CN106102162A - A kind of iterative estimate method for wireless sensor network three-dimensional localization - Google Patents

Abstract

The invention discloses a kind of iterative estimate method for wireless sensor network three-dimensional localization, belong to the technical field of wireless sensor network.The present invention utilizes current connection anchor node to be opened into the connection anchor node that three-dimensional barycenter alternative distances unknown node is farthest, opened at current connection anchor node and opened into three dimensions barycenter as positioning result with current connection anchor node when the distance between three dimensions barycenter and unknown node meets stopping criterion for iteration, opened into continuation iterative computation when the distance between three dimensions barycenter and unknown node is unsatisfactory for stopping criterion for iteration at current connection anchor node currently to connect anchor node and opened into three dimensions barycenter, the advantage not only maintaining former two dimension node positioning method, there is in the case of bigger node communication radius the positioning precision of the most former two-dimensional location method.

Description

A kind of iterative estimate method for wireless sensor network three-dimensional localization

Technical field

The invention discloses a kind of iterative estimate method for wireless sensor network three-dimensional localization, belong to wireless sensing The technical field of device network.

Background technology

Wireless sensor network is made up of the sensor node in a large number with perception, communication and signal handling capacity, is One of element of Internet of Things.Research for wireless sensor network comes from its application in military field, military The restriction of field applied environment requires that in network, sensor node has the feature of MANET and low-power consumption.Nowadays, along with relevant Scientific and technical is full-fledged, and the application of wireless sensor network technology also the most universal, relates to the aspect of people's life Face, such as environmental monitoring, medical treatment and nursing, target detection and tracking etc..Wireless sensor network must be exactly known sensor joint The positional information at some place, the information of this node institute perception just has the value of application.Therefore, sensor node leads in a network Crossing with communicating to self-position location between adjacent node is the basis that wireless sensor network is applied in practice.

Research for wireless sensor network node location is divided into node locating based on two dimensional surface and based on three-dimensional The node locating in space.Node locating based on two dimensional surface is owing to decreasing the estimation of third dimension information, relatively simple. Existing it is roughly divided into two classes based on two dimensional surface localization method: localization method based on range finding and based on non-ranging location side Method.Localization method based on range finding needs to carry out unknown node with the correlation distance connecting between anchor node or azimuth information Accurate calculating, node locating precision is higher, but node energy is often consumed bigger by position fixing process, it is impossible to meet wireless sensing The requirement to node low-power consumption of the device network, and affected relatively big by distance or orientation calculating error, anti-range measurement error Ability is poor.Based on non-ranging localization method need not calculate unknown node and connection anchor node between accurate distance or Azimuth information, estimates unknown node position merely with Connectivity etc., and positioning precision is relatively low.But, owing to it positions The consumption of process on node energy is less, greatly reduces overall location Calculation amount and the communication overhead of wireless sensor network, Application in practice is the most extensive.

Owing in actual applications, wireless sensor network node typically will not be distributed on absolute two dimensional surface, because of The 3-D positioning method of this research wireless sensor network more meets the location requirement of reality, has more preferable application prospect.Existing Having in wireless senser Network Three-dimensional localization method, Constrained-3D location algorithm is based on time of arrival (toa) (Time Ofarrival, is called for short TOA) method calculate required concrete range information, and realize making by oneself of node based on principle of triangulation Position, this wireless sensor network tri-dimensional node positioning method realizes node locating based on distance measurement method, and positioning precision is preferable, This technology document<Sensor Network Localization in Constrained3-D spaces>(Liang J L, Shao J, Xu Y., 2006.) in disclosed.But Constrained-3D location algorithm assumes all anchor Node distribution At grade, the actual application of this algorithm has been had a strong impact on.APIS algorithm with anchor node each in network as the centre of sphere, communication away from From for radius, whole three dimensions is divided into multiple sphere space, by judging the position of unknown node and each sphere space Relation, calculates all spheroid coincidence space comprising unknown node, and realizes wireless sensor node based on this coincidence three dimensions The three-dimensional localization of point, this technology is at document < Grid-Based Location Estimation Scheme using op In Counts for Multi-hop Wireless Sensor Networks > (Joo G L, Rao S V.A, 2004.) public Open.Although this APIS algorithm is without range finding, but overall calculation and communication overhead are bigger, it is desirable to anchor node has higher energy Deposit and communication capacity.APIT-3D location algorithm utilizes can uniquely not determine one at conplane any four anchor node Individual tetrahedron, carries out permutation and combination by the anchor node connected with unknown node, it may be determined that multiple different tetrahedrons, and passes through Judge the position relationship between unknown node and each tetrahedron, calculate all tetrahedron coincidence space comprising unknown node, and Realize the three-dimensional localization of wireless sensor node based on this coincidence three dimensions, this technology is at document " wireless sensor network three Dimension self-locating method " disclosed in (Liu Yuheng, Pu Juhua, He Yang, Xiong Zhang, 2008.).APIT-3D location algorithm amount of calculation Low, node power consumption is little, but easily occur for the erroneous judgement of position relationship between unknown node and tetrahedron, affect unknown node Positioning precision.

In sum, although not all wireless sensor network two-dimensional location method can be extended to three-dimensional space Between apply, but use for reference and based on relative maturity and positioning performance preferable two-dimensional location method principle, extended to Three dimensions is to realize node locating, and keeps the advantage of former two-dimensional location method, is to study and realize wireless sensor network The effective ways of three-dimensional localization.Wireless sensor network two-dimensional location method based on barycenter iterative estimate is by anchor node institute Surround the iterative computation of plane barycenter, constantly reduce unknown node two dimensional surface that may be present scope, improve node with this fixed Position precision.The method need not measure unknown node and the distance connecting between anchor node, has preferable anti-range measurement by mistake Difference performance, consumes less for node energy in position fixing process, and can obtain preferable positioning precision by successive ignition, this Technology in document " Localization Algorithm for Wireless Sensor Networks based on barycenter iterative estimate " (Jiang Rui, Yang Zhen, 2016.) Open.Known in two-dimensional location method, unknown node two dimensional surface that may be present region is the least, and its positioning precision is the best. In like manner, during three-dimensional localization, positioning precision the most constantly carries along with constantly reducing of three dimensions scope residing for unknown node High.Analyze based on above, it is contemplated that propose a kind of iterative estimate method for wireless sensor network three-dimensional localization, logical Cross repeatedly iterative estimate and constantly reduce three dimensions scope residing for unknown node, thus improve wireless sensor network three-dimensional nodes Positioning precision.

Summary of the invention

The goal of the invention of the present invention is the deficiency for above-mentioned background technology, it is provided that a kind of for wireless sensor network The iterative estimate method of three-dimensional localization, estimates constantly to reduce three dimensions scope residing for unknown node by successive ignition, thus Improve wireless sensor network three-dimensional nodes positioning precision, solve existing radio sensing network 3-D positioning method and there is application Limitation, reduce communication overhead and be difficult to, with improving positioning precision, the technical problem coordinated.

The present invention adopts the following technical scheme that for achieving the above object

A kind of iterative estimate method for wireless sensor network three-dimensional localization, utilizes current connection anchor node to be opened into The connection anchor node that three-dimensional barycenter alternative distances unknown node is farthest, is opened into three dimensions at current connection anchor node Three dimensions barycenter is opened into current connection anchor node when distance between barycenter with unknown node meets stopping criterion for iteration For positioning result, opened into the distance between three dimensions barycenter and unknown node at current connection anchor node and be unsatisfactory for iteration eventually Only continue iterative computation during condition currently to connect anchor node and opened into three dimensions barycenter.

Further, described a kind of in the iterative estimate method of wireless sensor network three-dimensional localization, work as utilizing Before front connection anchor node is opened into the connection anchor node that three-dimensional barycenter alternative distances unknown node is farthest, calculate current Connection anchor node and the RSSI of unknown node, currently connect anchor node according to order arrangement ascending for RSSI.

Further, described a kind of in the iterative estimate method of wireless sensor network three-dimensional localization, iteration ends Condition includesWithThe two criterion,Three dimensions barycenter is obtained by the m time iterationWith the unknown RSSI between node O,Three dimensions barycenter is obtained by the m-1 time iterationAnd the RSSI between unknown node O, ε₁ The energy threshold set when connection anchor node is opened into three dimensions inside, ε it is positioned at by unknown node₂It is positioned at even for unknown node The energy threshold that logical anchor node sets when being opened into three dimensions space outerpace, m is the integer more than or equal to 2, at the m time repeatedly When distance between generation obtained three dimensions barycenter and unknown node meets the requirement of arbitrary criterion, obtained with the m time iteration Three dimensions barycenter is positioning result.

Further, described a kind of in the iterative estimate method of wireless sensor network three-dimensional localization, the m time iteration Obtained three dimensions barycenterAnd the RSSI between unknown node O is designated as Wherein, N is the sum currently connecting anchor node, P_nRSSI, the n=1 between anchor node is connected with n-th for unknown node, 2 ..., N, M be span 3.24～4.5 normal parameter, A=-10log₁₀P₁, P₁For the reference at unknown node distance 1m RSSI, the span of general A value is 45～49, d_ijFor i-th connection anchor node connect with jth between anchor node away from From.

Further, described a kind of in the iterative estimate method of wireless sensor network three-dimensional localization, the m time iteration Obtained three dimensions barycenterCoordinate be designated as Wherein, (x_n,y_n,z_n) it is the coordinate of the n-th connection anchor node.

The present invention uses technique scheme, has the advantages that

(1) wireless sensor network two-dimensional location method is extended to three dimensions apply, to current connection anchor joint Point is opened into the relevant parameter of three dimensions barycenter and is calculated, and proposes to utilize current barycenter alternative distances unknown node farthest Connection anchor node, by successive ignition estimate realize wireless sensor network three-dimensional nodes hi-Fix, not only maintain The advantage of former two dimension node positioning method, has determining of the most former two-dimensional location method in the case of bigger node communication radius Position precision；

(2) at least there is the distance between a connection anchor node and unknown node more than between current barycenter and unknown node Distance, the new three dimensions scope one formed hence with the connection anchor node that current barycenter alternative distances unknown node is farthest Surely less than former three dimensions scope, i.e. localization method convergence；

(3) give localization method of the present invention concrete changing according to wireless sensor network environment concrete in three dimensions For end condition, under node locating precise manner is effectively ensured, save the communication overhead of network and the energy loss of node；

(4) (Received signal strength indication is called for short to have preferable anti-received signal strength RSSI) feature of measurement error ability, proposes to improve the inventive method by successive ignition under relatively low anchor node distribution situation Signal Coverage Percentage.

Accompanying drawing explanation

Fig. 1 is the connection anchor node number impact on positioning precision of the present invention.

Fig. 2 is two-dimensional location method and 3-D positioning method relative positioning error of the present invention contrast.

Fig. 3 is the impact on positioning precision of the present invention of the range measurement error.

Fig. 4 is the connection anchor node number impact on Signal Coverage Percentage of the present invention.

Fig. 5 is that iteration positions the number of times impact on Signal Coverage Percentage of the present invention.

Detailed description of the invention

Below in conjunction with the accompanying drawings the technical scheme of invention is described in detail.

Assume that there is true coordinate in three dimensions is (x, y, unknown node O z).In three dimensions, exist N number of Known anchor node S₁S₂S₃......S_NIt is connected with unknown node O, wherein, the n-th anchor node S_nCoordinate be (x_n,y_n,z_n), Then this anchor node S_nWith the spacing of unknown node O it is:

$\begin{array}{cc}{d}_n=\sqrt{{(x_n-x)}^2+{(y_n-y)}^2+{(z_n-z)}^2}& 1\&le;n\&le;N\end{array}---\left(1\right)$

By this N number of connection anchor node S₁S₂S₃......S_NOpen in three dimensions, current three dimensions barycenterCoordinate ForHave:

$\left\{\begin{array}{c}{x}_{{\hat{O}}_1}=\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{x}_n\\ y_{{\hat{O}}_1}=\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{y}_n\\ z_{{\hat{O}}_1}=\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{z}_n\end{array}\right.---\left(2\right)$

According to formula (1)-(2), can proper front three dimensions barycenterSpacing with unknown node OFor:

$d_{{\hat{O}}_1}=\sqrt{{\left(\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{x}_n-x\right)}^2+{\left(\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{y}_n-y\right)}^2+{\left(\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{z}_n-z\right)}^2}---\left(3\right)$

Wherein:

$\begin{array}{c}{\left(\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{x}_n-x\right)}^2=\frac{1}{N^2}{\left(\underset{n=1}{\overset{N}{\&Sigma;}}{x}_n-Nx\right)}^2=\frac{1}{N^2}{\&lsqb;\underset{n=1}{\overset{N}{\&Sigma;}}\left(x_n-x\right)\&rsqb;}^2\\ =\frac{1}{N^2}\&lsqb;\underset{n=1}{\overset{N}{\&Sigma;}}{\left(x_n-x\right)}^2+2\&CenterDot;\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}\left(x_i-x\right)\left(x_j-x\right)\&rsqb;\end{array}---\left(4\right)$

As i ≠ j, have:

$\begin{array}{c}2(x_i-x)(x_j-x)=2x_i{x}_j-2x_{i}x-2x_{j}x+2x^2\\ ={\left(x_i-x\right)}^2+{\left(x_j-x\right)}^2-{\left(x_i-x_j\right)}^2\end{array}---\left(5\right)$

Formula (5) is substituted into formula (4), can obtain:

${\left(\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{x}_n-x\right)}^2=\frac{1}{N^2}\&lsqb;N\underset{n=1}{\overset{N}{\&Sigma;}}{(x_n-x)}^2+\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{(x_i-x_j)}^2\&rsqb;---\left(6\right)$

In like manner can obtain:

${\left(\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{y}_n-y\right)}^2=\frac{1}{N^2}\&lsqb;N\underset{n=1}{\overset{N}{\&Sigma;}}{(y_n-y)}^2+\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{(y_i-y_j)}^2\&rsqb;---\left(7\right)$

${\left(\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{z}_n-z\right)}^2=\frac{1}{N^2}\&lsqb;N\underset{n=1}{\overset{N}{\&Sigma;}}{(z_n-z)}^2+\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{(z_i-z_j)}^2\&rsqb;---\left(8\right)$

Formula (6)-(8) are substituted into formula (3), have:

$d_{{\hat{O}}_1}=\frac{1}{N}\sqrt{N\underset{n=1}{\overset{N}{\&Sigma;}}{\left(d_n\right)}^2-\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{(x_i-x_j)}^2-\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{(y_i-y_j)}^2-\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{(z_i-z_j)}^2}---\left(9\right)$

(x_i,y_i,z_i) be i-th connection anchor node coordinate, (x_j,y_j,z_j) be jth connection anchor node coordinate.

Owing to connection anchor node coordinate is it is known that therefore according to formula (2) and formula (9), it is possible to obtain currently three dimensions BarycenterCoordinate and with the spacing of unknown node O.At this point it is possible to by current three dimensions barycenterIt is considered as new connection Anchor node, with the farthest a certain connection anchor node of its alternative distances unknown node O, thus reduces connection anchor node and is opened into three-dimensional Spatial dimension, and improve constantly positioning precision by successive ignition.

But, wireless sensor node localization method calculates the distance between anchor node and unknown node, can drastically increase Add computation complexity, the communication overhead of network and the energy loss of node.Accordingly, it is considered to utilize unknown node O with connect anchor joint RSSI information substitution range information between point, carries out space barycenterRelevant parameter calculate and the iteration of location algorithm, permissible Effectively reduce the communication overhead of network, reduce the loss for node energy.

Assume unknown node O and the n-th connection anchor node S_nSpacing be d_n, and known unknown node O and anchor node S_nBetween RSSI be P_n, can obtain according to the signal communication theory in free space:

$\frac{P_1}{P_n}={\left(\frac{d_n}{d_1}\right)}^M---\left(10\right)$

Wherein, M is normal parameter, P₁For with unknown node O distance d₁The reference RSSI at place.Make d₁=1, then P₁Represent with not Know the reference RSSI at node O distance 1m, substitute into formula (10), and do and simplify further and can obtain:

10log₁₀P_n=-[A+10M (log₁₀d_n)] (11)

Wherein:

A=-10log₁₀P₁ (12)

Different according to actual environment, the optimal set point of general M value is 3.24～4.5, and the optimal set point of A value is 45～49.According to formula (10)-(12), abbreviation can obtain:

$d_n=\sqrt{{10}^{-\frac{A}{5M}}{P_n}^{-\frac{2}{M}}}---\left(13\right)$

Carry it into formula (9), it is assumed that unknown node O and current barycenterRSSI beHave:

$P_{{\hat{O}}_1}=\frac{1}{{\&lsqb;\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}\left({P_n}^{-\frac{2}{M}}\right)-\frac{{10}^{\frac{A}{5M}}}{N^2}\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{\left(d_{ij}\right)}^2\&rsqb;}^{\frac{M}{2}}}---\left(14\right)$

Wherein, d_ijRepresent anchor node S_iWith S_jBetween distance, it may be assumed that

$\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{\left(d_{ij}\right)}^2=\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{\left(x_i-x_j\right)}^2+\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{\left(y_i-y_j\right)}^2+\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{\left(z_i-z_j\right)}^2---\left(15\right)$

In order to prove the location convergence of the inventive method further, formula (15) is substituted into formula (9), can be to space matter The heartSpacing with unknown node OExpression formula do further simplification, have:

${d_{{\hat{O}}_1}}^2=\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{\left(d_n\right)}^2-\frac{1}{N^2}\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{\left(d_{ij}\right)}^2---\left(16\right)$

Without loss of generality, it is assumed that have:

0<d₁≤d₂≤d₃......≤d_N-1≤d_N (17)

Therefore, according to formula (16)-(17), can obtain:

$\frac{1}{N}\underset{n=1}{\overset{N}{\&Sigma;}}{\left(d_n\right)}^2\&le;d_N---\left(18\right)$

$\frac{1}{N^2}\underset{i=1}{\overset{N-1}{\&Sigma;}}\underset{j=i+1}{\overset{N}{\&Sigma;}}{\left(d_{ij}\right)}^2>0---\left(19\right)$

Carry it into formula (16), have a conclusion:

$d_{{\hat{O}}_1}<d_N---\left(20\right)$

Obviously, current three dimensions barycenter is utilizedSubstitute anchor node S_NOpened into three dimensions scope necessarily less than former anchor Node is opened into three dimensions, is constantly reduced unknown node O place spatial dimension by successive ignition, improves node locating essence Degree, localization method proposed by the invention is restrained.

Based on the constringent proof of localization method proposed by the invention, illustrate that the positioning precision of the present invention is along with barycenter iteration The increase of number of times and improve constantly.But, along with anchor node is opened into constantly reducing of space, the inventive method iteration is not for Know that the improvement result of node locating precision also diminishes.Therefore, set suitable stopping criterion for iteration and node can be effectively ensured In the case of positioning precision, save communication overhead and the energy loss of node of network.

Consider that unknown node O is opened into two kinds of position relationships of existence between three dimensions, i.e. unknown joint with connection anchor node Point O be positioned at connection anchor node opened into interior volume be positioned at unknown node O connect anchor node opened into outside.Due to sky Between barycenter be necessarily positioned at interior volume, so when unknown node O be positioned at connection anchor node opened into interior volume time, along with this The increase of bright method iterations, it is more and more less that anchor node is opened into spatial dimension, and its space barycenter can constantly approach and there is no Limit is close to unknown node O.Now, it is considered to directly set the inventive method end condition and by unknown node O and obtained space matter The spacing of the heart is less than a certain threshold value.According to formula (14), i.e. set when the m time iteration obtained space barycenterWith the unknown Between node O, RSSI is more than a certain threshold value:

$P_{{\hat{O}}_m}>{\mathrm{\&epsiv;}}_1---\left(21\right)$

Wherein, ε₁For setting threshold value.When unknown node O be positioned at connection anchor node opened into outside time, along with this The increase of bright method iterations, its space barycenter constantly close to unknown node O, but but can not be infinitely close to the unknown Node O.Now, if still using formula (21) as stopping criterion for iteration, then the inventive method can be absorbed in endless loop.According to public affairs Formula (18), it is considered to set the RSSI rate of change between space barycenter and unknown node O less than a certain threshold value:

$P_{{\hat{O}}_m}-P_{{\hat{O}}_{m-1}}<{\mathrm{\&epsiv;}}_2---\left(22\right)$

Wherein, ε₂For setting threshold value.Now think that the inventive method iteration is less for the improvement result of positioning precision, this Inventive method has reached convergence.But, in actual three dimensions, it is impossible to quickly and accurately judge unknown node O and company Logical anchor node is opened into position relationship between space.Therefore, in order to ensure the location correct to unknown node O, set when the m time Iteration obtained space barycenterWhen meeting any condition in formula (21)-(22), the inventive method stops iteration.

The present invention uses based on non-ranging wireless sensor network tri-dimensional node positioning method, simulation results show this Bright method has preferable positioning precision and location spreadability, and anti-RSSI error ability is strong, it is adaptable to wireless sensor network Three-dimensional nodes location.The specific embodiment of the invention is as follows:

1) suitable localization method stopping criterion for iteration is determined according to wireless sensor network node communication radius.

2) connect anchor node with unknown node be ranked up according to RSSI value between itself and unknown node current.

3) calculate current anchor node surrounded region center-of-mass coordinate and and unknown node between RSSI value.

4) utilize the anchor node that current barycenter substitutes currently and between unknown node, RSSI value is minimum, thus obtain new connection Anchor node is opened into three dimensions, and is constantly reduced connection anchor node by successive ignition and opened into three dimensions scope.

In order to verify localization method performance of the present invention, by analogue simulation actual wireless sensor network environment, and change Affect the relevant important parameter of unknown node positioning precision, survey as node communication radius, anchor node distribution density and RSSI receive Amount errors etc., observe the inventive method positioning performance.

Definition unknown node actual position in three dimensions and location algorithm estimate the beeline between gained position Position error for algorithm.Assume that 3-D positioning method estimates that unknown node position isAccording to formula (1), then fixed Position error is:

$ERROR=\sqrt{{(x_{\hat{O}}-x)}^2+{(y_{\hat{O}}-y)}^2+{(z_{\hat{O}}-z)}^2}---\left(23\right)$

Positioning precision between the wireless sensor network different in order to preferably contrast node communication radius, in formula (23) On the basis of define relative positioning error be:

$\stackrel{\&OverBar;}{ERROR}=\frac{\underset{i=1}{\overset{K}{\&Sigma;}}{\mathrm{ERROR}}_i}{KR}---\left(24\right)$

Wherein, K is unknown node number in wireless sensor network, and R is node communication radius.Assume 100 × 100 × 100m³Three dimensions in 1000 nodes of random distribution.According to formula (13), map one by one owing to existing between RSSI and distance Relation, therefore directly set in emulation experiment stopping criterion for iteration as:

$\begin{array}{ccc}{d}_{{\hat{O}}_m}<0.1R& or& d_{{\hat{O}}_m}-d_{{\hat{O}}_{m-1}}<0.1R\end{array}---\left(25\right)$

The most respectively by changing communication radius and the anchor node ratio of wireless sensor network interior joint, with This explanation network connects the impact for positioning method accuracy of the present invention of the anchor node number with unknown node.It has been observed that in phase Under the conditions of anchor node ratio, node communication radius is the biggest, and the anchor node quantity connected with unknown node is the most, and the present invention positions Precision improves constantly the most therewith.In like manner, when node communication radius one timing, increase anchor node ratio in wireless sensor network same Sample can increase the anchor node quantity connected with unknown node, is effectively improved the present invention estimation essence for unknown node position Degree.In sum, by Monte Carlo simulation shown in Fig. 1 it is demonstrated experimentally that to increase the anchor node number that connects with unknown node permissible Improve the precision of localization method of the present invention.

Owing to localization method of the present invention is in three dimensions by two-dimensional location method expanded application, it is therefore desirable to two dimension is fixed Method for position and 3-D positioning method performance contrast, and analyzing three-dimensional localization method the most preferably remains former two-dimensional localization The good location performance of method.But, in two dimensional surface and three dimensions, residing for node, simulated environment is different, in order to really The positioning precision protecting two methods has comparability, it is desirable to node distribution situation in two dimensional surface and three dimensions is in statistics Upper holding concordance.Analyzing based on above, emulation is assumed at 100 × 100m²Two dimensional surface on 100 nodes of random distribution. The most either in two dimensional surface or three dimensions, it is satisfied by any one-dimensional direction averagely having one at interval of 10m Node.According to formula (25), set two-dimensional location method stopping criterion for iteration as:

Unknown node is positioned at and connects the surrounded internal plane of anchor node:Unknown joint Point is positioned at and connects the surrounded flat outer of anchor node:

Now, either wireless sensor network node distributional environment or localization method stopping criterion for iteration, two kinds of sides Method is respectively provided with preferable concordance.Regard two dimension node locating as three-dimensional nodes that all nodes are distributed in same plane Location, can obtain two-dimentional node locating error according to formula (23) is:

${\mathrm{ERROR}}_{2D}=\sqrt{{(x_{\hat{O}}-x)}^2+{(y_{\hat{O}}-y)}^2}---\left(28\right)$

Formula (28) is brought into formula (24) relative positioning error under two-dimensional condition.In order to fully contrast two Dimension localization method and 3-D positioning method, we choose the less R=25 of node communication radius and node communication radius relatively respectively Two kinds of situations of big R=40, observe two kinds of method relative positioning errors under the conditions of different anchor node ratio, as shown in Figure 2.

It has been observed that along with the increase of connection anchor node ratio, two-dimensional location method and three-dimensional in wireless sensor network Localization method estimated accuracy is all significantly improved, and its experimental result is the most identical with experimental result shown in Fig. 1.When node communication half When footpath is less, such as R=25, in the communication radius with unknown node as the centre of sphere, anchor node is identical with unknown node as the center of circle logical In letter radius, anchor node quantity is suitable, and now have the most similar node with 3-D positioning method the most fixed for two-dimensional location method Position error；But, when node communication radius is bigger, such as R=40, anchor node number in the communication radius with unknown node as the centre of sphere Being significantly more than anchor node quantity in the same communication radius with unknown node as the center of circle, localization method the most of the present invention is compared to two Dimension localization method, presents less node relative positioning error.Therefore, 3-D positioning method proposed by the invention not only keeps The advantage of former two dimension node positioning method, in the case of bigger node communication radius, has the most former two-dimensional location method Positioning precision.

In actual wireless sensor network, due to the interference of various noises, network can be caused to deposit for the measurement of RSSI In error.Localization method of the present invention need to utilize the RSSI between unknown node and anchor node estimate current three dimensions barycenter with not Know internodal RSSI value, therefore by analysis of simulation experiment rssi measurement error for positioning performance of the present invention impact particularly Important.In like manner, owing to there are mapping relations one by one between RSSI and distance, it is considered to directly utilize range measurement error and characterize RSSI survey Amount error, now range error for the impact i.e. rssi measurement error of positioning precision of the present invention for localization method of the present invention The impact of energy.Assume that range measurement error coefficient is μ, then have:

$\widehat{d_n}=(1+\mathrm{\&mu;}\&times;RAND(-1,1\left)\right)\&times;d_n---\left(29\right)$

Wherein, RAND (-1,1) is a random number, sets it without loss of generality and obeys uniform point in (-1,1) is interval Cloth.d_nWithIt is respectively unknown node and connects the distance actual value between anchor node and measured value with n-th.Obviously, range measurement Error coefficient μ determines the size of distance measure offset distance actual value.Error coefficient μ is the biggest in range measurement, and network is described The biggest with the range measurement error connected between anchor node to unknown node, during and if only if μ=0, distance measure is true with distance Real-valued equal, the most there is not range measurement error.

In order to more comprehensively analyze the impact on localization method performance of the present invention of the range measurement error, we choose node R=25 that communication radius is less and the bigger two kinds of situations of R=35 of node communication radius, and respectively in network anchor node ratio relatively Under the conditions of higher 45% two kind of 5% low and network anchor node ratio, viewing distance measurement error is for the present invention side of location The impact of method performance, as shown in Figure 3.Observation Fig. 3 finds, when communication radius is less and network anchor node ratio is relatively low, due to Connect anchor node negligible amounts with unknown node, now the inventive method location relative error is in higher level all the time.Along with Node communication radius increases and the raising of network anchor node ratio, connects anchor node quantity with unknown node and is consequently increased, this Inventive method positioning precision significantly improves.This experimental result is the most identical with experimental result shown in Fig. 1.Though localization method of the present invention So need to utilize the rssi measurement value between unknown node and anchor node to estimate between current three dimensions barycenter and unknown node RSSI value, but either actual RSSI value of measuring still calculates gained RSSI value, for node locating in position fixing process The impact of energy is mainly reflected in two aspects: first, and the magnitude relationship between localization method of the present invention needs by RSSI value will be even Logical anchor node is ranked up by the distance with unknown node spacing, thus determines in iterative process by current three dimensions Barycenter institute substitute node.The inaccurate measurement of RSSI value can cause anchor node sequence to make mistakes, and and if only if, and minimum RSSI value is corresponding When anchor node sequence makes mistakes, just localization method iterative process of the present invention can be produced impact, and only affect localization method and receive Hold back speed, less to location precision.Secondly, localization method of the present invention is by calculating current three dimensions barycenter and unknown joint RSSI value between point compares with set iteration ends threshold value, so that it is determined that localization method of the present invention when iteration is eventually Only.Therefore, inaccurate rssi measurement can affect localization method iterations, and more iterations does not interferes with positioning accurate Degree, but extra computation complexity can be increased；Less iterations can produce minor impact to positioning precision.Therefore exist In Fig. 3, no matter under less connection anchor node said conditions or under the conditions of more connection anchor node, range measurement error for The impact of positioning method accuracy of the present invention is the least, it was demonstrated that localization method of the present invention has preferable anti-rssi measurement error energy Power.

Except higher node locating precision and preferable anti-rssi measurement error ability, require wireless sensor network simultaneously Network node positioning method has preferable Signal Coverage Percentage.Assume that unknown node sum is K in wireless sensor network_all, profit Can be to wherein K with node positioning method_knownIndividual node carries out effective localization process, then Signal Coverage Percentage is:

Fig. 4 show the Signal Coverage Percentage of localization method of the present invention under different connection anchor node distribution occasion.Visible relatively Under the conditions of big node communication radius or bigger anchor node ratio, it is distributed the most intensive in three dimensions due to anchor node, because of This Signal Coverage Percentage of the present invention is preferable；But when node communication radius is less and anchor node ratio less in the case of, the present invention's Signal Coverage Percentage is poor.

But, because localization method of the present invention has preferable anti-rssi measurement error ability, therefore can be by new definition Unknown node be equivalent to the new anchor node with certain rssi measurement error, thus improve in wireless sensor network system Anchor node ratio, positions to improve the Signal Coverage Percentage of the inventive method by successive ignition.According to Fig. 4, the present invention is fixed Method for position is only less at node communication radius and anchor node ratio less in the case of, Signal Coverage Percentage is poor.So, we are at figure Only consider to improve node communication radius by successive ignition in 5 less, i.e. node communication radius R=20 and R=25, and anchor node Ratio is less, i.e. anchor node ratio is 5% and 10%, in the case of Signal Coverage Percentage.It has been observed that in most cases, this Inventive method has only to twice iteration location and is obtained with more satisfactory Signal Coverage Percentage, even if at node communication radius R =20 and poor anchor node distribution occasion that anchor node ratio is 5% under, can also be covered location by three iteration location Rate brings up to more than 90%.And under different node communication radiuses and anchor node distribution occasion, localization method of the present invention passes through 4-5 iteration location, Signal Coverage Percentage all can reach more than 99%, have fabulous practicality.

Claims (5)

1. the iterative estimate method for wireless sensor network three-dimensional localization, it is characterised in that: utilize and currently connect anchor Node is opened into the connection anchor node that three-dimensional barycenter alternative distances unknown node is farthest, is opened at current connection anchor node Currently to connect anchor node institute Zhang Chengsan when becoming the distance between three dimensions barycenter and unknown node to meet stopping criterion for iteration Dimension space barycenter is positioning result, is opened into the distance between three dimensions barycenter and unknown node not at current connection anchor node Continue iterative computation when meeting stopping criterion for iteration currently to connect anchor node and opened into three dimensions barycenter.

A kind of iterative estimate method for wireless sensor network three-dimensional localization, its feature exists In, utilize current connection anchor node opened into the farthest connection anchor node of three-dimensional barycenter alternative distances unknown node it Before, calculate the RSSI of current connection anchor node and unknown node, according to order arrangement current connection anchor joint ascending for RSSI Point.

A kind of iterative estimate method for wireless sensor network three-dimensional localization the most according to claim 1 or claim 2, its feature Being, described stopping criterion for iteration includesWithThe two criterion,Three-dimensional is obtained by the m time iteration Space barycenterAnd the RSSI between unknown node O,Three dimensions barycenter is obtained by the m-1 time iterationSave with the unknown RSSI, ε between some O₁The energy threshold set when connection anchor node is opened into three dimensions inside, ε it is positioned at by unknown node₂ Be positioned at the energy threshold set when connection anchor node is opened into three dimensions space outerpace by unknown node, m is more than or equal to 2 Integer, the distance between the m time iteration obtained three dimensions barycenter and unknown node meet arbitrary criterion require time, with The m time iteration obtained three dimensions barycenter is positioning result.

A kind of iterative estimate method for wireless sensor network three-dimensional localization, it is characterised in that m Secondary iteration obtained three dimensions barycenterAnd the RSSI between unknown node O is designated as Wherein, N is the sum currently connecting anchor node, P_nRSSI, the n=1 between anchor node is connected with n-th for unknown node, 2 ..., N, M be span 3.24～4.5 normal parameter, A=-10log₁₀P₁, P₁For the reference at unknown node distance 1m RSSI, the span of general A value is 45～49, d_ijFor i-th connection anchor node connect with jth between anchor node away from From.

A kind of iterative estimate method for wireless sensor network three-dimensional localization, it is characterised in that m Secondary iteration obtained three dimensions barycenterCoordinate be designated as Wherein, (x_n,y_n,z_n) it is the coordinate of the n-th connection anchor node.