Method and system for accelerating numerical ray tracing based on QP model

Abstract

The present invention discloses a method and system for accelerating numerical ray tracing based on the QP model. The method of the present invention first constructs a two-dimensional ionospheric electron density grid between the transmitting station and the receiving station, solves the ionospheric parameters of the midpoint and the great circle distance between the two stations, and then uses the theory of the QP model to synthesize the oblique ionospheric map trace. Based on the operating frequency of the transmitting station, the group path corresponding to the frequency is determined in the oblique map according to the operating frequency, and the initial elevation angle is calculated using the group path and the great circle distance. Finally, the elevation angle range of the operating frequency, that is, the #imgabs0# range near the initial elevation angle, is scanned by numerical ray tracing to obtain the ray tracing result. While ensuring that there is no loss of accuracy, the method of the present invention accelerates two-dimensional numerical ray tracing.

Description

Technical Field

[0001] The present invention belongs to the fields of radio physics and space exploration, and in particular relates to a method and system for accelerating numerical ray tracing based on a QP model (Quasi-Parabolic model). Background Art

[0002] Ray tracing is a widely used technique for analyzing high-frequency radio wave propagation. In the limits of geometric optics, radio wave propagation can be simplified to follow ray paths. The task of ray tracing is to determine the shape and propagation characteristics of these ray paths. Ray tracing plays a key role in studying radio wave propagation in the ionosphere, particularly in calculating the refraction, reflection, and bending of rays, as well as their propagation paths.

[0003] In ionospheric applications, as the problem scale increases, traditional numerical ray tracing methods often search for elevation angles over a wide range, resulting in low computational efficiency and high computational complexity. Therefore, developing efficient acceleration methods is crucial for improving the speed and real-time performance of ray tracing. Summary of the Invention

[0004] In response to the need for improvement in existing numerical ray tracing technology, the present invention proposes a method to accelerate numerical ray tracing based on the QP model. By constructing a two-dimensional ionospheric grid between transceiver stations to solve ionospheric parameters, synthesizing oblique ionogram tracing based on the QP model, selecting ray group paths, and solving and searching for initial ray elevation angles, the method accelerates two-dimensional numerical ray tracing without losing accuracy, thus solving the problem of large computational complexity and low efficiency of numerical ray tracing in simulation of radio wave propagation.

[0005] According to one aspect of the present invention, a method for accelerating numerical ray tracing based on a QP model is provided, comprising:

[0006] Construct a two-dimensional ionospheric grid between the signal transmitting station and the receiving station, obtain the ionospheric parameters of the midpoint of the grid, and calculate the great circle distance between the two stations;

[0007] According to the ionospheric parameters, a theoretical synthetic oblique ionogram trace based on the QP model is obtained;

[0008] According to the shortwave transmission frequency of the transmitting station, the ray group path corresponding to the frequency is selected in the synthesized oblique ionogram;

[0009] The initial ray elevation angle is calculated based on the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship;

[0010] According to the initial ray elevation angle, a preset angle range is selected as an elevation angle search range for numerical ray tracing.

[0011] As a further technical solution, according to the shortwave transmission frequency of the transmitting station, a ray group path corresponding to the frequency is selected in the synthesized oblique ionogram, including:

[0012] Based on the ionospheric parameters, the traversal is performed according to the set sweep frequency range and step interval, and the great circle distance between the ray landing point and the transmitting station is calculated using an iterative method;

[0013] Determine the absolute value of the difference between the calculated great circle distance and the great circle distance between the transmitting station and the receiving station. If it is less than the preset value, the ray is considered reachable and the corresponding elevation angle value is returned.

[0014] According to the reachable rays and their great circle distances and elevation angles, the corresponding ray group paths are solved.

[0015] As a further technical solution, after obtaining the ray group path corresponding to the shortwave transmission frequency of the transmitting station, the following is further included:

[0016] The current shortwave emission frequency is stored, and an oblique ionization map is traced based on an array of several shortwave emission frequencies and corresponding ray group paths.

[0017] As a further technical solution, when performing oblique ionization map tracing, the following is also included:

[0018] When shortwave multipath propagation occurs, all group paths within a preset range are found and grouped on the oblique ionogram trace according to the operating frequency of the transmitting station, and the average value of the group paths in each group is used as the corresponding group path of the current operating frequency.

[0019] As a further technical solution, all group paths corresponding to the preset range of shortwave transmission frequencies are classified, which also includes:

[0020] Taking the first group path value as a reference, subtract it from the remaining group path values. If the distance difference is less than the preset distance value, it is considered that the radio waves are reflected by the same layer, otherwise they are radio waves reflected by another layer.

[0021] As a further technical solution, the initial ray elevation angle is calculated based on the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship, and also includes:

[0022] Based on the inverse cosine trigonometric function, the great circle distance and the ray group path, the radian value is solved and obtained; and the angle obtained by converting the radian value is used as the initial ray elevation angle.

[0023] According to one aspect of the present invention, a system for accelerating numerical ray tracing based on a QP model is provided, comprising:

[0024] The first main module is used to construct a two-dimensional ionospheric grid between the signal transmitting station and the receiving station, obtain the ionospheric parameters of the middle point of the grid, and calculate the great circle distance between the two stations;

[0025] The second main module is used to synthesize the oblique ionogram trace based on the theory of the QP model according to the ionospheric parameters;

[0026] The third main module is used to select a ray group path corresponding to the frequency in the synthesized oblique ionogram according to the shortwave transmission frequency of the transmitting station;

[0027] The fourth main module is used to calculate the initial ray elevation angle based on the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship;

[0028] The fifth main module is configured to select a preset angle range as an elevation angle search range for numerical ray tracing according to the initial ray elevation angle.

[0029] According to one aspect of the present invention, a device for accelerating numerical ray tracing based on a QP model is provided, comprising a memory and a processor, wherein the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the steps of the method for accelerating numerical ray tracing based on the QP model.

[0030] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium stores computer instructions, wherein the computer instructions enable the computer to execute the steps of the method for accelerating numerical ray tracing based on the QP model.

[0031] Compared with the existing technology, the present invention can significantly improve the computing efficiency, which is specifically manifested in:

[0032] (1) The present invention first uses the QP model to perform a preliminary analysis of the group path and its corresponding frequency between the receiving station and the transmitting station based on the ionospheric parameters. Based on this preliminary result, the ionogram trace is obtained. In this step, although the elevation angle needs to be traversed and solved through iteration, the calculation speed is relatively fast because the process has a clear mathematical analytical formula and ignores the geomagnetic field and collision effects. Furthermore, the elevation angle at the operating frequency is determined based on the trace results and used as the initial elevation angle. Compared with the traditional numerical ray tracing method, the traditional method usually requires a large range of elevation angle search. This process relies on numerical approximation of the ray path and has high accuracy, but the calculation amount is huge and the computational overhead is large. The method of the present invention reduces the amount of calculation by narrowing the elevation angle range of the ray, thereby significantly improving the speed.

[0033] (2) After determining the initial elevation angle through analytical solution, the present invention uses a numerical ray tracing method to accurately search within a preset range of the initial elevation angle. Although the initial results obtained by the analytical solution are less accurate than those of the numerical solution, this gap can be effectively bridged by performing a local search near the elevation angle. Most importantly, the computational speed of ray tracing is significantly improved without compromising accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, a brief introduction will be given below to the drawings used in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 A schematic flow chart of a fast ray tracing method disclosed in an embodiment of the present invention;

[0036] Figure 2 This is an oblique measurement tracing result based on the QP model disclosed in an embodiment of the present invention;

[0037] Figure 3 A comparison of oblique measurement traces using traditional and fast calculation methods disclosed in an embodiment of the present invention;

[0038] Figure 4 This is a traditional numerical ray tracing result of a transmission frequency of 12.3 MHz disclosed in an embodiment of the present invention;

[0039] Figure 5 This is the ray tracing result of a fast calculation method for a transmission frequency of 12.3 MHz disclosed in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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 making creative work are within the scope of protection of the present invention. In addition, the technical features in the various embodiments or single embodiments provided by the present invention are arbitrarily combined with each other to form a new technical solution. This combination is not restricted by the sequence of steps and / or structural composition mode, but must be based on the ability of ordinary technicians in this field to implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that this combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0041] The embodiment of the present invention provides a method for accelerating numerical ray tracing based on the QP model, such as Figure 1 As shown in the figure, first, a two-dimensional ionospheric grid is constructed between the signal transmitting station and the receiving station, the ionospheric parameters of the middle point of the grid are obtained, and the great circle distance between the two stations is calculated; then, according to the ionospheric parameters, the oblique ionogram trace is synthesized based on the theory of the QP model; then, according to the shortwave transmission frequency of the transmitting station, the ray group path corresponding to the frequency is selected in the synthesized oblique ionogram; then, according to the great circle distance between the two stations and the ray group path, the initial ray elevation angle is calculated in combination with the trigonometric function relationship; finally, according to the initial ray elevation angle, a preset angle range is selected as the elevation angle search range of the numerical ray tracing.

[0042] After constructing a two-dimensional ionospheric grid between the two stations, the embodiment of the present invention obtains the maximum electron density at the middle point of the grid, and further obtains the critical frequency, peak height, and F layer half-thickness of the ionosphere; at the same time, the longitude and latitude coordinates of the signal transmitting station R1 and the receiving station R2 are obtained, and the great circle distance between the two stations is obtained by calculation.

[0043] Specifically, the equation for calculating the great circle distance between the two stations is:

[0044]

[0045] Where D is the great circle distance between the two stations, is the radius of the Earth, here we take 6370 kilometers, 、 are the latitude and longitude of the transmitting station, 、 are the latitude and longitude of the receiving station, respectively.

[0046] Specifically, the critical frequency is obtained by solving the maximum electron density , in MHz, and the formula is as follows:

[0047]

[0048] in, is the maximum electron density, in units of .

[0049] It should be noted that the peak height and the half thickness of the F layer can be obtained by using existing technologies, which will not be described in detail in the present invention.

[0050] In the embodiment of the present invention, the electron density distribution in the ionosphere is described according to the QP model, which is:

[0051]

[0052] in is the peak electron density, is the radial distance from the center of the Earth, is the peak height, is the half thickness of the F layer, is the bottom height of layer F, According to empirical values, take one third of the peak height.

[0053] After synthesizing the oblique ionogram traces by the QP model theory, the great circle distance D between the two stations and the ionospheric parameters are known. 、 (critical frequency), , traverse the frequency between 8-20MHz with an interval of 0.01MHz, and use the iterative method to obtain the great circle distance ,judge If the absolute value of the difference from the previously calculated D is less than 2 kilometers, the ray is considered reachable and the elevation angle value is returned. , and then calculate the ray group path P corresponding to the frequency.

[0054] Great Circle Distance The equation to be solved is:

[0055]

[0056] The equation for solving the group path P is:

[0057]

[0058] in, , is the incident angle of the ray at the bottom of the ionosphere, which is 5°-60° with an interval of 0.01°. is the ray elevation angle.

[0059] The oblique ionogram shows that when the frequency exceeds a certain value, multipath propagation occurs. Based on the frequency of a given transmitting station, find all the corresponding group paths around the frequency ±0.5MHz. , then classify the above group paths, taking the first group path value As a reference, respectively with the rest Subtract the distances. If the difference is less than 5 km, the waves are considered to have been reflected from the same layer. Otherwise, they are considered to have been reflected from a different layer. After classification, the average value of each group is taken as the group path P corresponding to that frequency.

[0060] Furthermore, the initial ray elevation angle is calculated from the great circle distance D and the group path P. , using the arc cosine trigonometric function, substitute as well as , solve the radian value, convert the radian value into an angle, and select the angle near the elevation angle As the range of ray tracing, the step is set to 0.01°.

[0061] The advantages of the present invention are illustrated below by comparing the fast calculation method of an embodiment of the present invention with a traditional method.

[0062] Step 1: First, construct a two-dimensional ionospheric grid between the stations. Then, obtain the ionospheric parameters of the midpoint through the electron density profile, including the maximum electron density, peak height, critical frequency, and F layer half-thickness, and calculate the great circle distance between the two stations through longitude and latitude.

[0063] Step 2: Use analytical ray tracing, set the sweep frequency range to 8-20 MHz, with a step of 0.01 MHz. The radius of the Earth is taken as 6370 km, the elevation angle range is taken as 5°-60°, with a step of 0.01°, and the bottom layer height of the F layer is equal to the peak height minus the half thickness of the F layer. Calculate the great circle distance between the ray landing point and the generating station, and subtract it from the great circle distance in step 1. If the absolute value is less than 2 km, the ray is considered to have arrived.

[0064] Step 3: The reachable ray passes through its great circle distance and elevation angle, and the corresponding group path is obtained. The shortwave frequency at this time is stored, and the array corresponding to the frequency and group path is obtained by analogy. This is used to perform oblique tracing of the ionogram, such as Figure 2 .

[0065] Step 4: According to the frequency of the transmitting station , select the trace closest to the frequency in the ionogram and return the corresponding group path. When the frequency increases to a certain level, the same frequency may correspond to two group path values, which is the shortwave multipath propagation phenomenon. To this end, it is necessary to classify the group paths and use the first group path value as the As a reference, respectively with the rest If the difference is less than 5 km, the waves are considered to have been reflected from the same layer; if the difference is larger, the waves are considered to have been reflected from different layers. After classification, the average value of each group is used as the group path corresponding to that frequency.

[0066] This step is based on the previously obtained oblique ionogram trace (frequency-group path). According to the input transmitting station operating frequency, all group paths in the vicinity are found on the trace, the group paths are distinguished (grouped), and the average within the group is taken as the group path corresponding to the input operating frequency. It is possible that one operating frequency corresponds to several group paths.

[0067] Step 5: Substitute the great circle distance and group path between the two stations into

[0068]

[0069] Get the radian value , and then convert the radian into an angle value, select the angle near the elevation As the range of ray tracing, the step is set to 0.01°.

[0070] Step 6: For traditional numerical ray tracing, the IRI model is used, and the sweep range, elevation angle, and step are consistent with step 2. By selecting the reachable ray and following the method in step 3, the ionospheric trace is obtained, and the result is as follows: Figure 3 Indicated by the dot (·).

[0071] In step 7, to verify the fast calculation method, fixed transmission frequencies are used, including 9 MHz, 9.3 MHz, 9.7 MHz, 10 MHz, 10.3 MHz, 10.7 MHz, 11 MHz, 11.3 MHz, 11.7 MHz, 12 MHz, 12.3 MHz, 12.7 MHz, 13 MHz, 13.3 MHz, 13.5 MHz, 13.7 MHz, 14 MHz and 14.5 MHz, and the frequency of the transmission frequency is 0. Figure 3 Specific results are shown in Table 1. The group path results show that the difference between the two methods is within 2 kilometers, which is within the tolerable range. Therefore, the accuracy of the fast calculation method is acceptable.

[0072] Table 1 Comparison of group paths between traditional and fast calculation methods at fixed transmission frequency

[0073]

[0074] Step 8: Simulate the ray propagation path with a frequency of 12.3 MHz, and use the traditional ray tracing method and the fast calculation method respectively. The ray propagation paths are plotted on Figure 4 and Figure 5 Simulation results show that the traditional ray tracing method requires the calculation of 5,500 ray data points, while the fast calculation method only needs to calculate 800 ray data points. This shows that the fast calculation method has significantly improved the search efficiency of ray tracing.

[0075] The implementation of each embodiment of the present invention is based on programmed processing performed by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of each embodiment of the present invention are encapsulated into various modules. Based on this reality, and in addition to the aforementioned embodiments, an embodiment of the present invention provides a system for accelerating numerical ray tracing based on a QP model. This system is used to implement the method for accelerating numerical ray tracing based on a QP model described in the aforementioned method embodiments.

[0076] The system includes: a first main module, used to construct a two-dimensional ionospheric grid between a signal transmitting station and a receiving station, obtain ionospheric parameters of the grid midpoint, and calculate the great circle distance between the two stations; a second main module, used to synthesize an oblique ionogram trace based on the theory of the QP model according to the ionospheric parameters; a third main module, used to select a ray group path corresponding to the frequency in the synthesized oblique ionogram according to the shortwave transmission frequency of the transmitting station; a fourth main module, used to solve the initial ray elevation angle based on the great circle distance between the two stations and the ray group path in combination with the trigonometric function relationship; and a fifth main module, used to select a preset angle range as the elevation angle search range for numerical ray tracing according to the initial ray elevation angle.

[0077] The system for accelerating numerical ray tracing based on the QP model provided in an embodiment of the present invention is designed to meet the needs for improving existing numerical ray tracing technology. It adopts the aforementioned modules to solve ionospheric parameters by constructing a two-dimensional ionospheric grid between transceiver stations, synthesize oblique ionogram traces based on the QP model, select ray group paths, and solve and search for initial ray elevation angles. This system accelerates two-dimensional numerical ray tracing without losing accuracy, thereby solving the problems of large computational complexity and low efficiency of numerical ray tracing in simulations of radio wave propagation.

[0078] It should be noted that the system embodiments provided by the present invention are not only used to implement the methods in the above-mentioned method embodiments, but also used to implement the methods in other method embodiments provided by the present invention. The only difference lies in the setting of corresponding functional modules, and the principles thereof are basically the same as the principles of the above-mentioned system embodiments provided by the present invention. As long as those skilled in the art refer to the specific technical solutions in other method embodiments on the basis of the above-mentioned system embodiments, obtain corresponding technical means and technical solutions composed of these technical means by combining technical features, and on the premise of ensuring the practicality of the technical solutions, improve the modules in the above-mentioned system embodiments to obtain corresponding system class embodiments for implementing the methods in other method class embodiments.

[0079] Based on the same inventive concept as the above embodiment, an embodiment of the present invention further provides a device for accelerating numerical ray tracing based on a QP model, comprising a memory and a processor, wherein the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the steps of the method for accelerating numerical ray tracing based on a QP model.

[0080] In an embodiment of the present invention, the memory may be a non-volatile memory, such as a hard disk drive (HDD) or a solid-state drive (SSD), or a volatile memory (volatile memory), such as a random-access memory (RAM). The memory is any other medium that can be used to carry or store desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited thereto. The memory in an embodiment of the present invention may also be a circuit or any other device that can implement a storage function, for storing program instructions and / or data.

[0081] In the embodiments of the present invention, the processor may be a general-purpose processor, a digital signal processor, an application-specific integrated circuit, a field-programmable gate array or other programmable logic device, a discrete gate or transistor logic device, or a discrete hardware component, and may implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. A general-purpose processor may be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of the present invention may be directly implemented and executed by a hardware processor, or by a combination of hardware and software modules within the processor.

[0082] Based on the same inventive concept as the above embodiment, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the steps of the method for accelerating numerical ray tracing based on the QP model.

[0083] In summary, the present invention discloses a fast calculation ray tracing method, which first constructs a two-dimensional ionospheric electron density grid between the transmitting station and the receiving station, solves the ionospheric parameters of the midpoint and the great circle distance between the two stations, and then uses the theory of the QP model to synthesize the oblique ionospheric map trace. Based on the operating frequency of the transmitting station, the group path corresponding to the frequency is determined in the oblique map according to the operating frequency, and then the initial elevation angle is calculated using the group path and the great circle distance. Finally, the elevation angle range of the operating frequency, i.e., the elevation angle near the initial elevation angle, is scanned by numerical ray tracing. The ray tracing results are obtained within the range. This method accelerates the two-dimensional numerical ray tracing without losing accuracy.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the technical solutions of the embodiments of the present invention.

Claims

1. A method for accelerating numerical ray tracing based on a QP model, characterized in that: include: Construct a two-dimensional ionospheric grid between the signal transmitting station and the receiving station, obtain the ionospheric parameters of the midpoint of the grid, and calculate the great circle distance between the two stations; According to the ionospheric parameters, a theoretical synthetic oblique ionogram trace based on the QP model is obtained; According to the shortwave transmission frequency of the transmitting station, the ray group path corresponding to the frequency is selected in the synthesized oblique ionogram; The initial ray elevation angle is calculated based on the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship; According to the initial ray elevation angle, a preset angle range is selected as an elevation angle search range for numerical ray tracing.

2. The method for accelerating numerical ray tracing based on the QP model according to claim 1, characterized in that: According to the shortwave transmission frequency of the transmitting station, the ray group path corresponding to the frequency is selected in the synthetic oblique ionogram, including: Based on the ionospheric parameters, the traversal is performed according to the set sweep frequency range and step interval, and the great circle distance between the ray landing point and the transmitting station is calculated using an iterative method; Determine the absolute value of the difference between the calculated great circle distance and the great circle distance between the transmitting station and the receiving station. If it is less than the preset value, the ray is considered reachable and the corresponding elevation angle value is returned. According to the reachable rays and their great circle distances and elevation angles, the corresponding ray group paths are solved.

3. The method for accelerating numerical ray tracing based on the QP model according to claim 2, characterized in that: After obtaining the ray group path corresponding to the shortwave transmission frequency of the transmitting station, it also includes: The current shortwave emission frequency is stored, and an oblique ionization map is traced based on an array of several shortwave emission frequencies and corresponding ray group paths.

4. The method for accelerating numerical ray tracing based on the QP model according to claim 3, characterized in that: When performing an oblique ionogram tracing, it also includes: When shortwave multipath propagation occurs, all group paths within a preset range are found and grouped on the oblique ionogram trace according to the operating frequency of the transmitting station, and the average value of the group paths in each group is used as the corresponding group path of the current operating frequency.

5. The method for accelerating numerical ray tracing based on the QP model according to claim 4, characterized in that: Classify all group paths corresponding to the preset range of shortwave transmission frequency, including: Taking the first group path value as a reference, subtract it from the remaining group path values. If the distance difference is less than the preset distance value, it is considered that the radio waves are reflected by the same layer, otherwise they are radio waves reflected by another layer.

6. The method for accelerating numerical ray tracing based on the QP model according to claim 1, characterized in that: Based on the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship, the initial ray elevation angle is calculated, including: Based on the inverse cosine trigonometric function, the great circle distance and the ray group path, the radian value is solved and obtained; and the angle obtained by converting the radian value is used as the initial ray elevation angle.

7. A system for accelerating numerical ray tracing based on a QP model, characterized in that: include: The first main module is used to construct a two-dimensional ionospheric grid between the signal transmitting station and the receiving station, obtain the ionospheric parameters of the middle point of the grid, and calculate the great circle distance between the two stations; The second main module is used to synthesize the oblique ionogram trace based on the theory of the QP model according to the ionospheric parameters; The third main module is used to select a ray group path corresponding to the frequency in the synthesized oblique ionogram according to the shortwave transmission frequency of the transmitting station; The fourth main module is used to calculate the initial ray elevation angle based on the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship; The fifth main module is configured to select a preset angle range as an elevation angle search range for numerical ray tracing according to the initial ray elevation angle.

8. A device for accelerating numerical ray tracing based on a QP model, characterized in that: The method comprises a memory and a processor, wherein the memory stores program instructions executed by the processor, and the processor calls the program instructions to execute the steps of the method for accelerating numerical ray tracing based on a QP model as described in any one of claims 1 to 6.

9. A non-transitory computer-readable storage medium, characterized in that The non-transitory computer-readable storage medium stores computer instructions, and the computer instructions enable the computer to execute the steps of the method for accelerating numerical ray tracing based on a QP model according to any one of claims 1 to 6.

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