CN111929643B - Transform domain electromagnetic situation perception and radiation source positioning method - Google Patents
Transform domain electromagnetic situation perception and radiation source positioning method Download PDFInfo
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Abstract
The invention provides an electromagnetic situation perception and radiation source positioning method based on a transform domain, which utilizes Fourier transform to realize conversion processing between two-dimensional domains, transforms a space-time domain to a frequency-wavenumber domain and realizes estimation of the phase and space position relation of vacant small sample data. And then the inverse transformation processing of the vacant small sample data is realized through two-dimensional inverse Fourier transform. And finally, performing superposition fitting with the original acquired data, restoring and reconstructing a complete and comprehensive electromagnetic situation, and deducing the position information of the radiation source. The method overcomes the defects of gradually increased error, increasingly complicated calculation, low filling efficiency and the like when a nearest neighbor interpolation method, a spline interpolation method, a discrete smooth interpolation method and a bilinear interpolation method deal with large-area data vacancy, and overcomes the defects of large calculated amount and relatively poor real-time performance of a kriging method; the inverse distance weighting method results in poor morphological overlap ratio and the like.
Description
Technical Field
The invention belongs to the technical field of electromagnetic wave detection, and particularly relates to a transform domain electromagnetic situation perception and radiation source positioning method.
Background
In view of the current technical means, the electromagnetic data acquired during detection aiming at the electromagnetic signal coverage condition often has a large-area vacancy, so that the full coverage perception of the electromagnetic situation of the target area is difficult to realize.
The classic data estimation and filling methods include nearest neighbor interpolation, spline interpolation, discrete smooth interpolation and bilinear interpolation studied in "estimating cursor mass loss on Franz Josef Land, Russian arc" and "Region-wide cursor mass partitions and area changes" for the central tie token between 1975and 1999using Hexagon KH-9image ", which are generally applied to the fields of image expansion and gridding resampling; methods such as a Kriging method and an Inverse distance weighting method researched in "Spatial variance of geological changes in the Swiss Alps associated from two digital elevation models" and "Inverse Spatial component analysis for geographic subsurface data interpretation" mainly realize estimation and filling of geological data, and are also applied to filling of data gaps.
The data estimation and filling methods with more outstanding performance are the kriging method and the inverse distance weighting method.
The kriging method is implemented as the attached figure 1, firstly, the distance between every two measured data points and the value of variance are calculated; secondly, a curve is searched to fit the distance and the half variance as much as possible, and the solution of the distance to the half variance is realized; thirdly, solving the half variance between the known points and the half variance between the point to be estimated and all the known points; then, solving the optimal coefficient of the target function; and finally, carrying in an objective function to obtain the value of the estimation point.
The flow of the inverse distance weighting method is shown in fig. 2, and the inverse distance weighting method is simple to implement. Firstly, obtaining a sample point; secondly, calculating the distance between all sample points and the point to be estimated; then, calculating the weights of all the sample points, wherein the weights are in direct proportion to the nth power of the distance; and finally, estimating the point to be estimated.
In summary, the prior art has the following disadvantages:
the nearest neighbor interpolation, spline interpolation, discrete smooth interpolation and bilinear interpolation studied in the "accumulating glacier mass loss on Franz Josef Land, Russian arc" and "Region-wide glacier mass headers and areas changes" all use peripheral data to calculate and process the vacant data, and when dealing with large-area data vacancy, there are disadvantages of increasing error, increasing computational complexity and low filling efficiency, etc. as the estimation advances inwards, the method of interpolation, spline interpolation, discrete smooth interpolation and bilinear interpolation is more convenient and more efficient. Geological data is estimated and filled by methods such as a Kriging method and an Inverse distance weighting method researched in "Spatial variance of geological changes in the Swiss Alps influenced from two digital elevation models" and "Inverse Spatial principal component analysis for geographic summary data interpolation", but the Kriging method is a processing method with higher precision, the calculated amount of the method is larger, the real-time performance is relatively poor, and the result form obtained by the Inverse distance weighting method is not as good as the Kriging method, especially the edge smoothness is not enough.
Disclosure of Invention
In order to solve the technical problem, the invention provides a transform domain electromagnetic situation sensing and radiation source positioning method, which is characterized by comprising the following steps:
the method comprises the following steps that firstly, an omnidirectional antenna of each sensing node randomly deployed in a target area is used for detecting electromagnetic signals in a sensitivity coverage range, and electromagnetic signal intensity data are obtained;
secondly, sending the detection data of each distributed sensing node to a data center for collection and storage, and processing the detection data by computing equipment of the data center to obtain an initial electromagnetic situation coverage map;
determining a cutoff wave value, determining a sampling matrix and iteration times, and predicting the data of the empty position based on the detected data; which comprises the substeps of
Step 3.1, determining a cutoff wave value k,
step 3.2, two-dimensional Fourier transform is carried out to the wave number domain and low-pass filtering is carried out,
step 3.3, performing two-dimensional Fourier inverse transformation to generate electromagnetic signal intensity data,
step 3.4, updating the filtering threshold value by using the replacement original data, executing N times of iteration on the data of the vacancy position points, solving predicted data,
filling the existing vacant positions with the prediction data, and further generating a complete electromagnetic situation coverage map capable of reflecting the real situation;
and step five, extracting the position of the radiation source.
Further, the second step further includes zero filling for the vacant positions and edge expanding for the data.
Further, the first step comprises: s is a vacancy sampling matrix for original vacancy data;
in which electromagnetic signal strength data d to be processed0And x and y are respectively the abscissa and the ordinate of the point to be estimated.
Further, in the substep 3.1, wherein T isk(u, v) conforms to the expression:
where (u, v) represents the actual coordinate value of the point to be estimated, and r represents the cut-off parameter T of the circular low-pass filterkDenotes a circular low-pass filter with a cut-off wavenumber k, where k is 1,2, … … ke，keThe final cut-off wavenumber.
Further, in step three, the space domain electromagnetic signal intensity data matrix d after the nth iterationnExpression:
dn(x,y)＝F-1{Tk[F(d0(x,y)+S(x,y)dn-1(x，y)]}n=1，2，3…，N
wherein, TkDenotes a circular low-pass filter with a cut-off wavenumber k, where k is 1,2, … … ke，keFinal cut-off wavenumber; n is the number of iterations, and N is the total number of iterations; f and F-1Representing the fourier transform and the inverse transform, respectively.
Preferably, the cut-off wave number is f (k) of a quadratic polynomial fitted by a least square method, and L is the cut-off wave number, and the determination method is as follows:
where row and column are rows and columns of the sampling matrix, respectively, and fix () represents an integer closest to the number in parentheses.
By adopting the cooperative sensing mechanism, the obtained energy image of the incomplete data is transformed from a space domain to a wave number domain for processing, and a complete electromagnetic signal equal-strength line situation graph of a target area is extracted through repeated iteration and filling estimation of the incomplete data, so that the full-coverage sensing of the electromagnetic situation under the condition of small sample incomplete data is realized, and the position of a radiation source can be extracted.
Drawings
FIG. 1 is a Critical method implementation flow;
FIG. 2 is a flow chart of an implementation of an inverse distance weighting method;
FIG. 3 is an electromagnetic situational awareness and radiation source localization method architecture;
fig. 4 is a data prediction and padding process.
Detailed Description
From the perspective of actual requirements and application, the electromagnetic situation perception and radiation source positioning method based on the transform domain is designed, the Fourier transform is mainly utilized to realize conversion processing between two-dimensional domains, namely, a space-time domain is transformed to a frequency-wavenumber domain, and estimation of the phase and space position relation of vacant small sample data is realized. And then the inverse transformation processing of the vacant small sample data is realized through two-dimensional inverse Fourier transform. And finally, performing superposition fitting with the original acquired data, restoring and reconstructing a complete and comprehensive electromagnetic situation, and deducing the position information of the radiation source.
The method mainly solves the problems that the nearest neighbor interpolation method, the spline interpolation method, the discrete smooth interpolation method and the bilinear interpolation method have the defects of gradually increased errors, increasingly complicated calculation, low filling efficiency and the like when the data vacancy of a large area is met, and the defects that the real-time performance is relatively poor due to the large calculated amount of the kriging method, the shape coincidence degree of the result of the inverse distance weighting method is poor, particularly the edge smoothness is not enough and the like.
The following detailed description of the present invention will be made with reference to fig. 3 and 4.
Electromagnetic situation perception and radiation source positioning method framework
When electromagnetic situation coverage detection and radiation source positioning are carried out, due to the fact that the situations that the terrain is complex or the area of the area to be detected is large and the like exist in the area to be detected, the situation that the electromagnetic signal coverage situation is comprehensively detected is often difficult to a certain extent. The method combines electromagnetic data cooperatively sensed by distributed sensing nodes with an electromagnetic situation based on a transform domain and a radiation source positioning method, and the architecture of the method is shown in FIG. 3.
Each sensing node randomly deployed in the target area can detect electromagnetic signals in the sensitivity coverage range by using the omnidirectional antenna of the sensing node to acquire electromagnetic signal intensity data. The detection data of each distributed sensing node is firstly gathered to the data center, and the data center processes the detection data to preliminarily obtain an electromagnetic situation coverage map. Due to the fact that the coverage range of each distributed sensing node is limited and the various adverse factors are existed, a large area of vacancy exists in the detected electromagnetic signal data, that is, the preliminarily obtained electromagnetic situation coverage map is often not in accordance with the actual coverage situation. Therefore, the empty positions must be predicted and filled up based on the detected data, and finally a complete electromagnetic situation coverage map reflecting the real situation is generated.
And (II) the electromagnetic situation perception and radiation source positioning method realizes the most critical part of the electromagnetic situation perception and radiation source positioning method to be data prediction and filling processing, and the basic process is as follows.
Setting electromagnetic signal intensity data d to be processed0S is a vacancy sampling matrix for original vacancy data, and x and y are respectively an abscissa and an ordinate of a point to be estimated:
thus obtaining the space domain electromagnetic signal intensity data matrix d after the nth iterationn：
dn(x，y)＝F-1{Tk[F(d0(x，y)+S(x，y)dn-1(x，y)]}n＝1，2，3，…，N (2)
TkDenotes a circular low-pass filter with a cut-off wavenumber k, where k is 1,2, … … ke，keFinal cut-off wavenumber; n is the number of iterations, and N is the total number of iterations; f and F-1Representing the fourier transform and the inverse transform, respectively.
Wherein T iskComprises the following steps:
(u, v) represents the actual coordinate value of the point to be estimated, and r represents the cutoff parameter of the circular low-pass filter.
Since the electromagnetic signal intensity data is greatly influenced by the terrain, the above formula needs to be improved to better fit the real situation:
dn(x，y)＝F-1{Tk[F(d0(x，y)+S(x，y)dn-1(x，y)]}n＝1，2，3，L，N-1 (4)
dN(x，y)＝d0(x，y)+S(x，y)dN-1(x，y) (5)
in the formula, N is iteration frequency, and N is total iteration frequency; the remaining parameters are the same as in equation (2).
Particularly, at the coverage edge of the electromagnetic signal intensity data, because the influence of the terrain and topography is more obvious, the obtained electromagnetic signal intensity data needs to be subjected to edge expansion processing at first, and then is intercepted after a complete electromagnetic signal intensity coverage map is generated.
The data prediction and filling processing flow in the electromagnetic situation perception and radiation source positioning method based on the transform domain is shown in fig. 4.
The energy of the electromagnetic signal has no turning point with obvious energy reduction in the wave number domain, namely, the radial average power spectrum of the vacancy data has no obvious inflection point. The cutoff wavenumber determination method of fig. 4 is as follows, in conjunction with the data characteristic of electromagnetic signal intensity.
And fitting the scatter data according to the radial average power spectrum by using a least square method, wherein the position of an inflection point is the minimum wave number corresponding to the second derivative of the curve being 0 and the third derivative being not 0. In order to calculate the second and third derivatives of the curve conveniently, polynomial curve fitting of a least square method is carried out according to the calculated radial average power spectrum, and the fitting result can meet the requirement when the polynomial degree is four. According to the fitted fourth-order polynomial curve, the radial average power can be observed to have an obvious inflection point at a certain position.
And (3) setting a quadratic polynomial curve fitted by a least square method as f (k) and L as a cut-off wave number, wherein the determination method comprises the following steps:
where row and column are rows and columns of the sampling matrix, respectively, and fix () represents an integer closest to the number in parentheses.
And the electromagnetic situation perception and radiation source positioning method based on the transform domain can be realized based on the result of data prediction and filling processing.
In view of the fact that the obtained result needs to be attached to the electromagnetic situation coverage real situation and the position of the radiation source as much as possible, the electromagnetic coverage state and the electromagnetic coverage parameter can be accurately reflected, and therefore three indexes, namely the contact ratio of the electromagnetic situation coverage graph, the root mean square error and the positioning offset of the radiation source, are selected for performance evaluation.
1. Contact ratio of electromagnetic situation coverage map
Because it is an accurate estimate of the electromagnetic situation coverage map, the resulting morphology fits the morphology of the original coverage map. The electromagnetic situation coverage map is greatly influenced by the topography and smoothness of the result cannot be achieved on one side, so the result form should reflect the position of the radiation source and the electromagnetic situation characteristics around the radiation source as much as possible.
2. Root mean square error is often used in the mathematical domain to measure the accuracy of the results, and is expressed as:
wherein T is0(x, y) represents the obtained result, and T (x, y) represents the actual value.
3. Offset of radiation source location
Because the application background of the patent is the prediction of the electromagnetic signal intensity, the result can well reflect the electromagnetic signal intensity coverage condition in the region to be detected, wherein the prediction of the number and the position of the electromagnetic radiation sources is an important index of the electromagnetic signal intensity coverage condition. And after the electromagnetic signal intensity data detected by the distributed sensing nodes are estimated and filled, a complete electromagnetic situation coverage map is obtained, and the position of the electromagnetic radiation source is positioned on the basis. The position of the electromagnetic radiation source is usually directly selected as the position of the maximum value of the signal intensity in the electromagnetic situation coverage map.
(III) technical effects
1. Experimental scene construction
The electromagnetic situation perception method researched by the invention is compared with a Kriging method and an inverse distance weighting method in performance from three aspects of electromagnetic situation coverage map contact ratio, root mean square error and radiation source positioning offset.
Without loss of generality, a 4G-LTE mobile communication network is taken as a simulation object. Intercepting an electromagnetic situation coverage map of the 4G-LTE mobile communication network with the area of 4000m multiplied by 4000m in the Brussel map as experimental background data, and observing a wave number domain image. The wave number domain image is a gray level image of the agent 8, and the higher the gray level value is, the stronger the energy is, and it can be observed that the energy of the wave number domain is more concentrated in the low frequency part. From the radial average power spectrum of the raw data obtained by the radial average power spectrum calculation method, it can be observed that the energy thereof tends to decrease with the increase of the wave number and the main energy is concentrated in the low frequency part. Therefore, the blank area can be subjected to data prediction by using low-frequency energy in a low-pass filtering mode.
And randomly distributing distributed sensing nodes in a target area to detect the electromagnetic intensity of the area, and uploading detection data to a data center to form an electromagnetic situation coverage map with blank undetected areas.
Electromagnetic intensity data exist in the detection radius of the distributed sensing nodes, and the electromagnetic intensity data cannot be detected outside the detection radius of the distributed sensing nodes, so that the electromagnetic data are vacant.
2. Effect analysis
As mentioned above, during the simulation experiment, the three indexes of the contact degree of the electromagnetic situation coverage map, the root mean square error and the positioning offset of the radiation source are adopted for performance evaluation.
And (3) carrying out zero filling on the electromagnetic intensity data containing the incomplete data, and then obtaining the electromagnetic intensity data according to the calculation step of the radial average power spectrum. The radial average power spectrum is observed, and the power is in a descending trend along with the increase of the wave number, which shows that the energy is still concentrated in a low-frequency region.
And fitting the radial average power by using a least square method according to an improved cut-off wave number determination method to obtain a fourth-order polynomial fitting curve. The cutoff wave number L, calculated according to equation (6), is 20, which corresponds to the tangent to the point of the fitted curve, and it can be seen that the curve after fitting has a sharp inflection point at that location.
In order to remove the edge distortion effect, the original data to be processed is firstly expanded to 400m, namely 20 unit pixels, and then situation perception is carried out, the obtained electromagnetic situation coverage map is processed by selecting a kriging method and an inverse distance weighting method with good effects in the existing methods, and the obtained results are compared.
(1) The electromagnetic situation coverage map has higher cutting degree
The three methods are good in overall shape, the data in the area near the radiation source can reflect the characteristics of the radiation source, the characteristics of geological terrain are more presented in the area far away from the radiation source, particularly in the area with weak communication strength, the large-area distortion condition does not exist, and the characteristics of electromagnetic situation data are met.
The kriging method and the reverse distance weighting method have poor results near one of the radiation sources, and cannot reflect the conditions that two radiation sources exist in the region to be measured, and the electromagnetic intensity is near the radiation sources and one of the radiation sources. The result obtained by the invention has good form, and can obviously reflect the condition that two radiation sources exist in the area to be measured.
(2) The positioning offset of the radiation source is smaller
The base station of the original data simultaneously evaluates the generation results of the three methods, and adopts the inferred and estimated radiation source (base station) to predict the position.
One of the communication base stations P1 can be clearly observed in the results of the Krigin method and the results of the inverse distance weighting method, but the other base station P2 is vaguer and cannot be positioned. The result of the invention can observe two obvious communication base stations and can accurately position. The differences in distance from the original data overlay location, respectively, result in table 2.
TABLE 2 base station positioning error Table
The positioning error of the Kriging method can be observed to be the largest through the positioning error, the result positioning error of the method and the inverse distance weighting method is smaller, and only the method can identify the positions of two base stations
Finally, it should be noted that the above embodiments are only used for illustrating the technical solutions of the embodiments of the present invention and not for limiting, and although the embodiments of the present invention are described in detail with reference to the above preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions can be made on the technical solutions of the embodiments of the present invention without departing from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (4)
1. A transform-domain electromagnetic situational awareness and radiation source localization method, comprising the steps of:
the method comprises the following steps that firstly, an omnidirectional antenna of each sensing node randomly deployed in a target area is used for detecting electromagnetic signals in a sensitivity coverage range, and electromagnetic signal intensity data are obtained;
secondly, sending the detection data of each distributed sensing node to a data center for collection and storage, and processing the detection data by computing equipment of the data center to obtain an initial electromagnetic situation coverage map;
determining a cutoff wave value, determining a sampling matrix and iteration times, and predicting the data of the empty position based on the detected data; the method comprises the following substeps:
step 3.1, determining a cutoff wave value k, wherein Tk(u, v) conforms to the expression:
where (u, v) represents the actual coordinate value of the point to be estimated, and r represents the cut-off parameter T of the circular low-pass filterkDenotes a circular low-pass filter with a cut-off wavenumber k, where k is 1,2, … … ke，keFinal cut-off wavenumber;
and f (k) of a quadratic polynomial is fitted by using a least square method for the cut-off wave number, L is the cut-off wave number, and the determination method comprises the following steps:
where row and column are the rows and columns of the sampling matrix, and fix () represents the nearest integer to the number in parentheses;
step 3.2, two-dimensional Fourier transform is carried out to the wave number domain and low-pass filtering is carried out,
step 3.3, performing two-dimensional Fourier inverse transformation to generate electromagnetic signal intensity data,
step 3.4, updating the filtering threshold value by using the replacement original data, executing N times of iteration on the data of the vacancy position points, solving predicted data,
filling the existing vacant positions with the prediction data, and further generating a complete electromagnetic situation coverage map capable of reflecting the real situation;
and step five, extracting the position of the radiation source.
2. The method for electromagnetic situational awareness and radiation source localization according to claim 1, wherein: and step two, zero filling and data edge expanding processing are further performed on the vacant positions.
3. The method for electromagnetic situational awareness and radiation source localization according to claim 1, wherein: the first step comprises the following steps: the vacancy sampling matrix S for the original vacancy data is as follows:
in which electromagnetic signal strength data d to be processed0And x and y are respectively the abscissa and the ordinate of the point to be estimated.
4. The method for electromagnetic situational awareness and radiation source localization according to claim 1, wherein: in the third step, the space domain electromagnetic signal intensity data matrix d after the nth iterationnExpression:
dn(x，y)＝F-1{Tk[F(d0(x，y)+S(x，y)dn-1(x，y)]} n＝1，2，3，...，N
wherein, TkDenotes a circular low-pass filter with a cut-off wavenumber k, where k is 1,2, … … ke，keFinal cut-off wavenumber; n is the number of iterations, and N is the total number of iterations; f and F-1The electromagnetic signal intensity data d0 represent Fourier transform and inverse transform respectively, x and y represent the abscissa and ordinate of the point to be estimated respectively, and S represents a vacancy sampling matrix for the original vacancy data.
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