A high-frequency sky-wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization

Abstract

The application discloses a high-frequency sky-wave radar ionosphere electron concentration inversion method based on QPS numerical ray tracing and multi-target optimization, first, FFT transformation is performed on radar echo data to construct a radar echo distance-Doppler matrix, according to the obtained radar echo distance-Doppler matrix, the distance of the direct wave group of the antenna and the ground distance between the transmitting station and the receiving station are determined; then, the best transmission elevation angle is determined by randomly generating ionosphere parameters; finally, the transmission elevation angle data corresponding to n groups of ionosphere parameters are used as an initial population, and the initial population is iteratively optimized by using a population optimization algorithm to obtain optimal ionosphere parameter results, so that the ionosphere electron concentration inversion is realized. The scheme combines radar echo data and randomly generated ionosphere parameters, significantly reduces the required calculation data amount, realizes accurate inversion of ionosphere parameters through ray tracing and multi-target optimization, has a simpler structure, does not depend on complex models or a large amount of experience data, can more quickly and effectively approach optimal ionosphere parameters, and improves the real-time performance and accuracy of the ionosphere electron concentration inversion.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of high-frequency sky-wave ionospheric inversion, and particularly relates to a high-frequency sky-wave radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-objective optimization. BACKGROUND

[0002] High-frequency sky-wave radar is a hybrid high-frequency over-the-horizon radar, which is a radar system capable of detecting long-range targets by reflecting electromagnetic waves in the ionosphere. Due to its ability to cover the target area beyond the horizon, high-frequency sky-wave radar has important application value in military early warning, long-range monitoring, and detection of large-scale sea and air targets.

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

[0004] Existing ionospheric electron concentration inversion methods mainly use the International Reference Ionosphere (IRI) model or ground-based ionosonde data. The above methods face some significant challenges in practical applications: the IRI model is an empirical model based on a large amount of historical data, although it can provide the average distribution of ionospheric electron concentration worldwide, it has limitations in reflecting real-time ionospheric state and local ionospheric disturbances; the complexity and high nonlinearity of the ionosphere make it difficult for the IRI model to accurately capture the rapidly changing ionospheric environment, especially during intense geomagnetic or solar activity, the prediction error of the model 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 ionosonde detects the height and electron concentration distribution of the ionosphere by transmitting and receiving high-frequency signals, and is usually used to obtain real-time data of local ionosphere, however, the limitation of ionosonde is its single location, which can only provide ionospheric information above a specific location, lacking the ability to cover a large area; the detection depth of ionosonde is limited, which is difficult to fully capture the overall picture of the ionosphere, especially in complex terrain or areas far from the ionosonde location, the obtained data may not reflect the actual ionospheric state. SUMMARY

[0005] In view of the above problems, the purpose of the present application is to provide a high-frequency 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 application is:

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

[0008] Step 1, FFT transform is performed on the radar echo data to construct a radar echo range-Doppler matrix;

[0009] Step 2, according to the obtained radar echo range-Doppler matrix, the distance element and Doppler of the sky-wave direct wave are determined based on the characteristics that the direct wave has the minimum attenuation and the maximum peak amplitude under ideal conditions;

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

[0011] Step 4, the initial parameter range of the ionosphere is set using the observation data of the ground ionosonde;

[0012] Step 5, n sets of ionospheric parameters are randomly generated based on the ionospheric parameter range, and the ionospheric state corresponding to each set of parameters is determined based on the QPS ionospheric model;

[0013] Step 6, the transmitting elevation angle is traversed, and the direct wave group distance set and the ground distance set corresponding to each set of ionospheric parameters are determined through ray tracing;

[0014] Step 7, the absolute value difference between the distance set and the real group distance of the radar direct wave is recorded as A1, the absolute value difference between the ground distance set and the real ground distance between the transmitting station and the receiving station is recorded as A2, and the elevation angle corresponding to the minimum sum of A1 and A2 is found and set as the transmitting elevation angle;

[0015] Step 8, the transmitting elevation angle data corresponding to the n sets of ionospheric parameters are used as the initial population, and the initial population is iteratively optimized using a population optimization algorithm to obtain the optimal ionospheric parameter result, thereby realizing ionospheric electron concentration inversion.

[0016] Compared with the prior art, the present application has the following advantages:

[0017] (1) The high-frequency sky-wave radar ionospheric electron concentration inversion method based on QPS ray tracing proposed by the present application realizes accurate inversion of ionospheric parameters through ray tracing and multi-objective optimization, and has a simpler structure and does not depend on complex models or a large amount of empirical data;

[0018] (2) The method of the application 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, the method can maintain high inversion accuracy with smaller data requirements;

[0019] (3) In the determination of the launch angle and the ray tracing process, the method of the application combines the over-the-horizon capability of the radar system to cover a wider detection range, effectively making up for the limited detection range of the altimeter, and is suitable for the inversion of ionospheric state in a large range.

[0020] (4) The method of the application can more quickly and effectively approach the optimal ionospheric parameter by iterative calculation and non-dominated sorting based on randomly generated ionospheric parameters, thereby improving the real-time performance and accuracy of ionospheric electron concentration inversion.

[0021] The application will be further described in conjunction with the specific embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 The flowchart of the ionospheric electron concentration inversion method of the application based on the QPS ray tracing of high-frequency sky-wave radar.

[0023] Figure 2 The schematic diagram of the direct wave propagation path of the sky-to-ground high-frequency over-the-horizon radar of the application.

[0024] Figure 3 The ionospheric propagation path diagram of different launch angles in the random ionospheric state of the application.

[0025] Figure 4 The comparison diagram of the QPS ionospheric model and the IRI model for ionospheric parameter inversion of the application.

[0026] Figure 5 The QPS ionospheric electron concentration inversion and propagation path diagram of a single launch angle at a certain time of the application.

[0027] Figure 6 The QPS ionospheric electron concentration inversion and propagation path diagram of a double launch angle at a certain time of the application.

[0028] Figure 7 The comparison diagram of the time variation of the ionospheric electron concentration of the QPS ionospheric model and the IRI model reflection height of the application.

[0029] Figure 8 The ionospheric electron concentration profile comparison diagram of the QPS ionospheric model and the IRI model at a certain time of the application. DETAILED DESCRIPTION

[0030] EMBODIMENT

[0031] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. The described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of the present application.

[0032] As shown in the present application and claims, unless the context clearly indicates otherwise, the words "one", "an", "a", and / or "the" do not mean to specify a single number, but also can include a plurality. Generally, the terms "comprising" and "including" only indicate including the steps and elements clearly identified, and these steps and elements do not constitute an exclusive list, and the method or device can also include other steps or elements.

[0033] Unless specifically stated otherwise, the relative arrangement of components and steps, numerical expressions, and numerical values set forth in these embodiments are not meant to limit the scope of the present application. Meanwhile, it should be understood that the sizes of the various parts shown in the drawings are not drawn in accordance with the actual proportional relationship. The technology, method and device known to those skilled in the related art can not be discussed in detail, but should be considered as part of the authorized description under appropriate circumstances. In all examples shown and discussed here, any specific value should be interpreted as merely exemplary, and not as a limitation. Therefore, other examples of exemplary embodiments can have different values. It should be noted that similar reference numbers and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further discussed in subsequent drawings.

[0034] In conjunction with Figure 1 A high-frequency 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, performing FFT transformation on radar echo data to construct a radar echo range-Doppler matrix:

[0036] Step 1-1, the number of antenna channels is M, the number of frames is N, and the number of distance units is P. An MxNXP distance dimension spectrum data containing all antenna channels and all frames is generated, denoted as X. For each antenna channel, the first FFT is performed on each frame data after windowing 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, ham is Hamming window;

[0039] Step 1-2, for data matrix FFT1, for each antenna channel, each distance unit is windowed and secondly FFT, FFT2 is obtained:

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

[0041] Wherein, k = 1, 2, 3…P, rn is a certain distance unit, FN is all frame numbers.

[0042] Step 2, according to the obtained radar echo distance-Doppler matrix, according to the characteristics that the sky wave direct wave is minimum and the peak amplitude is maximum in ideal case, the distance unit and Doppler of the sky wave direct wave are determined:

[0043] Step 2-1, based on the obtained radar echo distance-Doppler matrix, the background noise and peak power are determined:

[0044] The FFT2 data of the radar echo distance-Doppler matrix is converted into decibel result data, all frame numbers of a certain distance unit are sorted, the frame signal power after a certain position is used to estimate the decibel value of the background noise, 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, whether it is a direct wave is judged by comparing the power value of a certain distance unit with the power value difference of its adjacent units, and with the absolute value difference of the background noise and Maxval, if it is a direct wave, the distance unit and Doppler where it is located are recorded:

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

[0047] Wherein, Maxval is the maximum dB value in the search range, idx jFE is the minimum distance unit index, idx E is the maximum distance unit index.

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

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

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

[0051] Step 4, setting the initial ionospheric parameter range using the ground ionosonde observation data:

[0052] The ground ionosonde observation data of the days before and after the radar echo data is counted, in this embodiment, 3 days before and after the radar echo data, a total of 7 days of ground ionosonde observation data is selected, the upper and lower boundary data of the ionospheric parameters is obtained, and a dimx2 array is generated, denoted as bou, 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 parameter, and bou(dim, 1) represents the lower boundary of the ionospheric parameter.

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

[0054] Step 5-1, randomly generating n groups of ionospheric parameters based on the determined ionospheric parameter range:

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

[0056] where par represents the generated n groups of parameters, and rand refers to a randomly generated nxdim dimension (0-1) array;

[0057] Step 5-2, determining the ionospheric state corresponding to each group 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 ionosphere, r b is the distance from the bottom height of each layer in 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 of each layer in 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 represents the state parameter of the EF1 connecting layer in the ionosphere, represents the state parameter of the F1 layer in the ionosphere, N jFF , a jFF , b jFF , r jFF represents the state parameter of the F1F2 connecting layer in the ionosphere, represents the state parameter of the F2 layer in the ionosphere.

[0065] Step 6, traverse the transmission elevation angle, determine the direct wave group distance set and ground distance set corresponding to each set of ionospheric parameters by ray tracing:

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

[0067] The ray tracing method mainly solves the Haselgrove equation:

[0068]

[0069]

[0070] where r, θ, are the coordinates in 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 refractive index, c is the speed of light, f N is the plasma frequency, and f is the ray operating frequency;

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

[0072] In step 7, the absolute value difference between the distance set and the real group distance of the radar direct wave is recorded as A1, the absolute value difference between the ground distance set and the real ground distance between the transmitting station and the receiving station is recorded as A2, and the elevation angle corresponding to the minimum sum of A1 and A2 is found and set 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] The sets A1 and A2 are added, the set after addition is searched, the elevation angle corresponding to the minimum value is set as the transmitting elevation angle, and finally the optimal transmitting elevation angle corresponding to each set of ionospheric parameters is obtained.

[0075] In step 8, the transmitting elevation angle data corresponding to n sets of ionospheric parameters are used as the initial population, and the initial population is iteratively optimized by using the population optimization algorithm to obtain the optimal ionospheric parameter result, thereby realizing the inversion of the ionospheric electron concentration.

[0076] In step 8-1, n sets of ionospheric parameters and the transmitting elevation angle data corresponding thereto are used as the initial population.

[0077] In step 8-2, the initial population is subjected to non-dominated sorting and crowding calculation to form a parent population.

[0078] The non-dominated sorting and crowding calculation is mainly used for solving the multi-objective optimization problem when two direct wave echoes appear in the radar echo, that is, when high and low double-elevation angles appear. The non-dominated sorting is a process of sorting the solutions in the multi-objective optimization problem according to the dominance relationship between them, and the purpose is to divide the solution set into different non-dominated layers, and the solutions in each layer do not dominate other solutions and are not dominated by other solutions. The crowding calculation is used to measure the distribution density of the solution in the target space, and aims to maintain the diversity of the solution set. In multi-objective optimization, the solution set not only needs to have good performance in non-dominated sorting, but also needs to be uniformly distributed in the target space to cover a larger possible solution space.

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

[0080] After performing non-dominant sorting and crowdedness calculation, the individuals in the population are divided into different non-dominant layers, and individuals that perform well in non-dominant sorting and are evenly distributed in crowdedness calculation are preferentially selected as parents of the next generation; using a crossing operation, new children are generated by recombination from the selected parent individuals; the generated children are subjected to mutation operation to avoid the population from falling into local optimal solution and ensure that the population has sufficient diversity;

[0081] Step 8-4, merging the parent and child populations, performing non-dominant sorting and crowdedness calculation on the merged population to generate a new parent population, and returning to step 8-3 until the number of iterations is reached.

[0082] In this embodiment, the ionospheric electron concentration is inversed by using the measured echo data, the number of array elements is 8, and the number of pulses is 600. Figure 2 It is a schematic diagram of the direct wave propagation path of the high-frequency over-the-horizon radar. Figure 3 Then the ionospheric propagation path corresponding to different launch elevation angles under random ionospheric conditions is shown. 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 inversed by the QPS model and the corresponding propagation path under single-elevation and double-elevation conditions at a certain time are shown respectively. Through these charts, the feasibility of realizing ionospheric electron concentration inversion by QPS ray tracing is preliminarily proved.

[0083] Figure 7 The time variation comparison of the QPS model and the IRI model in the inversion of ionospheric electron concentration is shown. Figure 8 The inversion results of the ionospheric electron concentration profile by the QPS model and the IRI model at a certain time are shown. Compared with the IRI model, the QPS model has a simpler structure and requires less data for calculation. The QPS model realizes the ionospheric inversion work of the complex IRI system only by using ionospheric echo data.

[0084] In summary, the ionospheric electron concentration inversion method based on QPS ray tracing adopted by the present application has a more concise structure and smaller calculation amount, and has a faster inversion speed compared with the traditional IRI model. At the same time, compared with the altimeter, the detection range of the QPS model is larger, and it 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 application has effectiveness and advantages in the inversion of ionospheric electron concentration.

[0085] The above-described embodiments are merely illustrative of several embodiments of the present application, which are described in more detail and in a more specific and detailed manner, but should not be construed as limiting the scope of the patent. It should be noted that, for those skilled in the art, several modifications 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 should be subject to the appended claims.

Claims

1. A method for inverting ionospheric electron concentration using high-frequency ground-to-surface radar based on QPS numerical ray tracing and multi-target optimization, characterized in that, Includes the following steps: Step 1: Perform FFT transformation on the radar echo data to construct the radar echo range-Doppler matrix; Step 2: Based on the obtained radar echo range-Doppler matrix, and taking into account the ideal characteristics of the skywave direct wave having the minimum attenuation and the maximum peak amplitude, determine the range element and Doppler of the skywave direct wave. Step 3: Determine the direct antenna reach distance to the wave group and the ground distance between the transmitting station and the receiving station; Step 4: Use data from a ground-based vertical measuring instrument to set the initial parameter range for the ionosphere; Step 5: Randomly generate n' sets of ionospheric parameters based on the range of ionospheric parameters, and determine the ionospheric state corresponding to each set of parameters based on the QPS ionospheric model; Step 6: Traverse the emission elevation angles and determine the set of direct wave group distances and ground distances corresponding to each set of ionospheric parameters through ray tracing; Step 7: Denote the absolute difference between the range set and the true group distance of the radar direct wave as A1; denote the absolute difference between the ground range set and the true ground distance between the transmitting station and the receiving station as A2; find the minimum corresponding elevation angle when A1 and A2 are added together, and set it as the transmission elevation angle. The absolute difference between the antenna direct-to-group distance of a certain set of ionospheric parameters determined in step 6 and the actual antenna direct-to-group distance determined in step 3 is denoted as set A1, and the absolute difference between the ground distance determined in step 6 and the actual ground distance determined in step 3 is denoted as set A2. Add sets A1 and A2 together, search the set after addition, and set the elevation angle corresponding to the minimum value as the emission elevation angle. Finally, obtain the optimal emission elevation angle corresponding to each set of ionospheric parameters. Step 8: Use the emission elevation angle data corresponding to the n sets 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, thereby realizing the inversion of ionospheric electron concentration.

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

3. The method for inverting ionospheric electron concentration using high-frequency ground-to-surface radar based on QPS numerical ray tracing and multi-target optimization as described in claim 1, characterized in that, Step 2, determining the distance element and Doppler of the direct skywave, specifically involves: Step 2-1: Based on the acquired radar echo range-Doppler matrix, determine the background noise and peak power: Sort all frames for a given distance element, estimate the background noise in decibels using the signal power of frames that are ranked after a certain position, and determine the peak power. Step 2-2: Within the search range, determine whether a signal is a direct wave by comparing the power value of a certain range cell with the power values ​​of its immediate and adjacent cells, as well as with the absolute values ​​of the background noise and Maxval. If it is a direct wave, record its range cell and Doppler reading. Maxval=(max(avg((RN(idx min ,idx max ),:))) Where Maxval is the maximum dB value within the search range, and idx min idx is the minimum distance meta-index. max This is the maximum distance meta-index.

4. The method for inverting ionospheric electron concentration using high-frequency ground-to-surface radar based on QPS numerical ray tracing and multi-target optimization as described in claim 1, characterized in that, The determination of the antenna direct reach group distance in step 3 is specifically as follows: group=(Pst-Bias)×distRes+GrOrig Where group is the direct skywave group distance, Pst is the range cell of the direct skywave, Bias is the range cell offset of the skywave relative to the receiving station, distRes is the skywave range resolution, and GrOrig is the initial group distance.

5. The high-frequency terrestrial-to-ground radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-target optimization as described in claim 1, characterized in that, Step 4, which involves setting the initial parameter range of the ionosphere using data from a ground-based vertical logging instrument, specifically involves: By analyzing ground-based vertical logging data from several days before and after the radar echo data, the upper and lower bounds of ionospheric parameters are obtained, and a 2dim array, denoted as bou, is generated to store the range of ionospheric parameters. The dimension of the ionospheric parameter is represented by dim, bou(dim,2) represents the upper boundary of the ionospheric parameter, and bou(dim,1) represents the lower boundary of the ionospheric parameter.

6. The high-frequency terrestrial-to-ground radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-target optimization according to claim 5, characterized in that, The process of generating n' sets of ionospheric parameters and determining their corresponding ionospheric states in step 5 is as follows: Step 5-1: Randomly generate n' sets of ionospheric parameters based on the determined range of ionospheric parameters: par=bou(dim,1)+rand(n',dim)×(bou(dim,2)-bou(dim,1)) Where par represents the n' sets of parameters generated, and rand refers to the random generation of an 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 This represents the maximum electron density in each electron shell. r b y represents the distance from the Earth's center at the lowest level of each layer of the ionosphere. m N 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 Earth's center, and N is the distance from the peak electron concentration height in each layer of the ionosphere to the Earth's center. E ,a E ,b E ,r E N represents the state parameters of the E layer in the ionosphere. jFE ,a jFE ,b jFE ,r jFE This represents the state parameters of the EF1 linker layer in the ionosphere. N represents the state parameters of the F1 layer in the ionosphere. jFF ,a jFF ,b jFF ,r jFF This represents the state parameters of the F1F2 connecting layer in the ionosphere. This represents the state parameters of the F2 layer in the ionosphere.

7. The high-frequency terrestrial-to-ground radar ionospheric electron concentration inversion method based on QPS numerical ray tracing and multi-target optimization according to claim 5, characterized in that, The determination of the direct wave group distance set and ground distance set corresponding to each group of ionospheric parameters in step 6 is specifically as follows: By iterating through the radar's emission elevation angles and determining the ionospheric spatial state based on ionospheric parameters, ray tracing is used to determine the set of direct wave group distances and the set of ground distances corresponding to each set of ionospheric parameters. Where r, θ, k represents the coordinates in the spherical coordinate system along the ray path. r k θ , Here are the three components of the wave vector in spherical coordinates; H is the Hamiltonian operator, n is the phase refraction index, c is the speed of light, and f is the velocity of light. N f is the plasma frequency, and f is the X-ray operating frequency; The group distance and ground distance corresponding to different ray trajectories at each emission elevation angle are determined using the above set of equations.

8. The method for inverting ionospheric electron concentration using high-frequency ground-to-surface radar based on QPS numerical ray tracing and multi-target optimization according to claim 1, characterized in that, Step 8, which iteratively optimizes the initial population using a population optimization algorithm, specifically involves: Step 8-1: Use n' sets of ionospheric parameters and their corresponding emission 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: Select, crossover, and mutate the parent population to generate the offspring population, determine the ionospheric state of the offspring population, and determine 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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