CN107690184A - Joint TDOA AOA wireless sensor network Semidefinite Programming localization methods - Google Patents
Joint TDOA AOA wireless sensor network Semidefinite Programming localization methods Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
- H04W64/003—Locating users or terminals or network equipment for network management purposes, e.g. mobility management locating network equipment
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/025—Services making use of location information using location based information parameters
- H04W4/026—Services making use of location information using location based information parameters using orientation information, e.g. compass
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
- H04W64/006—Locating users or terminals or network equipment for network management purposes, e.g. mobility management with additional information processing, e.g. for direction or speed determination
Abstract
The present invention relates to one kind to combine TDOA AOA wireless sensor network Semidefinite Programming localization methods, including：In the reaching time-difference and angle of two-dimensional space arrangement wireless sensor network measurement destination node and reference mode.TDOA and AOA are performed an analysis, realize single-measurement location algorithm.Algorithms of different is merged, wireless sensor network target node locating problem is converted into the mathematical optimization problem of weighted least-squares WLS algorithms.The mathematical optimization problems of above-mentioned WLS algorithms is reconstructed optimization problem is converted into constrained optimization problem.By introducing redundant variables, using semidefinite decoding SDR technologies, weighted least-squares are converted into a Semidefinite Programming with linear equality constraints and linear inequality constraint and solution.
Description
Technical field
The invention belongs to wireless sensor network positioning field, is related to convex optimization method the two of joint TDOA-AOA measurements
Tie up the application in wireless sensor network target node locating.
Background technology
Because wireless sensor network (WSNs) is in radio communication, the neck such as indoor positioning and water sound sensor network (UASN)
The important application in domain, accurate Wireless Sensor Network Located Algorithm are of great interest in recent years.For reception signal
Different characteristic parameter, the localization method based on ranging mainly has RSS (received signal strength), TOA
Four kinds of (time of arrival), TDOA (time difference of arrival) and AOA (angle of arrival)
Method.Corresponding location algorithm can be selected for different positioning scenes and required precision.However, at non line of sight (NLOS)
Or under the limited complex environment of reference mode, greatly differed from each other using one of above-mentioned algorithm and pinpoint requirement.Therefore, join
The research for closing location algorithm is gradually taken seriously.
In order to improve the positioning precision under complex environment, corresponding alignment by union algorithm have TOA-AOA, AOA-RSS and
TDOA-AOA.In above-mentioned algorithm, TOA-AOA algorithms need high-precision time synchronized, higher to hardware requirement, improve
Position cost.And AOA-RSS is vulnerable to the influence of fading effect.By contrast, when TDOA-AOA alignment by union algorithm is to node
Between synchronously require low, strong antijamming capability.For TDOA-AOA alignment by union algorithms, in order to improve TDOA-AOA alignment by union
Precision, Li Cong et al. propose in two-dimensional space combine the step weighted least-squares of TDOA-AOA two (Two-Step LS)
Location algorithm, its arithmetic accuracy is higher than the positioning precision that TDOA is used alone.In order to reduce algorithm complex, there is scholar's proposition
By using joint TDOA-AOA constraint weighted least-squares methods (CWLS) positioning mobile base station, but when reference base station is few
Its positioning performance drastically declines even algorithm failure when 4.In order to cost-effective, the positioning performance under raising complex environment,
There is scholar to propose the positioning closed solutions based on TDOA-AOA under two base stations again in recent years, however, this method is only used for three-dimensional
The positioning in space, and the sum of ranks conditional number of weight matrix is limited to, it is poor that it positions robust property.It is above-mentioned to be calculated based on least square
The improvement of method is all Local Optimization Algorithm, can produce multiple locally optimal solutions in solution procedure, not ensure that and find the overall situation
Optimal solution, reduce positioning precision.
The content of the invention
The purpose of the present invention is overcome the deficiencies in the prior art, with reference to joint TDOA-AOA localization characteristics, there is provided a kind of line
Sensor network Semidefinite Programming localization method.The present invention can not only improve alignment by union stability, can also be in interstitial content
The positioning of destination node is realized under constrained environment, so as to improve the positioning precision of node.Technical scheme is such as
Under：
One kind joint TDOA-AOA wireless sensor network Semidefinite Programming localization methods, including following steps：
1) wireless sensor network is arranged in two-dimensional space, including N number of reference mode Xi=[xi,yi]T(i=
1 ..., N) and a destination node X=[x, y] to be positionedT, each reference mode measures target under the conditions of noisy
The reaching time-difference and angle of node and reference mode.
2) on the basis of the first step obtains reaching time-difference and angle, TDOA and AOA are performed an analysis respectively, realized single
One measurement and positioning algorithm.
3) algorithms of different in 2) is merged, wireless sensor network target node locating problem is converted into a weighting most young waiter in a wineshop or an inn
The mathematical optimization problem for multiplying WLS algorithms is solved：
Z=(GTW-1G)-1GTW-1h
Wherein z=[x-x1 y-y1 d1]T, wherein d1For node to be positioned and the range difference of first reference mode, G is connection
The coefficient matrix of positioning least square is closed, W is weight matrix, and h is constant term matrix.
4) the mathematical optimization problem of above-mentioned WLS algorithms is reconstructed, according to the pass of first reference mode and measured value
System, introduce constraintsObject function and constraints are decomposed, optimization problem is converted into constraint
Optimization problem, a quadratically constrained quadratic programming problem can be obtained：
Wherein Σ=diag (1,1, -1,0).
5) after previous step, object function and constraints are all nonlinear, by introducing redundant variables Z=zzT,
Using semidefinite decoding SDR technologies, that is, it is equivalent to two conditions：Rank (Z)=1 and Z is symmetrical positive semidefinite (PSD) matrix, is passed through
Weighted least-squares are converted to one and asked with linear equality constraints and the Semidefinite Programming of linear inequality constraint by relaxation order constraint
Topic.
For the present invention due to taking above technical scheme, it has advantages below：
The present invention is directed to TDOA-AOA alignment by union scenes, and nodal exactness position to be positioned is obtained by global optimization method
Put, when reference mode number is more, positioning precision is higher than existing algorithm, and positional information is provided in only two reference modes
When, classic algorithm such as Two-step LS and CWLS fail, and this paper algorithms can also realize the positioning under degree of precision.
In order to intuitively verify that this method positioning performance is better than existing algorithm, we and classic algorithm such as Two-step LS
CDF curve comparisons are carried out with CWLS, as shown in figure 3, wherein set angle variance and distance variance are respectively σθ=1 °, σd
=3m.It can be seen that in 2000 emulation experiments of progress, algorithm position error is put forward within 2m herein
Probability is close to 80%, higher than the 60% of other algorithms, therefore can prove that positioning performance of the present invention is substantially better than other two kinds of sides
Method, positioning precision is high, and robustness is more preferable.
Brief description of the drawings
Fig. 1 is emulation testing two dimensional wireless sensor network reference mode distribution map of the present invention.
Fig. 2 is TODA-AOA alignment by union measurement figures.
Fig. 3 is that the present invention becomes with other classical TDOA-AOA alignment by union algorithm root-mean-square errors (RMSE) with measurement error
The CDF curve maps of change.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
In order that technical scheme becomes apparent from, below in conjunction with accompanying drawing and example, the present invention is carried out further
Detailed description.This example is only limitted to a kind of implementation of the explanation present invention, does not represent the limit to coverage of the present invention
System.
We carry out 2000 Monte Carlo simulations to the alignment by union algorithm of proposition by MATLAB and tested, and we are main
Using position root-mean-square error (RMSE) comparative evaluation is carried out to set forth herein algorithm and existing algorithm.RMSE expression formula
It is as follows：
Wherein (x, y) is the tag coordinate by being calculated, (x0,y0) be label true coordinate.
Specific method implementation process is described as follows：
Step 1：Positioning scene is arranged：Emulation testing two dimensional wireless sensor network reference mode distribution form such as Fig. 1,
I.e. reference mode is randomly arranged in a square area, wherein, destination node is located at (50,100) m, reference mode number
Be set to 5, the position coordinates of reference mode is expressed as (0,0) m, (260,150) m, (0,300) m, (- 260,150) m and (200 ,-
150)m。
Step 2：Each reference mode measures arrival time and the angle of destination node signal under the conditions of noisy.
The true coordinate of i-th of reference mode is expressed as Xi=[xi,yi]T(i=1 ..., N), destination node to be positioned it is true
Coordinate representation is X=[x, y]T.Each reference mode measure under the conditions of noisy arrival time of destination node signal with
Angle, reaching time-difference is converted into reaches range difference to meet follow-up location requirement afterwards.It is first ginseng to reach range difference
Node and the range difference of i-th node and destination node are examined, i.e.,Assuming that TDOA and AOA measurement noise
Respectively ndiAnd nθi, the two obeys orthogonal Gaussian Profile, and sets its average and be respectively as zero varianceWith
Step 3：The weighted least square of destination node：Consider whole TDOA and the AOA measurement with measurement noise
Value, TDOA and AOA positions equation is built respectively, and then can must combine the mathematical optimization problem of weighted least-squares：
Z=(GTW-1G)-1GTW-1h
Wherein z=[x-x1 y-y1 d1]T, G is the coefficient matrix of alignment by union least square, and W is weight matrix, and h is normal
Several matrixes.
Step 4：For TDOA metrical informations, constraints is drawnBy object function and constraints
Be converted to a quadratically constrained quadratic programming problem：
Wherein Σ=diag (1,1, -1,0).
Step 5：By introducing redundant variables Z=zzTIt is excellent above-mentioned nonlinear optimal problem can be converted into linear restriction
Change problem, reapply semidefinite decoding (SDR) technology and constrained optimization problem be further converted into the convex optimization problem of Semidefinite Programming,
It is as follows：
Above formula can be solved by using interior point method such as SeDuMi to obtain half set pattern based on TDOA-AOA measurements
The optimal solution of (SDP) convex optimization problem is drawn, so as to complete the positioning to destination node.
Claims (1)
1. one kind joint TDOA-AOA wireless sensor network Semidefinite Programming localization methods, including following steps：
1) wireless sensor network is arranged in two-dimensional space, including N number of reference mode Xi=[xi,yi]T(i=1 ..., N)
With a destination node X=[x, y] to be positionedT, each reference mode measured under the conditions of noisy destination node with ginseng
Examine the reaching time-difference and angle of node；
2) on the basis of the first step obtains reaching time-difference and angle, TDOA and AOA is performed an analysis respectively, realize single-measurement
Location algorithm；
3) algorithms of different in 2) is merged, wireless sensor network target node locating problem is converted into weighted least-squares
The mathematical optimization problem of WLS algorithms is solved：
Z=(GTW-1G)-1GTW-1h
Wherein z=[x-x1 y-y1 d1]T, wherein d1For node to be positioned and the range difference of first reference mode, G is alignment by union
The coefficient matrix of least square, W are weight matrix, and h is constant term matrix；
4) the mathematical optimization problem of above-mentioned WLS algorithms is reconstructed, according to the relation of first reference mode and measured value, drawn
Enter constraintsObject function and constraints are decomposed, optimization problem is converted into constrained optimization asks
Topic, can obtain a quadratically constrained quadratic programming problem：
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Wherein Σ=diag (1,1, -1,0)；
5) after previous step, object function and constraints are all nonlinear, by introducing redundant variables Z=zzT, use
Semidefinite decoding SDR technologies, that is, it is equivalent to two conditions：Rank (Z)=1 and Z is symmetrical positive semidefinite (PSD) matrix, passes through relaxation
Order constraint, weighted least-squares are converted into a Semidefinite Programming with linear equality constraints and linear inequality constraint simultaneously
Solve.
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Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107703482A (en) * | 2017-10-20 | 2018-02-16 | 电子科技大学 | The AOA localization methods that a kind of closed solutions are combined with iterative algorithm |
| CN108717177A (en) * | 2018-06-21 | 2018-10-30 | 电子科技大学 | A kind of dual station TDOA-AOA two-step methods passive location method |
| CN108761384A (en) * | 2018-04-28 | 2018-11-06 | 西北工业大学 | A kind of sensor network target localization method of robust |
| CN109597023A (en) * | 2018-12-10 | 2019-04-09 | 中国人民解放军陆军工程大学 | The localization method of Semidefinite Programming based on NLOS error concealment |
| CN109884583A (en) * | 2019-03-26 | 2019-06-14 | 电子科技大学 | The convex optimization method of target three-dimensional coordinate is determined using one-dimensional direction finding |
| CN110221244A (en) * | 2019-05-24 | 2019-09-10 | 宁波大学 | Based on the robust positioning method of reaching time-difference under the conditions of non line of sight |
| CN110221245A (en) * | 2019-05-28 | 2019-09-10 | 宁波大学 | The robust TDOA localization method of Combined estimator target position and non-market value |
| CN110662290A (en) * | 2019-09-04 | 2020-01-07 | 宁波大学 | Wireless sensor network target positioning method based on ToA-AoA hybrid measurement |
| CN110662163A (en) * | 2019-08-23 | 2020-01-07 | 宁波大学 | RSS (really simple syndication) and AOA (automatic optical inspection) based three-dimensional wireless sensor network cooperative positioning method |
| CN111505575A (en) * | 2020-03-23 | 2020-08-07 | 宁波大学 | Sensor selection method aiming at TDOA (time difference of arrival) location based on conversion TOA (time of arrival) model |
| CN112230258A (en) * | 2020-09-29 | 2021-01-15 | 哈尔滨工业大学 | Enhanced GNSS broadband interference positioning method based on AOA/TDOA combination |
| CN113238217A (en) * | 2021-06-03 | 2021-08-10 | 哈尔滨工业大学 | Distributed high-frequency ground wave radar combined positioning method based on interior point method |
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Cited By (19)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107703482A (en) * | 2017-10-20 | 2018-02-16 | 电子科技大学 | The AOA localization methods that a kind of closed solutions are combined with iterative algorithm |
| CN108761384A (en) * | 2018-04-28 | 2018-11-06 | 西北工业大学 | A kind of sensor network target localization method of robust |
| CN108761384B (en) * | 2018-04-28 | 2022-04-19 | 西北工业大学 | Target positioning method for robust sensor network |
| CN108717177B (en) * | 2018-06-21 | 2021-07-06 | 电子科技大学 | Double-station TDOA-AOA two-step passive positioning method |
| CN108717177A (en) * | 2018-06-21 | 2018-10-30 | 电子科技大学 | A kind of dual station TDOA-AOA two-step methods passive location method |
| CN109597023A (en) * | 2018-12-10 | 2019-04-09 | 中国人民解放军陆军工程大学 | The localization method of Semidefinite Programming based on NLOS error concealment |
| CN109884583A (en) * | 2019-03-26 | 2019-06-14 | 电子科技大学 | The convex optimization method of target three-dimensional coordinate is determined using one-dimensional direction finding |
| CN109884583B (en) * | 2019-03-26 | 2023-03-14 | 电子科技大学 | Convex optimization method for determining three-dimensional coordinates of target by utilizing one-dimensional direction finding |
| CN110221244A (en) * | 2019-05-24 | 2019-09-10 | 宁波大学 | Based on the robust positioning method of reaching time-difference under the conditions of non line of sight |
| CN110221245A (en) * | 2019-05-28 | 2019-09-10 | 宁波大学 | The robust TDOA localization method of Combined estimator target position and non-market value |
| CN110221245B (en) * | 2019-05-28 | 2022-04-19 | 宁波大学 | Robust TDOA (time difference of arrival) positioning method for jointly estimating target position and non-line-of-sight error |
| CN110662163A (en) * | 2019-08-23 | 2020-01-07 | 宁波大学 | RSS (really simple syndication) and AOA (automatic optical inspection) based three-dimensional wireless sensor network cooperative positioning method |
| CN110662290A (en) * | 2019-09-04 | 2020-01-07 | 宁波大学 | Wireless sensor network target positioning method based on ToA-AoA hybrid measurement |
| CN111505575B (en) * | 2020-03-23 | 2022-02-11 | 宁波大学 | Sensor selection method aiming at TDOA (time difference of arrival) location based on conversion TOA (time of arrival) model |
| CN111505575A (en) * | 2020-03-23 | 2020-08-07 | 宁波大学 | Sensor selection method aiming at TDOA (time difference of arrival) location based on conversion TOA (time of arrival) model |
| CN112230258A (en) * | 2020-09-29 | 2021-01-15 | 哈尔滨工业大学 | Enhanced GNSS broadband interference positioning method based on AOA/TDOA combination |
| CN112230258B (en) * | 2020-09-29 | 2023-10-10 | 哈尔滨工业大学 | Enhanced GNSS broadband interference positioning method based on AOA/TDOA combination |
| CN113238217A (en) * | 2021-06-03 | 2021-08-10 | 哈尔滨工业大学 | Distributed high-frequency ground wave radar combined positioning method based on interior point method |
| CN113238217B (en) * | 2021-06-03 | 2024-03-08 | 哈尔滨工业大学 | Distributed high-frequency ground wave radar joint positioning method based on interior point method |
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