CN104507164B - A kind of WSN node positioning methods based on RSS and ranging unbiased esti-mator - Google Patents
A kind of WSN node positioning methods based on RSS and ranging unbiased esti-mator Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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Abstract
A kind of WSN node positioning methods based on RSS and ranging unbiased esti-mator, the present invention relates to node positioning method；It is affected by noise the present invention is to solve the WSN node locating algorithms based on RSS rangings and cause the analysis of range error insufficient, it is impossible to inherently to eliminate a kind of WSN node positioning methods based on RSS and ranging unbiased esti-mator due to the ranging deviation caused by noise the problem of and proposed.This method is by 1, sets unknown node U=(x, y), BiThe coordinate of signal is xi,yi；2nd, unknown node and beaconing nodes B are calculatediDistance vi；3rd, unbiased estimator is obtained4th, unknown node U to beaconing nodes B is calculatediDistance5th, unknown node U position x, y is solved using Newton iteration method；6th, obtain △ X7, obtain unknown node position location xk,ykRealized etc. step.The present invention is applied to node locating field.
Description
Technical field
The present invention relates to node positioning method, more particularly to a kind of WSN node locatings based on RSS and ranging unbiased esti-mator
Method.
Background technology
Wireless sensor network (Wireless Sensor Network, WSN) is that have perception, meter by disposing largely
The network calculated the sensor node with wireless communication ability and formed.Substantial amounts of sensor node cooperates with completion is specific to appoint each other
Business.In many cases, it is necessary to know accurate node location information.And substantial amounts of sensor node is often random in deployment
, the positional information that each node is obtained by manpower is worthless.In addition, to meet the needs of commercial Application, sensing
Device node is usually less expensive, it is impossible to by configuring a locating module (such as GPS module) to each node to carry out
Positioning.Therefore, it is necessary to obtain the positional information of WSN nodes by appropriate location algorithm.
WSN node locating algorithms based on RSS (Received Signal Strength) ranging are a kind of more commonly used
Method.Its general principle is the RSS values of each beaconing nodes (position known node) received by unknown node, and by
Certain signal propagation model, unknown node is calculated to the distance of each beaconing nodes, then utilizes the positioning of three sides, least square
The location algorithms such as method calculate the positional information of unknown node.Can be due to environment complexity and the influence of noise, RSS it is frequent
It is fluctuation.By theory analysis, in general propagation model, according to the unknown node that RSS is calculated to each beaconing nodes
Distance inherent variability be present.This limits the raising of node locating precision to a certain extent.
Although many researchers solve this problem by proposing various propagation models, for RSS institutes
Analysis that is affected by noise and causing range error is simultaneously insufficient, only attempts to optimize the parameter of propagation model, this can not
The ranging deviation caused by noise is inherently eliminated, is unfavorable for the raising of WSN node locating precision.Therefore, based on RSS
The application under some complex environments of the WSN node locating algorithms of ranging can be restricted.
The content of the invention
It is affected by noise and cause the invention aims to solve the WSN node locating algorithms based on RSS rangings
The analysis of range error is insufficient, it is impossible to inherently eliminates one due to the ranging deviation caused by noise the problem of and proposed
WSN node positioning method of the kind based on RSS and ranging unbiased esti-mator.
Above-mentioned goal of the invention is achieved through the following technical solutions：
Step 1: in sensor network working environment, M beaconing nodes are disposed in advance；If sensor network building ring
Domestic arbitrary unknown node U=(x, y), if U is received from beaconing nodes BiThe coordinate of signal is xi,yi, i=1,
2,...,N,N≤M；Wherein, N represents the number for the visible beaconing nodes of unknown node U；
Step 2: according in general signal propagation model, calculate under the influence of by Gaussian noise n, unknown node with
Beaconing nodes BiDistanceWherein, apart from beaconing nodes d0Place sets reference mode, reference node
Point receives beaconing nodes BiSignal power be Pi(d0)；Unknown node U and beaconing nodes BiDistance be di；Not by noise
In the case of, unknown node U receives beaconing nodes BiSignal power be Pi(di)；N is that average is 0, and variance isGauss make an uproar
Sound；α is path loss index；
Step 3: the v to step 2iExpectation value analysis is carried out to obtainIn order thatIntroduce unknown node U to beaconing nodes BiThe unbiased estimator of actual distanceWherein,N is that average is 0, and variance isGaussian noise；
Step 4: according to unknown node U=(x, y) in two dimensional surface and beaconing nodes Bi=(xi,yi) coordinate, calculate
Unknown node U to beaconing nodes BiDistanceMeet following formula：
Wherein, i=1,2 ..., N, N >=3；
Step 5: unknown node U position x, y is solved using Newton iteration method；By formula (1) in (xk-1,yk-1)TPlace is carried out
Taylor series expansion, and quadratic term is omitted, obtain：
Wherein,xk,ykSolved not for kth time Newton iteration method
Know node U position coordinateses；
Step 6: being solved with reference to least square method to formula (2), matrix form is obtained：
G △ X=b (3)
Wherein, △ X=[(x-xk-1) (y-yk-1)]T,
With reference to Least Square Theory, obtaining △ X is：
△ X=(GTG)-1GTb (6)
Step 7: take △ X=[(xk-xk-1) (yk-yk-1)]T, it is iterated and solves according to formula (4), (5) and (6)
To final unknown node position location xk,yk；Complete a kind of WSN node locating sides based on RSS and ranging unbiased esti-mator
Method.
Invention effect
The present invention is not intended to propose a kind of new propagation model, is also not intended to discuss that the parameter under a certain special scenes is excellent
Change, but utilize in general propagation model, RSS and intrinsic range error are analyzed, find a kind of nothing to actual distance
Estimate partially, and the optimal estimation of RSS rangings is realized by least square, and then improve the essence of the WSN node locatings based on RSS
Degree.There will be the distance estimations of inherent variability and unbiased esti-mator of the invention to be compared by the present invention.For Gaussian noise
Standard deviation is equal to 3 situation, and simulation result is as shown in figure 1, from the graph, it is apparent that traditional survey calculated according to RSS
Away from inherent variability between distance and actual distance being present, and the unbiased esti-mator to ranging distance of the present invention substantially can be with
Actual distance is consistent.
The present invention in the case where not increasing any hardware resource, can effectively improve the precision of node locating.Algorithm
Moderate complexity, WSN nodes can location-independent, can adapt to wireless-sensor network distribution type positioning demand.Ordinary circumstance
Under, it need to only consider the situation of plane positioning, three-dimensional case can similar popularization.
Brief description of the drawings
Fig. 1 is the proposition of embodiment one to the unbiased esti-mator of actual distance and the comparison schematic diagram of Biased estimator；
Fig. 2 is the localization region and Node distribution figure that embodiment one proposes；
Fig. 3 is the unbiased esti-mator and Biased estimator cumulative probability error profiles versus's schematic diagram that embodiment one proposes；
Fig. 4 is a kind of WSN node positioning method streams based on RSS and ranging unbiased esti-mator that embodiment one proposes
Cheng Tu.
Embodiment
Embodiment one：A kind of WSN node locating sides based on RSS and ranging unbiased esti-mator of present embodiment
Method, specifically prepared according to following steps：
Step 1: in sensor network working environment, M beaconing nodes are disposed in advance；If sensor network building ring
Domestic arbitrary unknown node U=(x, y), if U is received from beaconing nodes BiThe coordinate of signal is xi,yi, i.e. BiFor not
It is visible, i=1,2 ..., N, N≤M to know node U；Wherein, N represents the number for the visible beaconing nodes of unknown node U
Mesh；
Step 2: according in general signal propagation model, calculate under the influence of by Gaussian noise n, unknown node with
Beaconing nodes BiDistanceWherein, apart from beaconing nodes d0Place sets reference mode, reference
Node receives beaconing nodes BiSignal power be Pi(d0)；Unknown node U and beaconing nodes BiDistance be di；Not by noise
In the case of, unknown node U receives beaconing nodes BiSignal power be Pi(di)；N is that average is 0, and variance isGauss
Noise；α is path loss index, and when being free space for sensor network working environment, its value is typically taken as 2；viRelatively
In actual distance diInherent variability be present；
Step 3: the v to step 2iExpectation value analysis is carried out to obtainIn order thatIntroduce unknown node U to beaconing nodes BiThe unbiased estimator of actual distance (introduces unknown node U to beacon section
Point BiThe unbiased estimator of actual distance)Wherein, N is that average is 0, and variance isGaussian noise；
Step 4: according to unknown node U=(x, y) in two dimensional surface and beaconing nodes Bi=(xi,yi) coordinate, calculate
Unknown node U to beaconing nodes BiDistanceMeet following formula：
Wherein, i=1,2 ..., N, N >=3；
Step 5: unknown node U position x, y is solved using Newton iteration method；By in formula (1) in (xk-1,yk-1)TPlace is entered
Row Taylor series expansion, and quadratic term is omitted, obtain：
Wherein,xk,ykSolved not for kth time Newton iteration method
Know node U position coordinateses；
Step 6: being solved with reference to least square method to formula (2), matrix form is obtained：
G △ X=b (3)
Wherein, △ X=[(x-xk-1) (y-yk-1)]T,
With reference to Least Square Theory, obtaining △ X is：
△ X=(GTG)-1GTb (6)
Step 7: take △ X=[(xk-xk-1) (yk-yk-1)]T, it is iterated and solves according to formula (4), (5) and (6)
To final unknown node position location xk,yk；As Fig. 4 completes a kind of WSN nodes based on RSS and ranging unbiased esti-mator
Localization method.
Present embodiment effect：
Present embodiment is not intended to propose a kind of new propagation model, is also not intended to that the ginseng under a certain special scenes is discussed
Number optimization, but in general propagation model is utilized, RSS and intrinsic range error are analyzed, found a kind of to actual distance
Unbiased esti-mator, and realize by least square the optimal estimation of RSS rangings, and then improve the WSN node locatings based on RSS
Precision.There will be the unbiased esti-mator of the distance estimations of inherent variability and present embodiment to be compared for present embodiment.It is right
It is equal to 3 situation in the standard deviation of Gaussian noise, simulation result is as shown in figure 1, from the graph, it is apparent that traditional basis
Inherent variability be present between ranging distance and actual distance that RSS is calculated, and the nothing to ranging distance of present embodiment
Estimation can be consistent with actual distance substantially partially.
Present embodiment in the case where not increasing any hardware resource, can effectively improve the precision of node locating.Calculate
The moderate complexity of method, WSN nodes can location-independent, can adapt to wireless-sensor network distribution type positioning demand.Typically
In the case of, it need to only consider the situation of plane positioning, three-dimensional case can similar popularization.
Embodiment two：Present embodiment is unlike embodiment one：According in general in step 2
Signal propagation model, calculate under the influence of by noise n, unknown node and beaconing nodes BiDistance
Detailed process is：
P (d)=P (d0)-10αlg(d/d0) (7)
Wherein, d0Distance for reference point apart from beaconing nodes, takes d0=1m；N is that average is 0, and variance isGauss make an uproar
Sound；D is unknown node and the distance of beaconing nodes；Under the influence of by Gaussian noise, unknown node does not receive beaconing nodes
Signal power be P (d)；
According to the in general signal propagation model in formula (7), unknown node U and beaconing nodes BiDistance be di, by
In the case of noise, the signal power that unknown node receives beaconing nodes is P (d)=Pi(di)+n, Pi(d0) and viSubstitute into public
Formula (7)：
Pi(di)+n=Pi(d0)-10αlg(vi/d0) (8)
Due to d0=1m, produced according to formula (8)：
Wherein, i=1,2 ..., N.Other steps and parameter are identical with embodiment one.
Embodiment three：Present embodiment is unlike embodiment one or two：To step in step 3
Two viExpectation value analysis is carried out to obtainDetailed process is：
Obtained according to formula (8),
DefinitionN is that average is 0, and variance isGaussian noise,
For unknown node U and beaconing nodes BiBetween ranging distance vi, meet following probability density function：
Then viDesired value E (vi) be：
Wherein, i=1,2 ..., N.Other steps and parameter are identical with embodiment one or two.
Embodiment four：Unlike one of present embodiment and embodiment one to three：It is sharp in step 5
Unknown node U positions (x, y) is solved with Newton iteration method；By formula (1) in (xk-1,yk-1)TPlace carries out the tool of Taylor series expansion
Body process is：
According to formula (1), and makeTaylor series expansion is carried out, and is omitted secondary
Xiang get：
Wherein,Other steps and parameter and specific embodiment party
One of formula one to three is identical.
Embodiment five：Unlike one of present embodiment and embodiment one to four：Taken in step 7
△ X=[(xk-xk-1) (yk-yk-1)]TIt is as follows to be iterated the specific iterative process of solution：
(1) unknown node U initial position is set as x0,y0, i.e. the initial value of iteration；
(2) as k=1, G and b is obtained respectively according to formula (4), (5), and substitutes into △ X, the △ X=of formula (6) acquisition now
[(x1-x0) (y1-y0)]T, and then obtain the result x of first time iteration1,y1；If △ X two norms are less than the threshold value of setting,
Then exit iteration, unknown node U position (x, y)=(x1,y1), otherwise k+1 performs step (3)；Threshold value determines that iteration is moved back
The condition gone out, when △ X very littles, it is believed that iteration convergence；Threshold value can be set as 0.01；
(3) k is worked as>It is similar with step (2) when 1, G and b is obtained respectively according to formula (4), (5), and is substituted into formula (6) and obtained this
When △ X=[(xk-xk-1) (yk-yk-1)]T；When △ X two norms are less than threshold value, iteration, unknown node U position are exited
Put estimated result (xk,yk)；
(4) when △ X two norms are more than or equal to threshold value, by k+1, the step performed in (3) is returned to；Until △ X's
Untill two norms are less than threshold value, iteration, final unknown node positioning result x are exitedk,yk.Other steps and parameter with it is specific
One of embodiment one to four is identical.
Beneficial effects of the present invention are verified using following examples：
Embodiment one：
A kind of WSN node positioning methods based on RSS and ranging unbiased esti-mator of the present embodiment, specifically according to following steps
Prepare：
Assuming that localization region is 30 × 30 (m2) square area, the origin of coordinates is (0,0).Deployment 8 in advance
Beaconing nodes, the transmission power of each beaconing nodes is 1mW (0dBm).The information of each beaconing nodes is as shown in table 1：
The position coordinates of the beaconing nodes of table 1
| Beaconing nodes sequence number | x(m) | y(m) |
| 1 | 5 | 5 |
| 2 | 15 | 5 |
| 3 | 25 | 5 |
| 4 | 5 | 15 |
| 5 | 5 | 25 |
| 6 | 15 | 25 |
| 7 | 25 | 25 |
| 8 | 25 | 15 |
Node communication radius is set to 15 meters.The coordinate of unknown node is set to (12,17), for other positions, obtains
Positioning result it is similar.The design parameter of emulation is as shown in table 2：
The simulation parameter of table 2
| Variable | Parameter |
| Gaussian noise standard deviation | 3 |
| Simulation times | 10000 times |
| Iteration initial coordinate | (0,0) |
Fig. 2 gives localization region and Node distribution.Eight squares of periphery are beaconing nodes, and middle star represents not
Know the position of node.It is similar that unknown node chooses the result that other positions obtain.
This algorithm is emulated according to the simulation parameter in table 2, and contrasts least square when inherent variability be present and calculates
Method, the cumulative probability distribution of position error are as shown in Figure 3：
From figure 3, it can be seen that relative to there is an inclined least square location algorithm, a unbiased most young waiter in a wineshop or an inn used by this algorithm
Good positioning improvement can be obtained by multiplying WSN node locating algorithms.When it is 68% to position probability, i.e. one times of standard deviation, have partially
The position error of least square is 4.65m, and the position error of no offset minimum binary is 3.73m, and position error reduces 0.92 meter.
The amount of calculation of two kinds of algorithms is roughly the same, and therefore, this algorithm can effectively improve on the premise of amount of calculation is not increased
Positioning precision.
The present embodiment is not intended to propose a kind of new propagation model, is also not intended to that the parameter under a certain special scenes is discussed
Optimization, but utilize in general propagation model, analyze RSS and intrinsic range error, finds a kind of to actual distance
Unbiased esti-mator, and the optimal estimation of RSS rangings is realized by least square, and then improve the WSN node locatings based on RSS
Precision.There will be the unbiased esti-mator of the distance estimations of inherent variability and the present embodiment to be compared for the present embodiment.For Gauss
The standard deviation of noise is equal to 3 situation, and simulation result is as shown in figure 1, from the graph, it is apparent that traditional count according to RSS
Inherent variability between the ranging distance and actual distance of calculation be present, and the unbiased esti-mator base to ranging distance of the present embodiment
Originally can be consistent with actual distance.
The present embodiment in the case where not increasing any hardware resource, can effectively improve the precision of node locating.Algorithm
Moderate complexity, WSN nodes can location-independent, can adapt to wireless-sensor network distribution type positioning demand.General feelings
Under condition, the situation of plane positioning need to be only considered, three-dimensional case similar can be promoted.
The present invention can also have other various embodiments, in the case of without departing substantially from spirit of the invention and its essence, this area
Technical staff works as can make various corresponding changes and deformation according to the present invention, but these corresponding changes and deformation should all belong to
The protection domain of appended claims of the invention.
Claims (5)
1. a kind of WSN node positioning methods based on RSS and ranging unbiased esti-mator, it is characterised in that one kind is based on RSS and ranging
The WSN node positioning methods of unbiased esti-mator are specifically what is followed the steps below：
Step 1: in sensor network working environment, M beaconing nodes are disposed in advance；If in sensor network working environment
Arbitrary unknown node U=(x, y), if U is received from beaconing nodes BiThe coordinate of signal is xi,yi, i=1,2 ..., N, N
≤M；Wherein, N represents the number for the visible beaconing nodes of unknown node U；
Step 2: according in general signal propagation model, calculate under the influence of by Gaussian noise n, unknown node and beacon
Node BiDistanceWherein, apart from beaconing nodes d0Place sets reference mode, and reference mode connects
Receive beaconing nodes BiSignal power be Pi(d0)；Unknown node U and beaconing nodes BiDistance be di；Not by the situation of noise
Under, unknown node U receives beaconing nodes BiSignal power be Pi(di)；N is that average is 0, and variance isGaussian noise；α
For path loss index；
Step 3: the v to step 2iExpectation value analysis is carried out to obtainIn order that
Introduce unknown node U to beaconing nodes BiThe unbiased estimator of actual distanceWherein,N is that average is 0, and variance isGaussian noise；
Step 4: according to unknown node U=(x, y) in two dimensional surface and beaconing nodes Bi=(xi,yi) coordinate, calculate it is unknown
Node U to beaconing nodes BiDistanceMeet following formula：
Wherein, i=1,2 ..., N, N >=3；
Step 5: unknown node U position x, y is solved using Newton iteration method；By in formula (1) in (xk-1,yk-1)TPlace carries out safe
Series expansion is strangled, and omits quadratic term, is obtained：
Wherein,xk,ykUnknown section is solved for kth time Newton iteration method
Point U position coordinateses；
Step 6: being solved with reference to least square method to formula (2), matrix form is obtained：
G Δs X=b (3)
Wherein, Δ X=[(x-xk-1)(y-yk-1)]T,
With reference to Least Square Theory, obtaining Δ X is：
△ X=(GTG)-1GTb (6)
Step 7: take Δ X=[(xk-xk-1)(yk-yk-1)]T, solution is iterated according to formula (4), (5) and (6) and obtained finally
Unknown node position location xk,yk；Complete a kind of WSN node positioning methods based on RSS and ranging unbiased esti-mator.
A kind of 2. WSN node positioning methods based on RSS and ranging unbiased esti-mator according to claim 1, it is characterised in that：
According in general signal propagation model in step 2, calculate under the influence of by noise n, unknown node and beaconing nodes Bi's
DistanceDetailed process is：
P (d)=P (d0)-10αlg(d/d0) (7)
Wherein, d0Distance for reference point apart from beaconing nodes, takes d0=1m；N is that average is 0, and variance isGaussian noise；d
For unknown node and the distance of beaconing nodes；Under the influence of by Gaussian noise, unknown node does not receive the letter of beaconing nodes
Number power is P (d)；
According to the in general signal propagation model in formula (7), unknown node U and beaconing nodes BiDistance be di, by noise
In the case of, the signal power that unknown node receives beaconing nodes is P (d)=Pi(di)+n, Pi(d0) and viSubstitute into formula (7)
：
Pi(di)+n=Pi(d0)-10αlg(vi/d0) (8)
Due to d0=1m, produced according to formula (8)：
Wherein, i=1,2 ..., N.
A kind of 3. WSN node positioning methods based on RSS and ranging unbiased esti-mator according to claim 1, it is characterised in that：
To the v of step 2 in step 3iExpectation value analysis is carried out to obtainDetailed process is：
Obtained according to formula (8),
Definition N is that average is 0, and variance isGaussian noise,It is right
In unknown node U and beaconing nodes BiBetween ranging distance vi, meet following probability density function：
Then viDesired value E (vi) be：
Wherein, i=1,2 ..., N.
A kind of 4. WSN node positioning methods based on RSS and ranging unbiased esti-mator according to claim 1, it is characterised in that：
In step 5 unknown node U positions (x, y) is solved using Newton iteration method；By formula (1) in (xk-1,yk-1)TPlace carries out Taylor's level
Counting the detailed process deployed is：
According to formula (1), and makeTaylor series expansion is carried out, and omits quadratic term and obtains：
Wherein,
A kind of 5. WSN node positioning methods based on RSS and ranging unbiased esti-mator according to claim 1, it is characterised in that：
Δ X=[(x are taken in step 7k-xk-1)(yk-yk-1)]TIt is as follows to be iterated the specific iterative process of solution：
(1) unknown node U initial position is set as x0,y0, i.e. the initial value of iteration；
(2) as k=1, G and b is obtained respectively according to formula (4), (5), and substitutes into the Δ X, Δ X=[(x of formula (6) acquisition now1-
x0) (y1-y0)]T, and then obtain the result x of first time iteration1,y1；If Δ X two norms are less than the threshold value of setting, move back
Go out iteration, unknown node U position (x, y)=(x1,y1), otherwise k+1 performs step (3)；
(3) k is worked as>When 1, G and b is obtained respectively according to formula (4), (5), and substitutes into Δ the X=[(x of formula (6) acquisition nowk-xk-1)
(yk-yk-1)]T；When Δ X two norms are less than threshold value, iteration, unknown node U location estimation result (x are exitedk,yk)；
(4) when Δ X two norms are more than or equal to threshold value, by k+1, the step performed in (3) is returned to；Until Δ X two models
Untill number is less than threshold value, iteration, final unknown node positioning result x are exitedk,yk。
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| CN106610486B (en) * | 2015-10-23 | 2019-05-10 | 华为技术有限公司 | A kind of method and apparatus of node locating |
| CN106569222A (en) * | 2016-11-01 | 2017-04-19 | 湖北航天技术研究院总体设计所 | Azimuth measurement method based on distance measurement principle |
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| CN109561498B (en) * | 2018-12-04 | 2020-07-10 | 桂林电子科技大学 | Sensor node distributed positioning method based on improved Newton method |
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