CN110929396A - Electromagnetic situation generation method based on information geometry - Google Patents

Electromagnetic situation generation method based on information geometry Download PDF

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CN110929396A
CN110929396A CN201911137699.5A CN201911137699A CN110929396A CN 110929396 A CN110929396 A CN 110929396A CN 201911137699 A CN201911137699 A CN 201911137699A CN 110929396 A CN110929396 A CN 110929396A
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张怡
宋哲
唐成凯
于阳
郭淑霞
华翔
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Northwestern Polytechnical University
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Abstract

The invention provides an electromagnetic situation generating method based on information geometry. Compared with the traditional electromagnetic situation generating method based on field intensity synthesis, the method provided by the invention not only can reduce the calculation amount of situation generation and improve the operation speed, but also can reflect the detailed attributes of disturbance in the space for the generated electromagnetic situation distribution diagram. As can be seen from simulation results, the method is sensitive to the position and the scattering intensity of a scattering source introduced into the space, and the situation distribution diagram of the method has good relevance with the attribute of the scattering source. The method provides a new idea for the generation of the electromagnetic situation, and can accurately, quickly and effectively construct the electromagnetic situation distribution in a certain area range.

Description

Electromagnetic situation generation method based on information geometry
Technical Field
The invention belongs to the field of situation generation, and particularly relates to an electromagnetic situation generation method based on information geometry.
Background
As the informatization war develops, the information-dependent characteristics become more and more obvious. The electromagnetic waves carry battlefield information on a battlefield, and the electromagnetic waves transmit important information to each terminal like a courier. As modern war is more and more "informationized", its battlefield space is also gradually extended from traditional land, sea, air to space, electricity (electromagnetism) and match-play space. With the advent of the electromagnetic landscape, the battlefield environment has become increasingly complex. In addition to the wide application of electromagnetic technology and frequency-using equipment, the electromagnetic environment of a battlefield becomes increasingly complex, the electromagnetic spectrum is increasingly crowded, and how to obtain the initiative on the modern battlefield with abundant information elements is extremely important for the cognition of the electromagnetic environment and the comprehensive electromagnetic situation requirement.
In the military aspect, a commander needs a set of detailed electromagnetic situation distribution maps to know the distribution situation of the electromagnetic environment of the whole battlefield in the electronic countermeasure environment; in civil use, the electromagnetic situation distribution map is also required as a reference in the process of striking illegal stations so as to analyze the positions of the illegal stations (radiation sources). The traditional electromagnetic situation characterization and generation usually requires extracting a corresponding target signal from a noisy signal, and generating a corresponding electromagnetic environment situation after performing corresponding processing on the extracted signal. The document "field numerical analysis and measurement comparison of electromagnetic situation in complex urban environment, science report of electric wave, 2018, vol.33, No.6, p671-p 676" calculates propagation distribution of electromagnetic waves in a scene by using a ray model of consistent geometric diffraction theory and compares the propagation distribution with actual measurement, but because a signal extraction and numerical calculation method is adopted, the calculation complexity is high, the calculation time is long, and the generated electromagnetic situation cannot accurately reflect details in the scene, such as the position of a radiation source.
Disclosure of Invention
In order to solve the problems that the traditional electromagnetic situation generation method based on field intensity synthesis is complex in calculation, long in time consumption and incapable of accurately reflecting the incidence relation between the electromagnetic situation and a scene, the invention provides a method for representing and generating the electromagnetic situation by using an information geometric theory.
The technical scheme of the invention is as follows:
the electromagnetic situation generating method based on the information geometry is characterized by comprising the following steps: the method comprises the following steps:
step 1: performing grid division on a target area, wherein each grid node in the grid is provided with a sensor as an electromagnetic observation point;
step 2: collecting amplitude values of electromagnetic signals in a space by each electromagnetic observation point at a certain sampling rate, and forming sample statistical data X corresponding to each electromagnetic observation point after accumulation for a certain time; selecting a Gaussian mixture model as a statistical model, and solving a probability density function of a signal by combining sample statistical data X received by each electromagnetic observation point; after solving the probability density function of each electromagnetic receiving end, mapping each probability density function into a Riemann space, wherein each point on a statistical manifold in the Riemann space is determined by the corresponding parameter of each probability density function, and the distribution of each point on the statistical manifold forms an electromagnetic state psi under the current electromagnetic environment;
and step 3: for two electromagnetic states Ψ obtained by step 21And Ψ2Using the formula
Figure BDA0002280003750000021
Calculating the distance between the probability density functions corresponding to two electromagnetic states, wherein f (x) is the electromagnetic state Ψ1The probability density function ofModel, g (x) is the electromagnetic state Ψ2α corresponding to the probability density function ofiIs in the electromagnetic state Ψ1Corresponding mixing weight coefficient, mu, of ith Gaussian component in Gaussian mixture modeliIs in the electromagnetic state Ψ1The expectation of the ith gaussian component in the gaussian mixture model of (1),
Figure BDA0002280003750000022
is in the electromagnetic state Ψ1The variance of the ith Gaussian component in the Gaussian mixture model of (1), βjIs in the electromagnetic state Ψ2The mixing weight coefficient, v, of the jth Gaussian component in the corresponding Gaussian mixture modeljIs in the electromagnetic state Ψ2The expectation of the jth gaussian component in the corresponding gaussian mixture model,
Figure BDA0002280003750000023
is in the electromagnetic state Ψ2The variance of the jth Gaussian component in the corresponding Gaussian mixture model, N (-) is a Gaussian distribution function, and i' is a number for distinguishing i;
and 4, step 4: taking a gridded target area two-dimensional plane as an xoy plane of the electromagnetic situation diagram; and 3, determining the distance of each grid node position according to the distance between the probability density functions corresponding to the two electromagnetic states in the target area obtained by calculation in the step 3, taking the distance as the value of the electromagnetic situation map at the corresponding coordinate position, and drawing the electromagnetic situation distribution map in a contour line mode.
Further preferably, the electromagnetic situation generating method based on information geometry is characterized in that: and step 1, carrying out equal-interval meshing on the target area.
Further preferably, the electromagnetic situation generating method based on information geometry is characterized in that: in the step 2, an improved EM algorithm is adopted as a model fitting algorithm to solve the probability density function of the signal, and a stability factor delta is introduced in the iterative process of the solution.
Further preferably, the electromagnetic situation generating method based on information geometry is characterized in that: in step 2, nine adjacent grid points in the target region are divided into a group, for each group of grid points, the probability distribution function on the grid point at the intermediate position is firstly calculated, then the parameters of the probability distribution function on the grid point at the intermediate position are used as the initial values of the EM iteration of the other grid points, and the probability distribution functions on the other grid points are calculated.
Advantageous effects
The electromagnetic environment in the space is cluttered by the use of a large number of radio devices, and the complex electromagnetic situation caused by the cluttering of the radio devices can adversely affect the radio system, and the efficiency of the radio system is reduced to various degrees. Compared with the traditional electromagnetic situation generation method based on field intensity synthesis, the electromagnetic situation generation method based on the information geometry provided by the invention not only can reduce the calculation amount of situation generation and improve the operation speed, but also can reflect the detailed attributes of disturbance in the space for the generated electromagnetic situation distribution diagram. As can be seen from simulation results, the method is sensitive to the position and the scattering intensity of a scattering source introduced into the space, and the situation distribution diagram of the method has good relevance with the attribute of the scattering source. The method provides a new idea for the generation of the electromagnetic situation, and can accurately, quickly and effectively construct the electromagnetic situation distribution in a certain area range.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a system for electromagnetic situation generation using information geometry
FIG. 2 initial scene setup diagram
FIG. 3 electromagnetic situation diagram (front view and contour plot) for a target scattering intensity of-14 dB
FIG. 4 electromagnetic situation diagram (front view and contour plot) for a target scattering intensity of-34 dB
FIG. 5 is a graph of position versus electromagnetic situation for a target moving to (7km,6km,0.1km)
FIG. 6 is a graph of position versus electromagnetic situation for a target moving to (6km,7km,0.1km)
FIG. 7 is a graph of position versus electromagnetic situation for a target moving to (10km,10km,0.1km)
FIG. 8 is a graph of position versus electromagnetic situation for a target moving to (10km,10km,0.1km)
Detailed Description
In order to make the technical means of the invention easier to understand, the invention is further illustrated below with reference to specific examples. Assuming a target scene as a square area of 20km x 20km, there are two radiation sources in the scene, radiation source 1(AM) and radiation source 2(FM), respectively. The coordinates of the radiation source 1 are (6km, 14km and 0.2km), and the emission power is 10 kW; the coordinates of the radiation source 2 are (14km, 6km, 0.2km), and the emission power is 10 kW; the scattering source of the object moves in a planar space 100m from the ground. With the above conditions as background, simulation was performed with reference to the system flow shown in fig. 1.
Step 1: meshing regions
Firstly, grid division is carried out on the region, nodes contained in the grids are observation points, and the electromagnetic situation of each node can be calculated and generated after the position of each node is determined. The target area is divided into n × n grid areas at equal intervals, the target area range is assumed to be L × L, so that the side length of each grid in the area is L/n, and the number of grid nodes contained in the whole target area is (n +1) × (n + 1).
For the above simulation background, in this embodiment, the ground scene is divided into grids, the number of the grids is 50 × 50, the number of observation nodes is 51 × 51, and the grid interval is 400 m. Next, setting an initial scene, wherein the scattering source position coordinates are (6km,6km,0.1km), and the distribution of the whole scene is shown in fig. 2.
Step 2: signal processing at each node
Acquiring electromagnetic observation data by each observation point sensor in an electromagnetic space, and sampling electromagnetic signals in the space at a certain sampling rate fsCollecting amplitude values, and forming samples corresponding to the receiving ends after a certain time tau is accumulatedStatistical data X ═ X1,X2,…,X(n+1)×(n+1)}; the method comprises the steps of selecting a Gaussian Mixture Model (GMM) as a statistical model, combining sample statistical data X received by each receiving end to solve a probability density function of a signal, solving by adopting an improved EM algorithm as a model fitting algorithm, and introducing a stability factor delta in iteration to enable the robustness of the iteration process to be stronger and prevent the iteration process from falling into singular points; after solving the probability density function of each receiving point, mapping each probability density function to Riemann space, wherein the parameter (theta) corresponding to each probability density function1,θ2,…,θ(n+1)×(n+1)Determining each point on the statistical manifold in the Riemann space respectively, wherein the statistical manifold is determined by a selected statistical model, the statistical model defines a family of probability density functions, and the distribution of each point on the statistical manifold forms an electromagnetic state psi under the current electromagnetic environment:
Ψ＝{θ1,θ2,…,θ(n+1)×(n+1)},θ1,θ2,…,θ(n+1)×(n+1)∈θ
and theta is a parameter space of the selected statistical model.
As the Gaussian mixture model is selected as the statistical model, the number of mixture components of the statistical model needs to be determined. If the random variable x obeys a Gaussian Mixture Distribution (GMD), its probability density function is:
Figure BDA0002280003750000051
wherein k is the number of Gaussian components, lambdaiMixed weight coefficient, N, representing the ith Gaussian componenti(. h) represents the probability density function of the ith Gaussian component, μiExpressing the expectation of the ith Gaussian component, σi 2Representing the variance of the ith gaussian component. Before determining the number of components of the mixture model, it is necessary to define a range K of component numbers of the modelmin＜K＜KmaxAnd the optimum number of components K should be included in the range, and the formula for determining the optimum number of components is:
Figure BDA0002280003750000052
in the formula (I), the compound is shown in the specification,
Figure BDA0002280003750000053
represents the optimal component number estimate, C]A function representing a model selection criterion is used,
Figure BDA0002280003750000054
is a parameter estimate. The MML criterion is chosen here and is defined as follows:
Figure BDA0002280003750000055
in the formula, f (theta) is a prior probability function of the model parameter vector theta, L (x theta) is a likelihood function of the model, and | G (theta) | is a determinant value of the Fisher information matrix G (theta).
After the number of GMM mixing components is determined, each parameter of the mixing model needs to be fitted and solved by combining actually monitored data. Aiming at solving the parameters of the Gaussian mixture model, the improved EM algorithm is adopted, and the iterative process of the improved EM algorithm based on the Gaussian mixture model is as follows:
e, step E:
updating the hidden variable q according to the result of the parameter iteration of the first timenk：
Figure BDA0002280003750000061
And M:
according to the updated hidden variable
Figure BDA0002280003750000062
Model parameter lambda of update order l +1k、μk、
Figure BDA0002280003750000063
Figure BDA0002280003750000064
Figure BDA0002280003750000065
Figure BDA0002280003750000066
Where δ is an iterative stability factor, usually 10, to enhance the stability of the algorithm-7. And (3) calculating whether an iteration termination condition is reached or not by repeatedly executing the step E and the step M, namely calculating whether a log-likelihood function is converged or not:
ln[L(θ(l+1)；X)]-ln[L(θ(l)；X)]≤ζ
where ζ is the iterative convergence decision threshold, which is a very small positive number, typically 10-5。
And step 3: generation of electromagnetic situation
In the initial state, the electromagnetic environment data monitored by each observation point in the target area is processed through the step 2 to obtain an electromagnetic state psi in the environment1(ii) a When the electromagnetic environment in the region is disturbed, new electromagnetic environment data can be monitored through each observation point in the target region, and the electromagnetic state psi in the new environment can be obtained through the processing in the step 22(ii) a By calculating the electromagnetic state Ψ2Relative to the initial electromagnetic state Ψ1The electromagnetic situation distribution under the condition of disturbance can be obtained through the change of the electromagnetic situation. Since the electromagnetic state is determined by the set of probability density functions of the signal processed at each monitoring point in the scene, the requirement Ψ2Relative to Ψ1The variation of (2) is the difference between the probability density functions of the electromagnetic signals in the two states detected by each monitoring point, which is also called "distance". Due to the Gaussian Mixture Model (GMM) of the probability model used in step 2, a modified KLD calculation method is used to calculate the "distance" between the probability density functions of the detected signals at the two states at each monitoring point.
For two given Gaussian mixture distributions
Figure BDA0002280003750000067
And
Figure BDA0002280003750000068
its distance is usually expressed by KLD:
Figure BDA0002280003750000071
the above equation generally does not have a closed form solution, and can be approximately converted to the following equation using the Jensen inequality:
Figure BDA0002280003750000072
zii′＝∫fi(x)fi′(x)dx
since the mixture components of the Gaussian mixture distributions f (x) and g (x) are both Gaussian distributions, N (x; mu, sigma) for both Gaussian distributions2) And N (x; v, gamma2) The following equation holds true:
∫N(x；μ,σ2)N(x；ν,γ2)dx＝N(0；μ-ν,σ2+γ2)
where μ, v is the mean, σ, of two Gaussian distributions2,γ2Is the variance of two gaussian distributions. Then a closed-form solution for KLD between the two gaussian mixture models can be obtained:
Figure BDA0002280003750000073
wherein, αiIs in the electromagnetic state Ψ1Corresponding mixing weight coefficient, mu, of ith Gaussian component in Gaussian mixture modeliFor the expectation of the ith gaussian component in the state 1 model,
Figure BDA0002280003750000074
variance of the ith Gaussian component in the State 1 model, βjIs in the electromagnetic state Ψ2In corresponding Gaussian mixture modelCoefficient of mixing weight of jth Gaussian component, vjFor the expectation of the jth gaussian component in the state 2 model,
Figure BDA0002280003750000075
for the variance of the jth gaussian component in the state 2 model, N (-) is the gaussian distribution function and i' is the number that distinguishes i. The distance value on each node can be calculated through the formula,
in order to increase the speed of the electromagnetic situation generating operation, the electromagnetic situation of each region can be calculated in blocks in the calculating process. The electromagnetic space is divided into a plurality of grids, each grid point is an observation point, and a plurality of adjacent grid points are grouped into one group. Firstly, calculating a probability distribution function on each group of intermediate position observation points, and at the moment, adopting a method of selecting the best fitting result by multiple times of calculation to obtain a probability density function on the point; secondly, the obtained parameters of the probability density function are used as initial values of adjacent receiving points for EM iteration, and because the electromagnetic situations of the adjacent grid points are usually not very different, the parameter distributions of the probability density function at the two adjacent receiving points are similar, the initial values can be used as the initial values of the EM algorithm to avoid iteration falling into local maximum values, and meanwhile, the problem of selecting the initial values before each EM iteration is carried out is also reduced.
And 4, step 4: visualization of electromagnetic situation
Calculating the distance between the probability density functions of the signals detected under the two environments at each observation point in the target area through the step 3, wherein the distribution condition of the distance corresponds to the positions of grid nodes in the target area, taking a two-dimensional plane of the grid target area as an xoy plane of the electromagnetic situation map, calculating the distance between the electromagnetic signal distributions under the two scenes at each node position as a value on a corresponding coordinate position, and drawing the electromagnetic situation distribution map in a contour line mode. In the electromagnetic situation distribution diagram, since the introduction of the additional scattering (radiation) source can form a clear triangular cone in the diagram, the electromagnetic state Ψ can be determined according to the vertex position of the triangular cone2The position of the newly added scattering (radiation) source.
In this embodiment, the electromagnetic situation values on the nodes are obtained by calculation by using the method, correspond to the position coordinates of the nodes in the target scene, and the electromagnetic situation distribution map is drawn by using a contour line mode. Figures 3 and 4 show the electromagnetic situation resulting from the introduction of a scattering source of interest in an initial scenario, where figure 3 is the result of introducing a scattering source with a scattering intensity of-14 dB and figure 4 is the result of introducing a scattering source with a scattering intensity of-34 dB. Fig. 5, 6, 7 and 8 show the variation of the electromagnetic situation caused by the change of the source position under the condition of the same scattering intensity (-14 dB). As can be seen from the comparison graph, the electromagnetic situation generated by the electromagnetic situation generating method provided by the invention is still clear under the condition that the scattering intensity of a scattering source is very low; and the generated electromagnetic situation has a good correlation with the position of the scattering source.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (4)

1. An electromagnetic situation generating method based on information geometry is characterized in that: the method comprises the following steps:
step 1: performing grid division on a target area, wherein each grid node in the grid is provided with a sensor as an electromagnetic observation point;
step 2: collecting amplitude values of electromagnetic signals in a space by each electromagnetic observation point at a certain sampling rate, and forming sample statistical data X corresponding to each electromagnetic observation point after accumulation for a certain time; selecting a Gaussian mixture model as a statistical model, and solving a probability density function of a signal by combining sample statistical data X received by each electromagnetic observation point; after solving the probability density function of each electromagnetic receiving end, mapping each probability density function into a Riemann space, wherein each point on a statistical manifold in the Riemann space is determined by the corresponding parameter of each probability density function, and the distribution of each point on the statistical manifold forms an electromagnetic state psi under the current electromagnetic environment;
and step 3: for two electromagnetic states Ψ obtained by step 21And Ψ2Using the formula
Figure FDA0002280003740000011
Calculating the distance between the probability density functions corresponding to two electromagnetic states, wherein f (x) is the electromagnetic state Ψ1G (x) is the electromagnetic state psi2α corresponding to the probability density function ofiIs in the electromagnetic state Ψ1Corresponding mixing weight coefficient, mu, of ith Gaussian component in Gaussian mixture modeliIs in the electromagnetic state Ψ1The expectation of the ith gaussian component in the gaussian mixture model of (1),
Figure FDA0002280003740000012
is in the electromagnetic state Ψ1The variance of the ith Gaussian component in the Gaussian mixture model of (1), βjIs in the electromagnetic state Ψ2The mixing weight coefficient, v, of the jth Gaussian component in the corresponding Gaussian mixture modeljIs in the electromagnetic state Ψ2The expectation of the jth gaussian component in the corresponding gaussian mixture model,
Figure FDA0002280003740000013
is in the electromagnetic state Ψ2The variance of the jth Gaussian component in the corresponding Gaussian mixture model, N (-) is a Gaussian distribution function, and i' is a number for distinguishing i;
and 4, step 4: taking a gridded target area two-dimensional plane as an xoy plane of the electromagnetic situation diagram; and 3, determining the distance of each grid node position according to the distance between the probability density functions corresponding to the two electromagnetic states in the target area obtained by calculation in the step 3, taking the distance as the value of the electromagnetic situation map at the corresponding coordinate position, and drawing the electromagnetic situation distribution map in a contour line mode.
2. An electromagnetic situation generating method based on information geometry as claimed in claim 1, characterized in that: and step 1, carrying out equal-interval meshing on the target area.
3. An electromagnetic situation generating method based on information geometry as claimed in claim 1, characterized in that: in the step 2, an improved EM algorithm is adopted as a model fitting algorithm to solve the probability density function of the signal, and a stability factor delta is introduced in the iterative process of the solution.
4. An electromagnetic situation generating method based on information geometry as claimed in claim 1, characterized in that: in step 2, nine adjacent grid points in the target region are divided into a group, for each group of grid points, the probability distribution function on the grid point at the intermediate position is firstly calculated, then the parameters of the probability distribution function on the grid point at the intermediate position are used as the initial values of the EM iteration of the other grid points, and the probability distribution functions on the other grid points are calculated.
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