A method for extrapolating marine space field based on the parabolic equation model of radio wave propagation

Abstract

The present invention relates to a method for extrapolating marine space fields based on a parabolic equation model of radio wave propagation, and belongs to the field of computational electromagnetics. Aiming at the problem that the calculation height of the parabolic equation model of radio wave propagation is limited by the wavelength of the radiation source, resulting in a large amount of calculation for high-altitude areas, a method for extrapolating marine space fields based on a parabolic equation model of radio wave propagation is proposed, so as to break through the calculation height limit of the parabolic equation model, realize the calculation of electromagnetic field path loss in high altitude / near space, and improve the calculation efficiency of the radio wave propagation model in a large area environment. The present invention can be used for shipborne / shore-based radar power prediction.

Description

Technical Field

[0001] The present invention belongs to the field of computational electromagnetics. Background Art

[0002] For electromagnetic wave propagation problems in large, complex environments, parabolic equation models are often used to comprehensively consider the effects of atmospheric refraction and electromagnetic wave diffraction on electromagnetic wave path loss. However, the spatial grid division of the parabolic equation model is limited by the wavelength of the electromagnetic wave, making the parabolic equation model highly restricted and difficult to use for analyzing electromagnetic field coverage characteristics in high-altitude and near-space areas. In addition, the presence of atmospheric waveguides in the low-altitude atmospheric environment not only affects the low-altitude electromagnetic propagation characteristics, but also affects the electromagnetic field path loss in high-altitude and near-space areas. Summary of the Invention

[0003] In order to model high altitude / near space under different atmospheric environments and analyze the detection efficiency of radar equipment for targets with a sea surface altitude exceeding 1 km, the present invention proposes a marine space field extrapolation method based on the radio wave propagation parabolic equation model.

[0004] The present invention proposes a marine space field extrapolation method based on the parabolic equation model of radio wave propagation. The parabolic equation model is used to analyze the refraction and diffraction effects of low-altitude electromagnetic wave propagation. By extracting the spatial electromagnetic field distribution near the upper limit of the parabolic equation with distance, converting it into a function with angle through coordinate system transformation, and performing spatial field extrapolation on the electromagnetic field distribution in a linear refractive index environment, a model of electromagnetic wave propagation suitable for high altitude / near space is realized, which can be used to analyze the impact of the low-altitude atmospheric environment on high-altitude target detection. The present invention adopts the following technical solutions to achieve this:

[0005] Step 1: Calculate the initial electric field distribution based on the carrier frequency, height and vertical direction diagram of the radiation source;

[0006] Step 2: Model the electromagnetic wave propagation environment based on the atmospheric refractive index profile measured by forward modeling or inversion estimation;

[0007] Step 3: Using the parabolic equation model's split-step Fourier algorithm to calculate electromagnetic field propagation;

[0008] Step 4: Perform power calibration on the calculated electromagnetic field to obtain the electromagnetic wave spatial propagation loss and propagation factor;

[0009] Step 5: Calculate the Earth's equivalent radius R based on the atmospheric refractive index profile outside the parabolic equation's altitude limit. e ;

[0010] Step 6: Extract the curve of the electromagnetic wave propagation factor at the upper limit of the parabolic equation as a function of distance, and analyze its elevation angle relative to the radiation source through coordinate transformation;

[0011] Step 7: Establish a spatial field extrapolation grid coordinate system from the parabolic equation altitude limit to high altitude / near space, and interpolate the elevation angle-propagation factor curve obtained in step 6 to obtain the propagation factor of each point in the grid coordinate system;

[0012] Step 8: Calculate the free space path loss of each point in the spatial field extrapolation grid coordinate system, and after subtracting the propagation factor, obtain the electromagnetic field path loss of each point in the grid coordinate system.

[0013] Among them, step 5 of calculating the equivalent radius of the Earth includes:

[0014] First, by performing least squares fitting on the atmospheric refractive index profile from the upper limit of the parabolic equation to the target altitude, the intercept and gradient of the atmospheric refractive index in the area with altitude are analyzed to establish a linear refractive index environment.

[0015] Then: according to Fresnel's theorem, the linear refractive index environment is equivalent to the radius of the earth, and the equivalent factor of the earth's curvature radius is calculated;

[0016] Finally: According to the equivalent factor of the earth's curvature radius, the equivalent radius of the earth is calculated, and the electromagnetic wave propagation problem in the area from the upper limit of the parabolic equation to the target height is regarded as free propagation on the surface of the earth's equivalent radius.

[0017] Furthermore, step 6 of calculating the curve of the radiation source propagation factor changing with elevation angle includes:

[0018] Firstly, the electromagnetic field calculated by the parabolic equation model is calibrated to obtain the curves of electromagnetic wave propagation path loss and propagation factor varying with distance.

[0019] Then: according to the position of each point at the upper limit of the parabolic equation model, the coordinate system transformation method is used to establish the function of distance and elevation angle, and the electromagnetic wave propagation factor that changes with distance is mapped into a curve that changes with elevation angle;

[0020] Next: establish a uniform angle vector and interpolate the curve of propagation factor changing with elevation angle to obtain data in the same coordinate system;

[0021] Finally: Several heights near the upper limit of the parabolic equation model are selected for repeated calculation, and the median filtering method is used to reduce the error caused by multipath zero depth.

[0022] Furthermore, step 7 of calculating the propagation factor of the target location includes:

[0023] First: according to the target position, the coordinate system transformation method is used to calculate the radiation source elevation angle corresponding to the target position;

[0024] Then: according to the curve of the propagation factor at the upper limit of the parabolic equation model versus elevation angle, the propagation factor at the target position is obtained by linear interpolation.

[0025] This invention primarily extrapolates the spatial electromagnetic field calculated by the parabolic equation model using ray propagation theory, effectively addressing the computationally intensive nature of the parabolic equation model when modeling high-altitude regions. This spatial field extrapolation method not only overcomes the altitude limitations of parabolic equation calculations but also enables a more accurate analysis of the impact of low-altitude atmospheric refraction on high-altitude and near-space electromagnetic field path loss. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagram of the present invention.

[0027] Figure 2 Flowchart of the embodiments.

[0028] Figure 3 Calculation results of the parabolic equation model and space field extrapolation method under standard atmospheric environment.

[0029] Figure 4 Comparison of the calculation results of the parabolic equation model under standard atmospheric conditions and the calculation results of the space field extrapolation method. The left side shows the path loss (dB) result at an altitude of 5000m, and the right side shows the path loss (dB) result at a distance of 200km.

[0030] Figure 5 Calculation results of the parabolic equation model and spatial field extrapolation method under a typical evaporation duct environment.

[0031] Figure 6 Comparison of the parabolic equation model calculation results and the spatial field extrapolation method calculation results in a typical evaporation duct environment. The left side shows the path loss (dB) result at an altitude of 5000m, and the right side shows the path loss (dB) result at a distance of 200km. DETAILED DESCRIPTION

[0032] The present invention will be further explained below with reference to the accompanying drawings.

[0033] The marine space field extrapolation method based on the parabolic equation model of radio wave propagation proposed in the present invention can analyze the influence of refraction and diffraction effects on the electromagnetic wave propagation loss in high-altitude areas, such as the refraction effect of the atmospheric waveguide on the first interference enhancement lobe on the sea surface, and the leakage of electromagnetic waves at the top of the atmospheric waveguide. The parabolic equation model is mainly used to calculate the low-altitude electromagnetic wave propagation path loss in the area from the sea surface height to the upper limit of the parabolic equation height; near the upper limit of the parabolic equation height, the electromagnetic field power change information is extracted, and the electromagnetic wave propagation problem in the area from the upper limit of the parabolic equation height to the high altitude / near high altitude area is regarded as a ray propagation problem in a linear refractive index environment, thereby realizing the calculation of the electromagnetic wave propagation path loss in the high altitude / near space area, as shown in the schematic diagram. Figure 1 As shown in the figure, the present invention is mainly implemented through coordinate system transformation and spatial interpolation. Compared with the method of directly meshing the high-altitude area using the parabolic equation model, the amount of calculation can be reduced. The ratio of the reduction in the amount of calculation is approximately the ratio of the reduced amount of meshes to the total amount of meshes, which can reach more than 50%.

[0034] The preferred embodiment of the present invention is as follows Figure 2 , the steps are as follows:

[0035] Step 1: Calculate the initial electric field distribution based on the carrier frequency, height and vertical direction diagram of the radiation source;

[0036] Step 2: Model the electromagnetic wave propagation environment based on the atmospheric refractive index profile measured by forward modeling or inversion estimation;

[0037] Step 3: Using the parabolic equation model's split-step Fourier algorithm to calculate electromagnetic field propagation;

[0038] Step 4: Perform power calibration on the calculated electromagnetic field to obtain the electromagnetic wave spatial propagation loss and propagation factor;

[0039] Step 5: Calculate the Earth's equivalent radius R based on the atmospheric refractive index profile outside the parabolic equation's altitude limit. e ;

[0040] Step 6: Extract the curve of the electromagnetic wave propagation factor at the upper limit of the parabolic equation as a function of distance, and analyze its elevation angle relative to the radiation source through coordinate transformation;

[0041] Step 7: Establish a spatial field extrapolation grid coordinate system from the parabolic equation altitude limit to high altitude / near space, and interpolate the elevation angle-propagation factor curve obtained in step 6 to obtain the propagation factor of each point in the grid coordinate system;

[0042] Step 8: Calculate the free space path loss of each point in the spatial field extrapolation grid coordinate system, and after subtracting the propagation factor, obtain the electromagnetic field path loss of each point in the grid coordinate system.

[0043] The optimal process for calculating the equivalent radius of the Earth in step 5 is:

[0044] Step 5.1: Extract the atmospheric refractivity profile from the upper limit of the parabolic equation to the target altitude, and estimate the atmospheric refractivity gradient using the pseudo-inverse calculation method of the least squares method:

[0045]

[0046] Among them, M0 is the estimated atmospheric refractive index at the sea surface, g is the atmospheric refractive index gradient, matrix A is a two-dimensional matrix of m*2 dimensions, m is the number of atmospheric refractive index profile sampling points, all elements in the first column of matrix A are 1, and the elements in the second column are the heights of the atmospheric refractive index profile sampling points, M z A column vector of sampled values ​​of the atmospheric refractive index;

[0047] Step 5.2: Calculate the Earth's curvature radius equivalent factor k based on the estimated atmospheric refractive index gradient:

[0048]

[0049] Where R0 is the radius of the Earth, usually 6375km;

[0050] Step 5.3: Calculate the Earth's equivalent radius R based on the Earth's curvature radius equivalent factor k. e =k·R0.

[0051] Preferably, calculating the curve of the radiation source propagation factor varying with elevation angle in step 6 includes:

[0052] Step 6.1: Extract the curve of the electromagnetic wave field strength versus distance at the upper limit of the parabolic equation model. By spatially calibrating the electromagnetic field, calculate the path loss versus distance r at the upper limit of the parabolic equation model:

[0053] PL(h pe ,r)=20log 10 (E0(h ant ,△r) / E(h pe ,r))+10log 10 (4π△r 2 )

[0054] where h pe is the upper limit of the height of the parabola equation, h ant is the height of the radiation source above the sea level, △r is the grid step size of the parabolic equation model;

[0055] Step 6.2: Compare with the free-space path loss to obtain the propagation factor at the upper limit of the parabolic equation model:

[0056] PF(h pe ,r)=10log 10 (4πr 2 )-PL(h pe ,r);

[0057] Step 6.3: Calculate the elevation angle relative to the radiation source based on the position of each point at the upper limit of the parabolic equation model:

[0058]

[0059] Where r c To calculate the distance corresponding to the center point of the region, R e is the equivalent radius of the Earth calculated in step 5.3. Since the distance and elevation angle are monotonically mapped, the propagation factor at the upper limit of the parabolic equation model can be written as PF(h pe ,θ);

[0060] Step 6.4: Select several heights near the upper limit of the parabolic equation model and repeat steps 6.1-6.3. The propagation factor calculated for the i-th time is recorded as PF i (h pe ,θ), and establish a uniform angle vector in the range of [0,π / 2], denoted as θ0;

[0061] Step 6.5: Interpolate the propagation factor on θ0:

[0062] PF i (h pe ,θ0)=I0[θ,PF i (h pe ,θ),θ0]

[0063] Among them, I0 is the linear interpolation operator;

[0064] Step 6.7: Take the median of the obtained propagation factor sequence to avoid multipath nulls at high elevation angles:

[0065] PF(h pe ,θ0)=median i [PF i (h pe ,θ0)].

[0066] Preferably, calculating the propagation factor of the target position in step 7 includes:

[0067] Step 7.1. Calculate the elevation angle of the radiation source at the target location:

[0068]

[0069] Step 7.2: Based on the curve of the propagation factor at the upper limit of the parabolic equation model obtained in step 6.7, the propagation factor at the target position is obtained again by linear interpolation:

[0070] PF(h tar ,r)=I0[θ0,PF(h pe ,θ0),θ(h tar ,r)];

[0071] Step 7.3, considering free space path loss, we get:

[0072]

[0073] Preferably, the method for calculating the electromagnetic wave propagation path loss at the target position using the spatial field extrapolation method in step 8 is:

[0074]

[0075] like Figure 3 and Figure 5 As shown, the standard atmosphere is a linear refractive index environment with an atmospheric refractive index gradient of -46.9M / km, and the typical evaporation duct environment is an evaporation duct with a thickness of 20m and a strength of 5M; the parabolic equation height upper limit is selected as 1000m, that is, the parabolic equation model is used for calculation within the range of [0m, 1000m], and the spatial field extrapolation method is used for calculation within the range of [1000m, 5000m]. From the perspective of graphic texture, the calculation results of the two methods are similar. In order to verify the spatial field extrapolation method, the direct calculation results of the parabolic equation model and the calculation results of the spatial field extrapolation method are compared and verified. The verification figure is shown in FIG. Figure 4 and Figure 6 As shown in FIG, from the results of the path loss calculation curve, the root mean square error calculated by the spatial field extrapolation method is less than 3dB, which verifies the effectiveness of the present invention.

Claims

1. A method for extrapolating marine space field based on the parabolic equation model of radio wave propagation, characterized by: Step 1: Calculate the initial electric field distribution according to the carrier frequency, height and vertical direction diagram of the radiation source; Step 2: Model the electromagnetic wave propagation environment based on the atmospheric refractive index profile measured by forward modeling or inversion estimation; Step 3, using the step-by-step Fourier algorithm of the parabolic equation model to calculate the electromagnetic field propagation; Step 4: Perform power calibration on the calculated electromagnetic field to obtain the electromagnetic wave spatial propagation loss and propagation factor; Step 5: Calculate the Earth's equivalent radius R based on the atmospheric refractive index profile outside the parabolic equation height limit e ; Step 6: extract the curve of the electromagnetic wave propagation factor changing with the distance at the upper limit of the parabolic equation height, and analyze its elevation angle relative to the radiation source through coordinate transformation to form a curve of the propagation factor changing with the elevation angle; Step 7: Establish a spatial field extrapolation grid coordinate system from the upper limit of the parabolic equation height to the high altitude / near space, and interpolate the propagation factor obtained in step 6 according to the curve of the propagation factor changing with the elevation angle to obtain the propagation factor of each point in the grid coordinate system; Step 8: Calculate the free space path loss of each point in the spatial field extrapolation grid coordinate system, and after subtracting the propagation factor, obtain the electromagnetic field path loss of each point in the grid coordinate system.

2. The method for extrapolating marine space field based on the parabolic equation model of radio wave propagation according to claim 1 is characterized by: The calculation of the variation curve of the radiation source propagation factor with the elevation angle in step 6 includes: Step 6.1, extract the curve of the electromagnetic wave field strength at the upper limit of the parabolic equation model with distance, and calculate the path loss at the upper limit of the parabolic equation model with distance r by spatially calibrating the electromagnetic field: PL(h pe ,r)=20log 10 (E0(h ant ,Δr) / E(h pe ,r))+10log 10 (4πΔr 2 ) where h pe is the upper limit of the height of the parabolic equation, h ant is the height of the radiation source above the sea level, Δr is the grid step size of the parabolic equation model; Step 6.2: Compare with the free space path loss to obtain the propagation factor at the upper limit of the parabolic equation model: PF(h pe ,r)=10log 10 (4πr 2 )-PL(h pe ,r); Step 6.3: Calculate the elevation angle relative to the radiation source based on the position of each point at the upper limit of the parabolic equation model: In the formula, r c To calculate the corresponding distance of the center point of the region, R e is the calculated equivalent radius of the earth. Since the distance and elevation angle are monotonically mapped, the propagation factor at the upper limit of the parabolic equation model is PF(h pe ,θ); Step 6.4: Select 5 groups of curves with a height difference of 100m at the upper limit of the parabolic equation model, repeat steps 6.1-6.3, and record the propagation factor calculated for the i-th time as PF i (h pe ,θ), and establish a uniform angle vector in the range of [0,π / 2], denoted as θ0; Step 6.5: Interpolate the propagation factor on θ0: PF i (h pe ,θ0)=I0[θ,PF i (h pe ,θ),θ0] Among them, I0 is a linear interpolation operator; Step 6.7: Take the median of the obtained propagation factor sequence to avoid multipath zeros in the direction of large elevation angles: PF(h pe ,θ0)=median i [PF i (h pe ,θ0)]。 3. The method for extrapolating marine space field based on the parabolic equation model of radio wave propagation according to claim 2 is characterized by: The calculation of the propagation factor of the target position in step 7 includes: Step 7.1, calculate the elevation angle of the radiation source at the target location: Step 7.2: Based on the curve of the propagation factor at the upper limit of the parabolic equation model obtained in step 6 and the elevation angle, the propagation factor at the target position is obtained again by linear interpolation: PF(h tar ,r)=I0[θ0,PF(h pe ,θ0),θ(h tar ,r)]。

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