CN107144810A - Wireless multi-hop range-free localization method based on structural risk minimization - Google Patents
Wireless multi-hop range-free localization method based on structural risk minimization Download PDFInfo
- Publication number
- CN107144810A CN107144810A CN201611189753.7A CN201611189753A CN107144810A CN 107144810 A CN107144810 A CN 107144810A CN 201611189753 A CN201611189753 A CN 201611189753A CN 107144810 A CN107144810 A CN 107144810A
- Authority
- CN
- China
- Prior art keywords
- mrow
- msubsup
- mtd
- msub
- mtr
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Classifications
-
- 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
- G01S1/00—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith
- G01S1/02—Beacons or beacon systems transmitting signals having a characteristic or characteristics capable of being detected by non-directional receivers and defining directions, positions, or position lines fixed relatively to the beacon transmitters; Receivers co-operating therewith using radio waves
- G01S1/08—Systems for determining direction or position line
Landscapes
- Engineering & Computer Science (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Mobile Radio Communication Systems (AREA)
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
The present invention provides a kind of wireless multi-hop range-free localization method based on structural risk minimization, including initial phase, build hop count-apart from optimal mapping model and location estimation stage, use distance vector route switching agreement, after node communicates a period of time, make most short hop count and physical distance between all nodes acquisitions and reference mode in network, structure hop count-and apart from optimal mapping model, obtain respective physical distance under mapping model guide using the hop count of unknown node to reference mode；The estimated location of unknown node is obtained finally by three side methods.Present invention use risk structure minimum structure hop count-apart from mapping model, empiric risk is constrained using the fiducial range of structural risk minimization, the result that it is zero that calculating process, which is not present, so as to avoid the problem of position relationship has synteny between reference mode in smaller subregion or neighborhood.
Description
Technical field
The present invention relates to a kind of wireless multi-hop range-free localization method based on structural risk minimization.
Background technology
With the popularization of mobile device, the application based on wireless network is more and more more, and in many wireless applications, node
Positional information prerequisites that to be often other applied based on wireless network.For example：Wireless monitor and city in sewage discharge
In the wireless monitor of city's gas pipeline, when event occurs, the matter of utmost importance that monitoring personnel is concerned about is exactly occur suddenly tight
Urgent thing part occur where, the only definite particular location for knowing that burst is raw, such monitoring is just of practical significance, just can be with
It is rapid to solve bursting problem.The relation of information and position for wireless monitor, there is Document system discovery, about 80% wireless prison
Measurement information is relevant with position.
In the application of most of wireless monitors, wireless network node is randomly to be deployed to by machine in monitored area.
The positional information of node can obtain the position letter of event generation by the self-contained GPS of equipment or the method manually demarcated
Breath.Due to being limited by deployed environment, expense etc., whole nodes install GPS chip additional or artificial setting is often infeasible, thus
Monitored area, only small part node, which are realized, knows self-position, and most of nodes are not aware that itself specific position in advance
Information.In order that unknown node obtains global position information, it is necessary to by certain in the case of only a small amount of known location node
Method, algorithm carry out location estimation.By development for many years, scientific research personnel proposes the location estimation of numerous radio nodes
Strategy and method, according to e measurement technology whether is used in position fixing process, what wireless network location technology typically can be roughly is divided
For：The wireless location of wireless location and non-ranging technology based on ranging technology.Physical electromagnetic signal is passed through based on ranging localization
Measurement obtains distance (angle) information between radio node.After distance (angle) study is obtained, unknown node can be surveyed using three sides
Amount, triangulation or Maximum-likelihood estimation estimate its position.The wireless location method precision for being generally basede on ranging is of a relatively high,
But the precision of positioning performance heavy dependence physical measurement in itself.
It is often harsh to measurement hardware requirement so that expense becomes high or even is difficult in order to ensure range measurement accuracy
Receive, so as to cause the positioning based on distance measuring method to be not suitable for large-scale wireless application.To reduce the expense of hardware costs,
It is many in large-scale wireless network positioning that node location is estimated using the method unrelated with ranging.Range-free localization method is utilized
The characteristic for the self-organizing that wireless network innately has, i.e. wireless network data are to carry out data biography by way of multi-hop is propagated
Pass, thus in the case of no ranging hardware, using hop count can also come portray or approximate representation wireless network node between
Physical distance.However, range-free localization technical performance nevertheless suffers from many technical barrier puzzlements in actual applications, wherein most causing
Life is that range-free localization is only capable of obtaining comparatively ideal positioning result in the isotropism network that node density is high and is evenly distributed,
And under Node distribution inequality, the irregular anisotropic network of deployment, locating effect extreme difference, or even positioning result are unavailable.
It is that the hop count between node is obtained by the annexation between node based on most of non-ranging localization method,
And then to estimate the position of node.Therefore, non-ranging method does not need the distance and directional information between node so that it is adapted to big
The wireless network application of scale.The method that hop count is changed into approximate physical distance there are into many kinds, had presently the most famous：
DV-hop methods, Amorphous methods and PDM methods.
Wherein, DV-hop methods and Amorphous methods are all based on the algorithm of hop count, and they obtain more accurate position
Put estimation and all assume that network node topology is isotropism, i.e., deployment region rule, line-of-sight propagation and be evenly distributed between node.
Unfortunately, real network often due to it is random dispense, barrier block etc. reason cause deployment region it is irregular,
Node distribution is uneven.As shown in figure 1, in fig 1 a, node A to node B, C, D physical distance is identical, and between them
Hop count is 5,4,3 respectively；And for example in Figure 1b, node A to node B straight line physical distance is very short, because the original of shelter
The irregular hop count for causing node A to node B disposed caused by is very long.These problems all cause minimum hop count and actual physical
Deviation between distance.
The present invention will be around multi-hop, these three non-ranging and distributed characteristics, use for reference other range-free localization methods
A kind of non-ranging distributed wireless location method of multi-hop based on structural risk minimization is proposed on the basis of advantage, i.e.,：
Multi-hop Localization though Structural Risk Minimization, MLSRM.MLSRM methods are adopted
The hop count-apart from mapping relations between reference mode is built with structural risk minimization, each unknown node passes through distributed side
Formula estimates it to the reference mode distance that is connected using this relational model, and finally estimates unknown node position.
The content of the invention
It is an object of the invention to provide a kind of wireless multi-hop range-free localization method solution based on structural risk minimization,
The iptimum relationship of node hop count and distance is found using the structural risk minimization theories of learning, while playing structural risk minimization
Generalization ability improve hop count-apart from transfer capability, each last unknown node estimates its position using distributed computation schema
Put.
The present invention technical solution be：
A kind of wireless multi-hop range-free localization method based on structural risk minimization, including initial phase, structure are jumped
Number-apart from optimal mapping model and location estimation stage,
Initial phase, using distance vector route switching agreement, after node communicates a period of time, makes to own in network
Node obtains the most short hop count and physical distance between reference mode；
Structure hop count-and apart from optimal mapping model, after the most short hop count and physical distance between obtaining reference mode,
Obtain the predictor formula of distance：
In formula, I is unit diagonal matrix, and γ is the scale parameter of empiric risk and two kinds of risks of fiducial range,It is htIn
Vector after heartization processing,It is H column mean, centralization operation is carried out to hop count matrix H and Distance matrix D in calculating process,
Obtain corresponding matrixWith ForN rows stacking；
In the location estimation stage, respective physical is obtained under mapping model guide using the hop count of unknown node to reference mode
Distance；The estimated location of unknown node is obtained finally by three side methods.
Further, in initial phase, the most short hop count between all nodes acquisitions and reference mode, tool in network are made
Body process is：In monitored area, remaining node of reference mode into communication radius sends wide with own location information
Broadcast in information block, monitored area that each node is after grouping information is received, to the reference mode being connected under nodes records
Minimum hop count, while Jia 1 by the hop count field Hop_counts values in packet, but when node is received from same reference node,
Program ignores this packet automatically when hop count field value therein is not minimum value, using the above method, final whole monitoring section
All nodes all have recorded the minimum hop count for the reference mode that they are connected in domain.
Further, broadcast message packet, which is comprised at least, has reference mode to represent Field ID, co-ordinate position information and hop count word
Section Hop_counts, wherein co-ordinate position information include X and Y, and packet format is as follows：
Further, in the location estimation stage, in monitored area, unknown node t connections k are above with reference to node signal, k
>=3, there is coordinate-distance relation equation between reference mode and unknown node, i.e.,：
Wherein, (x, y) is the coordinate of unknown node, (x1,y1),(x2,y2),…,(xk,yk) it is reference mode coordinate, if
1st subtracts each other with k-th of equation respectively to the equation of kth -1, obtains：
Order
Formula (18) equation group is converted into Ax=b form, due to the presence of measurement error, the correct form of expression of equation group
For：Ax=b+ ε.In order to obtain the optimal solution of unknown node position, using the quadratic sum of error as criterion, i.e.,：
Formula (19) gradient is sought, it is 0 to make it, is obtained：
If with reference to not point-blank, square formation ATA can the inverse time, it is easy to obtain unknown node estimated coordinates：
The beneficial effects of the invention are as follows：Wireless multi-hop range-free localization method of this kind based on structural risk minimization, is adopted
Minimized with risk structure and build hop count-apart from mapping model, experience is constrained using the fiducial range of structural risk minimization
Risk, the result that it is zero that calculating process, which is not present, so as to avoid in smaller subregion or neighborhood position relationship between reference mode
The problem of there is synteny.In addition, centralization is taken to hop count, range data in calculating, running, so as to avoid jump
Count, apart from dimension transfer problem.MLSRM methods proposed by the present invention are optimal using experience in terms of the selection of regularisation parameter
Value, so as to avoid unnecessary optimization process.By further demonstrating the present invention to different deployment, the experiment of Node distribution
The method proposed is better than classical multi-hop range-free localization method.
Brief description of the drawings
Fig. 1 is the schematic diagram of anisotropic network.
Fig. 2 is the schematic flow sheet of the wireless multi-hop range-free localization method of the invention based on structural risk minimization.
Fig. 3 is the schematic diagram of four kinds of Node distribution situations, wherein, (a) unobstructed deployment, node random distribution, (b) is without screening
Stopper is affixed one's name to, node rule distribution, and (c) blocks deployment, node random distribution, and (d) blocks deployment, node rule distribution.
Fig. 4 is C-shaped region, the lower four kinds of Algorithm Error distribution maps of regular distribution, wherein, (a) DV-hop error maps,
(b) Amorphous error maps, (c) PDM error maps, (d) MLSRM error maps.
Fig. 5 is C-shaped deployment, four kinds of algorithm positioning result schematic diagrames of regular distribution.
Fig. 6 be view distance environment in, the lower four kinds of Algorithm Error distribution maps of regular distribution.
Fig. 7 be view distance environment in, four kinds of algorithm positioning result schematic diagrames of regular distribution.
Fig. 8 be view distance environment in, the lower four kinds of Algorithm Error distribution maps of random distribution.
Fig. 9 is C-shaped deployment, four kinds of algorithm positioning result schematic diagrames of random distribution.
Figure 10 be view distance environment in, the lower four kinds of Algorithm Error distribution maps of random distribution.
Figure 11 be view distance environment in, four kinds of algorithm positioning result schematic diagrames of random distribution.
Embodiment
The preferred embodiment that the invention will now be described in detail with reference to the accompanying drawings.
Embodiment
The positional parameter of embodiment is described as follows, without loss of generality, it is assumed that in a two dimensional surface, has n wirelessly
Network nodeWherein, preceding m, m ＜ n, the individual reference mode to equip the artificial set locations of GPS/BDS or prior.First
Stage beginning, method obtains the most short hop count vector between node using dijkstra's algorithm or Floyd algorithms, and reference is represented using h
Most short hop count vector between node, then corresponding most short hop count matrix is H；The physical distance matrix between reference mode is accordingly
D.The most short hop count vector of other reference modes is in order, i-th of reference mode to region：hi=[hi,1,…,hi,m]T；Accordingly
Reference mode between physical distance be expressed as：di=[di,1,…,di,m]T.Most short hop count of l-th of unknown node to reference mode
It is expressed as：Corresponding matrix is
In based on artificial intelligence, the location mechanism of machine learning, position fixing process be generally divided into two stages [7,11,
12], i.e.,：Training stage (offline training phase) and positioning stage (online localization phase).
In the training stage, by learning the measurement distance (hop count) known node and physical distance, train hop count and arrive distance
Mapping model；In positioning stage, unknown node arrives the hop count of reference mode, the mapping model obtained with the training stage by it
Unknown node is estimated to the distance of reference mode.
The non-ranging node positioning method of the multi-hop based on structural risk minimization of embodiment is carried out again to position fixing process
Divide, such as Fig. 2 is divided into：Initial phase, structure hop count-apart from optimal mapping model and location estimation stage.
First stage：Initial phase：Use for reference DV-hop methods and use distance vector route switching agreement, in node communication
After a period of time, make the most short hop count between all nodes acquisitions and reference mode in network.Detailed process is：In monitored area
Interior, remaining node of reference mode into communication radius sends the broadcast message with own location information and is grouped, and packet is at least
Include reference mode and represent Field ID, (Hop_counts, initialization value is for co-ordinate position information (X and Y) and hop count field
1), packet format is as follows：
| ID | X | Y | Hop_counts |
Each node is after grouping information is received in monitored area, to the minimum for the reference mode being connected under nodes records
Hop count, while Jia 1 by the hop count field Hop_counts values in packet, but when node is received from same reference node, wherein
Hop count field value when not being minimum value program ignore this packet automatically.Using the above method, in final whole monitored area
All nodes all have recorded the minimum hop count for the reference mode that they are connected.
Distance between reference mode can be obtained, i.e., according to own coordinate using physical distance formula：
Wherein, dijRepresent the i-th node to the Euclidean distance of jth node, (xi,yi)、(xj,yj) be reference mode i, j seat
Mark
Second stage：Structure hop count-apart from optimal mapping model.Most short hop count and physics between reference mode is obtained
After distance, due to, minimum hop count between reference mode has a kind of mapping relations with actual range, therefore, hop count with it is true
Relation of the actual distance between is expressed as：D=HT+V, wherein D be reference mode between physical distance, H be reference mode between most
Short hop count matrix, V is error matrix, and T is minimum hop count and the mapping relations of actual range.T every column vector can be by most
The mean square deviation of smallization error is obtained, i.e.,：
It is easy to get, column vector tiLeast square solution：
ti=(HTH)-1HTdi (6)
Risk functional is generally minimized using formula (5) as loss function, such minimum risk functional is otherwise known as
Empirical risk minimization (Empirical Risk Minimization, ERM).So, hop count-apart from optimum linearity convert
Empirical risk minimization is expressed as：
Minimized using experience point danger and build hop count-apart from mapping model, there is asking for heavy dependence reference mode quantity
Topic.The problem of node is excessively also easy to produce over-fitting, and node is also easy to produce poor fitting problem at least, sum it up, using experience point
Danger minimizes structure mapping model and there is the problem of generalization ability is weak.It is real in order to improve the Generalization Ability of hop count-distance model
The concept that example is tieed up from Statistical Learning Theory from VC is applied, using structural risk minimization (Structural Risk
Minimization, SRM) principle construction hop count-apart from mapping model.The mapping model minimized using structure point danger, in fact
Border risk is made up of two parts, and one is empiric risk, and another is fiducial range, the VC dimensions and its training sample of it and Learning machine
This number is relevant.In the case of limited reference mode quantity, not only to make empirical risk minimization, and to reduce fiducial range, this
Sample could obtain less practical risk, and keep preferable generalization to the prediction of unknown node to reference mode distance.Cause
This, further tries to achieve hop count and distance relation coefficient, i.e., on neighborhood using structural risk minimization：
Wherein, Remp(ti) it is empiric risk, φ (h/n) is fiducial range, and h ties up for VC, and n is sample number.Convolution (7),
It can be found that the difference of formula (8) and formula (6) is, fiducial range φ (h/n) constrains the empiric risk of formula (7) so that its is non-
Zero, so as to avoid the problem of position relationship has correlation between reference mode in smaller subregion or neighborhood.
Order, the penalty term of shrink variable is carried to the fiducial range selection in structural risk minimization, i.e.,：
φ (h/n)=γ | | β | |2,0≤γ≤1 (9)
In formula, γ is the scale parameter of two kinds of risks, then formula (8) is changed into：
It is apparent from, formula (10) is constrained extremal problem, unconditional extreme problem can be converted into by Lagrange's equation
Solved：
Wherein α=[α1,α2,…,αn]；αi∈Rn(i=1,2 ..., n) represent Lagrange multiplier.
The gradient of formula (11) is sought, it is 0 to make it, can obtain hop count-distance relation between reference mode：
The matrix form of formula (12) is：
At this point it is possible to find out matrixIn element tijRepresent the hop count away from j-th of reference mode to away from i-th of reference node
The influence of the physical distance of point.Middle the elements in a main diagonal tiiIt is considered as then the zoom factor that hop count is converted into distance.Thus
One unknown node can be defined as the hop count weighted sum to all reference modes to the physical distance of a reference mode.This
Be becauseIn store the distance features of all reference modes on all directions, soNode can accurately be described adjacent
Connect the anisotropy relation between distance and physical distance.And I γ promote to expand in the case of not multiple reference minutiaeIt is extensive
Ability so that hop count-distance relation is not only accurate near reference mode, away from reference modeMapping accuracy still
So keep.
When some unknown node t is obtaining its hop count vector h in monitored areatAfterwards, phase is acquired by formula (14)
The physical distance of reference mode is answered, formula (14) is specifically expressed as follows：
f(ht)=(I γ+HTH)-1HTDht (14)
Hop count and apart from different dimension ranks, it is contemplated that the dimension in hop count-distance relation transfer process is poor
It is different, centralization operation is carried out to hop count matrix H and Distance matrix D in calculating process, corresponding matrix is obtainedWithTherefore, away from
From predictor formula (14) be changed into：
In formula,It is htVector after centralization processing,It is H column mean,ForN rows stacking.
Phase III：The location estimation stage.In monitored area, unknown node t connection k (k >=3) are individual above with reference to node letter
Number, there is coordinate-distance relation equation between reference mode and unknown node, i.e.,：
Wherein, (x, y) is the coordinate of unknown node, (x1,y1),(x2,y2),…,(xk,yk) it is reference mode coordinate.If
1st subtracts each other with k-th of equation respectively to the equation of kth -1, can obtain：
Order
Formula (18) equation group can be converted into Ax=b form.Due to the presence of measurement error, equation group is correctly showed
Form is：Ax=b+ ε.In order to obtain the optimal solution of unknown node position, using the quadratic sum of error as criterion, i.e.,：
Formula (19) gradient is sought, it is 0 to make it, is obtained：
If with reference to not point-blank, square formation ATA can the inverse time, it is easy to obtain unknown node estimated coordinates：
MLSRM methods, by flooding, method transmits reference mode coordinate and hop count information, it is therefore desirable to spend O's (m) wide
Broadcast cost；The mapping relations for minimizing method structure hop count-distance using structure point danger then need O (m3) calculation cost；Each
The distance of reference mode is each arrived in the mapping relations estimation for utilization hop count-distance that unknown node can be distinguished, thus can be calculated
Make Distributed fusion process；Therefore, the time complexity of MLSRM methods can only consider what broadcast cost and mapping model were built
Calculation cost, i.e. O (m)+O (m3)。
Performance Evaluation
Multi-hop range-free localization method is especially suitable for the application under large scale scene, and application has wireless section on a large scale
The characteristics of point is numerous such.Therefore, the positioning application under checking large scale scene may need thousands of radio nodes up to a hundred to exist
Also it is not very real in the case of current experiment condition and one-house show；In addition, also being needed to the Performance Evaluation of location algorithm
To be verified under different scenes, sometimes need to also be in the parameter involved by adjustment algorithm under Same Scene, this causes workload
It is huge.Based on these above-mentioned reasons, in large-scale wireless network positions research, generally using simulation software MATLAB to wireless
Network positions algorithm performance is verified.
Amorphous, PDM algorithm also with same type is tested to compare.For the sake of justice, PDM methods pair
Characteristic value thresholding is given up in TSVD settings, if casting out characteristic value less than or equal to 3 corresponding characteristic vectors；The performance of MLSRM methods
Also relevant with scale parameter γ, it can be obtained by crosscheck or L-curve method, but its amount of calculation is larger, it is contemplated that one
As | | ATA | | ＜ 0.01 is uncomfortable set matrix, therefore experiment sets γ=0.01.
Experiment scene is set and parameter setting
The two kinds of deployment of multi-hop range-free localization Performance Evaluation Setup Experiments based on structural risk minimization and two kinds points
Cloth, altogether four kinds of experiment scenes.Two kinds of deployment are：It is unobstructed to dispose such as (a) and (b) in Fig. 3 and block in deployment such as Fig. 3
(c) with (d), wherein block deployment be due to there are larger barrier so that distributed areas present C-shaped.Have in deployment region
During larger barrier, non-line-of-sight propagation can be caused.Two kinds of distributions are：Regular distribution and random distribution.All four scenes it is big
Small is 1000m × 1000m, there are 500 nodes as schemed (2a, 2c) in random distribution scene；In regular distribution and line-of-sight propagation
Scene to deploy between 441 nodes, node spacing be 50m；285 are deployed in the scene of regular distribution and non-line-of-sight propagation
Spacing is 40m between node, node.
The universal performance issue of algorithm can not be represented in order to reduce an independent experimental result, experimental arrangement is in Same Scene
In, experiment is repeated repeatedly finally to take the end value of 50 times.Experiment is investigated not by the way of increase reference mode quantity
Know the precision of the final positioning result of node, the positive radius of communication that node is assumed in experiment is 100m.Distribution situation is pressed in experiment, point
Into two groups, i.e.,：Random distribution and regular distribution.
Regular distribution
In this group experiment, node deployment is divided into two kinds：(1) horizon communication between deployment region node；(2) deployment region section
There is barrier between point and cause non line-of-sight communication.
Fig. 4 is shown the error range figure of the multiple bearing of unobstructed regular distribution, the algorithm that embodiment is proposed with
And four kinds of classical non-ranging multi-hop positioning methods are being run multiple times, the Error Graph that is run multiple times under different reference mode environment.
For the advantage of the method mentioned by comparing embodiment, embodiment uses the box figure function (boxplot) in MATLAB to be retouched
State, box figure function can show the error range that algorithm is run multiple times, and error lumped values size, thus shown from side
The stability of algorithm.Reference node points are shown in the abscissa of Error Graph, and ordinate is RMS error, the specific table of RMS error
Show as follows：
In formula, n is unknown node number, (x in regioni,yi) it is unknown node true coordinate,For unknown node
Estimated coordinates.
DV-hop is easily found from Fig. 4, two methods of Amorphous are by the anisotropic influence of network topology, not only
Positioning precision is low, and the problems such as positioning calculation process fails to consider conllinear, the position directionality between reference mode, therefore
Location estimation result is very unstable.PDM and MLSRM methods mentioned by embodiment using hop count-distance using directly being mapped
Relation build transformation model, it is contemplated that the directionality of position, at the same in calculating process using rule method thus avoid
Conllinear problem.And the method that embodiment is carried optimizes the selection of risk structure parameter on forefathers' Research foundation, using center
Change method eliminates On The Dimension in hop count-distance mapping, therefore anisotropic network is presented in deployment region, and embodiment is carried
And algorithm is one kind of best performance in four kinds of non-ranging methods of multi-hop.
Four kinds of non-ranging multi-hops positioning that reference node points are certain computing in 35, C-shaped deployment region are shown in Fig. 5
Estimated result.Wherein circle represents unknown node, and square represents reference mode, the true coordinate of straight line connection unknown node and it
Estimated coordinates, straight line is longer, and position error is bigger.DV-hop RMS value is；Amorphous RMS value is；PDM RMS
It is worth and is；
The Node distribution figure of this experiment is shown in Fig. 5 a.The DV-hop methods that Fig. 5 b are shown are under this deployment scenario
Positioning result, it is easy to find to cause network topology structure that anisotropic is presented due to blocking, and then hop count is turned to distance
Distorted when changing, cause the evaluated error of DV-hop methods unknown node at C-shaped mouth especially huge.In DV-hop methods
On the basis of the Amorphous algorithms (Fig. 5 c) that develop in anisotropic environment, equally exist hop count to distance change when
The matching abnormal problem of generation.The positioning result of PDM methods is shown in Fig. 5 d.PDM methods are under least square method guidance
Optimum translation is carried out to hop count-distance relation using rule method, the node direction that method is considered in conversion is asked
Topic, and using failing centralization operational parameter in the extensive hop count-distance relation model, but PDM calculating processes of rule method
Cause dimension transfer problem and fail optimization to give up characteristic value thresholding.Fig. 5 e are carried algorithm MLSRM positioning knot by embodiment
Really, algorithm considers hop count-distance relation model dimension transfer problem, uses for reference the selection of forefathers' parameter, thus operation result is obvious
Better than preceding 4 kinds of classic algorithms.
Fig. 6 is shown in view distance environment, under node rule distribution situation, and repeatedly deployment, reference node points are different
Error range figure.Deployment anisotropic problem is not present in line-of-sight propagation environment, but two kinds of algorithms of DV-hop and Amorphous are fixed
Position result is still unstable, and position error is sometimes on the contrary with big when reference mode quantity is more.Because during node rule distribution,
Alignment is even more serious than random placement between reference mode.The MLSRM methods that PDM methods and embodiment are proposed make full use of portion
The reference mode in region is affixed one's name to, the conllinear problem between reference mode is avoided using rule method.MLSRM method positioning performances
Not only stablize but also better than PDM methods.
Fig. 7 is shown in view distance environment, when reference node points are 45,4 kinds of localization methods of regular distribution under sighting distance scene
Certain operation result.Fig. 6 b are DV-hop positioning results, and its RMS error is 31.1906；Fig. 6 c figures are Amorphous methods
Positioning result, its RMS error is 33.2699；Fig. 6 d figures are the positioning result of PDM methods, and its RMS error is 20.0773；Fig. 6 e
Figure is the positioning result for the MLSRM that embodiment is proposed, its RMS error is 17.7796.Due to it is conllinear the problem of, DV-hop and
Amorphous methods positioning performance is significantly lower than positioning performance in random placement environment.Due to using rule method PDM methods
Excellent characteristic can be still kept with MLSRM methods performance.
Random distribution
Node random distribution is most commonly that in true environment, Fig. 8 is shown in 1000m × 1000m region, deposited
In environment is blocked, the multiple bearing result of four kinds of multi-hop range-free localization methods of node random placement.
Easily find that the MLSRM methods that PDM methods and embodiment are proposed still have very high compared with DV-hop and Amorphous methods
Positioning precision.Although Amorphous methods are higher than DV-hop method distance estimations precision in theory, in actual tests
It was found that Amorphous methods are more sensitive to anisotropy, therefore its positioning performance in anisotropic network is markedly less than DV-
Hop methods.In addition, Amorphous methods are not considered than DV-hop method conllinear problem node, therefore multiple bearing knot
Fruit shows that two kinds of algorithm positioning precisions of DV-hop and Amorphous are not reduced with increasing for node, or even the feelings more than node
Positioning precision declines on the contrary under condition, such as when reference node points are 40, the positioning precision scopes of two algorithms almost with reference mode
When several 20 almost, and precision median is also very close to.MLSRM methods consider more comprehensive than PDM method in calculating process, because
This positioning performance is apparently higher than PDM methods.
C-shaped random placement is shown in Fig. 9, and reference node points are 35, certain operation result of four algorithms.It is different in items
Property network in, unknown node at C-shaped mouth because hop count-distance to match imbalance degree extremely big, therefore DV-hop methods exist
Unknown node evaluated error at C-shaped mouthful is also maximum.Amorphous localization methods are the improved methods of DV-hop methods, but its
The prior Connected degree for knowing adjacent domain is needed, prediction is easy in uniform, regular domain Connected degree, and in anisotropic network
Such prediction meeting error is bigger, so that it is extremely poor to cause Amorphous to be positioned at location estimation in anisotropic network.PDM
Method and MLSRM methods are built in mapping model, estimation deployment region using the hop count matrix and distance matrix of reference mode
All referring to the respective directionality of node, therefore two methods positioning result is substantially better than DV-hop and Amorphous methods.Figure
The RMS value of middle DV-hop methods is；The RMS value of Amorphous methods is；PDM methods and MLSRM method values are respectively：
Due to anisotropic problem being not present in sighting distance region, the main checking embodiment of this group experiment is proposed
Whether MLSRM methods remain to obtain superior performance.
The evaluated error areal map that four kinds of methods are repeatedly redeployed is shown in Figure 10, in multiple deployment experiment, I
Also counted influence of the assessment reference number of nodes to final positioning result by setting different reference nodes.With anisotropic network
Environment compares, from figure it is easy to see that two kinds of algorithms of DV-hop and Amorphous line-of-sight propagation environment positioning performance
It is obviously improved, and Amorphous methods give full play to estimation advantage of adjusting the distance, and positioning performance is substantially better than DV-hop.But DV-
Two kinds of algorithms of hop and Amorphous have not been considered relative position between reference mode, therefore with reference mode increasing number
Positioning performance is not obviously improved.From figure, it can be seen that the MLSRM methods positioning performance that PDM and embodiment are proposed is stable,
And better than DV-hop and two kinds of Amorphous, but PDM advantages are relatively weak.
Under Figure 11 is view distance environment, certain positioning result of four kinds of methods of node random placement, reference node is counted in Figure 11
For 45.Figure 11 b are DV-hop positioning results, and its RMS error is 26.6835；Figure 11 c are the positioning result of Amorphous methods,
Its RMS error is 19.8791；Figure 11 d are the positioning result of PDM methods, and its RMS error is 14.4452；Figure 11 e are embodiment
The MLSRM of proposition positioning result, its RMS error is 12.3378.It is apparent from from figure, the MLSRM methods that embodiment is proposed are determined
Position best performance, pdm methods are taken second place, and Amorphous positioning performances are less than MLSRM and PDM methods, but better than DV-hop methods.
Claims (4)
1. a kind of wireless multi-hop range-free localization method based on structural risk minimization, it is characterised in that：Including initialization rank
Section, structure hop count-apart from optimal mapping model and location estimation stage,
Initial phase, using distance vector route switching agreement, after node communicates a period of time, makes all nodes in network
Obtain the most short hop count and physical distance between reference mode；
Structure hop count-and apart from optimal mapping model, after the most short hop count and physical distance between obtaining reference mode, obtain
The predictor formula of distance：
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>k</mi>
<mi>t</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>I</mi>
<mi>&gamma;</mi>
<mo>+</mo>
<msup>
<mover>
<mi>H</mi>
<mo>~</mo>
</mover>
<mi>T</mi>
</msup>
<mover>
<mi>H</mi>
<mo>~</mo>
</mover>
<mo>)</mo>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msup>
<msup>
<mover>
<mi>H</mi>
<mo>~</mo>
</mover>
<mi>T</mi>
</msup>
<mover>
<mi>D</mi>
<mo>~</mo>
</mover>
<msub>
<mover>
<mi>h</mi>
<mo>~</mo>
</mover>
<mi>t</mi>
</msub>
<mo>+</mo>
<mi>r</mi>
<mi>e</mi>
<mi>p</mi>
<mi>m</mi>
<mi>a</mi>
<mi>t</mi>
<mrow>
<mo>(</mo>
<mover>
<mi>h</mi>
<mo>~</mo>
</mover>
<mo>,</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, I is unit diagonal matrix, and γ is the scale parameter of empiric risk and two kinds of risks of fiducial range,It is htCentralization
Vector after processing,It is H column mean, centralization operation is carried out to hop count matrix H and Distance matrix D in calculating process, obtained
Corresponding matrixWithForN rows stacking；
The location estimation stage, using unknown node to reference mode hop count mapping model guide under obtain respective physical away from
From；The estimated location of unknown node is obtained finally by three side methods.
2. the wireless multi-hop range-free localization method as claimed in claim 1 based on structural risk minimization, it is characterised in that：
In initial phase, make the most short hop count between all nodes acquisitions and reference mode in network, detailed process is：In monitoring section
In domain, remaining node of reference mode into communication radius sends the broadcast message with own location information and is grouped, monitoring section
Each node is after grouping information is received in domain, to the minimum hop count for the reference mode being connected under nodes records, while will divide
Hop count field Hop_counts values in group Jia 1, but when node is received from same reference node, hop count field value therein is not
Program ignores this packet automatically when being minimum value, using the above method, and all nodes are all recorded in final whole monitored area
The minimum hop count of the reference mode connected to them.
3. the wireless multi-hop range-free localization method as claimed in claim 1 or 2 based on structural risk minimization, its feature exists
In：Broadcast message packet, which is comprised at least, has reference mode to represent Field ID, co-ordinate position information and hop count field Hop_counts,
Wherein co-ordinate position information includes X and Y, and packet format is as follows：
4. the wireless multi-hop range-free localization method as claimed in claim 1 or 2 based on structural risk minimization, its feature exists
In：In the location estimation stage, in monitored area, unknown node t connections k are above with reference to node signal, k >=3, reference mode with
There is coordinate-distance relation equation between unknown node, i.e.,：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>d</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>d</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>+</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>=</mo>
<msubsup>
<mi>d</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
<mi>k</mi>
<mo>&GreaterEqual;</mo>
<mn>3</mn>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein, (x, y) is the coordinate of unknown node, (x1,y1),(x2,y2),…,(xk,yk) be reference mode coordinate, if the 1st to
The equation of kth -1 subtracts each other with k-th of equation respectively, obtains：
<mrow>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>y</mi>
<mo>=</mo>
<msubsup>
<mi>d</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>d</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>y</mi>
<mo>=</mo>
<msubsup>
<mi>d</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>d</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>x</mi>
<mo>+</mo>
<mn>2</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mi>y</mi>
<mo>=</mo>
<msubsup>
<mi>d</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>d</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>17</mn>
<mo>)</mo>
</mrow>
</mrow>
Order
<mrow>
<mi>A</mi>
<mo>=</mo>
<mn>2</mn>
<mo>&times;</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>a</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>b</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>d</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>d</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>d</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>d</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>.</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msubsup>
<mi>x</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>y</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>y</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>d</mi>
<mi>k</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>d</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mn>2</mn>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mi>b</mi>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>x</mi>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mi>x</mi>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>y</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>18</mn>
<mo>)</mo>
</mrow>
</mrow>
Formula (18) equation group is converted into Ax=b form, due to the presence of measurement error, and the correct form of expression of equation group is：
Ax=b+ ε.In order to obtain the optimal solution of unknown node position, using the quadratic sum of error as criterion, i.e.,：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>arg</mi>
<mi> </mi>
<mi>min</mi>
<msup>
<mrow>
<mo>(</mo>
<mi>b</mi>
<mo>-</mo>
<mi>A</mi>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mi>T</mi>
</msup>
<mrow>
<mo>(</mo>
<mi>b</mi>
<mo>-</mo>
<mi>A</mi>
<mi>x</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&DoubleRightArrow;</mo>
<mi>arg</mi>
<mi> </mi>
<mi>min</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>x</mi>
<mi>T</mi>
</msup>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>A</mi>
<mi>x</mi>
<mo>-</mo>
<mn>2</mn>
<msup>
<mi>b</mi>
<mi>T</mi>
</msup>
<mi>A</mi>
<mi>x</mi>
<mo>+</mo>
<msup>
<mi>b</mi>
<mi>T</mi>
</msup>
<mi>b</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>19</mn>
<mo>)</mo>
</mrow>
</mrow>
Formula (19) gradient is sought, it is 0 to make it, is obtained：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mn>2</mn>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>b</mi>
<mo>+</mo>
<mn>2</mn>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>A</mi>
<mi>x</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>&DoubleRightArrow;</mo>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>b</mi>
<mo>=</mo>
<msup>
<mi>A</mi>
<mi>T</mi>
</msup>
<mi>A</mi>
<mi>x</mi>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>20</mn>
<mo>)</mo>
</mrow>
</mrow>
If with reference to not point-blank, square formation ATA can the inverse time, it is easy to obtain unknown node estimated coordinates：
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611189753.7A CN107144810B (en) | 2016-12-20 | 2016-12-20 | Wireless multi-hop non-ranging positioning method based on structure risk minimization |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611189753.7A CN107144810B (en) | 2016-12-20 | 2016-12-20 | Wireless multi-hop non-ranging positioning method based on structure risk minimization |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN107144810A true CN107144810A (en) | 2017-09-08 |
| CN107144810B CN107144810B (en) | 2020-10-13 |
Family
ID=59783280
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611189753.7A Active CN107144810B (en) | 2016-12-20 | 2016-12-20 | Wireless multi-hop non-ranging positioning method based on structure risk minimization |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN107144810B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101651951A (en) * | 2009-09-15 | 2010-02-17 | 哈尔滨工业大学 | Establishing method and positioning method of indoor positioning network of support vector machine based on WLAN |
| CN102547977A (en) * | 2011-12-28 | 2012-07-04 | 南昌大学 | Sensor network positioning method based on hop counts |
| CN102547918A (en) * | 2012-01-05 | 2012-07-04 | 重庆大学 | Non-ranging-based wireless sensor network three-dimensional node positioning method |
| US20150002337A1 (en) * | 2010-07-14 | 2015-01-01 | Zih Corp. | Frequency channel diversity for real-time locating systems, methods, and computer program products |
| CN105828434A (en) * | 2016-05-18 | 2016-08-03 | 金陵科技学院 | Subnetting type DV-hop wireless sensor network positioning algorithm |
-
2016
- 2016-12-20 CN CN201611189753.7A patent/CN107144810B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101651951A (en) * | 2009-09-15 | 2010-02-17 | 哈尔滨工业大学 | Establishing method and positioning method of indoor positioning network of support vector machine based on WLAN |
| US20150002337A1 (en) * | 2010-07-14 | 2015-01-01 | Zih Corp. | Frequency channel diversity for real-time locating systems, methods, and computer program products |
| CN102547977A (en) * | 2011-12-28 | 2012-07-04 | 南昌大学 | Sensor network positioning method based on hop counts |
| CN102547918A (en) * | 2012-01-05 | 2012-07-04 | 重庆大学 | Non-ranging-based wireless sensor network three-dimensional node positioning method |
| CN105828434A (en) * | 2016-05-18 | 2016-08-03 | 金陵科技学院 | Subnetting type DV-hop wireless sensor network positioning algorithm |
Non-Patent Citations (4)
| Title |
|---|
| SLIM ZAIDI等: "Accurate Range-Free Localization in Multi-Hop Wireless Sensor Networks", 《IEEE TRANSACTIONS ON COMMUNICATIONS》 * |
| 严筱永: "无线传感器网络节点定位技术研究", 《中国博士学位论文全文数据库信息科技辑》 * |
| 赵炜等: "核回归在异构无线传感网节点定位中的应用", 《金陵科技学院学报》 * |
| 郑久虎等: "基于核Tikhonov规则化的多跳非测距定位方法", 《南京理工大学学报》 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN107144810B (en) | 2020-10-13 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Xiao et al. | An RSSI based DV-hop algorithm for wireless sensor networks | |
| Niculescu et al. | Position and orientation in ad hoc networks | |
| JP6596516B2 (en) | Method and apparatus for improving the positioning performance of an artificial neural network | |
| Chen et al. | An improved DV-Hop localization algorithm with reduced node location error for wireless sensor networks | |
| Lee et al. | A new range-free localization method using quadratic programming | |
| CN103270801B (en) | Method of and system for locating the position of user equipment | |
| CN102665274B (en) | Method and device for positioning sensor network node | |
| US20120039316A1 (en) | Method of generating map, and method of measuring location of terminal using the map | |
| CN105592420B (en) | Environmental characteristic library generates and indoor orientation method and device based on environmental characteristic library | |
| Hol et al. | Ultra-wideband calibration for indoor positioning | |
| Zhang et al. | An optimal roadside unit placement method for vanet localization | |
| Kanwar et al. | DV-Hop based localization methods for additionally deployed nodes in wireless sensor network using genetic algorithm | |
| Shit et al. | AI-enabled fingerprinting and crowdsource-based vehicle localization for resilient and safe transportation systems | |
| Fan et al. | Fault-tolerant cooperative localization of 3D mobile networks via two-layer filter multidimensional scaling | |
| Sun et al. | Geomagnetic positioning-aided Wi-Fi FTM localization algorithm for NLOS environments | |
| CN107144810A (en) | Wireless multi-hop range-free localization method based on structural risk minimization | |
| CN104540095B (en) | Localization method during anchor node limited amount based on propagated error minimum principle | |
| CN104215990B (en) | Auxiliary global positioning system (GPS) location method and system based on wireless network single node | |
| CN109874149A (en) | Localization method, device and the computer readable storage medium of mobile terminal | |
| Shioda et al. | Cooperative localization revisited: Error bound, scaling, and convergence | |
| Ran et al. | Impact of irregular radio and faulty nodes on localization in industrial WSNs | |
| Jing et al. | Community detection based reference points clustering for indoor localization in WLAN | |
| Zhou et al. | An improved DV-HOP localization algorithm | |
| Zhou et al. | A map registration localization approach based on mobile beacons for wireless sensor networks | |
| Sharon Priya et al. | Localization of WSN using IDV and Trilateration Algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |