CN115776724A - Sensor node layout optimization method and system for electromagnetic spectrum mapping - Google Patents

Sensor node layout optimization method and system for electromagnetic spectrum mapping Download PDF

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CN115776724A
CN115776724A CN202310091981.4A CN202310091981A CN115776724A CN 115776724 A CN115776724 A CN 115776724A CN 202310091981 A CN202310091981 A CN 202310091981A CN 115776724 A CN115776724 A CN 115776724A
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CN115776724B (en
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朱秋明
赵翼
林志鹏
王洁
黄洋
李婕
吴启晖
仲伟志
高钱豪
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Nanjing University of Aeronautics and Astronautics
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Abstract

A sensor node layout optimization method and system for electromagnetic spectrum mapping comprises the following steps: carrying out mobile initialization acquisition on frequency spectrum data of a region to be detected to obtain initial frequency spectrum data; pairing the sampling positions pairwise by using the initial frequency spectrum data to obtain an empirical half variance value data point; clustering and grouping the empirical half variance value data points; determining the minimum number of sampling nodes according to the half variance value data points after clustering grouping; optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes; and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance until the total number of the sampling nodes. The invention comprehensively considers the spatial correlation of the radio wave propagation model and the frequency spectrum data, and can obtain the least number of sampling nodes and the optimal position for the multi-node sensor collaborative frequency spectrum mapping task under the unknown scene, thereby achieving the purpose of realizing the optimal frequency spectrum mapping performance by utilizing the least number of nodes.

Description

Sensor node layout optimization method and system for electromagnetic spectrum mapping
Technical Field
The invention belongs to the field of wireless information transmission, and particularly relates to a sensor node layout optimization method and system for electromagnetic spectrum mapping, in particular to electromagnetic spectrum mapping application in a multi-node sensor collaborative sensing scene.
Background
With the rapid development of information technology and wireless communication technology, various wireless communication network devices are rapidly increased, and the electromagnetic spectrum space is increasingly complex. The electromagnetic spectrum map can quantitatively represent and visualize related information of the frequency spectrum including time, frequency, received signal strength and position, and is expected to play a role in multiple fields of illegal radio frequency signal detection, radiation source positioning, frequency spectrum resource management and the like. Therefore, it is becoming more and more important how to perform accurate electromagnetic spectrum mapping.
For a wide-area three-dimensional geographic space, electromagnetic spectrum mapping faces challenges such as limited number of acquisition nodes, limited acquisition time, complex and variable acquisition environment and the like. In addition, the final accuracy of the spectrum map depends on the number of sampling nodes and the specific positions of the sampling nodes. The more the number of sampling nodes is, the more accurately the electromagnetic spectrum of the region to be measured can be reconstructed, but the acquisition workload is increased. Therefore, how to select the optimal position for layout and sampling under the condition of giving the number of sampling nodes is a compromise solution which gives consideration to both performance and efficiency.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a sensor node layout optimization method and system for electromagnetic spectrum mapping, which comprehensively consider the spatial correlation between a radio wave propagation model and spectrum data, and can obtain the minimum number of sampling nodes and the optimal position for a multi-node sensor collaborative spectrum mapping task under an unknown scene, thereby achieving the purpose of realizing the optimal spectrum mapping performance by using the minimum number of nodes.
In order to realize the purpose, the invention adopts the following technical scheme:
a sensor node layout optimization method for electromagnetic spectrum mapping is characterized by comprising the following steps:
step 1: carrying out mobile initialization collection on the frequency spectrum data of the area to be detected according to a random track or a uniform track by utilizing collection equipment to obtain initial frequency spectrum data;
step 2: pairing the sampling positions pairwise by using the obtained initial frequency spectrum data, calculating a half variance value, and obtaining an empirical half variance value data point;
and step 3: clustering and grouping the empirical half-variance value data points to obtain clustered and grouped half-variance value data points;
and 4, step 4: according to the clustered and grouped half variance value data points, fitting to obtain a spatial global half-variation function, and according to the obtained spatial global half-variation function, determining the minimum number of sampling nodes;
and 5: optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes;
and 6: and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance according to the data acquired from the optimized initial sampling node position until the total number of the sampling nodes.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in step 1, the initial spectrum data M is represented as:
Figure SMS_1
，
in the formula (I), the compound is shown in the specification,
Figure SMS_2
is a firstiSampling node position
Figure SMS_3
Department collectionTThe average received power over time is calculated,
Figure SMS_4
is composed of
Figure SMS_5
At the positiontThe instantaneous voltage of the moment in time,
Figure SMS_6
and
Figure SMS_7
respectively are uniformly collected at equal intervals in the transverse direction and the longitudinal direction;Lis the length of the region to be measured,Wis the width of the region to be measured,Nfor the total number of sampling nodes to be counted,t 1 indicating an arbitrary starting instant.
Further, in the step 2, empirical half-variance value data points
Figure SMS_8
The calculation of (c) is as follows:
Figure SMS_9
，
in the formula (I), the compound is shown in the specification,dis shown asiA sampling node and the secondjThe distance of the individual sampling nodes,
Figure SMS_10
denotes the firstiA sampling node and the secondjThe half variance value of each sampling node,
Figure SMS_11
means any two distances ofdThe value of the half-variance of the sampling node of (c),
Figure SMS_12
indicating distancedThe empirical half variance value of (a); will be at a distance ofdAny ofTwo sampling nodes are called a distance ofdThe group of nodes of (a) is,N d is a distance ofdThe number of groups of node groups.
Further, the step 3 specifically includes the following steps:
step 3.1: selecting a distance variable composition set in empirical half-variance data points
Figure SMS_13
As a variable of the clustering group, there is,
Figure SMS_14
is shown asepnDistance variables for the empirical half variance value data points; random selectionKUsing non-repetitive samples as clustering center
Figure SMS_15
(ii) a By using
Figure SMS_16
Is shown askThe number of points of the semi-variance data values within the group,kthe value of (b) is 1 toKEach group is aggregated into
Figure SMS_17
Then it is firstkCluster center of group
Figure SMS_18
Comprises the following steps:
Figure SMS_19
；
step 3.2: calculating a distance variable in each half variance value data point
Figure SMS_20
With each cluster center
Figure SMS_21
Euclidean distance of
Figure SMS_22
：
Figure SMS_23
，
In the formula (I), the compound is shown in the specification,epthe value of (1) ~epn；
Step 3.3: according to the calculated Euclidean distance, dividing each sample into a group with the nearest one in turn, and then recalculating the clustering center
Figure SMS_24
If, if
Figure SMS_25
Then will be
Figure SMS_26
Update the value of (2) to cluster center
Figure SMS_27
；
Step 3.4: repeating the step 3.2 and the step 3.3, iterating until the clustering center is not changed, ending the algorithm after convergence is reached, and outputting the final clustering grouping result
Figure SMS_28
；
Step 3.5: empirical half-variance data points
Figure SMS_29
According to post-clustering partitioningKThe groups are averaged to obtain a semi-variance data point set after clustering grouping
Figure SMS_30
Wherein
Figure SMS_31
Representing the semi-variance value data points after clustering grouping,
Figure SMS_32
denotes the firstKThe distance variable of the grouped half variance value data points of each cluster,
Figure SMS_33
is the firstKSemi-variance value after clustering groupingThe variance of the data points.
Further, the step 4 specifically includes:
grouping the data points according to the clustering
Figure SMS_34
Fitting to obtain a spatial global semi-variogram
Figure SMS_35
The optimization target is as follows:
Figure SMS_36
，
in the formula (I), the compound is shown in the specification,
Figure SMS_37
the function of the object is represented by,
Figure SMS_38
is shown askThe distance variable of the grouped half variance value data points of each cluster,
Figure SMS_39
is shown askThe variance of the grouped half variance value data points,
Figure SMS_40
is the parameter to be determined and is,c 0 is the half-variance zero-offset value,cis the half-variance scaling factor and is,
Figure SMS_41
is a distance scaling factor;
will be provided with
Figure SMS_42
Distance at which stability tends to occurdRecord the associated distanced 0 At this time
Figure SMS_43
Is the critical space variation valueCDetermining the minimum number of sampling nodes according to the following equal interval constraint formulaP：
Figure SMS_44
，
In the formula (I), the compound is shown in the specification,
Figure SMS_45
is the fluctuation threshold.
Further, the step 5 specifically includes the following steps:
step 5.1: initializing solution space X, search speed V andPinitial sampling node location:
Figure SMS_46
，
in the formula (I), the compound is shown in the specification,
Figure SMS_47
is the first in solution spaceqThe number of the solutions is one,
Figure SMS_48
is as followsqThe speed of the search of the individual solutions,
Figure SMS_49
is as followsqThe 1 st node position in the solution,
Figure SMS_50
is the firstqThe search speed of the 1 st node in the solution,
Figure SMS_51
is the optimal initial sampling node position in the initial solution space X; the function initialize represents initialization;
step 5.2: computingPHalf-variance value of initial sampling node
Figure SMS_52
；
Step 5.3: calculating an optimization objective function:
Figure SMS_53
；
step 5.4: the solution space is updated and the global optimum is obtained according to the following principle:
Figure SMS_54
，
in the formula (I), the compound is shown in the specification,
Figure SMS_55
is the firstt+1 iteration timeqThe speed of the search of the individual solutions,
Figure SMS_56
is the firsttAfter the second iterationqThe optimal situation of the individual solutions is,
Figure SMS_57
is the firsttThe optimal node position situation after the sub-iteration,
Figure SMS_58
is a firstt(iii) on +1 iterationqThe solution, function update, indicates the situation of obtaining the optimal node position from the solution space X and updating into Gb,wis the weight of the inertia, and,r 1 、r 2 is a random number subject to uniform distribution, and the function max represents taking the maximum value;
step 5.5: repeating the step 5.2 to the step 5.4, iterating until the algorithm is finished after convergence, and outputting the optimized initial sampling node position
Figure SMS_59
。
Further, the step 6 specifically includes the following steps:
step 6.1: first, the weight coefficients are solved using the following formula:
Figure SMS_60
，
in the formula (I), the compound is shown in the specification,
Figure SMS_61
is the sampling node position
Figure SMS_62
And a non-sampled position
Figure SMS_63
The value of the half-variance of (c),
Figure SMS_64
is the coefficient to be solved;
the kriging variance values at each unknown sampling location are then calculated using the following equation
Figure SMS_65
：
Figure SMS_66
；
Step 6.2: taking the position with the maximum Kriging variance value
Figure SMS_67
For the next sampled node location, and add the sampled node location set
Figure SMS_68
Updating the number of sampled nodesn =n+1；
Step 6.3: repeating the step 6.1 and the step 6.2 until the total number of sampling nodes is reachedNAnd outputting the final sampling node position optimization result.
The invention also provides a sensor node layout optimization system for electromagnetic spectrum mapping, which is characterized by comprising the following steps:
the acquisition equipment is used for carrying out mobile initialization acquisition on the frequency spectrum data of the area to be detected according to a random track or a uniform track to obtain initial frequency spectrum data;
the calculation module is used for pairing the sampling positions pairwise by using the obtained initial spectrum data, calculating a half variance value and obtaining an empirical half variance value data point; clustering and grouping the empirical half-variance value data points to obtain half-variance value data points after clustering and grouping; according to the clustered and grouped half variance value data points, fitting to obtain a spatial global half-variation function, and according to the obtained spatial global half-variation function, determining the minimum number of sampling nodes;
the optimization module is used for optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes; and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance according to the data acquired from the optimized initial sampling node position until the total number of the sampling nodes.
The beneficial effects of the invention are:
1) According to the sensor node layout optimization method and system for electromagnetic spectrum mapping, which are provided by the invention, the spatial correlation between the radio wave propagation model and the spectrum data is comprehensively considered, and the accurate electromagnetic spectrum map can be obtained by using the least number of sensors;
2) According to the sensor node layout optimization scheme provided by the invention, based on the spectrum data spatial correlation model and the kriging variance model which are constructed in a mixed mode, sampling node layout optimization and sequential node optimization are combined, and the calculation complexity is effectively reduced.
Drawings
FIG. 1 is a flow chart of a sensor node layout optimization method for electromagnetic spectrum mapping according to the present invention.
Fig. 2 is a global spectrum map of an embodiment.
Fig. 3 is a schematic diagram of the spectral data acquired by the equal interval initialization of the embodiment.
Fig. 4 is a graph of the calculation results of the empirical half variance values of the example.
Fig. 5 is a schematic diagram of a cluster center according to an embodiment.
Fig. 6 is a diagram of the calculation results of the fitting global spatial half-variance function according to the embodiment.
Fig. 7a to 7d are graphs of results of initial sampling node optimization according to an embodiment, where fig. 7a shows initialized 25 node positions, fig. 7b shows 25 node positions after 10 iterations, fig. 7c shows 25 node positions after 20 iterations, and fig. 7d shows 25 node positions after final optimization.
Fig. 8a to 8d are graphs of the final output result of the sampling node optimization according to the embodiment, where fig. 8a shows the optimized positions of 50 nodes, fig. 8b shows the optimized positions of 100 nodes, fig. 8c shows the optimized positions of 150 nodes, and fig. 8d shows the optimized positions of 256 nodes.
Detailed description of the preferred embodiments
The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
In an embodiment, as shown in fig. 1, the present invention provides a sensor node layout optimization method oriented to electromagnetic spectrum mapping. The global spectrum map of this embodiment is shown in fig. 2, and the number of transmitters is 8 in the scene to be measured. Location parameters corresponding to transmitters
Figure SMS_69
Frequency of transmissionfAnd transmit power
Figure SMS_70
As shown in table 1.
Table 1 transmitter configuration parameters
Figure SMS_71
。
The specific implementation steps are as follows:
the first step is as follows: user sets length of area to be measuredL = 500m and widthW = 500m, frequency band to be measuredf = 2450Mhz; user setting total sampling node numberN =256. The embodiment adopts a scheme of uniform equal interval arrangement. Carrying out equal-interval acquisition according to the constraint condition of the formula (1), and transversely spacing
Figure SMS_72
= 30mAnd at a longitudinal interval
Figure SMS_73
= 30mObtaining the initially acquired frequency spectrum data MAs shown in fig. 3.
Figure SMS_74
（1）
In the formula (I), the compound is shown in the specification,
Figure SMS_75
is as followsiSampling node position
Figure SMS_76
Department collectionTThe average received power over time is determined by,
Figure SMS_77
is composed of
Figure SMS_78
At the positiontInstantaneous voltage at a time;t 1 indicating an arbitrary starting instant.
The second step is that: pairing every two sampling nodes according to the initially acquired frequency spectrum data M, and calculating by using a formula (2) to obtain an empirical half-variance value data point
Figure SMS_79
As shown in fig. 4.
Figure SMS_80
（2）
In the formula (I), the compound is shown in the specification,dis shown asiA sampling node and the secondjThe distance of the individual sampling nodes,
Figure SMS_81
denotes the firstiA sampling node and the secondjThe half variance value of each sampling node,
Figure SMS_82
means any two distances ofdThe value of the half-variance of the sampling node of (c),
Figure SMS_83
indicating distancedThe empirical half variance value of; will be at a distance ofdAny two samples ofThe node is called a distance ofdThe group of nodes of (a) is,N d is a distance ofdThe number of groups of node groups.
To the obtained empirical half-variance value
Figure SMS_84
Clustering groups, clustering the number of groupsKAnd =12. The distance vector of each group is calculated by using formula (3), distance measurement is performed by using formula (4) until convergence is completed, and the mean half-variance of each class is calculated according to the clustering result, as shown in fig. 5.
Figure SMS_85
（3）
Figure SMS_86
（4）
In the formula, the distance variables in the empirical half-variance data points form a set
Figure SMS_87
As a variable of the clustering group, there is,
Figure SMS_88
is shown asepnDistance variables for the empirical half-variance data points; random selectionKUsing non-repetitive samples as clustering center
Figure SMS_89
(ii) a By using
Figure SMS_90
Is shown askThe number of points of the semi-variance data values within the group,kthe value of (1) ~KEach group is assembled as
Figure SMS_91
，
Figure SMS_92
Denotes the firstkThe center of the cluster of the group is,epthe value of (1) ~epn。
The fourth step: according to the semi-variance mean value after clustering grouping, fitting to obtain a global space semi-variation function
Figure SMS_93
As shown in fig. 6, the optimization objectives are:
Figure SMS_94
（5）
in the formula (I), the compound is shown in the specification,
Figure SMS_95
the representation of the objective function is shown as,
Figure SMS_96
denotes the firstkThe distance variable of the grouped half variance value data points of each cluster,
Figure SMS_97
is shown askThe variance of the grouped half variance value data points,
Figure SMS_98
is the parameter to be determined and,c 0 is the value of the half-variance zero offset,cis the half-variance scaling factor and is,
Figure SMS_99
is a distance scaling factor.
Will be provided with
Figure SMS_100
Distance at which stability tends to occurdRecord as the correlation distanced 0 At this time
Figure SMS_101
Is the critical space variation valueCDetermined according to equation (6)d 0 10m, minimum number of initial layout pointsP =25。
Figure SMS_102
（6）
In the formula (I), the compound is shown in the specification,
Figure SMS_103
is the fluctuation threshold.
The fifth step: and solving and obtaining the initial sampling node optimization position based on a random optimization algorithm. The concrete implementation steps are as follows:
s5.1: initializing the solution space, the search speed and the optimal node position by using formula (7):
Figure SMS_104
（7）
in the formula (I), the compound is shown in the specification,
Figure SMS_105
is the first in solution spaceqThe number of the solutions is one,
Figure SMS_106
is as followsqThe speed of the search of the individual solutions,
Figure SMS_107
is as followsqThe 1 st node position in the solution,
Figure SMS_108
is the firstqThe search speed of the 1 st node in the solution,
Figure SMS_109
is the optimal initial sampling node position in the initial solution space X, and the function initialization represents initialization.
S5.2: calculating according to the method of the second step and the third stepPHalf-variance value of initial sampling node
Figure SMS_110
。
S5.3: the objective function value is calculated using equation (8):
Figure SMS_111
（8）
s5.4: and (3) updating the solution space, the search speed and the optimal initial node position by using the formula (9):
Figure SMS_112
（9）
in the formula (I), the compound is shown in the specification,
Figure SMS_113
is the firstt+1 iteration timeqThe speed of the search of the individual solutions,
Figure SMS_114
is the firsttAfter the second iterationqThe optimal situation of the individual solutions is,
Figure SMS_115
is the firsttThe optimal node location situation after the sub-iteration,
Figure SMS_116
is a firstt(iii) on +1 iterationqThe solution, function update, indicates the situation of obtaining the optimal node position from the solution space X and updating into Gb,wis the weight of the inertia, and,r 1 、r 2 is a random number obeying a uniform distribution and the function max represents taking the maximum value.
Repeating S5.2 to S5.4, iterating until the algorithm is ended after convergence, and outputting the optimal sampling node position
Figure SMS_117
As shown in fig. 7a to 7d, the detailed sampling coordinates are shown in table 2.
Table 2 detailed sample coordinates
Figure SMS_118
。
And a sixth step: initializing number of sampled nodesn=P=25, performing sequential optimization on the remaining nodes based on the principle of maximum kriging variance until the total number of sampling nodes is reachedN=256. The method comprises the following concrete steps:
s6.1: the kriging variance value for each non-sampled position is calculated using equations (10) and (11):
Figure SMS_119
（10）
Figure SMS_120
（11）
in the formula (I), the compound is shown in the specification,
Figure SMS_121
is sampling node position
Figure SMS_122
And a non-sampled position
Figure SMS_123
The value of the half-variance of (c),
Figure SMS_124
is the coefficient to be solved.
S6.2: the non-sampling position with the maximum Kriging variance value is set as the next sampling node position
Figure SMS_125
And adding the location to the sampled node set
Figure SMS_126
. Updating the number of sampled nodesn=n+1。
S6.3: repeating S6.1 and S6.2 until the total number of sampling nodes is reachedN=256, and a final sampling node position optimization result is output as shown in fig. 8a to 8 d.
In another embodiment, the present invention further provides a system corresponding to the method for optimizing a sensor node layout for electromagnetic spectrum mapping proposed in the first embodiment, that is, a system for optimizing a sensor node layout for electromagnetic spectrum mapping, specifically including:
the acquisition equipment is used for carrying out mobile initialization acquisition on the frequency spectrum data of the area to be detected according to a random track or a uniform track to obtain initial frequency spectrum data;
the calculation module is used for pairing the sampling positions pairwise by using the obtained initial spectrum data, calculating a half variance value and obtaining an empirical half variance value data point; clustering and grouping the empirical half-variance value data points to obtain clustered and grouped half-variance value data points; according to the clustered and grouped half variance value data points, fitting to obtain a spatial global half-variation function, and according to the obtained spatial global half-variation function, determining the minimum number of sampling nodes;
the optimization module is used for optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes; and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance according to the data acquired from the optimized initial sampling node position until the total number of the sampling nodes.
In the sensor node layout optimization system for electromagnetic spectrum mapping, the specific working mode and implementation steps of each device/module are the same as those of the sensor node layout optimization method for electromagnetic spectrum mapping, so that repeated description is omitted.
The above are only preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples, and all technical solutions that fall under the spirit of the present invention belong to the scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (8)

1. A sensor node layout optimization method for electromagnetic spectrum mapping is characterized by comprising the following steps:
step 1: carrying out mobile initialization collection on the frequency spectrum data of the area to be detected according to a random track or a uniform track by utilizing collection equipment to obtain initial frequency spectrum data;
step 2: pairing the sampling positions pairwise by using the obtained initial frequency spectrum data, calculating a half variance value, and obtaining an empirical half variance value data point;
and 3, step 3: clustering and grouping the empirical half-variance value data points to obtain clustered and grouped half-variance value data points;
and 4, step 4: according to the clustered and grouped half variance value data points, fitting to obtain a spatial global half-variation function, and according to the obtained spatial global half-variation function, determining the minimum number of sampling nodes;
and 5: optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes;
and 6: and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance according to the data acquired from the optimized initial sampling node position until the total number of the sampling nodes.
2. The method for optimizing the layout of the sensor nodes for electromagnetic spectrum mapping as claimed in claim 1, wherein: in step 1, the initial spectrum data M is represented as:
Figure QLYQS_1
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_3
is as follows
Figure QLYQS_8
Sampling node position
Figure QLYQS_13
Department collection
Figure QLYQS_5
The average received power over time is determined by,
Figure QLYQS_9
is composed of
Figure QLYQS_11
At the position
Figure QLYQS_14
Instantaneous electricity of time of dayThe pressure is applied to the inner wall of the cylinder,
Figure QLYQS_2
and
Figure QLYQS_6
respectively are uniformly collected at equal intervals in the transverse direction and the longitudinal direction;
Figure QLYQS_10
is the length of the region to be measured,
Figure QLYQS_12
is the width of the region to be measured,
Figure QLYQS_4
for the total number of sampling nodes to be counted,
Figure QLYQS_7
indicating an arbitrary starting moment.
3. The method for optimizing the layout of the sensor nodes for electromagnetic spectrum mapping as claimed in claim 2, wherein: in the step 2, empirical half-variance data points
Figure QLYQS_15
The calculation method of (c) is as follows:
Figure QLYQS_16
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_18
is shown as
Figure QLYQS_22
A sampling node and the second
Figure QLYQS_28
The distance of the individual sampling nodes,
Figure QLYQS_20
is shown as
Figure QLYQS_23
A sampling node and the second
Figure QLYQS_27
The half variance value of each sampling node,
Figure QLYQS_30
means any two distances of
Figure QLYQS_17
The value of the half-variance of the sampling node of (a),
Figure QLYQS_21
indicating distance
Figure QLYQS_25
The empirical half variance value of; will be at a distance of
Figure QLYQS_29
Any two sampling nodes of are referred to as a distance of
Figure QLYQS_19
The group of nodes of (a) is,
Figure QLYQS_24
is a distance of
Figure QLYQS_26
The number of groups of node groups.
4. The method for optimizing the layout of sensor nodes for electromagnetic spectrum mapping as claimed in claim 3, wherein: the step 3 specifically comprises the following steps:
step 3.1: selecting a set of distance variables from empirical half-variance data points
Figure QLYQS_33
As a variable of the clustering group, there is,
Figure QLYQS_37
is shown as
Figure QLYQS_39
Distance variables for the empirical half variance value data points; random selection
Figure QLYQS_34
Using non-repetitive samples as clustering center
Figure QLYQS_36
(ii) a By using
Figure QLYQS_40
Is shown as
Figure QLYQS_42
The number of points of the semi-variance data values within the group,
Figure QLYQS_31
is taken as
Figure QLYQS_35
Each group is aggregated into
Figure QLYQS_38
Then it is first
Figure QLYQS_41
Cluster center of group
Figure QLYQS_32
Comprises the following steps:
Figure QLYQS_43
；
step 3.2: calculating each half variance valueDistance variables in data points
Figure QLYQS_44
With each cluster center
Figure QLYQS_45
Euclidean distance of
Figure QLYQS_46
：
Figure QLYQS_47
，
In the formula (I), the compound is shown in the specification,
Figure QLYQS_48
is taken as
Figure QLYQS_49
；
Step 3.3: according to the calculated Euclidean distance, dividing each sample into a group with the nearest one in turn, and then recalculating the clustering center
Figure QLYQS_50
If, if
Figure QLYQS_51
Then will be
Figure QLYQS_52
Update the value of (2) to cluster center
Figure QLYQS_53
；
Step 3.4: repeating the step 3.2 and the step 3.3, iterating until the clustering center is not changed, ending the algorithm after convergence is reached, and outputting the final clustering grouping result
Figure QLYQS_54
；
Step 3.5: empirical half-variance valuesData points
Figure QLYQS_57
According to post-clustering partitioning
Figure QLYQS_59
The groups are averaged to obtain a semi-variance data point set after clustering grouping
Figure QLYQS_60
Wherein
Figure QLYQS_56
Representing the semi-variance value data points after clustering grouping,
Figure QLYQS_58
is shown as
Figure QLYQS_61
Distance variables for the grouped half variance value data points,
Figure QLYQS_62
is the first
Figure QLYQS_55
And the variance value of the grouped half variance value data points is variable.
5. The method for optimizing the layout of the sensor nodes for electromagnetic spectrum mapping as claimed in claim 4, wherein: the step 4 is specifically as follows:
grouping the data points according to the clustering
Figure QLYQS_63
Fitting to obtain a spatial global semi-variogram
Figure QLYQS_64
The optimization target is as follows:
Figure QLYQS_65
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_67
the representation of the objective function is shown as,
Figure QLYQS_70
is shown as
Figure QLYQS_72
The distance variable of the grouped half variance value data points of each cluster,
Figure QLYQS_68
denotes the first
Figure QLYQS_71
The variance of the grouped half variance value data points,
Figure QLYQS_73
is the parameter to be determined and is,
Figure QLYQS_74
is the value of the half-variance zero offset,
Figure QLYQS_66
is the half-variance scaling factor and is,
Figure QLYQS_69
is a distance scaling factor;
will be provided with
Figure QLYQS_75
Distance at which stability tends to occur
Figure QLYQS_76
Record as the correlation distance
Figure QLYQS_77
At this time
Figure QLYQS_78
Is the critical space variation value
Figure QLYQS_79
Determining the minimum number of sampling nodes according to the following equal interval constraint formula
Figure QLYQS_80
：
Figure QLYQS_81
，
In the formula (I), the compound is shown in the specification,
Figure QLYQS_82
is the fluctuation threshold.
6. The method for optimizing the layout of sensor nodes for electromagnetic spectrum mapping as claimed in claim 5, wherein: the step 5 specifically comprises the following steps:
step 5.1: initializing solution space X, search speed V and
Figure QLYQS_83
initial sampling node location:
Figure QLYQS_84
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_86
is the first in solution space
Figure QLYQS_89
The number of the solutions is one,
Figure QLYQS_91
is as follows
Figure QLYQS_87
The speed of the search of the individual solutions,
Figure QLYQS_90
is as follows
Figure QLYQS_92
The 1 st node position in the solution,
Figure QLYQS_93
is the first
Figure QLYQS_85
The search speed of the 1 st node in the solution,
Figure QLYQS_88
the position of the optimal initial sampling node in the initial solution space X is shown, and the initialization is represented by the function initialization;
step 5.2: computingPHalf-variance value of initial sampling node
Figure QLYQS_94
；
Step 5.3: calculating an optimization objective function:
Figure QLYQS_95
；
step 5.4: the solution space is updated and the global optimum is obtained according to the following principle:
Figure QLYQS_96
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_97
is the firstt+1 iteration timeqThe speed of the search of the individual solutions,
Figure QLYQS_98
is the firsttAfter the second iterationqThe optimal situation of the individual solutions is,
Figure QLYQS_99
is the firsttThe optimal node position situation after the sub-iteration,
Figure QLYQS_100
is as followstThe first of +1 iterationsqThe solution, function update, indicates the situation of obtaining the optimal node position from the solution space X and updating into Gb,
Figure QLYQS_101
it is the weight of the inertia that,
Figure QLYQS_102
、
Figure QLYQS_103
is a random number subject to uniform distribution, and the function max represents taking the maximum value;
step 5.5: repeating the step 5.2 to the step 5.4, iterating until the algorithm is finished after convergence, and outputting the optimized initial sampling node position
Figure QLYQS_104
。
7. The method for optimizing the layout of sensor nodes based on electromagnetic spectrum mapping as claimed in claim 6, wherein: the step 6 specifically comprises the following steps:
step 6.1: first, the weight coefficients are solved using the following formula:
Figure QLYQS_105
，
in the formula (I), the compound is shown in the specification,
Figure QLYQS_106
is the sampling node position
Figure QLYQS_107
And a non-sampled position
Figure QLYQS_108
The value of the half-variance of (c),
Figure QLYQS_109
is the coefficient to be solved;
and then calculating the kriging variance value at each unknown sampling position by using the following formula
Figure QLYQS_110
：
Figure QLYQS_111
；
Step 6.2: taking the position with the maximum Kriging variance value
Figure QLYQS_112
For the next sampled node location, and add the sampled node location set
Figure QLYQS_113
Updating the number of sampled nodes
Figure QLYQS_114
；
Step 6.3: repeating the step 6.1 and the step 6.2 until the total number of sampling nodes is reachedNAnd outputting the final sampling node position optimization result.
8. A sensor node layout optimization system oriented to electromagnetic spectrum mapping is characterized by comprising:
the acquisition equipment is used for carrying out mobile initialization acquisition on the frequency spectrum data of the area to be detected according to a random track or a uniform track to obtain initial frequency spectrum data;
the calculation module is used for pairing the sampling positions pairwise by using the obtained initial spectrum data, calculating a half variance value and obtaining an empirical half variance value data point; clustering and grouping the empirical half-variance value data points to obtain clustered and grouped half-variance value data points; according to the clustered and grouped half variance value data points, fitting to obtain a spatial global half-variation function, and according to the obtained spatial global half-variation function, determining the minimum number of sampling nodes;
the optimization module is used for optimizing the position of the initial sampling node based on a random optimization algorithm according to the minimum number of the sampling nodes; and performing sequential optimization on the positions of the rest sampling nodes based on the principle of maximum kriging variance according to the data acquired from the optimized initial sampling node position until the total number of the sampling nodes.
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