Method and system for accelerating numerical ray tracing based on vertical measurement frequency and height map

Abstract

The present invention discloses a method for accelerating numerical ray tracing based on a vertical frequency-height map. The method first constructs an ionospheric electron density grid between the transmitting and receiving stations and calculates the great-circle distance between the two stations. Subsequently, a vertical ionogram is generated using the electron density profile at the midpoint and converted into an oblique ionogram. Based on the operating frequency of the transmitting station, the group path corresponding to the operating frequency is determined in the oblique map, and the initial elevation angle is calculated using the group path and the great-circle distance. Finally, numerical ray tracing is used to scan the elevation angle range of the operating frequency, i.e., the range near the initial elevation angle, to obtain ray tracing results. This method significantly improves the computational efficiency of numerical ray tracing without compromising computational accuracy.

Description

Technical Field

[0001] The present invention belongs to the fields of radio physics and space detection, and particularly relates to a method for accelerating numerical ray tracing based on a vertical frequency-height map. Background Art

[0002] Ray tracing is a commonly used analytical tool in the study of high-frequency radio wave propagation. Based on the principles of geometric optics, this technique abstracts radio wave propagation paths into rays, allowing the geometric characteristics and propagation parameters of these rays to be studied. Ray tracing demonstrates unique value in analyzing radio wave propagation in the ionospheric environment, effectively characterizing propagation characteristics such as refraction, reflection, and bending of radio waves.

[0003] Traditional numerical ray tracing methods for ionospheric propagation typically employ a broad elevation angle search strategy, which often results in low computational efficiency and excessive computational complexity when applied to large-scale problems. Therefore, developing efficient acceleration algorithms is crucial for improving the computational efficiency and real-time processing capabilities of ray tracing and is a key research topic. Summary of the Invention

[0004] To address the problems of high computational complexity and low operational efficiency in existing numerical ray tracing technology, the present invention proposes a method to accelerate numerical ray tracing based on vertical frequency-height maps. By optimizing key algorithm links and improving computational efficiency, this method provides a more efficient solution for the numerical simulation of radio wave propagation.

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

[0006] Step 1: Obtain the latitude and longitude coordinates of the signal transmitting station and the receiving station, and calculate the great circle distance between the two stations;

[0007] Step 2: Construct an ionospheric grid between the signal transmitting station and the receiving station, calculate the electron density profile at the midpoint of the grid, and generate a vertical ionogram based on the electron density profile;

[0008] Step 3: Convert the vertical ionogram in step 2 into an oblique ionogram trace;

[0009] Step 4: Based on the radio wave transmission frequency of the transmitting station in step 1, select the ray group path corresponding to the radio wave transmission frequency from the oblique ionogram obtained in step 3. When ray multipath propagation occurs, classify all group paths within a preset frequency range centered on the transmitting station frequency according to the clustering concept, and use the average value of each group path after classification as the group path corresponding to the transmitting station frequency;

[0010] Step 5: Substitute the great circle distance between the two stations in step 1 and the ray group path in step 4 into the trigonometric relationship to solve for the initial ray elevation angle;

[0011] Step 6: With the initial ray elevation angle in step 5 as the center, search for the elevation angle of the numerical ray tracing within the preset angle range.

[0012] As a further technical solution, step 2 further includes:

[0013] Based on the electron density profile, the frequency scanning range and step are set, the reflection height corresponding to each frequency is calculated, and the electron density at the reflection height is obtained by linear interpolation. According to the relationship between the reflection virtual height and the vertical measurement frequency, a vertical measurement ionization map is constructed.

[0014] As a further technical solution, the step 3 converts the vertical power diagram into the oblique power diagram using the following formula:

[0015] ,

[0016] in is the oblique frequency, is the vertical measurement frequency, P is the group path, D is the great circle distance between the two stations, It is a false reflection.

[0017] As a further technical solution, all group paths are classified according to the clustering idea, which also includes:

[0018] Taking the minimum group path as a reference, respectively calculating the difference between the minimum group path and the remaining group paths, and when the difference is less than a threshold, it is considered to belong to the same layer propagation;

[0019] For the remaining group paths, the minimum group path is first calculated, and then the difference between the minimum group path and the remaining group paths is calculated in sequence, and the groups are screened and classified one by one to obtain several groups of group paths.

[0020] As a further technical solution, the method further includes:

[0021] When the propagation mode is greater than or equal to 3, ray tracing is performed using a degenerate wide-range search elevation angle method;

[0022] When the propagation mode is less than 3, the initial ray elevation angle is returned one by one according to the number of modes, and ray tracing is performed near the initial ray elevation angle.

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

[0024] The first main module is used to obtain the longitude and latitude coordinates of the signal transmitting station and the receiving station and calculate the great circle distance between the two stations;

[0025] The second main module is used to construct an ionospheric grid between the signal transmitting station and the receiving station, calculate the electron density profile at the midpoint of the grid, and generate a vertical ionogram based on the electron density profile;

[0026] The third main module is used to convert the generated vertical ionogram into an oblique ionogram trace;

[0027] The fourth main module is used to select a ray group path corresponding to the radio wave transmission frequency from the obtained oblique ionization map based on the radio wave transmission frequency of the transmitting station;

[0028] The fifth main module is used to substitute the great circle distance and ray group path between the two stations into the trigonometric relationship to solve the initial ray elevation angle;

[0029] The sixth main module is used to search for the elevation angle of the numerical ray tracing within a preset angle range with the initial ray elevation angle as the center.

[0030] According to one aspect of the present invention, there is provided a device for accelerating the speed of numerical ray tracing based on a vertical frequency height map, 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 the speed of numerical ray tracing based on a vertical frequency height map.

[0031] 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, and the computer instructions enable the computer to execute the steps of the method for accelerating numerical ray tracing based on a vertical frequency map.

[0032] Compared with the existing technology, the present invention can significantly improve the computing efficiency, which is specifically manifested in:

[0033] (1) The present invention first constructs an ionospheric grid and, based on the electron density profile, generates a vertical ionogram by scanning the propagation height corresponding to each frequency, and converts it into an oblique ionogram. Furthermore, the elevation angle at the operating frequency is determined based on the tracing results and used as the initial elevation angle. Compared with traditional numerical ray tracing methods, traditional methods usually require a large range of elevation angle searches and rely on numerical approximation of ray paths. Although the accuracy is high, the computational complexity and overhead are large. The present invention significantly reduces the computational complexity by narrowing the elevation angle search range, thereby greatly improving the computational efficiency.

[0034] (2) The present invention determines the initial elevation angle by obliquely measuring the ionogram and uses a numerical ray tracing method to perform a precise search within a preset angle range of the initial elevation angle. Although the initial results of this method are slightly less accurate than those of direct numerical ray tracing, the accuracy gap can be effectively compensated by performing a local search near the initial elevation angle. Most importantly, this method significantly improves the computational efficiency of ray tracing without compromising accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] 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.

[0036] Figure 1 A schematic flow chart of a method for accelerating numerical ray tracing based on a vertical frequency-height map disclosed in an embodiment of the present invention;

[0037] Figure 2 A schematic diagram of a vertical ionization diagram between two stations disclosed in an embodiment of the present invention;

[0038] Figure 3 A schematic diagram of converting a vertical ionization diagram into an oblique tracing diagram disclosed in an embodiment of the present invention;

[0039] Figure 4 A schematic diagram showing the comparison results between a fast calculation method disclosed in an embodiment of the present invention and a traditional method;

[0040] Figure 5 This is a schematic diagram of ray tracing results of a traditional method using a transmission frequency of 12.7 MHz disclosed in an embodiment of the present invention;

[0041] Figure 6 This is a schematic diagram of ray tracing results of a fast calculation method for a transmission frequency of 12.7 MHz disclosed in an embodiment of the present invention. DETAILED DESCRIPTION

[0042] 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.

[0043] To address the efficiency bottlenecks of traditional numerical ray tracing algorithms in radio wave propagation simulation, this paper proposes an improved accelerated ray tracing method, namely, a method that accelerates numerical ray tracing based on vertical frequency-height maps. This method primarily addresses the high computational complexity and low operational efficiency issues inherent in existing numerical ray tracing techniques. By optimizing key algorithmic steps and improving computational efficiency, it provides a more efficient solution for numerical simulation of radio wave propagation.

[0044] The embodiment of the present invention provides a method for accelerating numerical ray tracing based on vertical frequency height map, such as Figure 1 As shown, the following steps are included:

[0045] Step (1): Obtain the latitude and longitude coordinates of the signal transmitting station R1 and the receiving station R2, and calculate the great circle distance between the two.

[0046] In step (1), the great circle distance equation between the two stations is calculated based on the longitude and latitude of the two stations:

[0047]

[0048] 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.

[0049] Step (2): Construct an ionospheric grid between the signal transmitting station R1 and the receiving station R2, calculate the electron density profile at the midpoint of the grid, and generate a vertical ionogram based on the profile.

[0050] The vertical ionization map is obtained in step (2), specifically: based on the given electron density profile, the frequency scanning range is set to 1-20MHz, the step is 0.01MHz, the reflection height corresponding to each frequency is calculated, and the electron density at the height is obtained by linear interpolation, and the reflection virtual height is calculated according to the reflection virtual height. and vertical frequency The relationship between the vertical ionization diagram is constructed.

[0051] Step (3): Convert the vertical ionogram in step (2) into an oblique ionogram trace.

[0052] In step (3), the vertical ionogram is converted to an oblique ionogram trace, and the formula is as follows:

[0053]

[0054] in is the oblique frequency, is the vertical measurement frequency, P is the group path, It is a false reflection.

[0055] Step (4): Based on the radio wave transmission frequency of the transmitting station in step (1), select the ray group path corresponding to the frequency in the oblique ionization map generated in step (3).

[0056] The step (4) solves the group path. Since the ray multipath propagation phenomenon will occur when the frequency exceeds a certain value, the following scheme is adopted: according to the frequency of the transmitting station, all corresponding group paths are found within the range of ±0.5MHz of the frequency. , then classify the above group paths and take the minimum group path value As a reference, calculate the rest and Differences are calculated using an 8 km threshold. Data points with a difference less than 8 km are considered to belong to the same layer. For the remaining data, the minimum value is calculated, and then this minimum value is subtracted from each data point in turn, dividing the data into several groups. Points within each group are considered to have propagated through the same layer. After classification, the average value of each group is taken as the group path P corresponding to that frequency.

[0057] This method uses a vertical frequency-height map, encompassing all layers. After a single grouping, the remaining patterns from the previous group are grouped again, using the same method to separate the cluster paths until no more patterns are found. When the number of propagation modes is greater than or equal to three, the fast calculation algorithm directly degenerates to a wide-range elevation search (i.e., 5-60°) and ray tracing. If the number is less than three, the algorithm returns to the initial elevation angle one by one based on the number of patterns, and ray tracing is performed near the initial elevation angle.

[0058] Step (5): Substitute the great circle distance between the stations in step (1) and the ray group path in step (4) into the trigonometric relationship to solve for the initial ray elevation angle.

[0059] Step (5) solves the initial ray elevation angle Specifically: Calculate the initial ray elevation angle from the great circle distance D and the group path P , using the arc cosine trigonometric function, substitute as well as , solve the radian, convert the radian value into an angle, the initial ray elevation angle value Ray tracing is performed near the target, with the step size set to 0.01°. The initial ray elevation angle is calculated as follows:

[0060]

[0061] Where P is the group path and D is the great circle distance.

[0062] Step (6): According to the initial ray elevation angle in step (5), select the The interval within the range serves as the elevation angle search range for numerical ray tracing.

[0063] The present invention demonstrates its technical advantages through comparative experiments with traditional methods, focusing on the significant improvement in the balance between computational efficiency and accuracy.

[0064] (1) First, an ionospheric grid is constructed between the stations. Then, the vertical ionogram is obtained through the electron density profile, and the great circle distance between the two stations is calculated using the longitude and latitude.

[0065] (2) Draw the vertical ionization map through the electron density profile, and check the ray reflection conditions by scanning the frequency from 1-20MHz with an interval of 0.01MHz to obtain the corresponding virtual height at each frequency. The results are as follows Figure 2 shown.

[0066] (3) Convert the vertical ionogram in the above steps into an oblique ionogram. First, perform median filtering on the virtual height data of the vertical ionogram to remove noise. Then, combine the great circle distance and the virtual height parameter to analyze the correspondence between the frequency and the group path, and finally generate the oblique ionogram, as shown in Figure 3 shown.

[0067] (4) According to the frequency of the transmitting station , classify the group paths, and find all corresponding group paths within the frequency ±0.5MHz range , then classify the above group paths and take the minimum group path value As a reference, calculate the rest and Differences are calculated using an 8 km threshold. Data points with a difference less than 8 km are considered to belong to the same layer. For the remaining data, the minimum value is calculated, and then this minimum value is subtracted from each data point in turn, dividing the data into several groups. Points within each group are considered to have propagated through the same layer. After classification, the average value of each group is taken as the group path P corresponding to that frequency.

[0068] (5) Calculate the arc value based on the great circle distance and group path between the two stations, and convert it into an angle value as the initial ray elevation angle. In the ray tracing process, take the initial ray elevation angle as the center and select The range is used as the search interval, and the step parameter is set to 0.01° to achieve high-precision path calculation.

[0069] (6) For traditional numerical ray tracing, the IRI model is used, with a sweep frequency range of 1-20 MHz, a step of 0.01 MHz, an elevation angle of 5°-60°, and a step of 0.01°. The rays that reach the receiving station within 2 km are considered to be reachable, and the group path of the rays is obtained, and then the ray tracing results of the traditional method are obtained, such as Figure 4 The circle (·) symbol.

[0070] (7) To verify the fast calculation method, the working transmission frequencies are used here, including 5 MHz, 9 MHz, 9.7 MHz, 11 MHz, 12.3 MHz, 13 MHz, 15 MHz, and 16 MHz. Figure 4 The group path results for operating frequencies of 9 MHz, 9.7 MHz, 11 MHz, and 12.3 MHz are shown in Table 1. 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.

[0071] Table 1 Comparison of group paths between the traditional method and the fast calculation method of the present invention at the working transmission frequency

[0072]

[0073] (8) Simulate the ray propagation path with a frequency of 12.7 MHz, and use the traditional ray tracing method and the fast calculation method respectively. The ray propagation paths are plotted on Figure 5 and Figure 6 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.

[0074] The various embodiments of the present invention are implemented through programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functionalities of the various embodiments of the present invention are packaged into various modules. Based on this reality, and in addition to the aforementioned embodiments, embodiments of the present invention provide a system for accelerating numerical ray tracing using a vertical frequency-height map. This system is used to implement the method for accelerating numerical ray tracing using a vertical frequency-height map described in the aforementioned method embodiments.

[0075] The system includes: a first main module for obtaining the latitude and longitude coordinates of a signal transmitting station and a receiving station and calculating the great circle distance between the two stations; a second main module for constructing an ionospheric grid between the signal transmitting station and the receiving station, calculating the electron density profile at the midpoint of the grid, and generating a vertical ionogram based on the electron density profile; a third main module for converting the generated vertical ionogram into an oblique ionogram trace; a fourth main module for selecting a ray group path corresponding to the radio wave transmission frequency from the obtained oblique ionogram based on the radio wave transmission frequency of the transmitting station; when multipath propagation of rays occurs, all group paths within a preset frequency range with the transmitting station frequency as the center are classified according to the clustering concept, and the average value of each group path after classification is used as the group path corresponding to the transmitting station frequency; a fifth main module for substituting the great circle distance between the two stations and the ray group path into a trigonometric relationship to solve the initial ray elevation angle; and a sixth main module for searching for the elevation angle of numerical ray tracing within a preset angle range with the initial ray elevation angle as the center.

[0076] The system for accelerating numerical ray tracing based on vertical frequency-height maps provided in an embodiment of the present invention addresses the problems of high computational complexity and low operational efficiency in existing numerical ray tracing technologies. By adopting several of the aforementioned modules and optimizing key algorithm links, the computational efficiency is improved, providing a more efficient solution for the numerical simulation of radio wave propagation.

[0077] 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.

[0078] Based on the same inventive concept as the above-mentioned embodiment, an embodiment of the present invention also provides a device for accelerating the speed of numerical ray tracing based on a vertical frequency height map, 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 the speed of numerical ray tracing based on a vertical frequency height map.

[0079] 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.

[0080] 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.

[0081] 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 storing computer instructions. The computer instructions cause the computer to execute the following steps of the method for accelerating numerical ray tracing based on a vertical frequency-height map:

[0082] Step 1: Obtain the latitude and longitude coordinates of the signal transmitting station and the receiving station, and calculate the great circle distance between the two stations;

[0083] Step 2: Construct an ionospheric grid between the signal transmitting station and the receiving station, calculate the electron density profile at the midpoint of the grid, and generate a vertical ionogram based on the electron density profile;

[0084] Step 3: Convert the vertical ionogram in step 2 into an oblique ionogram trace;

[0085] Step 4: Based on the radio wave transmission frequency of the transmitting station in step 1, select the ray group path corresponding to the radio wave transmission frequency from the oblique ionogram obtained in step 3. When ray multipath propagation occurs, classify all group paths within a preset frequency range centered on the transmitting station frequency according to the clustering concept, and use the average value of each group path after classification as the group path corresponding to the transmitting station frequency;

[0086] Step 5: Substitute the great circle distance between the two stations in step 1 and the ray group path in step 4 into the trigonometric relationship to solve for the initial ray elevation angle;

[0087] Step 6: With the initial ray elevation angle in step 5 as the center, search for the elevation angle of the numerical ray tracing within the preset angle range.

[0088] In summary, the present invention discloses a fast calculation ray tracing method, which first constructs an ionospheric electron density grid between the transmitting station and the receiving station, and calculates the great circle distance between the two stations. Subsequently, the electron density profile of the intermediate point is used to generate a vertical ionization map, and the map is converted into an oblique ionization map. 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, i.e., the elevation angle near the initial elevation angle, is scanned by numerical ray tracing. The ray tracing results are obtained by adjusting the range. This method significantly improves the computational efficiency of numerical ray tracing without reducing the computational accuracy.

[0089] 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 vertical frequency-height maps, characterized in that: include: Step 1: Obtain the latitude and longitude coordinates of the signal transmitting station and the receiving station, and calculate the great circle distance between the two stations; Step 2: Construct an ionospheric grid between the signal transmitting station and the receiving station, calculate the electron density profile at the midpoint of the grid, and generate a vertical ionogram based on the electron density profile; Step 3: Convert the vertical ionogram in step 2 into an oblique ionogram trace; Step 4: Based on the radio wave transmission frequency of the transmitting station in step 1, select the ray group path corresponding to the radio wave transmission frequency from the oblique ionogram obtained in step 3. When ray multipath propagation occurs, classify all group paths within a preset frequency range centered on the transmitting station frequency according to the clustering concept, and use the average value of each group path after classification as the group path corresponding to the transmitting station frequency; Step 5: Substitute the great circle distance between the two stations in step 1 and the ray group path in step 4 into the trigonometric relationship to solve for the initial ray elevation angle; Step 6: With the initial ray elevation angle in step 5 as the center, search for the elevation angle of the numerical ray tracing within the preset angle range.

2. The method for accelerating numerical ray tracing based on vertical frequency-height maps according to claim 1, characterized in that: The step 2 further comprises: Based on the electron density profile, the frequency scanning range and step are set, the reflection height corresponding to each frequency is calculated, and the electron density at the reflection height is obtained by linear interpolation. According to the relationship between the reflection virtual height and the vertical measurement frequency, a vertical measurement ionization map is constructed.

3. The method for accelerating numerical ray tracing based on vertical frequency-height maps according to claim 1, characterized in that: The step 3 converts the vertical power diagram into the oblique power diagram using the following formula: ， in is the oblique frequency, is the vertical measurement frequency, P is the group path, D is the great circle distance between the two stations, It is a false reflection.

4. The method for accelerating numerical ray tracing based on vertical frequency-height maps according to claim 1, characterized in that: All group paths are classified according to the clustering idea, including: Taking the minimum group path as a reference, respectively calculating the difference between the minimum group path and the remaining group paths, and when the difference is less than a threshold, it is considered to belong to the same layer propagation; For the remaining group paths, the minimum group path is first calculated, and then the difference between the minimum group path and the remaining group paths is calculated in sequence, and the groups are screened and classified one by one to obtain several groups of group paths.

5. The method for accelerating numerical ray tracing based on vertical frequency-height map according to claim 4, characterized in that: The method further comprises: When the propagation mode is greater than or equal to 3, ray tracing is performed using a degenerate wide-range search elevation angle method; When the propagation mode is less than 3, the initial ray elevation angle is returned one by one according to the number of modes, and ray tracing is performed near the initial ray elevation angle.

6. A system for accelerating numerical ray tracing based on vertical frequency and height maps, characterized in that: include: The first main module is used to obtain the longitude and latitude coordinates of the signal transmitting station and the receiving station and calculate the great circle distance between the two stations; The second main module is used to construct an ionospheric grid between the signal transmitting station and the receiving station, calculate the electron density profile at the midpoint of the grid, and generate a vertical ionogram based on the electron density profile; The third main module is used to convert the generated vertical ionogram into an oblique ionogram trace; The fourth main module is configured to select a ray group path corresponding to the radio wave transmission frequency from the oblique ionogram obtained based on the radio wave transmission frequency of the transmitting station. When multipath propagation of rays occurs, all group paths within a preset frequency range centered on the transmitting station frequency are classified, and the average value of each group path after classification is used as the group path corresponding to the transmitting station frequency. The fifth main module is used to substitute the great circle distance and ray group path between the two stations into the trigonometric relationship to solve the initial ray elevation angle; The sixth main module is used to search for the elevation angle of the numerical ray tracing within a preset angle range with the initial ray elevation angle as the center.

7. A device for accelerating numerical ray tracing based on vertical frequency-height maps, 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 vertical frequency height map as described in any one of claims 1 to 5.

8. 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 vertical frequency map according to any one of claims 1 to 5.

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