Method and system for increasing numerical ray tracing speed based on QP model

Abstract

The invention discloses a method and a system for increasing numerical ray tracing speed based on a QP model. The method comprises the steps of firstly constructing a two-dimensional ionosphere electron density grid between a transmitting station and a receiving station, solving ionosphere parameters of a middle point and a large circle distance between the two stations, then synthesizing an oblique measurement ionosphere map trace by utilizing a QP model theory, determining a group path corresponding to a working frequency in an oblique measurement map according to the working frequency on the basis of the working frequency of the transmitting station, and finally obtaining a group path corresponding to the group path. And calculating an initial elevation angle by using the group path and the great circle distance. And finally, scanning the elevation angle range of the working frequency, namely the # imgabs0 # range near the initial elevation angle, through numerical ray tracing scanning to obtain a ray tracing result. The method accelerates the two-dimensional numerical ray tracing under the condition of ensuring that the accuracy is not lost.

Description

Technical Field

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

[0002] Ray tracing is a technology widely used in the analysis of high-frequency radio wave propagation. In the limit of geometric optics, the propagation of radio waves can be simplified to propagate along ray paths, and the task of ray tracing is to determine the shapes and propagation characteristics of these ray paths. Ray tracing technology plays a key role in studying the propagation of radio waves in the ionosphere, especially when calculating the refraction, reflection, bending of rays and their propagation paths.

[0003] In ionospheric applications, as the scale of the problem increases, traditional numerical ray tracing methods often search for elevation angles over a large range, facing problems of low computational efficiency and large computational volume. Therefore, developing efficient acceleration methods is of great significance for improving the speed and real-time performance of ray tracing. Summary of the Invention

[0004] In response to the improvement requirements of existing numerical ray tracing technologies, the present invention proposes a method for accelerating the numerical ray tracing speed based on the QP model. By constructing a two-dimensional ionospheric grid between the transmitting and receiving stations to solve the ionospheric parameters, synthesizing oblique ionograms based on the QP model for tracing, selecting ray group paths, calculating and searching for the initial ray elevation angle, the two-dimensional numerical ray tracing is accelerated without loss of accuracy, and the problems of large computational volume and low efficiency in numerical ray tracing in the simulation of radio wave propagation are solved.

[0005] According to one aspect of the specification of the present invention, there is provided a method for accelerating the numerical ray tracing speed based on the QP model, including: Constructing a two-dimensional ionospheric grid between the signal transmitting station and the receiving station, obtaining the ionospheric parameters of the midpoint of the grid, and calculating the great circle distance between the two stations; Synthesizing an oblique ionogram trace based on the theory of the QP model according to the ionospheric parameters; Selecting the ray group path corresponding to the frequency in the synthesized oblique ionogram according to the shortwave transmission frequency of the transmitting station; Calculating the initial ray elevation angle according to the great circle distance between the two stations and the ray group path, in combination with the trigonometric function relationship; Selecting a preset angle range as the elevation angle search range for numerical ray tracing according to the initial ray elevation angle.

[0006] As a further technical solution, according to the short-wave emission frequency of the transmitting station, select the ray group path corresponding to this frequency in the synthesized oblique sounding ionogram, including: Based on the ionospheric parameters, traverse according to the set frequency sweep range and step interval, and use the iterative method to calculate the great circle distance from the ray landing point to the transmitting station; Judge 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, consider this ray reachable and return the corresponding elevation angle value; According to the reachable rays and their great circle distances and elevation angle values, solve to obtain the corresponding ray group path.

[0007] As a further technical solution, after obtaining the ray group path corresponding to the short-wave emission frequency of the transmitting station, it further includes: Store the current short-wave emission frequency, and perform oblique sounding ionogram tracing according to the array of several short-wave emission frequencies and the corresponding ray group paths.

[0008] As a further technical solution, when performing oblique sounding ionogram tracing, it further includes: When the short-wave multipath propagation phenomenon occurs, according to the working frequency of the transmitting station, find all group paths within the preset range on the oblique sounding ionogram tracing and group them, and use the average value of the group paths within each group as the corresponding group path of the current working frequency.

[0009] As a further technical solution, when classifying all group paths corresponding to the preset range of the short-wave emission frequency, it further includes: Taking the first group path value as a reference, subtract it from the other group path values respectively. If the distance difference is less than the preset distance value, it is considered that the radio wave is reflected through the same layer, otherwise it is the radio wave reflected by another layer.

[0010] As a further technical solution, according to the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship, calculate the initial ray elevation angle, and it further includes: Based on the inverse cosine trigonometric function, the great circle distance and the ray group path, solve to obtain the radian value; convert the radian value to an angle as the initial ray elevation angle.

[0011] According to one aspect of the specification of the present invention, a system for accelerating the numerical ray tracing speed based on the QP model is provided, including: 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 grid midpoint, and calculate the great circle distance between the two stations; The second main module is used to perform oblique sounding ionogram tracing based on the QP model theory according to the ionospheric parameters; The third main module is used to select the ray group path corresponding to the shortwave transmission frequency of the transmitting station in the synthesized oblique ionogram. The fourth main module is used to calculate the initial ray elevation angle according to the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship. The fifth main module is used to select a preset angle range as the elevation angle search range for numerical ray tracing according to the initial ray elevation angle.

[0012] According to one aspect of the specification of the present invention, there is provided a device for accelerating the numerical ray tracing speed based on the QP model, including a memory and a processor. 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 the numerical ray tracing speed based on the QP model.

[0013] According to one aspect of the specification of the present invention, there is provided a non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the steps of the method for accelerating the numerical ray tracing speed based on the QP model.

[0014] Compared with the prior art, the present invention can significantly improve the calculation efficiency, specifically manifested in: (1) The present invention first preliminarily analyzes the group path and its corresponding frequency between the receiving station and the transmitting station by using the QP model according to the ionospheric parameters. Based on this preliminary result, an ionogram trace is obtained. In this step, although the elevation angle needs to be traversed and solved iteratively, since this process has a clear mathematical analysis formula and ignores the geomagnetic field and collision effects, the calculation speed is relatively fast. Further, the elevation angle at the operating frequency is determined according to the trace result 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 searches. This process relies on numerical approximation of the ray path, with high accuracy but a large amount of calculation and high calculation overhead. 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.

[0015] (2) After determining the initial elevation angle by the analytical solution, the present invention then uses the numerical ray tracing method to perform an accurate search within the preset range of the initial elevation angle. Although the accuracy of the preliminary result obtained by the analytical solution is lower than that of the numerical solution, this gap can be effectively compensated by performing a local search near the elevation angle. Most importantly, without reducing the accuracy, the calculation speed of ray tracing is significantly improved. Description of the Drawings

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0017] Figure 1 It is a schematic flow chart of a fast ray tracing method disclosed in an embodiment of the present invention; Figure 2 It is an oblique measurement trace result based on the QP model disclosed in an embodiment of the present invention; Figure 3 It is a comparison of oblique measurement traces using traditional and fast calculation methods respectively disclosed in an embodiment of the present invention; Figure 4 It is a traditional numerical ray tracing result with a transmission frequency of 12.3 MHz disclosed in an embodiment of the present invention; Figure 5 It is a ray tracing result of a fast calculation method with a transmission frequency of 12.3 MHz disclosed in an embodiment of the present invention. Detailed implementation manners

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention. In addition, the technical features in each embodiment or individual embodiment provided by the present invention can be combined with each other arbitrarily to form a new technical solution. This combination is not restricted by the order of steps and / or the mode of structural composition, but must be based on the fact that those of ordinary skill in the art can implement it. When the combination of technical solutions results in contradictions or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0019] The embodiments of the present invention provide a method for accelerating the speed of numerical ray tracing based on the QP model, as Figure 1As shown in the figure, first, a two-dimensional ionospheric grid is constructed between the signal transmitting station and the receiving station, the ionospheric parameters at the midpoint of the grid are obtained, and the great circle distance between the two stations is calculated; then, based on the ionospheric parameters, the synthetic oblique ionogram trace is described according to the QP model theory; subsequently, according to the shortwave transmission frequency of the transmitting station, the ray group path corresponding to this frequency is selected in the synthetic oblique ionogram; then, according to 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 solved; finally, according to the initial ray elevation angle, a preset angle range is selected as the elevation angle search range for numerical ray tracing.

[0020] In the embodiment of the present invention, after constructing the two-dimensional ionospheric grid between the two stations, the maximum electron density at the midpoint of the grid is obtained, and further the critical frequency, peak height and F-layer half thickness of the ionosphere are obtained; 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 calculated.

[0021] Specifically, the calculation equation for calculating the great circle distance between the two stations from their longitudes and latitudes is:

[0022] where D is the great circle distance between the two stations, is the radius of the earth, which is taken as 6370 km here, 、 are the latitude and longitude of the transmitting station respectively, 、 are the latitude and longitude of the receiving station respectively.

[0023] Specifically, the critical frequency is obtained by solving from the maximum electron density, with the unit of MHz, and its formula is as follows:

[0024] where, is the maximum electron density, with the unit of .

[0025] It should be noted that the peak height and the F-layer half thickness can both be obtained by existing technologies, and the present invention will not elaborate here.

[0026] In the embodiment of the present invention, the QP model is used to describe the electron density distribution in the ionosphere. The QP model is:

[0027] where is the peak electron density, is the radial distance measured from the center of the earth, is the peak height, is the F-layer half thickness, is the bottom height of the F layer Take one-third of the peak height according to the empirical value

[0028] After synthesizing the oblique ionogram trace by the QP model theory, given the great circle distance D between two known stations and the ionospheric parameters 、 (critical frequency), , traverse the frequency from 8 - 20 MHz with an interval of 0.01 MHz, and use the iterative method to obtain the great circle distance , judge the absolute value of the difference between and the previously calculated D. If it is less than 2 km, consider this ray reachable and return the elevation angle value , and then calculate the ray group path P corresponding to this frequency

[0029] Great circle distance The equation for solving is:

[0030] The equation for solving the group path P is:

[0031] where , is the incident angle of the ray at the bottom of the ionosphere, taking values from 5° - 60° with an interval of 0.01°, is the ray elevation angle

[0032] As shown by the oblique ionogram, when the frequency exceeds a certain value, ray multipath propagation occurs. According to the frequency of the given transmitting station, find all the corresponding group paths near this frequency ±0.5 MHz , and then classify the above group paths. Taking the first group path value as a reference, subtract it from the rest respectively. If the distance difference is less than 5 km, it is considered that the radio wave is reflected through the same layer; otherwise, it is the radio wave reflected by another layer. After classification, take the average value of each group as the group path P corresponding to this frequency

[0033] Furthermore, calculate the initial elevation angle of the ray from the great circle distance D and the group path P, use the inverse cosine trigonometric function, substitute and , solve to obtain the radian value, convert the radian value to an angle, and select the range near this elevation angle as the ray tracking range, with a step size set to 0.01°

[0034] Next, the advantages of the present invention are compared and described by using the fast calculation method and the traditional method of the embodiments of the present invention

[0035] Step 1: First, construct a two-dimensional ionospheric grid between stations. Then, obtain the ionospheric parameters at the intermediate points from the electron density profile, including the maximum electron density, peak height, critical frequency, and F-layer half-thickness. Calculate the great circle distance between the two stations based on the longitude and latitude.

[0036] Step 2: Through analytical ray tracing, set the frequency sweep range from 8 to 20 MHz with a step of 0.01 MHz. Take the Earth's radius as 6370 km here, and the elevation angle range as 5° - 60° with a step of 0.01°. The height of the bottom layer of the F-layer is equal to the peak height minus the F-layer half-thickness. Calculate the great circle distance from the ray landing point to the transmitting station, and subtract it from the great circle distance in Step 1. If the absolute value is less than 2 km, it is considered that the ray arrives.

[0037] Step 3: For the reachable rays, obtain the corresponding group paths through their great circle distances and elevation angles, and store the short-wave frequencies at this time. By analogy, obtain an array with one-to-one correspondence between frequencies and group paths, and use this to perform ionogram oblique sounding tracing, as Figure 2 .

[0038] Step 4: According to the frequency at which the transmitting station operates , select the tracing closest to this frequency in the ionogram and return the corresponding group path. When the frequency increases to a certain extent, the same frequency may correspond to two group path values, i.e., the short-wave multipath propagation phenomenon. Therefore, it is necessary to classify the group paths. Taking the first group path value as a reference, subtract it from the rest respectively. If the difference is less than 5 km, it is considered that the radio wave is reflected by the same layer; if the difference is large, it is considered that the radio wave is reflected by different layers. After classification, the average value of each group is used as the group path corresponding to this frequency.

[0039] This step is based on the previously obtained oblique sounding ionogram tracing (frequency---group path). According to the input operating frequency of the transmitting station, find all group paths within its vicinity range on the tracing, distinguish the group paths (grouping), and take the average within the grouping, which is used as the group path corresponding to the input operating frequency. It is possible that one operating frequency corresponds to several group paths.

[0040] Step 5: Substitute the great circle distance between the two stations and the group path into

[0041] to obtain the radian value , then convert it to an angular value through the radian. Select the vicinity of this elevation angle ° as the ray tracing range, and set the step to 0.01°.

[0042] Step 6, for traditional numerical ray tracing, the IRI model is adopted, and the sweep frequency range, elevation angle, and step are the same as those in Step 2. By selecting the reachable rays and following the method in Step 3, the ionospheric trace is obtained, and the result is as shown by the dot (·) in Figure 3 the figure.

[0043] Step 7, to verify the fast calculation method, fixed transmission frequencies are used here, 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 they are marked with asterisks (*) in Figure 3 the figure. Some specific results are shown in Table 1. From the group path results, the difference between the two methods is within 2 km, which is within the tolerable range. Therefore, the accuracy of the fast calculation method is acceptable.

[0044] Table 1 Comparison of group paths between traditional and fast calculation methods at fixed transmission frequencies

[0045] Step 8, simulate the ray propagation path at a frequency of 12.3 MHz, and the traditional ray tracing method and the fast calculation method are respectively adopted. The ray propagation paths are respectively plotted in Figure 4 and Figure 5 the figure. The simulation results show that the traditional ray tracing method needs to calculate 5500 ray data, while the fast calculation method only needs to calculate 800 ray data. It can be seen that the fast calculation method has a significant improvement in the search efficiency of ray tracing.

[0046] The implementation basis of each embodiment of the present invention is achieved through programmed processing by a device with processor functions. Therefore, in engineering practice, the technical solutions and functions of each embodiment of the present invention are encapsulated into various modules. Based on this actual situation, on the basis of the above embodiments, the embodiments of the present invention provide a system for accelerating the numerical ray tracing speed based on the QP model, and this system is used to execute the method for accelerating the numerical ray tracing speed based on the QP model in the above method embodiments.

[0047] The system includes: a first main module, which is used to construct a two-dimensional ionospheric grid between a signal transmitting station and a receiving station, obtain the ionospheric parameters of the midpoint of the grid, and calculate the great circle distance between the two stations; a second main module, which is used to perform a synthetic oblique ionogram trace based on the QP model according to the ionospheric parameters; a third main module, which is used to select a ray group path corresponding to the frequency in the synthetic oblique ionogram according to the shortwave emission frequency of the transmitting station; a fourth main module, which is used to calculate the initial ray elevation angle according to the great circle distance between the two stations and the ray group path in combination with the trigonometric function relationship; a fifth main module, which is used to select a preset angle range as the elevation angle search range for numerical ray tracing according to the initial ray elevation angle.

[0048] The system for accelerating the numerical ray tracing speed based on the QP model provided by the embodiment of the present invention is aimed at the improvement requirements of the existing numerical ray tracing technology. By using the foregoing several modules, it solves the problems of large computational amount and low efficiency in numerical ray tracing in the simulation of radio wave propagation by constructing a two-dimensional ionospheric grid between the transceiver stations to solve the ionospheric parameters, synthesizing an oblique ionogram trace based on the QP model, selecting the ray group path, calculating and searching for the initial ray elevation angle, and accelerating the two-dimensional numerical ray tracing without loss of accuracy.

[0049] It should be noted that the system embodiment provided by the present invention, in addition to being used to implement the method in the above method embodiment, is also used to implement the methods in other method embodiments provided by the present invention. The difference is only in setting the corresponding functional modules, and its principle is basically the same as that of the above system embodiment provided by the present invention. As long as those skilled in the art, on the basis of the above system embodiment, refer to the specific technical solutions in other method embodiments, obtain the corresponding technical means by combining technical features, and the technical solutions constituted by these technical means, and on the premise of ensuring the practicability of the technical solutions, improve the modules in the above system embodiment to obtain the corresponding system type embodiments for implementing the methods in other method type embodiments.

[0050] Based on the same inventive concept as the above embodiment, the embodiment of the present invention also provides a device for accelerating the numerical ray tracing speed based on the QP model, including a memory and a processor. 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 the numerical ray tracing speed based on the QP model.

[0051] 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), etc., or may also be a volatile memory, such as a random-access memory (RAM). The memory is any other medium that can be used to carry or store the 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 the embodiment of the present invention may also be a circuit or any other device capable of implementing a storage function, for storing program instructions and / or data.

[0052] In an embodiment 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 devices, discrete gate or transistor logic devices, discrete hardware components, and can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present invention may be directly embodied as being executed by a hardware processor, or may be executed by a combination of hardware and software modules in the processor.

[0053] Based on the same inventive concept as the above embodiments, the embodiment of the present invention further provides a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions cause the computer to execute the steps of the method for accelerating the numerical ray tracing speed based on the QP model.

[0054] In summary of the above embodiments, the present invention discloses a ray tracing method for fast calculation. The method first constructs a two-dimensional ionospheric electron density grid between the transmitting station and the receiving station, solves the ionospheric parameters of the intermediate point and the great circle distance between the two stations, and then uses the theory of the QP model to synthesize the oblique ionogram tracing. Based on the operating frequency of the transmitting station, the group path corresponding to this frequency is determined on the oblique ionogram, and then the initial elevation angle is calculated using the group path and the great circle distance. Finally, the elevation angle range of this operating frequency, that is, the range near the initial elevation angle, is scanned through numerical ray tracing to obtain the ray tracing result. Without sacrificing accuracy, this method accelerates the two-dimensional numerical ray tracing. range to obtain the ray tracing result. Without sacrificing accuracy, this method accelerates the two-dimensional numerical ray tracing.

[0055] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for accelerating the numerical ray tracing speed based on the QP model, characterized in that Including: Construct a two-dimensional ionospheric grid between the signal transmitting station and the receiving station, obtain the ionospheric parameters of the grid midpoint, and calculate the great circle distance between the two stations; Based on the ionospheric parameters, trace the synthetic oblique ionogram according to the theory of the QP model; According to the shortwave emission frequency of the transmitting station, select the ray group path corresponding to this frequency in the synthesized oblique ionogram; According to the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship, solve for the initial ray elevation angle; According to the initial ray elevation angle, select a preset angle range as the elevation angle search range for numerical ray tracing.

2. The method for accelerating the numerical ray tracing speed based on the QP model according to claim 1, wherein According to the shortwave emission frequency of the transmitting station, select the ray group path corresponding to this frequency in the synthesized oblique ionogram, including: Based on the ionospheric parameters, traverse according to the set frequency sweep range and step interval, and use the iterative method to solve for the great circle distance from the ray landing point to the transmitting station; Judge the absolute value of the difference between the solved great circle distance and the great circle distance between the transmitting station and the receiving station. If it is less than the preset value, consider this ray reachable and return the corresponding elevation angle value; According to the reachable rays and their great circle distances and elevation angle values, solve to obtain the corresponding ray group path.

3. The method for accelerating the numerical ray tracing speed based on the QP model according to claim 2, wherein After obtaining the ray group path corresponding to the shortwave emission frequency of the transmitting station, it further includes: Store the current shortwave emission frequency, and perform oblique ionogram tracing according to the array of several shortwave emission frequencies and the corresponding ray group paths.

4. The method for accelerating the numerical ray tracing speed based on the QP model according to claim 3, characterized in that, When performing oblique ionogram tracing, it further includes: When the shortwave multipath propagation phenomenon occurs, according to the operating frequency of the transmitting station, find all the group paths within the preset range on the oblique ionogram tracing and group them, and use the average value of the group paths within each group as the corresponding group path of the current operating frequency.

5. The method for accelerating the numerical ray tracing speed based on the QP model according to claim 4, wherein Classifying all the group paths corresponding to the preset range of the shortwave emission frequency further includes: Taking the first group path value as a reference, subtract it from the other group path values respectively. If the distance difference is less than the preset distance value, it is considered that the radio wave is reflected through the same layer, otherwise it is the radio wave reflected by another layer.

6. The method for accelerating the numerical ray tracing speed based on the QP model according to claim 1, wherein According to the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship, solve for the initial ray elevation angle, and it further includes: Based on the inverse cosine trigonometric function, the great circle distance and the ray group path, solve for the radian value; convert the radian value to an angle as the initial ray elevation angle.

7. A system for accelerating the numerical ray tracing speed based on the QP model, characterized in that Including: 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 grid midpoint, and calculate the great circle distance between the two stations; The second main module is used to trace the synthetic oblique ionogram according to the theory of the QP model based on the ionospheric parameters; The third main module is used to select the ray group path corresponding to the shortwave emission frequency of the transmitting station in the synthesized oblique ionogram; The fourth main module is used to solve for the initial ray elevation angle according to the great circle distance between the two stations and the ray group path, combined with the trigonometric function relationship; The fifth main module is used to select a preset angle range as the elevation angle search range for numerical ray tracing according to the initial ray elevation angle.

8. An apparatus for accelerating the numerical ray tracing speed based on the QP model, characterized in that, It includes a memory and a processor. The memory stores program instructions to be executed by the processor. The processor calls the program instructions to execute the steps of the method for accelerating the numerical ray tracing speed based on the QP model according to 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 cause the computer to execute the steps of the method for accelerating the numerical ray tracing speed based on the QP model according to any one of claims 1 to 6.

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