High-frequency sky-ground wave radar ionosphere electron concentration inversion method based on QPS numerical ray tracing and multi-target optimization

Abstract

The invention discloses a QPS numerical ray tracing and multi-target optimization-based high-frequency sky-ground wave radar ionosphere electron concentration inversion method, which comprises the following steps of: firstly, carrying out FFT (Fast Fourier Transform) on radar echo data, constructing a radar echo distance-Doppler matrix, and according to the obtained radar echo distance-Doppler matrix, calculating the electron concentration of a high-frequency sky-ground wave radar ionosphere according to the obtained radar echo distance-Doppler matrix; determining an antenna direct wave group distance and a transmitting station-receiving station ground distance; then determining an optimal emission elevation angle by using randomly generated ionosphere parameters; and finally, taking the emission elevation angle data corresponding to the n groups of ionosphere parameters as an initial population, and carrying out iterative optimization on the initial population by utilizing a population optimization algorithm to obtain an optimal ionosphere parameter result, thereby realizing ionosphere electron concentration inversion. According to the scheme, the radar echo data and the randomly generated ionosphere parameters are combined, the amount of data needing to be calculated is remarkably reduced, accurate inversion of the ionosphere parameters is achieved through ray tracing and multi-target optimization, the structure is simpler, the method does not depend on a complex model or a large amount of experience data, and the method is suitable for large-scale popularization and application. The optimal ionosphere parameter can be approached more quickly and effectively, and the real-time performance and accuracy of ionosphere electron concentration inversion are improved.

Description

Technical Field

[0001] The invention belongs to the field of high-frequency sky-ground wave ionosphere inversion, and specifically relates to a high-frequency sky-ground wave radar ionosphere electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization. Background Art

[0002] High-frequency ground-to-air wave radar is a hybrid high-frequency over-the-horizon radar, a radar system that can detect distant targets by using the reflection of electromagnetic waves from the ionosphere. Because it can cover target areas beyond the horizon, high-frequency ground-to-air wave radar has important application value in military early warning, long-range monitoring, and detection of large-scale ocean and air targets.

[0003] The ionosphere is a layer of charged particles in the Earth's atmosphere formed by ionized gas molecules and atoms by solar radiation. The electron concentration in the ionosphere has a direct impact on the refraction, reflection and absorption of electromagnetic waves, which in turn affects the working performance of high-frequency radars. Since the electron concentration in the ionosphere changes with time, location, season, solar activity and other factors, the dynamic changes in the propagation path of electromagnetic waves make the interpretation of radar echo signals complicated. Therefore, accurately inverting the distribution of ionospheric electron concentration can help correct the calculation of the propagation path of electromagnetic waves and improve the detection accuracy and reliability of radar systems.

[0004] The existing methods for inverting ionospheric electron concentration mainly rely on the International Reference Ionosphere (IRI) or ground altimeter data. The above methods face some significant challenges in practical applications: the IRI model is an empirical model built on a large amount of historical data. Although it can provide the average distribution of ionospheric electron concentration on a global scale, it is insufficient in reflecting the real-time ionospheric state and local ionospheric disturbances; the ionospheric structure is complex and highly nonlinear, making it difficult for the IRI model to accurately capture the rapidly changing ionospheric environment, especially during periods of intense geomagnetic or solar activity, the model's prediction error may be large; the complexity of the IRI model also makes it difficult to perform fast and accurate calculations in some specific applications. Ground-based altimeters detect the height and electron concentration distribution of the ionosphere by transmitting and receiving high-frequency signals. They are usually used to obtain real-time data on the local ionosphere. However, the limitation of altimeters lies in their single location. They can usually only provide ionospheric information above a specific location and lack the ability to cover a large area. The detection depth of altimeters is limited, making it difficult to fully capture the entire picture of the ionosphere, especially in areas with complex terrain or far away from the altimeter location. The data obtained may not reflect the actual state of the ionosphere. Summary of the invention

[0005] In view of the above problems, the object of the present invention is to provide a high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization.

[0006] The specific technical solution for achieving the purpose of the present invention is:

[0007] A high-frequency ground-to-earth wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization includes the following steps:

[0008] Step 1, perform FFT transformation on the radar echo data to construct the radar echo range-Doppler matrix;

[0009] Step 2, according to the radar echo range-Doppler matrix obtained, based on the ideal characteristics of the sky wave direct wave with the minimum attenuation and the maximum peak amplitude, determine the range element and Doppler of the sky wave direct wave;

[0010] Step 3, determine the antenna direct wave group distance and the ground distance between the transmitting station and the receiving station;

[0011] Step 4: Use the ground vertical meter observation data to set the initial ionospheric parameter range;

[0012] Step 5: randomly generate n groups of ionospheric parameters based on the ionospheric parameter range, and determine the ionospheric state corresponding to each group of parameters based on the QPS ionospheric model;

[0013] Step 6, traverse the launch elevation angles, and determine the direct wave group distance set and ground distance set corresponding to each set of ionospheric parameters by ray tracing;

[0014] Step 7, record the absolute value difference between the distance set and the real group distance of the radar direct wave as A1; record the absolute value difference between the ground distance set and the real ground distance between the transmitting station and the receiving station as A2; find the minimum corresponding elevation angle of A1 plus A2, and set it as the transmitting elevation angle;

[0015] Step 8: Use the transmission elevation angle data corresponding to the n groups of ionospheric parameters as the initial population, and use the population optimization algorithm to iteratively optimize the initial population to obtain the optimal ionospheric parameter results and realize the inversion of ionospheric electron concentration.

[0016] Compared with the prior art, the present invention has the following beneficial effects:

[0017] (1) The high-frequency ground-to-ground wave radar ionospheric electron concentration inversion method based on QPS ray tracing proposed in the present invention realizes accurate inversion of ionospheric parameters through ray tracing and multi-objective optimization. It has a simpler structure and does not rely on complex models or a large amount of empirical data.

[0018] (2) The method of the present invention significantly reduces the amount of data required for calculation by combining radar echo data with randomly generated ionospheric parameters. Compared with the traditional IRI model, this method can maintain high inversion accuracy with smaller data requirements;

[0019] (3) In the process of determining the emission elevation angle and ray tracing, the present invention combines the beyond-horizon capability of the radar system to cover a wider detection range, effectively making up for the deficiency of the limited detection range of the altimeter, and is suitable for the inversion of a large range of ionospheric states.

[0020] (4) The present invention uses a multi-objective optimization method to perform iterative calculation and non-dominated sorting based on randomly generated ionospheric parameters, which can more quickly and effectively approach the optimal ionospheric parameters and improve the real-time and accuracy of ionospheric electron concentration inversion.

[0021] The present invention is further described below in conjunction with specific implementation modes. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The present invention is a flow chart of the method for inverting the ionospheric electron concentration of high-frequency ground-to-sky wave radar based on QPS ray tracing.

[0023] Figure 2 It is a schematic diagram of the propagation path of the direct wave of the high-frequency over-the-horizon radar for transmitting and receiving high-frequency waves on the ground according to the present invention.

[0024] Figure 3 It is a diagram of ionospheric propagation paths at different transmission elevation angles under the random ionospheric state of the present invention.

[0025] Figure 4 It is a comparison diagram of ionospheric parameters inverted by the QPS ionospheric model and the IRI model of the present invention.

[0026] Figure 5 This is the single elevation angle QPS inversion ionospheric electron concentration and propagation path diagram at a certain moment of the present invention.

[0027] Figure 6 This is the dual-elevation-angle QPS inversion ionospheric electron concentration and propagation path diagram at a certain moment of the present invention.

[0028] Figure 7 This is a comparison of the time variation of the electron concentration in the ionosphere reflected by the QPS ionosphere model of the present invention and the IRI model.

[0029] Figure 8 This is a comparison diagram of the ionospheric electron concentration profile inverted by the QPS ionospheric model and the IRI model at a certain moment of the present invention. DETAILED DESCRIPTION

[0030] Example

[0031] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. The described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0032] As shown in this application and claims, unless the context clearly indicates an exception, the words "a", "an", "an kind" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "include" and "comprise" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0033] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values ​​of the parts and steps set forth in these embodiments do not limit the scope of the present application. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to those of ordinary skill in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be considered as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so that once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0034] Combination Figure 1 , a high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization, comprising the following steps:

[0035] Step 1: Perform FFT transformation on the radar echo data to construct the radar echo range-Doppler matrix:

[0036] Step 1-1, the number of antenna channels is M, the number of frames is N, the number of distance units is P, generate an M×N×P distance dimension spectrum data containing all antenna channels and all frames, denoted as X, and perform windowing and the first FFT on each antenna channel and each frame data to obtain FFT1:

[0037] FFT1=fftshift(FFT(X(a(i),:,fr(j))×ham(RN)))

[0038] Wherein, i = 1, 2, 3 ... M, j = 1, 2, 3 ... N, a is a certain antenna channel, fr is a certain data frame, RN is all distance units, FFT is fast Fourier transform, fftshift is to move the zero-frequency component in the FFT result to the center position, and ham is the Hamming window;

[0039] Step 1-2: For the data matrix FFT1, perform windowing and a second FFT for each antenna channel and each distance unit to obtain FFT2:

[0040] FFT2=fftshift(FFT(FFT1(a(i),rn(k),:)×ham(FN)))

[0041] Wherein, k = 1, 2, 3…P, rn is a certain distance unit, and FN is the number of all frames.

[0042] Step 2: According to the radar echo range-Doppler matrix obtained, based on the ideal characteristics of the sky wave direct wave with the minimum attenuation and the maximum peak amplitude, determine the distance element and Doppler of the sky wave direct wave:

[0043] Step 2-1: Determine the background noise and peak power based on the acquired radar echo range-Doppler matrix:

[0044] The FFT2 data of the radar echo range-Doppler matrix is ​​converted into decibel result data, all the frame numbers of a certain range element are sorted, and the decibel value of the background noise is estimated by using the frame signal power after a certain position, and the peak power is determined; in this embodiment, the 1 / 3 position of the sorted signal power is selected to estimate the dB value of the background noise;

[0045] Step 2-2: In the search range, determine whether it is a direct wave by comparing the power value of a certain distance element with the power value difference of its adjacent elements before and after, as well as the absolute value difference with the background noise and Maxval. If it is a direct wave, record its distance element and Doppler:

[0046] Maxval=(max(avg((RN(idx min ,idx max ),:)))

[0047] Among them, Maxval is the maximum dB value in the search range, idx min is the minimum distance element index, idx max is the maximum distance element index.

[0048] Step 3: Determine the antenna direct wave group distance and the ground distance between the transmitting station and the receiving station:

[0049] group=(Pst-Bias)×distRes+GrOrig

[0050] Among them, group is the skywave direct wave group distance, Pst is the distance element where the skywave direct wave is located, Bias is the distance element bias of the skywave relative to the receiving station, distRes is the skywave distance resolution, and GrOrig is the initial group distance.

[0051] Step 4: Use the ground vertical meter observation data to set the initial ionospheric parameter range:

[0052] The ground vertical instrument observation data of several days before and after the radar echo data are counted. In this embodiment, the ground vertical instrument observation data of 7 days, 3 days before and after the echo data, are selected to obtain the upper and lower bounds of the ionospheric parameters, and generate a dim×2 array, denoted as bou, which is used to store the ionospheric parameter range, and dim is used to represent the ionospheric parameter dimension, bou(dim,2) represents the upper boundary of the ionospheric parameters, and bou(dim,1) represents the lower boundary of the ionospheric parameters.

[0053] Step 5: Randomly generate n groups of ionospheric parameters based on the ionospheric parameter range, and determine the ionospheric state corresponding to each group of parameters based on the QPS ionospheric model:

[0054] Step 5-1: Randomly generate n groups of ionospheric parameters based on the determined ionospheric parameter range:

[0055] par=bou(dim,1)+rand(n,dim)×(bou(dim,2)-bou(dim,1))

[0056] Among them, par represents the generated n sets of parameters, and rand refers to the randomly generated n×dim-dimensional (0~1) array;

[0057] Step 5-2: Determine the ionospheric state corresponding to each set of ionospheric parameters based on the QPS ionospheric model:

[0058]

[0059] a jFE =a E ;

[0060]

[0061]

[0062] r jFE =r E

[0063]

[0064] Where a = N m , N m is the maximum electron density of each layer in the electron layer, r b is the distance from the bottom layer of each layer of the ionosphere to the center of the earth, y m is the half thickness of each layer in the ionosphere, r is the distance from the peak electron concentration height in each layer of the ionosphere to the center of the earth, N E ,a E ,b E ,r E Represents the state parameter of the E layer in the ionosphere, N jFE ,a jFE ,b jFE ,r jFE Indicates the state parameters of the EF1 connection layer in the ionosphere, Represents the state parameters of the F1 layer in the ionosphere, N jFF ,a jFF ,b jFF ,r jFF Represents the state parameters of the F1F2 connection layer in the ionosphere, Represents the state parameters of the F2 layer in the ionosphere.

[0065] Step 6: Traverse the launch elevation angles and determine the direct wave group distance set and ground distance set corresponding to each set of ionospheric parameters by ray tracing:

[0066] Traversing the radar transmission elevation angle, based on the ionospheric space state determined by the ionospheric parameters, ray tracing is used to determine the direct wave group distance set and ground distance set corresponding to each set of ionospheric parameters:

[0067] The ray tracing method is mainly to solve the Haselgrove equation:

[0068]

[0069]

[0070] Among them, r, θ, is the coordinate of the spherical coordinate system on the ray path; k r , k θ , are the three components of the wave vector in the spherical coordinate system; H is the Hamiltonian operator, n is the phase refractive index, c is the speed of light, and f is the N is the plasma frequency, f is the ray working frequency;

[0071] The group distance and ground distance corresponding to different ray trajectories at each emission elevation angle are determined by the above equation group, wherein the above Haselgrove equation group can be numerically solved using the Runge-Kutta algorithm. The position coordinates and wave vector of the ray path point can be obtained for each step change in the group distance, and the complete ray trajectory can be obtained; finally, by traversing the emission elevation angle (3 to 81° in this embodiment), the group distance and ground distance corresponding to different ray trajectories can be obtained.

[0072] Step 7: record the absolute value difference between the distance set and the real group distance of the radar direct wave as A1; record the absolute value difference between the ground distance set and the real ground distance between the transmitting station and the receiving station as A2; find the minimum corresponding elevation angle of A1 plus A2, and set it as the transmitting elevation angle:

[0073] Specifically, the absolute value difference between the antenna direct wave group distance of a certain set of ionospheric parameters determined in step 7 and the real antenna direct wave group distance determined in step 3 is recorded as set A1, and the absolute value difference between the ground distance determined in step 7 and the real ground distance determined in step 3 is recorded as set A2;

[0074] Sets A1 and A2 are added together, and the added sets are searched. The elevation angle corresponding to the minimum value is set as the transmission elevation angle, and finally the optimal transmission elevation angle corresponding to each set of ionospheric parameters is obtained.

[0075] Step 8: Take the transmission elevation angle data corresponding to n groups of ionospheric parameters as the initial population, and use the population optimization algorithm to iteratively optimize the initial population to obtain the optimal ionospheric parameter results and realize the ionospheric electron concentration inversion:

[0076] Step 8-1, taking n groups of ionospheric parameters and their corresponding transmission elevation angle data as the initial population;

[0077] Step 8-2: Perform non-dominated sorting and crowding calculation on the initial population to form the parent population;

[0078] Non-dominated sorting and crowding calculation are mainly methods proposed for solving multi-objective optimization problems when there are two direct wave echoes in the radar echo, that is, when there are high and low double elevation angles. Non-dominated sorting is a process of sorting the solutions in a multi-objective optimization problem according to their mutual dominance relationship. The purpose is to divide the solution set into different non-dominated layers. The solutions in each layer do not dominate other solutions, nor are they dominated by other solutions. Crowding calculation is used to measure the distribution density of solutions in the target space, aiming to maintain the diversity of the solution set. In multi-objective optimization, the solution set must not only perform well in non-dominated sorting, but also be evenly distributed in the target space to cover a larger possible solution space.

[0079] Step 8-3, selecting, crossing over, and mutating the parent population to generate a child population, determining the ionospheric state of the child population, and determining the emission elevation angle corresponding to the ionospheric state;

[0080] After performing non-dominated sorting and crowding calculation, individuals in the population will be divided into different non-dominated layers, and individuals that perform well in non-dominated sorting and are evenly distributed in crowding calculation will be selected as parents of the next generation. Using crossover operation, new offspring are generated through recombination from the selected parent individuals. Mutation operation is performed on the generated offspring to prevent the population from falling into a local optimal solution and ensure that the population has sufficient diversity.

[0081] Step 8-4: merge the parent and child populations, perform non-dominated sorting and crowding calculation on the merged population, generate a new parent population, and return to step 8-3 until the number of iterations is reached.

[0082] In this embodiment, the measured echo data is used to invert the ionospheric electron concentration, the number of array elements is 8, and the number of pulses is 600. Figure 2 This is a schematic diagram of the propagation path of the direct wave of the high-frequency over-the-horizon radar sent to the sky and received on the ground. Figure 3 It shows the ionospheric propagation paths corresponding to different launch elevation angles under random ionospheric conditions. Figure 4 The ionospheric parameter inversion results of the QPS ionospheric model and the IRI model are compared. Figure 5 and Figure 6 The ionospheric electron concentration inverted by the QPS model and its corresponding propagation path under single elevation angle and double elevation angle conditions at a certain moment are shown respectively. Through these charts, the feasibility of inverting the ionospheric electron concentration through QPS ray tracing is preliminarily proved.

[0083] Figure 7 The comparison of the temporal variation of the ionospheric electron concentration inverted by the QPS model and the IRI model is shown. Figure 8 The comparison of the inversion results of the ionospheric electron concentration profile by the QPS model and the IRI model at a certain moment is shown. Compared with the IRI model, the QPS model has a simpler structure and requires less data to be calculated. The QPS model uses only ionospheric echo data to achieve the ionospheric inversion of the IRI complex system.

[0084] In general, the ionospheric electron concentration inversion method based on QPS ray tracing adopted by the present invention is simpler in structure, has less computational effort, and has a faster inversion speed than the traditional IRI model. At the same time, compared with the altimeter, the QPS model has a larger detection range and can more effectively capture the global changes of the ionosphere. Through the verification of this embodiment, it can be confirmed that the method of the present invention is effective and advantageous in the inversion of ionospheric electron concentration.

[0085] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A high-frequency ground-to-air wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization, characterized in that: The following steps are involved: Step 1, perform FFT transformation on the radar echo data to construct the radar echo range-Doppler matrix; Step 2, according to the radar echo range-Doppler matrix obtained, based on the ideal characteristics of the sky wave direct wave with the minimum attenuation and the maximum peak amplitude, determine the range element and Doppler of the sky wave direct wave; Step 3, determine the antenna direct wave group distance and the ground distance between the transmitting station and the receiving station; Step 4: Use the ground vertical meter observation data to set the initial ionospheric parameter range; Step 5: randomly generate n groups of ionospheric parameters based on the ionospheric parameter range, and determine the ionospheric state corresponding to each group of parameters based on the QPS ionospheric model; Step 6, traverse the launch elevation angles, and determine the direct wave group distance set and ground distance set corresponding to each set of ionospheric parameters by ray tracing; Step 7, record the absolute value difference between the distance set and the real group distance of the radar direct wave as A1; record the absolute value difference between the ground distance set and the real ground distance between the transmitting station and the receiving station as A2; find the minimum corresponding elevation angle of A1 plus A2, and set it as the transmitting elevation angle; Step 8: Use the transmission elevation angle data corresponding to the n groups of ionospheric parameters as the initial population, and use the population optimization algorithm to iteratively optimize the initial population to obtain the optimal ionospheric parameter results and realize the inversion of ionospheric electron concentration.

2. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 1 is characterized in that: The construction of the radar echo range-Doppler matrix in step 1 is specifically as follows: Step 1-1, the number of antenna channels is M, the number of frames is N, the number of distance units is P, generate an M×N×P distance dimension spectrum data containing all antenna channels and all frames, denoted as X, and perform windowing and the first FFT on each antenna channel and each frame data to obtain FFT1: FFT1=fftshift(FFT(X(a(i),:, fr(j))×ham(RN))) Wherein, i = 1, 2, 3 ... M, j = 1, 2, 3 ... N, a is a certain antenna channel, fr is a certain data frame, RN is all distance units, FFT is fast Fourier transform, fftshift is to move the zero-frequency component in the FFT result to the center position, and ham is the Hamming window; Step 1-2: For the data matrix FFT1, perform windowing and a second FFT for each antenna channel and each distance unit to obtain FFT2: FFT2=fftshift(FFT(FFT1(a(i),rn(k),:)×ham(FN))) Wherein, k = 1, 2, 3…P, rn is a certain distance unit, and FN is the number of all frames.

3. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 1 is characterized in that: The step 2 of determining the distance element and Doppler of the sky wave direct wave is specifically as follows: Step 2-1: Determine the background noise and peak power based on the acquired radar echo range-Doppler matrix: Sort all the frames of a certain distance element, use the frame signal power after a certain position to estimate the decibel value of the background noise, and determine the peak power; Step 2-2: In the search range, determine whether it is a direct wave by comparing the power value of a certain distance element with the power value difference of its adjacent elements before and after, as well as the absolute value difference with the background noise and Maxval. If it is a direct wave, record its distance element and Doppler: Maxval=(max(avg((RN(idx min ,idx max ),:))) Among them, Maxval is the maximum dB value in the search range, idx min is the minimum distance element index, idx max is the maximum distance element index.

4. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 1 is characterized in that: Determining the antenna direct wave group distance in step 3 is specifically: group=(Pst-Bias)×distRes+GrOrig Among them, group is the skywave direct wave group distance, Pst is the distance element where the skywave direct wave is located, Bias is the distance element bias of the skywave relative to the receiving station, distRes is the skywave distance resolution, and GrOrig is the initial group distance.

5. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 1 is characterized in that: The step 4 uses the ground vertical meter observation data to set the initial ionospheric parameter range, specifically: The ground vertical instrument observation data of several days before and after the radar echo data are statistically analyzed to obtain the upper and lower bounds of the ionospheric parameters, and generate a dim×2 array, denoted as bou, which is used to store the ionospheric parameter range. Dim is used to represent the ionospheric parameter dimension, bou(dim, 2) represents the upper bound of the ionospheric parameters, and bou(dim, 1) represents the lower bound of the ionospheric parameters.

6. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 5 is characterized in that: The step 5 of generating n groups of ionospheric parameters and determining the corresponding ionospheric states is specifically as follows: Step 5-1: Randomly generate n groups of ionospheric parameters based on the determined ionospheric parameter range: par=bou(dim,1)+rand(n,dim)×(bou(dim,2)-bou(dim,1)) Among them, par represents the generated n sets of parameters, and rand refers to the randomly generated n×dim-dimensional (0~1) array; Step 5-2: Determine the ionospheric state corresponding to each set of ionospheric parameters based on the QPS ionospheric model: r jFE ＝r E Where a = N m , N m is the maximum electron density in each layer of the electron layer, r b is the distance from the bottom layer of each layer of the ionosphere to the center of the earth, y m is the half thickness of each layer in the ionosphere, r is the distance from the peak electron concentration height in each layer of the ionosphere to the center of the earth, N E , a E , b E , r E Represents the state parameter of the E layer in the ionosphere, N jFE , a jFE , b jFE , r jFE Indicates the state parameters of the EF1 connection layer in the ionosphere, Represents the state parameters of the F1 layer in the ionosphere, N jFF , a jFF , b jFF , r jFF Represents the state parameters of the F1F2 connection layer in the ionosphere, Represents the state parameters of the F2 layer in the ionosphere.

7. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 5 is characterized in that: Determining the direct wave group distance set and the ground distance set corresponding to each set of ionospheric parameters in step 6 is specifically: Traversing the radar transmission elevation angle, based on the ionospheric space state determined by the ionospheric parameters, ray tracing is used to determine the direct wave group distance set and ground distance set corresponding to each set of ionospheric parameters: Among them, r, θ, is the coordinate of the spherical coordinate system on the ray path; k r , k θ , are the three components of the wave vector in the spherical coordinate system; H is the Hamiltonian operator, n is the phase refractive index, c is the speed of light, and f N is the plasma frequency, f is the ray working frequency; The group distance and ground distance corresponding to different ray trajectories at each emission elevation angle are determined by the above equations.

8. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 1 is characterized in that: The absolute value difference between the antenna direct wave group distance of a certain set of ionospheric parameters determined in step 7 and the real antenna direct wave group distance determined in step 3 is recorded as set A1, and the absolute value difference between the ground distance determined in step 7 and the real ground distance determined in step 3 is recorded as set A2; Sets A1 and A2 are added together, and the added sets are searched. The elevation angle corresponding to the minimum value is set as the transmission elevation angle, and finally the optimal transmission elevation angle corresponding to each set of ionospheric parameters is obtained.

9. The high-frequency ground-to-sky wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization according to claim 1 is characterized in that: The step 8 uses a population optimization algorithm to iteratively optimize the initial population, specifically: Step 8-1, taking n groups of ionospheric parameters and their corresponding transmission elevation angle data as the initial population; Step 8-2: Perform non-dominated sorting and crowding calculation on the initial population to form the parent population; Step 8-3, selecting, crossing over, and mutating the parent population to generate a child population, determining the ionospheric state of the child population, and determining the emission elevation angle corresponding to the ionospheric state; Step 8-4: merge the parent and child populations, perform non-dominated sorting and crowding calculation on the merged population, generate a new parent population, and return to step 8-3 until the number of iterations is reached.

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