CN116008671A - Lightning positioning method based on time difference and clustering - Google Patents
Lightning positioning method based on time difference and clustering Download PDFInfo
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Abstract
The invention discloses a lightning positioning method based on time difference and clustering, which comprises the following steps: four-station combined positioning is carried out on lightning strike-back data based on the arrival time difference principle, initial lightning positioning data are obtained, an initial lightning positioning data set is formed, a k-means clustering algorithm is adopted to carry out clustering analysis on the initial lightning positioning data set to obtain k clustering cluster sets, and the cluster center with the largest lightning positioning data point in the k clustering cluster sets is selected to be output and used as a final lightning positioning result. And removing the locating outliers to obtain a final accurate locating value. The invention can effectively improve the lightning positioning precision and reduce the influence of factors such as data coarse difference, station network layout and the like on the lightning positioning effect.
Description
Technical Field
The invention belongs to the technical field of meteorological lightning positioning, and particularly relates to a lightning positioning method based on time difference and clustering.
Background
Lightning is an electrical discharge phenomenon in the atmosphere, often accompanied by strong convective weather processes such as hail and heavy rain. Lightning has the physical effects of strong current, electromagnetic radiation, hot high temperature and the like, so lightning stroke disasters are often caused, including huge damages to buildings, power equipment, information communication equipment, oil tank storage and transportation and the like. The monitoring and early warning of lightning and accurate positioning have important significance for reducing lightning disaster accidents.
The lightning positioning system utilizes the electromagnetic field characteristics of lightning strike back radiation to telemetering the occurrence time, position, intensity and polarity, and has been applied to the fields of weather, electric power, aerospace and the like. Positioning accuracy is a key technical index for evaluating lightning positioning systems. The time difference of arrival (Time Difference Of Arrival, TDOA) positioning method has become the mainstream lightning positioning method due to the high positioning accuracy. The method is to determine a positioning hyperbola based on the distance difference between each lightning detection station and a lightning radiation source, and determine the relative position of a lightning radiation source signal relative to each detection station by solving a hyperbola equation set.
The TDOA positioning method is based on time difference positioning, because the lightning electromagnetic field is interfered by the factors such as topography, earth conductivity and the like in the propagation process, the original lightning data for positioning can contain rough differences under the influence of various error factors, so that the TDOA algorithm positioning curve cannot intersect at one point, and the method has the problems of inaccurate positioning, poor anti-interference performance and the like.
Disclosure of Invention
Aiming at the problems, the invention provides a lightning positioning method based on time difference and clustering, which improves the lightning positioning precision and further reduces the influence of factors such as data rough difference, station network layout and the like on the lightning positioning effect.
The clustering algorithm can extract needed information from a large amount of fuzzy, noisy or random actual data, a TDOA four-station positioning method is adopted to carry out combined positioning on lightning strike-back data to obtain a preliminary lightning positioning result, then the k-means clustering algorithm is utilized to classify the obtained preliminary positioning result, outliers are removed to obtain a final lightning positioning result, and positioning accuracy and anti-interference capability are improved.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
in a first aspect, a lightning location method based on time difference and clustering is provided, including:
s1, acquiring lightning data information to be positioned, wherein the lightning data information comprises lightning strike-back data of the lightning signal to be positioned received by at least four lightning detection stations; the lightning strike-back data comprises site position information of a lightning detection station and lightning arrival time;
s2, combining the lightning data information to obtain a plurality of groups of lightning data, wherein each group of lightning data comprises lightning strike-back data of the lightning detection station which receives the lightning signal to be positioned;
s3, positioning lightning radiation sources of each group of lightning data by adopting a four-station time difference positioning method to obtain initial lightning positioning data; all the initial lightning location data constitute a lightning location data set;
s4, performing cluster analysis on all lightning positioning data in the lightning positioning data set by adopting a k-means clustering algorithm to obtain k cluster sets;
s5, selecting and outputting a cluster center n with the largest lightning location data point in the k cluster sets p And p is more than or equal to 1 and less than or equal to k, and is used as a final lightning positioning result.
In some embodiments, in step S1, the site location information is site longitude and latitude height information, and further includes converting the site longitude and latitude height information into coordinates x, y, z located under a space rectangular coordinate system;
the longitude L, the latitude B and the height H, e of the lightning detection station are the first eccentricity of an ellipsoid, and N is the radius of curvature of a mortise ring of the ellipsoid.
In some embodiments, step S2 comprises: traversing all lightning detection stations, and combining lightning data information of every four stations to obtain
And (3) group lightning data, wherein n is the total number of lightning detection stations.
In some embodiments, in step S3, the lightning radiation sources are respectively positioned by using a four-station time difference positioning method, so as to obtain lightning initial positioning data, including:
according to the TDOA positioning principle, the distance difference equation is as follows:
wherein the lightning is generated at the position (x, y, z), the generation time is t, and the coordinate position of the ith lightning detection station is (x i ,y i ,z i ) Time of arrival t i The method comprises the steps of carrying out a first treatment on the surface of the i=0 represents the primary station, i=1, 2,3 … n represents the secondary station; lightning to the main station (x) 0 ,y 0 ,z 0 ) Distance r of (2) 0 Distance to the ith secondary station is r i ，Δr i R is i And r 0 C is the propagation rate of the electromagnetic wave signal;
the number of the detecting stations is 4, i.e. i=0, 1,2,3; the formula (1) is changed as follows:
ri2-r02＝di-d0 (2)
wherein d is i ＝(x-x i ) 2 +(y-y i ) 2 +(z-z i ) 2 ,d 0 ＝(x-x 0 ) 2 +(y-y 0 ) 2 +(z-z 0 ) 2 ；
And (3) performing term transfer, squaring and finishing reduction on the formula (2) to obtain:
in formula (3), i=1, 2,3 is a system of nonlinear equations for (x, y, z, t), r 0 As a known quantity, a matrix expression is obtained:
AX＝B (4)
namely:
when the lightning detection stations are not deployed on the same plane, the rank of the coefficient matrix a is equal to 3, and the following is obtained:
X ＝ (A T A) -1 A T B (6)
taking X into equation (1) yields the equation:
ar 0 2 +br 0 +c＝0 (7)
solving a unitary quadratic equation (7) to obtain r 0 After numerical solution of (2), r is determined 0 And (3) reversely substituting the space rectangular coordinate system of the lightning radiation source into the space rectangular coordinate system (6).
When delta=b 2 When-4 ac > 0, r 0 There are two solutions r 01 、r 02 I.e. the hyperboloid has two points of intersection; r is (r) 0 Indicating that the distance must be a positive number, r 01 、r 02 Selecting a positive root as a positioning solution when positive is negative; r is (r) 01 、r 02 When the two are positive numbers, the positioning ambiguity is eliminated by adding azimuth auxiliary information;
when delta=b 2 -r when 4ac=0 0 There is a unique solution and no problem of positioning ambiguity.
In some embodiments, step S4, performing cluster analysis on all lightning location data in the lightning location data set using a k-means clustering algorithm, includes:
s41, randomly extracting k objects in the lightning location data set X to form a first training subset T 1 (T 2 E, X), wherein K is less than n, constructing a local model containing K clusters by using a K-means algorithm to obtain K preliminary cluster centers;
s42, extracting C from X randomly on the basis of the first time 2 Each is other than T 1 Subjects other than the subject form training subset 2T 2 (T 2 ∈X-T 1 ) The method comprises the steps of carrying out a first treatment on the surface of the T is calculated by using K-means algorithm 2 Adding the objects in the plurality of clusters into k clusters, and updating the cluster center of each cluster; similarly, iterating the steps S41 to S42 repeatedly until reaching the preset iteration stop condition to obtain a final set S= { S of k class clusters 1 ，S 2 ，S 3 ，…，S k }。
Further, in some embodiments, step S4 comprises:
randomly selecting k lightning locations in a lightning location data set XThe data sample points are taken as initial clustering centers and marked as n (0) ＝(n 1 (0) ，…，n l (0) ，…，n k (0) ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein k is less than n, n is the total number of lightning detection stations; wherein in the m-dimensional vector lightning location data set X, the sample point X i ∈X，x i ＝(x 1i ，x 2i ，…，x mi ) T ；
For a fixed cluster center n (t) ＝(n 1 (t) ，…，n l (t) ，…，n k (t) ) Wherein n is l (t) Is a cluster S l Clustering the lightning location data sample points according to the distance between the sample points and the clustering center:
calculating the distance between each sample point and the center of the class cluster, and enabling each lightning positioning data sample point to belong to the class cluster with the smallest distance according to the calculated distance to obtain a set S= { S of k class clusters 1 ，S 2 ，S 3 ，…，S k Generating a preliminary clustering result C (t) ；
For clustering result C (t) Calculating the sample mean value u of each current class cluster i ：
Wherein x is i Locating data sample points, s, for lightning in category l (i) Is x i Belonging to the category, wherein z is the total number of sample points in each category cluster; taking the mean value as a new clustering center u (t+1) ＝(u 1 (t+1) ,…,u l (t+1) ,…,u k (t+1) )；
Defining the sum of distances between lightning location data sample points and their belonging class centers as a final loss function W (C):
wherein the method comprises the steps of
A cluster center of the first cluster; />
I (C (I) =l) represents an indicator function having a value of 0 or 1; the function W (C) represents the similarity degree of sample points in the same class of clusters; k-means clustering translates into a solution to an optimization problem:
outputting the final clustering result C if the iteration converges or the iteration stop condition is satisfied, i.e. the loss function W (C) reaches the minimum * ＝C (t) Otherwise, continuing the iteration, enabling the iteration times t=t+1 and returning to recalculate the loss function.
In some embodiments, step S5 further comprises: converting the lightning positioning result from the x, y and z coordinates positioned under the space rectangular coordinate system into longitude and latitude height information under the space geodetic coordinate system; the solving formula of longitude L, latitude B and altitude H in the WGS-84 ellipsoid model is as follows:
wherein a and b are the major and minor half shafts of an ellipsoid respectively, a=6378.137 km, b= 6356.752km; e is the first eccentricity of the ellipsoid, and N is the radius of curvature of the unitary mortise ring of the ellipsoid.
In a second aspect, the invention provides a lightning positioning device based on time difference and clustering, which comprises a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate in accordance with the instructions to perform the steps of the method according to the first aspect.
In a third aspect, the present invention provides a storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the method of the first aspect.
According to the invention, a TDOA four-station positioning method is adopted to carry out combined positioning on lightning strike-back data to obtain a lightning positioning result, then a k-means clustering algorithm is utilized to classify the obtained positioning result and reject outliers to obtain a final positioning result, and the problems of inaccurate positioning, poor anti-interference performance and the like in the traditional method are solved. Finally, the test proves that the method has better positioning effect.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a lightning positioning method based on time difference and clustering. The TDOA positioning method is based on time difference positioning, because the lightning electromagnetic field is interfered by the factors such as topography, earth conductivity and the like in the propagation process, the original lightning data for positioning can contain rough differences under the influence of various error factors, so that the TDOA algorithm positioning curve cannot intersect at one point, and the method has the problems of inaccurate positioning, poor anti-interference performance and the like. The clustering algorithm can extract needed information from a large amount of fuzzy, noisy or random actual data, and a lightning positioning method based on the clustering algorithm is provided. And then, classifying the obtained positioning result by using a k-means clustering algorithm, removing outliers to obtain a final positioning result, and improving the positioning accuracy and the anti-interference capability.
Drawings
FIG. 1 is a schematic diagram of TDOA location according to an embodiment of the invention.
Fig. 2 is a schematic view of a lightning location system arrangement according to an embodiment of the invention.
FIG. 3 is a flow chart of a lightning location method according to an embodiment of the invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples. The following examples are only for more clearly illustrating the technical aspects of the present invention, and are not intended to limit the scope of the present invention.
In the description of the present invention, the meaning of a number is one or more, the meaning of a number is two or more, and greater than, less than, exceeding, etc. are understood to exclude the present number, and the meaning of a number is understood to include the present number. The description of the first and second is for the purpose of distinguishing between technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, the descriptions of the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Example 1
A lightning positioning method based on time difference and clustering comprises the following steps:
s1, acquiring lightning data information to be positioned, wherein the lightning data information comprises lightning strike-back data of the lightning signal to be positioned received by at least four lightning detection stations; the lightning strike-back data comprises site position information of a lightning detection station and lightning arrival time;
s2, combining the lightning data information to obtain a plurality of groups of lightning data, wherein each group of lightning data comprises lightning strike-back data of the lightning detection station which receives the lightning signal to be positioned;
s3, positioning lightning radiation sources of each group of lightning data by adopting a four-station time difference positioning method to obtain initial lightning positioning data; all the initial lightning location data constitute a lightning location data set;
s4, performing cluster analysis on all lightning positioning data in the lightning positioning data set by adopting a k-means clustering algorithm to obtain k cluster sets;
s5, selecting and outputting a cluster center n with the largest lightning location data point in the k cluster sets p And p is more than or equal to 1 and less than or equal to k, and is used as a final lightning positioning result.
S4, clustering analysis is carried out on all lightning positioning data in the lightning positioning data set by adopting a k-means clustering algorithm, wherein the clustering analysis comprises the following steps:
s41, randomly extracting k objects in the lightning location data set X to form a first training subset T 1 (T 2 E, X), wherein K is less than n, constructing a local model containing K clusters by using a K-means algorithm to obtain K preliminary cluster centers;
s42, extracting C from X randomly on the basis of the first time 2 Each is other than T 1 Subjects other than the subject form training subset 2T 2 (T 2 ∈X-T 1 ) The method comprises the steps of carrying out a first treatment on the surface of the T is calculated by using K-means algorithm 2 Adding the objects in the plurality of clusters into k clusters, and updating the cluster center of each cluster; similarly, iterating the steps S41 to S42 repeatedly until reaching the preset iteration stop condition to obtain a final set S= { S of k class clusters 1 ,S 2 ,S 3 ,…,S k }。
In some embodiments, as shown in FIG. 1, which is a schematic diagram of TDOA location, TDOA is a wireless location method that requires three or more lightning detection stations of known location coordinates for location. In fig. 1 there are three lightning detection stations A, B, C, S being the lightning occurrence locations. Let the distance of the lightning radiation source S to the detection station A, B, C be r, respectively 1 、r 2 And r 3 In practice the distance is unknown. The lightning detection stations A and B can measure the time of the electromagnetic wave signal emitted by the lightning strike-back radiation source S reaching the respective detection stations, the two stations have time difference, and the distance difference r between the two stations can be determined by multiplying the time difference by the propagation speed of the lightning signal 21 ＝r 2 -r 1 Forms a distance difference r with the detecting station A, B as a focus 21 Hyperbola L as long axis 2 The lightning occurs on the hyperbolaIs a certain point of the above. The detection station C and the lightning detection station B can also form another positioning hyperbola L 1 The intersection point S of the two hyperbolas is the position of the lightning radiation source.
As shown in fig. 2, a schematic view of a lightning location system is shown. Assuming that the lightning occurs at the position S (x, y, z), the time of occurrence is t, and the coordinate position of the ith lightning detection station is (x i ,y i ,z i ) Time of arrival t i . i=0 represents the primary station, and i=1, 2,3 … n represents the secondary station.
In some embodiments, as shown in fig. 3, fig. 3 is a lightning location flow chart, comprising:
1) The lightning detection station receives lightning strike-back data X of the same lightning signal;
2) Combining all lightning detection stations every four stations, at most, can obtain
A seed combination;
3) The lightning radiation source is respectively positioned by using a four-station time difference positioning method, so that a lightning positioning data set X= { p can be obtained 1 ,p 2 ,p 3 ,…,p m }；
4) The k-means clustering algorithm is adopted to perform clustering analysis on all positioning data, data points which do not contain noise or have smaller noise can be clustered into one type due to better aggregative property, data points which have larger noise are clustered into another type or types, and k types are formed: s is(s) 1 、s 2 、s 3 …、s k ；
5) Selecting and outputting k cluster sets { s } 1 ,s 2 ,s 3 ,…,s k The cluster center n with the most lightning location data points p P is more than or equal to 1 and less than or equal to k, and the p is taken as a final lightning positioning result to exclude interference positioning points in the positioning result;
6) And analyzing the positioning performance of the algorithm according to the actual positioning result.
According to the TDOA positioning principle, the distance difference equation is as follows:
wherein the lightning is generated at the position (x, y, z), the generation time is t, and the coordinate position of the ith lightning detection station is (x i ,y i ,z i ) Time of arrival t i The method comprises the steps of carrying out a first treatment on the surface of the i=0 represents the primary station, i=1, 2,3 … n represents the secondary station; lightning to the main station (x) 0 ,y 0 ,z 0 ) Distance r of (2) 0 Distance to the ith secondary station is r i ，Δr i R is i And r 0 C is the propagation rate of the electromagnetic wave signal;
if the number of the detecting stations is 4, i.e. i=0, 1,2,3; the formula (1) is changed as follows:
ri2-r02＝di-d0 (2)
wherein d is i ＝(x-x i ) 2 +(y-y i ) 2 +(z-z i ) 2 ,d 0 ＝(x-x 0 ) 2 +(y-y 0 ) 2 +(z-z 0 ) 2 ；
And (3) performing term transfer, squaring and finishing reduction on the formula (2) to obtain:
in formula (3), i=1, 2,3 is a system of nonlinear equations for (x, y, z, t), r 0 As a known quantity, a matrix expression is obtained:
AX＝B (4)
when the lightning detection stations are not deployed on the same plane, the rank of the coefficient matrix a is equal to 3, and the following is obtained:
X ＝ (A T A) -1 A T B (6)
taking X into equation (1) yields the equation:
ar 0 2 +br 0 +c＝0 (7)
solving a unitary quadratic equation (7) to obtain r 0 After numerical solution of (2), r is determined 0 And (3) reversely substituting the space rectangular coordinate system of the lightning radiation source into the space rectangular coordinate system (6).
Further, the method further comprises the following steps: and converting the obtained coordinates x, y and z positioned under the space rectangular coordinate system of the lightning radiation source into longitude and latitude height information under the space geodetic coordinate system.
The lightning strike-back data recorded by the lightning positioning system is longitude, latitude and altitude information (space geodetic coordinate system) of each lightning detection station, and the space geodetic coordinate system and the space rectangular coordinate system need to be converted.
Since the real shape of the earth's surface is not a perfect regular sphere, the WGS-84 ellipsoid model is used as a lightning location reference model. The solving formula of longitude L, latitude B and altitude H in the WGS-84 ellipsoid model is as follows:
wherein a and b are the major and minor half shafts of the ellipsoid respectively, a=6378.137 km, and b= 6356.752km. e is the first eccentricity of the ellipsoid, and N is the radius of curvature of the unitary mortise ring of the ellipsoid.
The solving formula of the coordinates x, y and z positioned under the space rectangular coordinate system under the same reference is as follows:
in summary, after the lightning positioning system records the longitude and latitude height information and the arrival time of the station receiving lightning strike back data, coordinate transformation is carried out through the equation (9), and the distance r is obtained through the calculation of the equation (7) 0 Is solved by (1), r 0 The position of the lightning radiation source under the space rectangular coordinate system can be obtained by the carrying-in type (6)And finally obtaining the longitude and latitude high position of lightning through the formula (8).
In some embodiments, equation (7) may appear ambiguous of the solution:
when delta=b 2 When-4 ac > 0, r 0 There are two solutions r 01 、r 02 I.e. the hyperboloid has two points of intersection; r is (r) 0 Indicating that the distance must be a positive number, r 01 、r 02 Selecting a positive root as a positioning solution when positive is negative; r is (r) 01 、r 02 When the two are positive numbers, the positioning ambiguity is eliminated by adding azimuth auxiliary information;
Δ＝b 2 -r when 4ac=0 0 The method has unique solutions and does not have the problem of positioning ambiguity;
Δ＝b 2 -r when 4ac < 0 0 Without solution, the lightning radiation source cannot be located.
In some embodiments, step 4) comprises the steps of:
the lightning location sample centroid is first initialized. In the m-dimensional vector lightning location data set X, sample element X i ∈X，x i ＝(x 1i ,x 2i ,…,x mi ) T . Randomly selecting k (k < n) lightning location data sample points from the set X as initialized clustering center points in the initial iteration, and marking as n (0) ＝(n 1 (0) ,…,n l (0) ,…,n k (0) )。
For a fixed cluster center n (t) ＝(n 1 (t) ,…,n l (t) ,…,n k (t) ) Wherein n is l (t) Is a cluster S l And clustering the lightning location data sample points according to the distance between the sample points and the initial clustering center. For sample point x i And the clustering center point n j The minpoint distance between them is:
the Euclidean distance is used to calculate the distance of each lightning location data sample point in the lightning data set X to the cluster center. P=2 in formula (10) can be expressed as a euclidean distance:
calculating the distance from each sample point to the center of the class cluster according to the formula (11), and enabling each lightning location data sample point to belong to the class cluster with the smallest distance according to the calculated distance, so as to obtain a set S= { S of k class clusters 1 ,S 2 ,S 3 ,…,S k Generating a preliminary clustering result C (t) 。
For clustering result C (t) Calculating the sample mean value of each current class cluster:
wherein x is i For lightning data sample points, s, in category l (i) Is x i Belonging to the class, z is the total number of sample points in each class cluster. Taking the mean value as a new clustering center point u (t+1) ＝(u 1 (t+1) ,…,u l (t+1) ,…,u k (t+1) ). Defining the sum of distances between lightning sample points and class centers to which the lightning sample points belong as a final loss function:
wherein the method comprises the steps of
Is the centroid of the first class (i.e., the cluster center point). />
I (C (I) =l) represents an indicator function having a value of 0 or 1. The function W (C) represents the degree of similarity of sample points in the same class of clusters. k-means clustering translates into a solution to an optimization problem:
outputting the final clustering result C if the iteration converges or the iteration stop condition is satisfied, i.e., the sum of squares of errors W (C) in equation (13) reaches a minimum * ＝C (t) Otherwise, continuing the iteration, and enabling the iteration times t=t+1 to return to the formula (14) for recalculation.
The invention provides a lightning positioning method based on time difference and clustering, and the method and the way for realizing the technical scheme are numerous, the above is only a preferred embodiment of the invention, and it should be pointed out that a plurality of improvements and modifications can be made to those skilled in the art without departing from the principle of the invention, and the improvements and modifications are also considered as the protection scope of the invention. The components not explicitly described in this embodiment can be implemented by using the prior art.
Example 2
In a second aspect, the present embodiment provides a lightning location device based on time difference and clustering, including a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is operative according to the instructions to perform the steps of the method according to embodiment 1.
Example 3
In a third aspect, the present embodiment provides a storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the method described in embodiment 1.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The foregoing is only a preferred embodiment of the invention, it being noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.
Claims (10)
1. A lightning location method based on time difference and clustering, comprising:
s1, acquiring lightning data information to be positioned, wherein the lightning data information comprises lightning strike-back data of the lightning signal to be positioned received by at least four lightning detection stations; the lightning strike-back data comprises site position information of a lightning detection station and lightning arrival time;
s2, combining the lightning data information to obtain a plurality of groups of lightning data, wherein each group of lightning data comprises lightning strike-back data of the lightning detection station which receives the lightning signal to be positioned;
s3, positioning lightning radiation sources of each group of lightning data by adopting a four-station time difference positioning method to obtain initial lightning positioning data; all the initial lightning location data constitute a lightning location data set;
s4, performing cluster analysis on all lightning positioning data in the lightning positioning data set by adopting a k-means clustering algorithm to obtain k cluster sets;
and S5, selecting and outputting the cluster center with the largest lightning location data point in the k cluster sets as a final lightning location result.
2. The method according to claim 1, wherein in step S1, the station position information is station longitude and latitude information, and further comprising converting the station longitude and latitude information into coordinates x, y, z located under a space rectangular coordinate system;
the longitude L, the latitude B and the height H, e of the lightning detection station are the first eccentricity of an ellipsoid, and N is the radius of curvature of a mortise ring of the ellipsoid.
3. The method according to claim 1, wherein step S2 comprises: traversing all lightning detection stations, and combining lightning data information of every four stations to obtain
And (3) group lightning data, wherein n is the total number of lightning detection stations.
4. The method according to claim 1, wherein in step S3, the lightning radiation sources are respectively positioned by using a four-station time difference positioning method to obtain lightning initial positioning data, including:
according to the TDOA positioning principle, the distance difference equation is as follows:
wherein the lightning is generated at the position (x, y, z), the generation time is t, and the coordinate position of the ith lightning detection station is (x i ,y i ,z i ) Time of arrival t i The method comprises the steps of carrying out a first treatment on the surface of the i=0 represents the primary station, i=1, 2,3 … n represents the secondary station; lightning to the main station (x) 0 ,y 0 ,z 0 ) Distance r of (2) 0 Distance to the ith secondary station is r i ，Δr i R is i And r 0 C is the propagation rate of the electromagnetic wave signal;
the number of the detecting stations is 4, i.e. i=0, 1,2,3; the formula (1) is changed as follows:
r i 2 -r 0 2 ＝d i -d 0 (2)
wherein d is i ＝(x-x i ) 2 +(y-y i ) 2 +(z-z i ) 2 ,d 0 ＝(x-x 0 ) 2 +(y-y 0 ) 2 +(z-z 0 ) 2 ；
And (3) performing term transfer, squaring and finishing reduction on the formula (2) to obtain:
in formula (3), i=1, 2,3, a system of nonlinear equations for (x, y, z, t), will r 0 As a known quantity, a matrix expression is obtained:
AX＝B (4)
namely:
when the lightning detection stations are not deployed on the same plane, the rank of the coefficient matrix a is equal to 3, and the following is obtained:
X＝(A T A) -1 A T B (6)
taking X into equation (1) yields the equation:
ar 0 2 +br 0 +c＝0 (7)
solving a unitary quadratic equation (7) to obtain r 0 After numerical solution of (2), r is determined 0 And (3) reversely substituting the space rectangular coordinate system of the lightning radiation source into the space rectangular coordinate system (6).
5. The method of claim 4, wherein the step of determining the position of the first electrode is performed,
when delta=b 2 When-4 ac > 0, r 0 There are two solutions r 01 、r 02 I.e. the hyperboloid has two points of intersection; r is (r) 0 Indicating that the distance must be a positive number, r 01 、r 02 Selecting a positive root as a positioning solution when positive is negative; r is (r) 01 、r 02 When the two are positive numbers, the positioning ambiguity is eliminated by adding azimuth auxiliary information;
when delta=b 2 -r when 4ac=0 0 There is a unique solution and no problem of positioning ambiguity.
6. The method according to claim 1, wherein step S4 of performing a cluster analysis on all lightning location data in the lightning location data set using a k-means clustering algorithm comprises:
s41, randomly extracting k objects in the lightning location data set X to form a first training subset T 1 (T 1 E X), where k < n, liConstructing a local model containing K clusters by using a K-means algorithm to obtain K preliminary cluster centers;
s42, extracting C from X randomly on the basis of the first time 2 Each is other than T 1 Subjects other than the subject form training subset 2T 2 (T 2 ∈X-T 1 ) The method comprises the steps of carrying out a first treatment on the surface of the T is calculated by using K-means algorithm 2 Adding the objects in the plurality of clusters into k clusters, and updating the cluster center of each cluster; similarly, iterating the steps S41 to S42 repeatedly until reaching the preset iteration stop condition to obtain a final set S= { S of k class clusters 1 ,S 2 ,S 3 ,…,S k }。
7. The method of claim 6, wherein step S4 comprises:
randomly selecting k lightning positioning data sample points from the lightning positioning data set X as initial clustering centers, and marking the initial clustering centers as n (0) ＝(n 1 (0) ,…,n l (0) ,…,n k (0) ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein k is less than n, n is the total number of lightning detection stations; wherein in the m-dimensional vector lightning location data set X, the sample point X i ∈X，x i ＝(x 1i ,x 2i ,…,x mi ) T ；
For a fixed cluster center n (t) ＝(n 1 (t) ,…,n l (t) ,…,n k (t) ) Wherein n is l (t) Is a cluster S l Clustering the lightning location data sample points according to the distance between the sample points and the clustering center:
calculating the distance between each sample point and the center of the class cluster, and enabling each lightning positioning data sample point to belong to the class cluster with the smallest distance according to the calculated distance to obtain a set S= { S of k class clusters 1 ,S 2 ,S 3 ,…,S k Generating a preliminary clustering result C (t) ；
For clustering result C (t) Calculating the sample mean value u of each current class cluster l ：
Wherein x is i Locating data sample points, s, for lightning in category l (i) Is x i Belonging to the category, wherein z is the total number of sample points in each category cluster; taking the mean value as a new clustering center u (t+1) ＝(u 1 (t+1) ,…,u l (t+1) ,…,u k (t+1) )；
Defining the sum of distances between lightning location data sample points and their belonging class centers as a final loss function W (C):
wherein the method comprises the steps of
A cluster center of the first cluster; />
I (C (I) =l) represents an indicator function having a value of 0 or 1; the function W (C) represents the similarity degree of sample points in the same class of clusters; k-means clustering translates into a solution to an optimization problem:
outputting the final clustering result C if the iteration converges or the iteration stop condition is satisfied, i.e. the loss function W (C) reaches the minimum * ＝C (t) Otherwise, continuing the iteration, enabling the iteration times t=t+1 and returning to recalculate the loss function.
8. The method according to claim 1, wherein step S5 further comprises: converting the lightning positioning result from the x, y and z coordinates positioned under the space rectangular coordinate system into longitude and latitude height information under the space geodetic coordinate system; the solving formula of longitude L, latitude B and altitude H in the WGS-84 ellipsoid model is as follows:
wherein a and b are the major and minor half shafts of an ellipsoid respectively, a=6378.137 km, b= 6356.752km; e is the first eccentricity of the ellipsoid, and N is the radius of curvature of the unitary mortise ring of the ellipsoid.
9. A lightning positioning device based on time difference and clustering, which is characterized by comprising a processor and a storage medium;
the storage medium is used for storing instructions;
the processor being operative according to the instructions to perform the steps of the method according to any one of claims 1 to 8.
10. A storage medium having stored thereon a computer program, which when executed by a processor performs the steps of the method according to any of claims 1 to 8.
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| CN116430127A (en) * | 2023-06-14 | 2023-07-14 | 云南电力试验研究院(集团)有限公司 | Method for reducing lightning positioning ground flash error |
| CN116500703A (en) * | 2023-06-28 | 2023-07-28 | 成都信息工程大学 | Thunderstorm monomer identification method and device |
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| CN116430127A (en) * | 2023-06-14 | 2023-07-14 | 云南电力试验研究院(集团)有限公司 | Method for reducing lightning positioning ground flash error |
| CN116430127B (en) * | 2023-06-14 | 2023-10-20 | 云南电力试验研究院(集团)有限公司 | Method for reducing lightning positioning ground flash error |
| CN116500703A (en) * | 2023-06-28 | 2023-07-28 | 成都信息工程大学 | Thunderstorm monomer identification method and device |
| CN116500703B (en) * | 2023-06-28 | 2023-09-01 | 成都信息工程大学 | Thunderstorm monomer identification method and device |
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