ij}}\left(q\right)\right)$

$r_i=\arg \underset{1\≤q\≤Q}{\max }p\left(r_i\left(q\right)\right)$

P () be gaussian probability estimate, obtain after dimensionality reduction two dimension perception matrix S ' _{m × N}with the measurement vector R ' of one dimension _{m × 1}.

Optionally, when the area of described sample areas is less than the area in described region to be monitored, gridding interpolation process is carried out to the perception matrix after described migration, obtains the high resolving power perception matrix after moving, comprising:

In force, because the meshes number of zones of different is identical, the size increasing grid along with the area in region or the length of link also can increase, and this will cause the resolution of location to decline, and then causes the precision of locating to reduce.Therefore when the area in region increases, in order to reach at least identical with former region grid resolution, needing the link number of increase new region thus dividing more grid.

When the meshes number of new region increases, need to increase perception entry of a matrix element number after former zone migration, thus reach the object improving positioning precision.Because the RSS value of link is similar when target is in adjacent position, therefore use the RSS value of adjoining position to draw the RSS value of all newly-increased grids by interpolation, thus obtain the high resolving power perception matrix after moving.

Concrete for sample areas and Liang Ge region, region to be monitored, when the area l × a of sample areas is less than the area u × b in region to be monitored, when number of grid is N, the grid length of side of sample areas is ω _l, the grid length of side in region to be monitored is ω _u, namely linkage length is that l becomes u, and the grid length of side is by ω _lbecome ω _u.

In order to increase the grid resolution in region to be monitored, need by each stress and strain model in region to be monitored be individual sub-grid, the length of side of each sub-grid is the quantity of sub-grid is concrete enforcement, by increasing the link number in region to be monitored thus dividing more grid, needs to dispose M × [u/l] individual link and obtains the grid resolution identical with sample areas.

Corresponding, need the perception matrix after by migration to carry out interpolation.Choose the grid at sub-grid i' place and 8 adjacent mesh nearest with this grid distance, totally 9 grids form adjacent grid, and as shown in Figure 6, each grid is divided into 4 sub-grids.The RSS value of corresponding sub-grid i' is obtained by following formula:

$s_{i\′}=\underset{j=1}{\overset{9}{\mathrm{\Σ}}}\frac{s_i}{d_{j}D},$

Wherein s _i'and s _ithe RSS value of grid j and i' respectively, d _jboth Euclidean distances.Obtained the RSS value of sub-grid i' by interpolation, and then obtain the high resolving power perception matrix after moving.

Optionally, according to the measurement vector after the perception matrix after migration and migration, utilize compressive sensing theory to recover the position of target, comprising:

In force, theoretical according to CS, there is following formula

R' _M×1＝S' _M×N·θ _N×1+N

S ' _{m × N}with R ' _{m × 1}the perception matrix after dimensionality reduction and measurement vector.N is noise figure.θ _{n × 1}=[θ ₁..., θ _j... θ _n] ^tfor position vector, and θ _j∈ { 0,1}, the θ when a jth grid there being target _j=1, otherwise be 0.By utilize compressed sensing reconstruction algorithm ( algorithm) can position vector θ be obtained:

Wherein, be pseudoinverse operator, c>0 is a constant.δ is also a constant but can not be tending towards 1, obtains the location that namely θ completes region to be monitored internal object.

The concrete use flow process of above formula, comprises the related contents such as the detailed explanation of pseudo-operation.

It should be noted that to be ripe prior art to the above-mentioned mode of position utilizing compressive sensing theory to recover target here, therefore repeat no more herein.

The Passive Location based on spatial migration compressed sensing proposed in the present embodiment, by the perception matrix of sample areas and the measurement vector of monitored area are moved, and utilize the localization method of compressed sensing, avoid and treat monitored area and carry out perception matrix and rebuild the manpower consumption and communication overhead that bring, improve the feasibility utilizing compressed sensing to realize zones of different location.

In the process of above-mentioned migration formula passive positioning, use two variable as theoretical foundation, be specially:

If theorem one move after perception matrix S ' often row RSS value all meet Gaussian distribution, simultaneously M=O (K log (N/K)), so satisfied to the K sparse vector Θ that all N tie up, S'

$(1-\mathrm{\δ})\≤\frac{{\left|\right|S^{\′}\mathrm{\Θ}\left|\right|}_2^2}{{\left|\right|\mathrm{\Θ}\left|\right|}_2^2}\≤(1+\mathrm{\δ})$

Probability level off to 1, wherein δ ∈ [0,1].

Prove: in order to prove theorem above, we demonstrate first by experiment the perception matrix S after migration ' often row Gaussian distributed.Then, in order to simplified pr oof, S' is standardized as if E (S ' _ij) ₌μ, Var (S ' _ij)=E ((S ' _ij) ²)=σ, then inner product expectation and variance be

$E(<\frac{1}{\sqrt{\mathrm{\&sigma;M}}}{S}_i^{\&prime;},\mathrm{\&Theta;}>)=\frac{1}{\sqrt{\mathrm{\&sigma;M}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}E\left(S_{\mathrm{ij}}^{\&prime;}\right){\mathrm{\&theta;}}_j=\frac{\mathrm{K\&mu;}}{\sqrt{\mathrm{\&sigma;M}}},$

$\mathrm{Var}(<\frac{1}{\sqrt{\mathrm{\&sigma;M}}}{S}_i^{\&prime;},\mathrm{\&Theta;}>)=\frac{1}{\sqrt{\mathrm{\&sigma;M}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{Var}\left(S_{\mathrm{ij}}^{\&prime;}\right){\mathrm{\&theta;}}_j^2=\frac{{\left|\right|\mathrm{\&Theta;}\left|\right|}_2^2}{M}.$

And then obtain expectation:

$E\left({\left|\right|S^{\&prime;}\mathrm{\&Theta;}\left|\right|}_2^2\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}\mathrm{Var}(<\sqrt{\frac{1}{\mathrm{\&sigma;M}}{S}_i^{\&prime;}},\mathrm{\&Theta;}>)={\left|\right|\mathrm{\&Theta;}\left|\right|}_2^2.$

Theoretical by the Random observations on random observations:Sparse signal acquisition and processing of M.A.Davenport., have:

$p\left(\right|\frac{{\left|\right|s^{\&prime;}\mathrm{\&Theta;}\left|\right|}_2^2}{{\left|\right|\mathrm{\&Theta;}\left|\right|}_2^2}-1|\&GreaterEqual;\mathrm{\&delta;})\&le;2\exp \left(\frac{-M{\mathrm{\&delta;}}^2}{c}\right),$

Wherein c is constant.To S''s individual N n-dimensional subspace n, K sparse vector Θ meets $|\frac{{\left|\right|s^{\&prime;}\mathrm{\&Theta;}\left|\right|}_2^2}{{\left|\right|\mathrm{\&Theta;}\left|\right|}_2^2}-1|\&GreaterEqual;\mathrm{\&delta;}$ Probability be:

${\left(\frac{\mathrm{eN}}{K}\right)}^K\&CenterDot;2\exp \left(\frac{-M{\mathrm{\&delta;}}^2}{c}\right)=2\exp (\frac{-M{\mathrm{\&delta;}}^2}{c}+K\log \left(\frac{N}{K}\right)+1)$

M=O (K log (N/K)) simultaneously, then S' meets the K sparse vector Θ that all N tie up

$(1-\mathrm{\&delta;})\&le;\frac{{\left|\right|s^{\&prime;}\mathrm{\&Theta;}\left|\right|}_2^2}{{\left|\right|\mathrm{\&Theta;}\left|\right|}_2^2}\&le;(1+\mathrm{\&delta;})$

Probability level off to 1.

Theorem two, for the perception matrix S after the migration of M × N dimension ', measurement vector R' and the K sparse vector Θ after migration is tieed up in M × 1.Order for the solution (solution of formula (8)) of algorithm.Then at least with probability, restoration errors meet:

${\left|\right|\mathrm{\&Theta;}\widehat{-}\mathrm{\&Theta;}\left|\right|}_2^2\&le;\frac{8{(\sqrt{2\log M}+2)}^2}{{(1-(2K-1)\mathrm{\&mu;})}^2}(1+\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\min ({\left|\mathrm{\&Theta;}\left(i\right)\right|}^2,1)),$

Wherein s ' _iwith S ' _jbe respectively the i of S' ^thand j ^thcolumn vector.

Prove: frequently general, if δ=1, | Θ (1) | >=| Θ (2) | >=... .. >=| Θ (K) |, | Θ (i) |=0, wherein i > K.Order $a=R^{\&prime;}-S^{\&prime;}\widehat{\mathrm{\&Theta;}}.$ Definition event critical field on Gauss's tail probabilities shows:

Namely the probability that event A occurs is at least in ensuing part, we establish event A to occur, namely

Order β ₁=Θ (i): i=1,2 ... .., k ₀, β ₂={ Θ (i): k ₀₊₁... .., K}, and Θ=β ₁+ β ₂.Obviously, as i > k ₀time, | i:| Θ (i) |>=1}|≤k ₀, | Θ (i) | < 1.Therefore,

${\left|\right|{\mathrm{\&beta;}}_2\left|\right|}_1=\underset{i=k_0+1}{\overset{K}{\mathrm{\&Sigma;}}}\left|\mathrm{\&Theta;}\left(i\right)\right|<K-k_0$

${\left|\right|{\mathrm{\&beta;}}_2\left|\right|}_2=\sqrt{\underset{i=k_0+1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\mathrm{\&Theta;}\left(i\right)\right|}^2}=\sqrt{\underset{i=k_0+1}{\overset{K}{\mathrm{\&Sigma;}}}\min ({\left|\mathrm{\&Theta;}\left(i\right)\right|}^2,1)}\&le;\sqrt{k_0}$

First we prove β ₁it is a feasible solution of formula (8).In fact, for the i of S' ^th(1≤i≤M) column vector S ' _ihave:

Wherein, by the Uncertainty principles and ideal atomic decomposition of D.L.Donoho, when nothing is made an uproar namely have

$|<S_i^{\&prime;},S^{\&prime;}{\mathrm{\&beta;}}_1-R^{\&prime;}>|\&le;\sqrt{2\log M}+\frac{3}{2}\&le;\sqrt{2\log M}$

Above formula shows β ₁it is the feasible solution of formula (8).Therefore by the Stable recovery of sparsesignals and an oracle inequality of L.Wang, obtain

${\left|\right|\widehat{\mathrm{\&Theta;}}-{\mathrm{\&beta;}}_1\left|\right|}_2\&le;\frac{2\sqrt{2}(\sqrt{2\log M}+2)\sqrt{k_0}}{1-({2k}_0-1)\mathrm{\&mu;}}-\sqrt{k_0}$

Next have

${\left|\right|\widehat{\mathrm{\&Theta;}}-\mathrm{\&Theta;}\left|\right|}_2\&le;{\left|\right|\widehat{\mathrm{\&Theta;}}-{\mathrm{\&beta;}}_1\left|\right|}_2+{\left|\right|{\mathrm{\&beta;}}_2\left|\right|}_2\frac{2\sqrt{2}(\sqrt{2\log M}+2)\sqrt{k_0}}{1-({2k}_0-1)\mathrm{\&mu;}}$

Therefore restoration errors meets

${\left|\right|\widehat{\mathrm{\&Theta;}}-\mathrm{\&Theta;}\left|\right|}_2^2\&le;\frac{8{(\sqrt{2\log M}+2)}^2\sqrt{k_0}}{{(1-(2K-1)\mathrm{\&mu;})}^2}\&le;\frac{8{(\sqrt{2\log M}+2)}^2}{{(1-(2K-1))}^2}(1+\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}({\left|\mathrm{\&Theta;}\left(i\right)\right|}^2,i)).$

To sum up, the passive type localization method based on spatial migration compressed sensing provided in the present invention meets above-mentioned theory basis, has realizability.

Invention Performance Evaluation

We attempt going from following three aspects to assess the present invention: positioning performance, manpower consumption and communication overhead.

Positioning performance: Fig. 7 is the positioning error accumulated probability distribution plan (CDF) of linkage length when moving to 12m from 4m.The locating area that wherein it is 4m and 12m that CS w/o Trans. represents for linkage length builds perception matrix respectively and directly utilizes the method for compressed sensing to position; RTI is the method utilizing tomography to position, and RTI w/Trans. represents and moves, and RTI w/o Trans. represents and do not move; RASS method is the method based on study that top proposes, and utilizes support vector machine to position, and RTI w/Trans. represents and moves, and RTI w/o Trans. represents and do not move.Compared by the TCL method that the present invention proposed and additive method, result shows that the performance of TCL is close to CS w/o Trans., and for the net point for 50% and 80%, positioning error is respectively 0.87m and 1.23m.And RTI method and RASS method are for the net point of 80%, carry out the later positioning error of migration and improve 58% and 66% respectively compared to not carrying out moving, illustrating when passing through after locating area area change to move the perception matrix obtained in advance, can re-use in new monitored area.

Manpower consumption: in general, the RSS measured value of a new guarded region manually obtains.We went to check manpower consumption with the time disposing front cost.Locating area has been divided into the grid that the length of side is 0.5m, and in each grid, collects 100 measured values continuously, each measured value used time 1.5s.Therefore for 4m*4m and 12m*12m region, structure perception matrix times cost is at least 2.67 and 24 hours.Fig. 8 is the time loss comparison diagram under three kinds of different linkage lengths migrations, when linkage length be 3m move to 6m time, manpower consumption reduces 41%, and when moving to 12m from 4m, manpower consumption reduces 88%, and when moving to 12m from 3m, manpower consumption reduces 93%.As can be seen here, moving method provided by the invention can greatly reduce the manpower consumption that re-training perception matrix brings when locating area changes.

Communication overhead: the energy ezpenditure of TCL, RASS w/Trans. and RTI w/Trans. three contrasts by we, by increasing the quantity of link, until the precision of location reaches the consumption that a definite value removes to estimate the energy.According to single order radio model, on link, the energy consumption of each bag passes through E _radio=e _lbb ²+ 2BE _elccalculate.Wherein, B is the size of the bag with binary representation, and b is linkage length, e _l=100pJ/ (bit/m ²), E _elc=50nJ/bit.In experiment, B=320bits, b=12m, and each transmission 100 bags.Then the energy consumption of M bar link is M × 3.66mJ.Then for diverse ways, the link number realized needed for identical positioning precision is different.Fig. 9 is the comparison of several method energy consumption under different positioning error.Visible when positioning error is less than 1m, the energy consumption of TCL, RASS w/Trans. and RTIw/Trans. is respectively 18.3mJ, 47.59mJ, 54.91mJ, show that RTI and RASS method needs more measured value compared to TCL, therefore TCL method can reduce the energy ezpenditure that communication overhead causes.

To sum up, the embodiment of the present invention proposes a kind of passive type localization method based on spatial migration compressed sensing, by the perception matrix of sample areas and the measurement vector of monitored area are moved, and utilize the localization method of compressed sensing, determine the positional information of target in monitored area, thus avoid and treat monitored area and carry out perception matrix and rebuild the manpower consumption and communication overhead that bring, improve the feasibility utilizing compressed sensing to realize zones of different location.

It should be noted that: the migration formula Passive Location that above-described embodiment provides carries out the embodiment of glue coating, only as explanation in actual applications in this migration formula Passive Location, can also use in other application scenarioss according to actual needs and by above-mentioned migration formula Passive Location, its specific implementation process is similar to above-described embodiment, repeats no more here.

Each sequence number in above-described embodiment, just to describing, not to represent in the assembling of each parts or use procedure to obtain sequencing.

The foregoing is only embodiments of the invention, not in order to limit the present invention, within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (10)

1. based on a passive type localization method for spatial migration compressed sensing, it is characterized in that, the described passive type localization method based on spatial migration compressed sensing comprises:

Step one, disposes sensor node respectively in sample areas and region to be monitored;

Step 2, by the RSS matrix of reference position in described sensor node collecting sample region and region to be monitored;

Step 3, according to the described RSS matrix in described sample areas and region to be monitored, obtains moving function;

Step 4, by the sample RSS value in described sensor node collecting sample region, is combined as perception matrix by described sample RSS value;

Step 5, gathers the location RSS value in region to be monitored by described sensor node, described location RSS value be combined as and measure vector;

Step 6, according to described migration function, moves the measurement vector in the perception matrix of described sample areas and described region to be monitored, obtains the measurement vector after the perception matrix after moving and migration;

Step 7, when the area of described sample areas is less than the area in described region to be monitored, carries out gridding interpolation process to the perception matrix after migration, obtains the high resolving power perception matrix after moving;

Step 8, according to the measurement vector after the perception matrix after migration and migration, utilizes compressive sensing theory to recover the position of target.

2. the passive type localization method based on spatial migration compressed sensing according to claim 1, is characterized in that, the described passive type localization method based on spatial migration compressed sensing, also comprises:

When the area of described sample areas is not less than the area in described region to be monitored, after completing steps six, directly carry out step 8.

3. the passive type localization method based on spatial migration compressed sensing according to claim 1, is characterized in that, describedly disposes sensor node respectively in sample areas and region to be monitored, comprising:

If the size l × a of sample areas, the size in region to be monitored is u × b, the wireless link length formed at the node of sample areas deployment is l, the wireless link length that the node of regional deployment to be monitored is formed is u, and l ≠ u, the link number of sample areas and regional deployment to be monitored is M.

4. the passive type localization method based on spatial migration compressed sensing according to claim 1, is characterized in that, the described RSS matrix by reference position in described sensor node collecting sample region and region to be monitored, comprising:

First sample areas and region to be monitored are all divided into N number of square net, then choose identical reference position point respectively in sample areas and region to be monitored, use 1,2 respectively ... n and 1 ', 2 ' ... n ' expression, n=n '≤N.

Then allow target stand in grid place selected in sample areas and region to be monitored respectively successively, record the RSS matrix s of sample areas ^lwith the RSS matrix s in region to be monitored ^u, wherein;

$s^l=(s_{11}^l,\&CenterDot;\&CenterDot;\&CenterDot;,s_{M1}^l,\&CenterDot;\&CenterDot;\&CenterDot;,s_{1j}^l,\&CenterDot;\&CenterDot;\&CenterDot;,s_{\mathrm{Mj}}^l,\&CenterDot;\&CenterDot;\&CenterDot;,s_{\ln }^l,\&CenterDot;\&CenterDot;\&CenterDot;,s_{\mathrm{Mn}}^l),$

$s^u=(s_{11^{\&prime;}}^u,\&CenterDot;\&CenterDot;\&CenterDot;,s_{M{1}^{\&prime;}}^u,\&CenterDot;\&CenterDot;\&CenterDot;,s_{1j^{\&prime;}}^u,\&CenterDot;\&CenterDot;\&CenterDot;,s_{M{j}^{\&prime;}}^u,\&CenterDot;\&CenterDot;\&CenterDot;,s_{l{n}^{\&prime;}}^u,\&CenterDot;\&CenterDot;\&CenterDot;,s_{M{n}^{\&prime;}}^u),$

And s _ij={ s _ij(1) ..., s _ij(q) ..., s _ij(Q) } ^tq continuous print RSS value of i-th link when representing that target is in jth grid.

5. the passive type localization method based on spatial migration compressed sensing according to claim 1, is characterized in that, according to the described RSS matrix in described sample areas and region to be monitored, obtains moving function, comprising:

According to the described RSS matrix s of described sample areas ^lwith the described RSS matrix s in region to be monitored ^u, by s ^land s ^lproject respectively, obtain y ^l=Ws ^l, y ^u=Ws ^u, make x=(x ^l, x ^u), y=(y ^l, y ^u), constructor y=Wx, makes y ^land y ^ube distributed on projector space similar as far as possible, namely

Described F (W) is for measuring y ^ldistribution p _l(y) and y ^udistribution p _uthe majorized function of the spacing of (y);

By projective distribution range observation function D _w(p _l|| p _u) substitute into formula (1), obtain

Be migration function.

6. the passive type localization method based on spatial migration compressed sensing according to claim 1, is characterized in that, described by the sample RSS value in described sensor node collecting sample region, described sample RSS value is combined as perception matrix, comprises:

Allow target stand in all grid places of sample areas successively, the RSS value measuring each grid place obtains perception matrix

$S_{M\&times;N\&times;Q}=\left[\begin{array}{ccc}{S}_{11}& ...& S_{M1}\\ .& & .\\ .& S_{\mathrm{ij}}& .\\ .& & .\\ S_{M1}& ...& S_{\mathrm{MN}}\end{array}\right],$

Wherein, s _ij={ s _ij(1) ..., s _ij(q) ..., s _ij(Q) } ^t.

7. the passive type localization method based on spatial migration compressed sensing according to claim 1, is characterized in that, is gathered the location RSS value in region to be monitored by described sensor node, described location RSS value is combined as and measures vector, comprising:

When record object is in region to be monitored, the RSS value of every bar link, obtains measuring vectorial R _{m × 1 × Q}=[r ₁..., r _i..., r _m] ^t, wherein, r _i={ r _i(1) ..., r _i(q) ..., r _i(Q) } ^t.

8. the passive type localization method based on spatial migration compressed sensing according to claim 1, it is characterized in that, described according to described migration function, measurement vector in the perception matrix of described sample areas and described region to be monitored is moved, obtain the measurement vector after the perception matrix after moving and migration, comprising:

Perception matrix is multiplied with migration function W respectively with measurement vector, obtains the perception matrix after moving $S_{M\&times;N\&times;Q}^{\&prime;}=\left({\mathrm{Ws}}_{\mathrm{ij}}^l\right),i\&Element;[1,M],j\&Element;[1,M]$ With the measurement vector after migration $R_{M\&times;1\&times;Q}^{\&prime;}=\left({\mathrm{Wr}}_i^u\right),i\&Element;[1,M];$

Dimension-reduction treatment is carried out to the perception matrix after described migration and the measurement vector after described migration, obtains the perception matrix after dimensionality reduction and measure vector.

9. the passive type localization method based on spatial migration compressed sensing according to claim 1, it is characterized in that, when the described area when described sample areas is less than the area in described region to be monitored, gridding interpolation process is carried out to described sample areas, obtain the high resolving power perception matrix after moving, comprising:

First, when the area l × a of described sample areas is less than the area u × b in described region to be monitored, when number of grid is N, the grid length of side of sample areas is ω _l, the grid length of side in region to be monitored is ω _u;

Secondly, each grid in described region to be monitored is divided into individual sub-grid, the length of side of described each sub-grid is the quantity of described sub-grid is

Finally, choose the grid at sub-grid i' place and 8 adjacent mesh nearest with this grid distance, totally 9 grids form adjacent grid, are obtained the RSS value of sub-grid i' by interpolation, and then obtain the high resolving power perception matrix after moving.

10. the passive type localization method based on spatial migration compressed sensing according to claim 1, is characterized in that, according to the measurement vector after the perception matrix after migration and migration, utilizes compressive sensing theory to recover the position of target, comprising:

By utilizing compressed sensing reconstruction algorithm (l ₁-minimization algorithm) can position vector θ be obtained:

Wherein, be pseudoinverse operator, c>0 is a constant, and δ is also a constant but can not be tending towards 1, obtains the location that namely θ completes region to be monitored internal object, and

θ＝[θ ₁,…,θ _j,…θ _N] ^T，

Wherein, θ _j∈ { 0,1}, the θ when a jth grid there being target _j=1, otherwise be 0.