CN114826933B - Non-cooperative topology inference method based on unknown node positions - Google Patents

Non-cooperative topology inference method based on unknown node positions Download PDF

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CN114826933B
CN114826933B CN202210748002.3A CN202210748002A CN114826933B CN 114826933 B CN114826933 B CN 114826933B CN 202210748002 A CN202210748002 A CN 202210748002A CN 114826933 B CN114826933 B CN 114826933B
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CN114826933A (en
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束妮娜
牛钊
马涛
李强
黄郡
马春来
常超
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Abstract

The invention relates to a non-cooperative topology inference method based on unknown node positions, which comprises the following steps: using random distribution within a given area L
Figure DEST_PATH_IMAGE001
Monitoring the power of a non-cooperative network in a given area L by each sensor node; dividing a given area L into
Figure 796242DEST_PATH_IMAGE001
The grids with the same size are obtained according to the power detected by the sensor nodes; inputting the power of each grid into a neural network to obtain the coordinate position of a non-cooperative node; monitoring a time sequence of non-cooperative nodes by using a sensor network; constructing non-cooperative nodes according to time sequence of non-cooperative nodes
Figure 633748DEST_PATH_IMAGE002
And
Figure DEST_PATH_IMAGE003
an autoregressive model of the composed node pairs; constructing statistics using sum of squares of residuals from autoregressive models
Figure 9978DEST_PATH_IMAGE004
(ii) a According to
Figure 249329DEST_PATH_IMAGE004
Obtaining non-cooperative nodes
Figure 236002DEST_PATH_IMAGE005
And
Figure 810072DEST_PATH_IMAGE006
the cause and effect relationship of (1). The invention discloses a non-cooperative topology inference method based on unknown node positions, which combines node positioning and causal inference into a system to realize topology inference when the node positions are unknown.

Description

Non-cooperative topology inference method based on unknown node positions
Technical Field
The invention belongs to the technical field of positioning and topology inference, and relates to a non-cooperative topology inference method based on unknown node positions.
Background
The internet is becoming ubiquitous in today's world. From climate research to cancer research, from computational neuroscience to metrological economics, a scenario can be modeled as a network with multiple interaction variables. In the study of these networks, one of the main goals is to determine how certain variables affect other variables.
In network research, inferring causal relationships between network nodes will help to better understand how the different components of a network interact. In wireless network management, topology reasoning can provide information support for administrators, help them to remove faults and enhance the safety and the robustness of a network. For monitoring wireless networks, especially in the field of electronic warfare, topological reasoning can help identify and combat key nodes and key links in enemy networks. In addition, information can be mined from the topological information, the fighting intention of enemies can be inferred, and the information advantage on a battlefield can be realized.
However, in the conventional research, only one aspect is considered from topology inference alone, and the situation that the node position is unknown is not considered.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a non-collaborative topology inference method based on unknown node positions. The technical problem to be solved by the invention is realized by the following technical scheme:
the embodiment of the invention provides a non-cooperative topology inference method based on unknown node positions, which comprises the following steps:
step 1, using random distribution in a given area L
Figure 392208DEST_PATH_IMAGE001
A sensor network consisting of sensor nodes monitors the power of an uncooperative network in the given area L, the uncooperative network comprising
Figure 247032DEST_PATH_IMAGE002
A plurality of non-cooperative nodes;
step 2, dividing the given area L into
Figure 902135DEST_PATH_IMAGE001
The grids with the same size are obtained, and the power of each grid is obtained according to the power detected by the sensor nodes;
step 3, inputting the power of each grid into a trained neural network model to obtain the coordinate position of the uncooperative node;
step 4, after the coordinate position of the non-cooperative node is obtained, monitoring the time sequence of the non-cooperative node in the non-cooperative network by using the sensor network;
step 5, constructing the non-cooperative nodes according to the time sequence of the non-cooperative nodes
Figure 172711DEST_PATH_IMAGE003
And non-cooperative nodes
Figure 862449DEST_PATH_IMAGE004
An autoregressive model of the composed node pairs;
step 6, utilizing the residual sum of squares of the autoregressive model to construct statistics
Figure 560278DEST_PATH_IMAGE005
；
Step 7, according to the statistic quantity
Figure 764994DEST_PATH_IMAGE005
Obtaining the non-cooperative node
Figure 901577DEST_PATH_IMAGE004
And the non-cooperative node
Figure 445822DEST_PATH_IMAGE006
The cause and effect relationship of (1).
In one embodiment of the present invention, the step 1 comprises:
step 1.1, randomly setting the given area L
Figure 376869DEST_PATH_IMAGE001
A plurality of sensor nodes, wherein the locations of the sensor nodes are known;
step 1.2, utilizing the
Figure 68882DEST_PATH_IMAGE001
Each sensor node monitors the power of the uncooperative network in the given area L, wherein
Figure 692979DEST_PATH_IMAGE007
The monitored power of each sensor node is as follows:
Figure 154047DEST_PATH_IMAGE009
wherein,
Figure 521574DEST_PATH_IMAGE010
denotes the first
Figure 700883DEST_PATH_IMAGE011
A sensor node monitors
Figure 913690DEST_PATH_IMAGE012
The power of the individual non-cooperating nodes,
Figure 494844DEST_PATH_IMAGE013
，
Figure 767693DEST_PATH_IMAGE014
is shown as
Figure 371981DEST_PATH_IMAGE015
Transmit power of a plurality of non-cooperating nodes, wherein,
Figure 388479DEST_PATH_IMAGE016
，
Figure 824139DEST_PATH_IMAGE017
，
Figure 533469DEST_PATH_IMAGE018
representing the total number of uncooperative nodes in the uncooperative network,
Figure 421791DEST_PATH_IMAGE019
the antenna gain of the transmitting antenna is indicated,
Figure 241979DEST_PATH_IMAGE020
which represents the antenna gain of the receiving antenna,
Figure 469829DEST_PATH_IMAGE021
which is indicative of the wavelength of the light,
Figure 350061DEST_PATH_IMAGE022
denotes the first
Figure 725678DEST_PATH_IMAGE023
A sensor node monitors
Figure 21662DEST_PATH_IMAGE024
Distance between the non-cooperating nodes.
In one embodiment of the invention, the first
Figure 431914DEST_PATH_IMAGE025
The power of each grid is:
Figure 483047DEST_PATH_IMAGE026
wherein,
Figure 345961DEST_PATH_IMAGE027
denotes the first
Figure 445635DEST_PATH_IMAGE028
The power of the individual grids is,
Figure 444815DEST_PATH_IMAGE029
is shown as
Figure 666849DEST_PATH_IMAGE028
The number of sensors contained in each grid, wherein,
Figure 892425DEST_PATH_IMAGE030
。
in one embodiment of the present invention, the training method of the neural network model includes:
s1, obtaining a training set, wherein the training set comprises a plurality of non-cooperative training nodes;
s2, dividing the area where the non-cooperative training nodes are located into
Figure 858107DEST_PATH_IMAGE031
Training grids of the same size, wherein,
Figure 903337DEST_PATH_IMAGE032
；
s3, calculating
Figure 765114DEST_PATH_IMAGE033
Individual sensor training node and
Figure 805882DEST_PATH_IMAGE034
distance between non-cooperative training nodes
Figure 247359DEST_PATH_IMAGE035
；
S4, according to the distance
Figure 221131DEST_PATH_IMAGE036
To obtain the first
Figure 722651DEST_PATH_IMAGE037
Individual sensor training node to
Figure 985136DEST_PATH_IMAGE038
Training power of each non-cooperative training node;
s5, connecting a plurality of input-output pairs
Figure 27041DEST_PATH_IMAGE039
Inputting the data into the neural network model to train the neural network model to obtain a trained neural network model, wherein,
Figure 58582DEST_PATH_IMAGE040
is the training power of the uncooperative training node,
Figure 731003DEST_PATH_IMAGE041
and the mesh is the real position of the non-cooperative training node.
In one embodiment of the present invention, the step 3 comprises:
step 3.1, inputting the power of each grid into a trained neural network model to obtain a positioning result of the non-cooperative node so as to determine the grid where the non-cooperative node is located;
and 3.2, taking the central position of the network of the non-cooperative node as the coordinate position of the non-cooperative node.
In an embodiment of the present invention, the time sequence of the non-cooperative node is:
Figure 949626DEST_PATH_IMAGE042
wherein,
Figure 326381DEST_PATH_IMAGE043
a time series representing the non-cooperative node,
Figure 946849DEST_PATH_IMAGE044
the function of the index is expressed,
Figure 790171DEST_PATH_IMAGE045
which indicates the amount of time information that is to be transmitted,
Figure 89566DEST_PATH_IMAGE046
which represents the period of the sampling,
Figure 410957DEST_PATH_IMAGE047
indicating sensor
Figure 213828DEST_PATH_IMAGE048
Slave node
Figure 228051DEST_PATH_IMAGE049
The start time and the end time of an observed set of transmission events.
In one embodiment of the invention, the non-cooperative nodes
Figure 686845DEST_PATH_IMAGE050
And the non-cooperative node
Figure 761329DEST_PATH_IMAGE051
The autoregressive model of (a) is:
Figure 621969DEST_PATH_IMAGE052
Figure 807094DEST_PATH_IMAGE053
wherein,
Figure 815501DEST_PATH_IMAGE054
a constrained regression model is represented that has a constraint on the regression model,
Figure 681957DEST_PATH_IMAGE055
an unconstrained regression model is represented that is,
Figure 334786DEST_PATH_IMAGE056
representing the non-cooperative node
Figure 753129DEST_PATH_IMAGE057
The time series of (a) and (b),
Figure 858620DEST_PATH_IMAGE058
representing the non-cooperative node
Figure 528767DEST_PATH_IMAGE059
The time series of (a) and (b),
Figure 98419DEST_PATH_IMAGE060
、
Figure 625347DEST_PATH_IMAGE061
、
Figure 483712DEST_PATH_IMAGE062
is a constant number of times, and is,
Figure 691971DEST_PATH_IMAGE063
representing the non-cooperative node
Figure 178447DEST_PATH_IMAGE064
The number of the lag terms of (a) is,
Figure 67819DEST_PATH_IMAGE065
representing the non-cooperative node
Figure 210219DEST_PATH_IMAGE066
The number of the lag terms of (a) is,
Figure 222168DEST_PATH_IMAGE067
and
Figure 438517DEST_PATH_IMAGE068
indicating uncorrelated additive white noise.
In one embodiment of the invention, the statistics
Figure 635143DEST_PATH_IMAGE069
Comprises the following steps:
Figure 202522DEST_PATH_IMAGE071
wherein,
Figure 752583DEST_PATH_IMAGE072
representing the sum of squared residuals of the constrained regression model,
Figure 151335DEST_PATH_IMAGE073
representing the sum of squared residuals of the unconstrained regression model,
Figure 518862DEST_PATH_IMAGE074
the volume of the sample is represented by,
Figure 245641DEST_PATH_IMAGE075
representing the non-cooperative node
Figure 661710DEST_PATH_IMAGE076
The number of the lag terms of (a) is,
Figure 180547DEST_PATH_IMAGE077
representing the non-cooperative node
Figure 391080DEST_PATH_IMAGE078
The number of the lag terms of (a) is,
Figure 57684DEST_PATH_IMAGE079
representing compliance
Figure 23584DEST_PATH_IMAGE080
The distribution of the water content is controlled by the control system,
Figure 396927DEST_PATH_IMAGE081
representing a degree of freedom of
Figure 778361DEST_PATH_IMAGE082
And
Figure 869945DEST_PATH_IMAGE083
f distribution of (3).
In one embodiment of the present invention, the step 7 includes:
step 7.1, set original hypothesis
Figure 627817DEST_PATH_IMAGE084
Comprises the following steps: the non-cooperative node
Figure 917984DEST_PATH_IMAGE085
Not to cause said non-cooperative node
Figure 735898DEST_PATH_IMAGE086
The cause of the change glange;
step 7.2, judgment
Figure 49199DEST_PATH_IMAGE087
And
Figure 282865DEST_PATH_IMAGE088
in relation to the threshold value of (1), if
Figure 568484DEST_PATH_IMAGE089
Is present from the non-cooperative node
Figure 354038DEST_PATH_IMAGE090
To the non-cooperative node
Figure 154635DEST_PATH_IMAGE086
Otherwise there is no link from the non-cooperative node
Figure 254309DEST_PATH_IMAGE090
To the non-cooperative node
Figure 456751DEST_PATH_IMAGE086
The link of (2).
Compared with the prior art, the invention has the following beneficial effects:
the invention discloses a non-cooperative topology inference method based on unknown node positions, which combines node positioning and causal inference into a system to realize topology inference work when the node positions are unknown.
The positioning method of the invention adopts a machine learning method to realize the positioning of the non-cooperative nodes.
Other aspects and features of the present invention will become apparent from the following detailed description, which proceeds with reference to the accompanying drawings. It is to be understood, however, that the drawings are designed solely for purposes of illustration and not as a definition of the limits of the invention, for which reference should be made to the appended claims. It should be further understood that the drawings are not necessarily drawn to scale and that, unless otherwise indicated, they are merely intended to conceptually illustrate the structures and procedures described herein.
Drawings
Fig. 1 is a schematic flowchart of a non-collaborative topology inference method based on unknown node positions according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a non-cooperative network including sensor nodes according to an embodiment of the present invention;
fig. 3 is a schematic diagram of inference accuracy of a non-cooperative network topology according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
Referring to fig. 1, fig. 1 is a schematic flow chart of a non-collaborative topology inference method based on unknown node positions according to an embodiment of the present invention, and the present invention provides a non-collaborative topology inference method based on unknown node positions, where the non-collaborative topology inference method includes steps 1 to 7, where:
step 1, using random distribution in a given area L
Figure 678785DEST_PATH_IMAGE091
A sensor network composed of sensor nodes monitors the power of a non-cooperative network in a given area L, wherein the non-cooperative network comprises
Figure 28995DEST_PATH_IMAGE092
A non-cooperative node.
In a particular embodiment, step 1 may particularly comprise steps 1.1-1.2, wherein:
step 1.1, randomly setting in a given area L
Figure 666781DEST_PATH_IMAGE091
A sensor node, wherein the location of the sensor node is known.
Specifically, referring to fig. 2, an embodiment of the present invention provides a schematic diagram of an uncooperative network including sensor nodes, where the uncooperative network includes
Figure 774328DEST_PATH_IMAGE092
A sensor network consisting of
Figure 104946DEST_PATH_IMAGE091
Each sensor node and a sink node (the sink node is used for collecting data sent by all other nodes and carrying out related processing and the like),
Figure 942452DEST_PATH_IMAGE091
the sensor nodes are scattered in a given area randomly, and the coordinates of the sensor nodes are
Figure 446246DEST_PATH_IMAGE093
，
Figure 420018DEST_PATH_IMAGE094
Which represents the transpose of the matrix,
Figure 983854DEST_PATH_IMAGE095
a set of real numbers is represented as,
Figure 308657DEST_PATH_IMAGE096
to represent
Figure 288245DEST_PATH_IMAGE091
Real matrix of row 2 column, no
Figure 319786DEST_PATH_IMAGE097
The coordinates of each sensor are
Figure 54524DEST_PATH_IMAGE098
。
Step 1.2, use
Figure 538726DEST_PATH_IMAGE091
Each sensor node monitors the power of the uncooperative network within a given area L.
In particular, according to
Figure 649901DEST_PATH_IMAGE091
The sensor nodes detect the energy distribution in a given area, and each sensor node obtains the receiving power at the position of the sensor node.
In this embodiment, the sensor monitors the power of the uncooperative node to obtain
Figure 598266DEST_PATH_IMAGE099
First, of
Figure 441588DEST_PATH_IMAGE100
The monitored power of each sensor node is as follows:
Figure 475403DEST_PATH_IMAGE101
wherein,
Figure 796794DEST_PATH_IMAGE102
denotes the first
Figure 865244DEST_PATH_IMAGE103
A sensor node monitors
Figure 941785DEST_PATH_IMAGE104
The power of the individual non-cooperating nodes,
Figure 321950DEST_PATH_IMAGE105
，
Figure 650295DEST_PATH_IMAGE106
is shown as
Figure 510935DEST_PATH_IMAGE107
Transmit power of a plurality of non-cooperating nodes, wherein,
Figure 758376DEST_PATH_IMAGE108
，
Figure 704467DEST_PATH_IMAGE109
，
Figure 492294DEST_PATH_IMAGE110
representing the total number of non-cooperating nodes in the non-cooperating network,
Figure 31659DEST_PATH_IMAGE111
the antenna gain of the transmitting antenna is indicated,
Figure 528631DEST_PATH_IMAGE112
which represents the antenna gain of the receiving antenna,
Figure 617809DEST_PATH_IMAGE113
which is indicative of the wavelength of the light,
Figure 350273DEST_PATH_IMAGE114
is shown as
Figure 982243DEST_PATH_IMAGE115
Individual sensor node monitorMeasured to the first
Figure 509170DEST_PATH_IMAGE116
Distance between the non-cooperating nodes.
Step 2, dividing the given area L into
Figure 633115DEST_PATH_IMAGE117
And obtaining the power of each grid according to the power detected by the sensor nodes.
Specifically, a given area L is divided by the number of sensors
Figure 762745DEST_PATH_IMAGE117
The power data for each grid is then obtained based on the power data obtained for each sensor and the known sensor location information.
In this embodiment, the power data monitored by each sensor is obtained by the above-mentioned method
Figure 390167DEST_PATH_IMAGE117
The power distribution of the grid, i.e.
Figure 212629DEST_PATH_IMAGE118
Wherein the first
Figure 417346DEST_PATH_IMAGE119
The power of each grid is represented as:
Figure 366978DEST_PATH_IMAGE120
，
Figure 832595DEST_PATH_IMAGE121
denotes the first
Figure 966904DEST_PATH_IMAGE122
The number of sensors contained in each grid, wherein,
Figure 393337DEST_PATH_IMAGE123
。
and 3, inputting the power of each grid into the trained neural network model to obtain the coordinate position of the non-cooperative node.
In this embodiment, the training method of the neural network model includes:
s1, obtaining a training set, wherein the training set comprises a plurality of non-cooperative training nodes, and the non-cooperative training nodes are non-cooperative nodes for training.
In particular, the training set consists of data that can monitor some of the non-cooperating nodes and can derive their location.
S2, dividing the area where the non-cooperative training nodes are located into
Figure 333611DEST_PATH_IMAGE124
Training grids of the same size, wherein,
Figure 732363DEST_PATH_IMAGE125
。
s3, calculating
Figure 834311DEST_PATH_IMAGE126
Individual sensor training node and
Figure 888986DEST_PATH_IMAGE127
distance between non-cooperative training nodes
Figure 305055DEST_PATH_IMAGE128
。
Specifically, the training set consists of data that can monitor and derive the location of some of the non-cooperative nodes, say
Figure 608911DEST_PATH_IMAGE127
The coordinates of each non-cooperative training node are
Figure 85023DEST_PATH_IMAGE129
(ii) a The distance between each uncooperative training node and each sensor training node (i.e., the sensor node used for training) is then calculatedFrom, to
Figure 423731DEST_PATH_IMAGE130
Individual sensor training node and
Figure 643491DEST_PATH_IMAGE127
distance between non-cooperative training nodes
Figure 79152DEST_PATH_IMAGE131
Comprises the following steps:
Figure 460585DEST_PATH_IMAGE133
wherein,
Figure 552169DEST_PATH_IMAGE134
is as follows
Figure 310041DEST_PATH_IMAGE135
Coordinates of the individual sensor training nodes.
S4, according to distance
Figure 600208DEST_PATH_IMAGE136
To obtain the first
Figure 152543DEST_PATH_IMAGE137
The sensor trains the node to the first
Figure 465844DEST_PATH_IMAGE138
Training power of each non-cooperative training node.
In particular, the distance is measured
Figure 27406DEST_PATH_IMAGE139
Substituting the power formula of step 1.2 to obtain the second
Figure 109763DEST_PATH_IMAGE140
Individual sensor training node to
Figure 98579DEST_PATH_IMAGE138
Received power of each uncooperative training node.
S5, connecting a plurality of input-output pairs
Figure 961493DEST_PATH_IMAGE141
Inputting the data into a neural network model to train the neural network model to obtain a trained neural network model, wherein,
Figure 123484DEST_PATH_IMAGE142
is the training power of the non-cooperative training nodes,
Figure 388243DEST_PATH_IMAGE143
and training grids in which the real positions of the non-cooperative training nodes are located.
Specifically, a combination of uncooperative training nodes is created, and assuming that there are n uncooperative training nodes, the total number of combinations of uncooperative training nodes that may appear in each grid is:
Figure 547960DEST_PATH_IMAGE145
will train the set
Figure 632591DEST_PATH_IMAGE146
Input into a neural network model, wherein
Figure 598273DEST_PATH_IMAGE147
To be an input-output pair, the input-output pair,
Figure 729257DEST_PATH_IMAGE148
in order to acquire the power data of the power,
Figure 122192DEST_PATH_IMAGE149
and training the weight parameters of the neural network model for the training grid where the real position of the non-cooperative node is located to obtain the trained neural network model.
In a particular embodiment, step 3 may particularly comprise steps 3.1-3.2, wherein:
and 3.1, inputting the power of each grid into the trained neural network model to obtain a positioning result of the non-cooperative node so as to determine the grid where the non-cooperative node is located.
And 3.2, taking the central position of the network of the non-cooperative node as the coordinate position of the non-cooperative node.
Specifically, when the sensor network monitors a given area, power data of a scene to be measured is obtained
Figure 959698DEST_PATH_IMAGE150
The data is used as the input of a trained neural network model, the neural network model outputs the positioning result of the non-cooperative node, namely, the non-cooperative node is positioned in a certain grid, and then the central position of the grid is positioned
Figure 463492DEST_PATH_IMAGE151
As coordinates of non-cooperative nodes, wherein
Figure 437264DEST_PATH_IMAGE152
Is shown as
Figure 1101DEST_PATH_IMAGE153
Coordinates of the individual nodes.
And 4, after the coordinate position of the non-cooperative node is obtained, monitoring the time sequence of the non-cooperative node in the non-cooperative network by using the sensor network.
Specifically, after coordinate position information of the non-cooperative node is obtained, the sensor node records the time when the non-cooperative node sends information.
In this embodiment, the sensor monitors the network by observing information transmissions by uncooperative nodes in an RF (radio frequency) environment. The topology of the entire network is inferred from the observation of the sensors. Since the sensors cannot access the uncooperative network, i.e. cannot obtain the internal state of the network, externally observable features must be used. Radio station fingerprint identification technology by combining information such as frequency, interception time and the like of signalsDifferentiation of communication signals between nodes in the network may be achieved, i.e. the sensor node determines by which node the detected signal is emitted. The sensors collect the IDs of the uncooperative nodes they observe and the time series of transmitted information. Each node in the network requires a time series representation, e.g. sensor node monitoring for uncooperative nodes
Figure 60324DEST_PATH_IMAGE154
Time series of
Figure 367808DEST_PATH_IMAGE155
The feature obtained from each sensor node is a set of non-uniformly sampled events
Figure 461666DEST_PATH_IMAGE156
Wherein
Figure 134087DEST_PATH_IMAGE157
Is the time of a set of transmission events. To obtain a time series representation, events must be represented
Figure 680606DEST_PATH_IMAGE158
Resampling to form a time series:
Figure 526202DEST_PATH_IMAGE159
wherein
Figure 474567DEST_PATH_IMAGE160
A time series representing the non-cooperative node,
Figure 380206DEST_PATH_IMAGE161
the function of the index is expressed,
Figure 414021DEST_PATH_IMAGE162
which indicates the amount of time information that is to be transmitted,
Figure 63308DEST_PATH_IMAGE163
which represents the period of the sampling,
Figure 69441DEST_PATH_IMAGE164
indicating sensor
Figure 145982DEST_PATH_IMAGE165
Slave node
Figure 401514DEST_PATH_IMAGE166
The start time and end time of an observed set of transmission events, if
Figure 854492DEST_PATH_IMAGE164
At intervals of
Figure 777448DEST_PATH_IMAGE167
An event (whether the transmission is started or completed) is included, the value is 1, otherwise, the value is 0.
Step 5, constructing the non-cooperative nodes according to the time sequence of the non-cooperative nodes
Figure 24890DEST_PATH_IMAGE168
And non-cooperative nodes
Figure 767718DEST_PATH_IMAGE169
An autoregressive model of the constituent node pairs.
In particular, uncooperative nodes
Figure 696491DEST_PATH_IMAGE168
And the non-cooperative node
Figure 411637DEST_PATH_IMAGE169
The autoregressive model of (a) is:
Figure 767663DEST_PATH_IMAGE170
Figure 189331DEST_PATH_IMAGE171
wherein,
Figure 656216DEST_PATH_IMAGE172
a constrained regression model is represented that has a constraint on the regression model,
Figure 491448DEST_PATH_IMAGE173
an unconstrained regression model is represented that is,
Figure 18375DEST_PATH_IMAGE174
representing non-cooperative nodes
Figure 735795DEST_PATH_IMAGE175
The time series of (a) and (b),
Figure 6371DEST_PATH_IMAGE176
representing non-cooperative nodes
Figure 696109DEST_PATH_IMAGE177
The time series of (a) and (b),
Figure 393938DEST_PATH_IMAGE178
、
Figure 536337DEST_PATH_IMAGE179
、
Figure 672921DEST_PATH_IMAGE180
is constant, is calculated by using Ordinary Least Squares (OLS),
Figure 217166DEST_PATH_IMAGE181
representing the non-cooperative node
Figure 148213DEST_PATH_IMAGE182
The number of the lag terms of (a) is,
Figure 777908DEST_PATH_IMAGE183
representing the non-cooperative node
Figure 655865DEST_PATH_IMAGE184
Number of lag terms of, i.e.
Figure 54617DEST_PATH_IMAGE185
And
Figure 156565DEST_PATH_IMAGE186
the maximum number of lag-behind periods is indicated,
Figure 537473DEST_PATH_IMAGE187
and
Figure 15859DEST_PATH_IMAGE188
indicating uncorrelated additive white noise. If, in the above-described model,
Figure 269117DEST_PATH_IMAGE189
constant of the foregoing
Figure 807545DEST_PATH_IMAGE190
All zeros, or values negligible, are apparent nodes
Figure 146254DEST_PATH_IMAGE191
Will not affect the node
Figure 366014DEST_PATH_IMAGE192
. I.e. nodes
Figure 536095DEST_PATH_IMAGE191
Is not a node
Figure 183108DEST_PATH_IMAGE192
The reason for (1) and vice versa. Of course, if the coefficient
Figure 71430DEST_PATH_IMAGE193
、
Figure 829301DEST_PATH_IMAGE194
Are not zero, then the node
Figure 57151DEST_PATH_IMAGE191
Is a node
Figure 937383DEST_PATH_IMAGE192
Because of the presence of a slave node
Figure 250684DEST_PATH_IMAGE191
Pointing node
Figure 812246DEST_PATH_IMAGE192
The link of (2).
Step 6, utilizing the residual sum of squares of the autoregressive model to construct statistics
Figure 956920DEST_PATH_IMAGE195
Wherein the statistic
Figure 742473DEST_PATH_IMAGE195
Comprises the following steps:
Figure 531351DEST_PATH_IMAGE197
wherein,
Figure 693342DEST_PATH_IMAGE198
representing the sum of the squared residuals of the constrained regression model,
Figure 895785DEST_PATH_IMAGE199
represents the sum of the squared residuals of the unconstrained regression model,
Figure 117818DEST_PATH_IMAGE200
the volume of the sample is represented by,
Figure 202449DEST_PATH_IMAGE201
representing non-cooperative nodes
Figure 371393DEST_PATH_IMAGE202
The number of the lag terms of (a) is,
Figure 162763DEST_PATH_IMAGE203
representing non-cooperative nodes
Figure 555698DEST_PATH_IMAGE204
The number of the lag terms of (a) is,
Figure 330887DEST_PATH_IMAGE205
representing compliance
Figure 569102DEST_PATH_IMAGE206
The distribution of the water content is carried out,
Figure 808453DEST_PATH_IMAGE207
representing a degree of freedom of
Figure 309973DEST_PATH_IMAGE208
And
Figure 369196DEST_PATH_IMAGE209
the F distribution is a sampling distribution of the ratio of two independent random variables subjected to chi-square distribution after the independent random variables are divided by the degree of freedom of the independent random variables, is an asymmetric distribution, and is not interchangeable in position. Unconstrained residual sum of squares
Figure 614363DEST_PATH_IMAGE210
Is to the current non-cooperative node
Figure 708221DEST_PATH_IMAGE211
For all the lagged terms
Figure 380642DEST_PATH_IMAGE212
Making a regression, but not including a lag term in this regression
Figure 927161DEST_PATH_IMAGE213
. Similarly, there is a constrained sum of squares of residuals
Figure 772758DEST_PATH_IMAGE214
Is to the current non-cooperative node
Figure 658805DEST_PATH_IMAGE215
For all the lag terms
Figure 564444DEST_PATH_IMAGE216
And a lag term
Figure 535942DEST_PATH_IMAGE217
And (6) making regression.
Step 7, according to the statistic
Figure 185230DEST_PATH_IMAGE218
Obtaining non-cooperative nodes
Figure 937502DEST_PATH_IMAGE184
And non-cooperative nodes
Figure 14043DEST_PATH_IMAGE219
The cause and effect relationship of (1).
In a particular embodiment, step 7 may particularly comprise steps 7.1-7.2, wherein:
step 7.1, setting original hypothesis
Figure 472837DEST_PATH_IMAGE220
Comprises the following steps: non-cooperative node
Figure 925815DEST_PATH_IMAGE221
Not to cause non-cooperative nodes
Figure 520876DEST_PATH_IMAGE184
The cause of the change granger.
Step 7.2, judgment
Figure 768317DEST_PATH_IMAGE222
And
Figure 776725DEST_PATH_IMAGE223
in relation to the threshold value of (1), if
Figure 705498DEST_PATH_IMAGE224
If there is a secondary non-cooperative node
Figure 420644DEST_PATH_IMAGE221
To non-cooperative nodes
Figure 838987DEST_PATH_IMAGE184
Otherwise there is no slave non-cooperative node
Figure 272373DEST_PATH_IMAGE221
To non-cooperative nodes
Figure 801575DEST_PATH_IMAGE184
The link(s) of (a) is (are),
Figure 371227DEST_PATH_IMAGE225
is a distribution case, which is selected to correspond to a critical confidence level
Figure 163734DEST_PATH_IMAGE226
The value of (d) is a threshold value, the threshold value is a constant.
In particular, the original hypothesis
Figure 881154DEST_PATH_IMAGE227
Is expressed as
Figure 151730DEST_PATH_IMAGE228
，
Figure 903785DEST_PATH_IMAGE229
Representing a constant, by calculation using Ordinary Least Squares (OLS), if
Figure 601614DEST_PATH_IMAGE230
A threshold value of
Figure 806330DEST_PATH_IMAGE231
Significantly different from 0, so the original hypothesis is rejected
Figure 880597DEST_PATH_IMAGE232
Is ready to storeAt a slave non-cooperative node
Figure 487158DEST_PATH_IMAGE221
To non-cooperative nodes
Figure 344170DEST_PATH_IMAGE184
Otherwise, the original hypothesis cannot be rejected
Figure 36182DEST_PATH_IMAGE232
I.e. there is no slave non-cooperative node
Figure 710877DEST_PATH_IMAGE221
To non-cooperative nodes
Figure 109629DEST_PATH_IMAGE184
The link of (2). Repeating the steps 4 to 7, and checking whether all node pairs meet the original hypothesis
Figure 477156DEST_PATH_IMAGE232
To determine the links between the various uncooperative nodes.
That is, it is assumed that there is a network
Figure 594148DEST_PATH_IMAGE233
Repeating the steps 4 to 7, traversing all node pairs, constructing an autoregressive model of the nodes, and constructing the uncooperative nodes
Figure 744637DEST_PATH_IMAGE234
Statistics, judging whether the node pair satisfies the original hypothesis
Figure 263475DEST_PATH_IMAGE235
I.e. whether a causal relationship exists between pairs of nodes. Thereby obtaining topology inference results of the entire network.
It is worth noting that the granger causal relationship test is sometimes sensitive to the choice of lag phase length, and different lag phases may yield completely different test results. Therefore, it is first necessary to perform checks for different lag period lengths.
The effectiveness of the non-collaborative topology inference method based on unknown node positions in the embodiment is verified through experiments.
Specifically, energy distribution conditions in the non-cooperative area are detected through a sensor, and coarse positioning is carried out on the non-cooperative nodes. Specifically, the power monitored by each sensor is put into a trained neural network for training, and the positioning result of the uncooperative node is obtained. Then, through effective monitoring of non-cooperative nodes, after an autoregressive model of the nodes is constructed, statistics are constructed
Figure 474007DEST_PATH_IMAGE236
Judging whether the node pair satisfies the original assumption
Figure 140612DEST_PATH_IMAGE235
I.e. whether there is a causal relationship between pairs of nodes, thereby obtaining a topology inference of the entire network.
In the simulation, the antenna type of the non-cooperative node is set to be an omnidirectional antenna, a given area is divided into grids equal to the number of sensors, and fig. 3 shows the topology inference accuracy of the non-cooperative network topology.
The invention provides a non-cooperative topology inference method based on unknown node positions, wherein under the condition of unknown node positions, a sensor node collects the power distribution condition of a given area L, feeds the power distribution condition into a trained neural network model to obtain the positioning result of a non-cooperative node, uses the distance and frame interval information between nodes as the characteristics for judging whether a communication relation exists between the nodes, and feeds the trained classification model to obtain an inferred topology.
The positioning method of the invention adopts a machine learning method to realize the positioning of the non-cooperative nodes.
The invention combines node positioning and causal inference into a system to realize topology inference work when the node position is unknown based on a non-collaborative topology inference method with unknown node position.
Example two
Yet another aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the non-collaborative topology inference method based on node location unknown according to any of the above embodiments.
In the description of the invention, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or to imply that the number of indicated technical features is significant. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic data point described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristic data points described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples described in this specification can be combined and combined by those skilled in the art.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (9)

1. A non-cooperative topology inference method based on unknown node positions is characterized by comprising the following steps:
step 1, using random distribution in a given area L
Figure 123104DEST_PATH_IMAGE001
A sensor network consisting of sensor nodes monitors the power of an uncooperative network in the given area L, the uncooperative network comprising
Figure 102562DEST_PATH_IMAGE002
A plurality of non-cooperative nodes;
step 2, dividing the given area L into
Figure 475774DEST_PATH_IMAGE001
The grids with the same size are obtained, and the power of each grid is obtained according to the power detected by the sensor nodes;
step 3, inputting the power of each grid into a trained neural network model to obtain the coordinate position of the uncooperative node;
step 4, after the coordinate position of the non-cooperative node is obtained, monitoring the time sequence of the non-cooperative node in the non-cooperative network by using the sensor network;
step 5, constructing the non-cooperative nodes according to the time sequence of the non-cooperative nodes
Figure 339825DEST_PATH_IMAGE003
And non-cooperative nodes
Figure 216514DEST_PATH_IMAGE004
An autoregressive model of the composed node pairs;
step 6, utilizing the residual sum of squares of the autoregressive model to construct statistics
Figure 632452DEST_PATH_IMAGE005
；
Step 7, according to the statistic quantity
Figure 961802DEST_PATH_IMAGE005
Obtaining the non-cooperative node
Figure 629544DEST_PATH_IMAGE006
And the non-cooperative node
Figure 891898DEST_PATH_IMAGE003
The cause and effect relationship of (c).
2. The method for non-cooperative topology inference based on unknown node locations according to claim 1, wherein the step 1 comprises:
step 1.1, randomly setting the given area L
Figure 947579DEST_PATH_IMAGE007
A plurality of sensor nodes, wherein the locations of the sensor nodes are known;
step 1.2, utilizing the
Figure 170749DEST_PATH_IMAGE007
Each sensor node monitors the power of the uncooperative network in the given area L, wherein
Figure 501237DEST_PATH_IMAGE008
The monitored power of each sensor node is as follows:
Figure 86939DEST_PATH_IMAGE009
wherein,
Figure 985625DEST_PATH_IMAGE010
is shown as
Figure 289567DEST_PATH_IMAGE011
A sensor node monitors
Figure 158166DEST_PATH_IMAGE012
The power of the individual non-cooperating nodes,
Figure 270478DEST_PATH_IMAGE013
，
Figure 199120DEST_PATH_IMAGE014
is shown as
Figure 990359DEST_PATH_IMAGE015
Transmit power of a plurality of non-cooperating nodes, wherein,
Figure 538015DEST_PATH_IMAGE016
，
Figure 629467DEST_PATH_IMAGE017
，
Figure 869956DEST_PATH_IMAGE018
representing the total number of non-cooperating nodes in the non-cooperating network,
Figure 882911DEST_PATH_IMAGE019
the antenna gain of the transmitting antenna is indicated,
Figure 358892DEST_PATH_IMAGE020
which represents the antenna gain of the receiving antenna,
Figure 773693DEST_PATH_IMAGE021
which is indicative of the wavelength of the light,
Figure 185083DEST_PATH_IMAGE022
is shown as
Figure 216492DEST_PATH_IMAGE023
A sensor node monitors
Figure 699426DEST_PATH_IMAGE024
Distance between the non-cooperating nodes.
3. The method of claim 2, wherein the first step is to determine the topology of the non-cooperative topology based on the unknown node location
Figure 640838DEST_PATH_IMAGE025
The power of each grid is:
Figure 347762DEST_PATH_IMAGE026
wherein,
Figure 335310DEST_PATH_IMAGE027
denotes the first
Figure 28460DEST_PATH_IMAGE028
The power of the individual grids is determined,
Figure 152273DEST_PATH_IMAGE029
is shown as
Figure 30100DEST_PATH_IMAGE028
The number of sensors contained in each grid, wherein,
Figure 504943DEST_PATH_IMAGE030
。
4. the method of claim 1, wherein the training of the neural network model comprises:
s1, obtaining a training set, wherein the training set comprises a plurality of non-cooperative training nodes;
s2, dividing the area where the non-cooperative training nodes are located into
Figure 1784DEST_PATH_IMAGE031
Training grids of the same size, wherein,
Figure 776842DEST_PATH_IMAGE032
；
s3, calculating
Figure 28831DEST_PATH_IMAGE033
Individual sensor training node and
Figure 397496DEST_PATH_IMAGE034
distance between non-cooperative training nodes
Figure 25923DEST_PATH_IMAGE035
；
S4, according to the distance
Figure 921067DEST_PATH_IMAGE035
To obtain the first
Figure 750483DEST_PATH_IMAGE036
Individual sensor training node to
Figure 199919DEST_PATH_IMAGE037
Training power of each non-cooperative training node;
s5, connecting a plurality of input-output pairs
Figure 987414DEST_PATH_IMAGE038
Inputting the data into the neural network model to train the neural network model to obtain a trained neural network model, wherein,
Figure 346851DEST_PATH_IMAGE039
is the training power of the uncooperative training node,
Figure 737381DEST_PATH_IMAGE040
and training grids in which the real positions of the non-cooperative training nodes are located.
5. The method of claim 1, wherein step 3 comprises:
step 3.1, inputting the power of each grid into a trained neural network model to obtain a positioning result of the non-cooperative node so as to determine the grid where the non-cooperative node is located;
and 3.2, taking the central position of the grid with the non-cooperative node as the coordinate position of the non-cooperative node.
6. The method of claim 1, wherein the time series of the uncooperative nodes is:
Figure 408534DEST_PATH_IMAGE041
wherein,
Figure 50868DEST_PATH_IMAGE042
a time series representing the non-cooperative node,
Figure 655025DEST_PATH_IMAGE043
the function of the index is expressed,
Figure 91822DEST_PATH_IMAGE044
which indicates the amount of time information that is to be transmitted,
Figure 250271DEST_PATH_IMAGE045
which represents the period of the sampling,
Figure 555351DEST_PATH_IMAGE046
indicating sensor
Figure 889380DEST_PATH_IMAGE047
Slave node
Figure 621713DEST_PATH_IMAGE048
The start time and the end time of an observed set of transmission events.
7. The method of claim 1, wherein the uncooperative nodes are unknown based on location of the nodes
Figure 673982DEST_PATH_IMAGE049
And the non-cooperative node
Figure 517173DEST_PATH_IMAGE050
The autoregressive model of (a) is:
Figure 971288DEST_PATH_IMAGE051
Figure 343364DEST_PATH_IMAGE052
wherein,
Figure 7563DEST_PATH_IMAGE053
a constrained regression model is represented that has a constraint on the regression model,
Figure 529812DEST_PATH_IMAGE054
an unconstrained regression model is represented that is,
Figure 963067DEST_PATH_IMAGE055
representing the non-cooperative node
Figure 912568DEST_PATH_IMAGE056
The time series of (a) and (b),
Figure 267326DEST_PATH_IMAGE057
representing the non-cooperative node
Figure 717899DEST_PATH_IMAGE058
The time series of (a) and (b),
Figure 881027DEST_PATH_IMAGE059
、
Figure 126064DEST_PATH_IMAGE060
、
Figure 640222DEST_PATH_IMAGE062
is a constant number of times, and is,
Figure 628906DEST_PATH_IMAGE063
representing the non-cooperative node
Figure 240016DEST_PATH_IMAGE064
The number of the lag terms of (a) is,
Figure 796900DEST_PATH_IMAGE065
representing the non-cooperative node
Figure 657408DEST_PATH_IMAGE066
The number of the lag terms of (a) is,
Figure 325150DEST_PATH_IMAGE068
and
Figure 790766DEST_PATH_IMAGE070
indicating uncorrelated additive white noise.
8. The method of claim 7, wherein the statistics are based on an unknown location of the node
Figure 643185DEST_PATH_IMAGE071
Comprises the following steps:
Figure 866356DEST_PATH_IMAGE072
wherein,
Figure 196843DEST_PATH_IMAGE073
representing the sum of the squared residuals of the constrained regression model,
Figure 189070DEST_PATH_IMAGE074
representing the sum of the squared residuals of the unconstrained regression model,
Figure 681231DEST_PATH_IMAGE075
the volume of the sample is represented by,
Figure 250753DEST_PATH_IMAGE076
representing the non-cooperative node
Figure 260297DEST_PATH_IMAGE077
The number of the lag terms of (a) is,
Figure 497243DEST_PATH_IMAGE078
representing the non-cooperative node
Figure 301251DEST_PATH_IMAGE079
The number of the lag terms of (a) is,
Figure 623648DEST_PATH_IMAGE080
representing compliance
Figure 764779DEST_PATH_IMAGE081
The distribution of the water content is controlled by the control system,
Figure 731598DEST_PATH_IMAGE082
representing a degree of freedom of
Figure 831141DEST_PATH_IMAGE083
And
Figure 109676DEST_PATH_IMAGE084
f distribution of (3).
9. The method of claim 8, wherein the step 7 comprises:
step 7.1, set original hypothesis
Figure 461023DEST_PATH_IMAGE085
Comprises the following steps: the non-cooperative node
Figure 406982DEST_PATH_IMAGE086
Not to cause the non-cooperative node
Figure 411847DEST_PATH_IMAGE087
The cause of the change glange;
step 7.2, judgment
Figure 318623DEST_PATH_IMAGE088
And
Figure 332716DEST_PATH_IMAGE089
in relation to the threshold value of (1), if
Figure 867602DEST_PATH_IMAGE090
Is present from the non-cooperative node
Figure 184314DEST_PATH_IMAGE091
To the non-cooperative node
Figure 703020DEST_PATH_IMAGE092
Otherwise there is no link from the non-cooperative node
Figure 130590DEST_PATH_IMAGE093
To the non-cooperative node
Figure 797281DEST_PATH_IMAGE092
The link of (2).
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