Two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinate system

Abstract

The present application relates to the field of radio propagation technology, and discloses a radio atmospheric propagation two-dimensional ray tracing method based on a geocentric polar coordinate system, obtains geographical position parameters of a transmitting point, establishes a geocentric polar coordinate system with the earth center as a pole, takes radial distance and geocentric angle as coordinate axes, divides the atmosphere into several layers in the radial direction; iteratively solves a ray propagation differential equation in a continuous numerical integral manner in the geocentric polar coordinate system to generate a ray path point sequence; establishes an analytical mapping relationship between the geocentric polar coordinate system and a specified output coordinate system for coordinate conversion, and outputs path data for calculating atmospheric propagation delay or refraction correction. The present application reduces three-dimensional tracking to two dimensions, is compatible with atmospheric statistical models in a geocentric reference system, can directly calculate atmospheric statistical information, does not need complex coordinate transformation, and is suitable for real-time or quasi-real-time application scenarios such as satellite navigation, radar detection, communication link diagnosis, etc.

Description

Technical Field

[0001] This invention belongs to the field of radio propagation technology and relates to a two-dimensional ray tracing technology for atmospheric propagation of radio signals based on geocentric polar coordinates. Background Technology

[0002] When radio signals propagate through the atmosphere, their propagation path is curved due to the influence of atmospheric refractive index distribution. The radio signal atmospheric propagation path ray tracing method refers to a technique based on geometric optics that calculates propagation characteristics such as signal propagation delay and curvature angle by tracing the geometric path of radio signals propagating through the Earth's atmosphere (mainly the troposphere). This technique is widely used in fields such as satellite navigation (GNSS), very long baseline interferometry (VLBI), radar detection, and wireless communication network planning, and is a fundamental technical means for space geodesy and radio propagation research.

[0003] Early research on ray tracing methods was primarily based on the assumption of a spherically layered atmosphere. Snell's law was used to calculate the propagation trajectory of rays within the spherical atmosphere, analyzing the functional relationships between parameters such as the ray's initial direction, length, and refraction point location, and the atmospheric refractive index gradient. Limited by the accuracy of atmospheric refractive index observations, it was generally assumed that the atmosphere only varied vertically or that ray paths were traced within a specific horizontal atmospheric profile (such as a fixed azimuth plane), resulting in one-dimensional and two-dimensional ray tracing respectively. With the continuous improvement of the spatiotemporal resolution of numerical weather prediction models (such as the European Centre for Medium-Range Weather Forecasts' Generation 5 Atmospheric Reanalysis Dataset (ERA5)), the refined construction of three-dimensional refractive index fields became possible. This led to the development of a three-dimensional ray tracing method based on a three-dimensional refractive index field constructed from meteorological data. This method is currently the most accurate ray tracing method for the atmospheric propagation path of radio signals.

[0004] Existing mainstream ray tracing technologies are mainly divided into two categories: 3D ray tracing and 2D ray tracing. Their technical solutions are described below: (I) Three-dimensional ray tracing technology solution First, a three-dimensional atmospheric refractive index field is constructed within the signal propagation space. This is typically achieved by acquiring three-dimensional grid meteorological data (including air pressure, temperature, and humidity) from high spatiotemporal resolution numerical weather prediction (NWP) data (such as ERA5), and then calculating the three-dimensional atmospheric refractive index field within the signal propagation space using Thayer's empirical formula for refractive index. Second, based on the principles of geometric optics, a system of ordinary differential equations concerning the ray position vector and propagation direction vector is established. Solving these ray differential equations accurately describes the ray propagation path (see Nilsson et al., 2013). When solving these differential equations, the starting point is generally the radio signal transmitter, with initial conditions including the signal's elevation angle and azimuth angle. Numerical integration is performed stepwise along the ray propagation direction using the Runge-Kutta method. During each stepwise integration, the atmospheric refractive index at the integration point is interpolated using the three-dimensional grid points surrounding the integration point, while also considering atmospheric gradient information, to calculate the atmospheric refractive index radially in the spherical coordinate system. Azimuth and latitude By progressively solving for the partial derivatives in three directions, the propagation path of the signal in the atmosphere is determined. See Appendix for details. Figure 1 O represents the Earth's center. n ( r , l , f ) represents grid points ( r , l , f Atmospheric refractive index, The subscripted symbols represent the refractive index sampled values ​​on the corresponding discrete grid nodes; n ( r , l , f The θ represents the atmospheric refractive index gradient, which determines the curvature of the ray. By establishing this spherical discrete grid, the system can interpolate the refractive index and its spatial partial derivative at the current point using the refractive index data of the surrounding grid points in each step of the numerical integration. Thus, combined with the initial emission angle, it can accurately depict the curved propagation path of radio waves in a complex atmospheric environment.

[0005] (II) Two-dimensional ray tracing technology solution Two-dimensional ray tracing also requires first obtaining the three-dimensional atmospheric refractive index field within the signal propagation space from high spatiotemporal resolution NWP data. Ignoring lateral bending of the rays and assuming the Earth's atmosphere has a spherically symmetrical structure (i.e., the atmosphere is horizontally uniformly distributed, and the refractive index varies only with altitude), the signal propagation path in the atmosphere is determined layer by layer based on Snell's law, given the starting position of the ray tracing (longitude, latitude, and geodetic height) and the ray's starting direction (elevation angle and azimuth angle). (Appendix) Figure 2The diagram illustrates a piecewise linear two-dimensional ray tracing method based on Snell's law, where O represents the Earth's center. This represents the radial height corresponding to each atmospheric layer interface. This indicates the instantaneous exit angle of the ray in each layer. The atmosphere is generally divided into several parallel, uniform thin layers along the altitude, and the refractive index of each layer is... The ray is a constant. It emerges from the point of origin with an initial elevation angle θ0. At each interface, according to Snell's law in spherical coordinates... The angle of refraction is calculated, and the ray path is calculated by layer-by-layer geometric recursion (see (Hofmeister, 2016)).

[0006] Currently, the three-dimensional ray tracing method is theoretically the most rigorous and has the highest accuracy. However, this method requires high-frequency numerical solutions and spatial interpolation of ordinary differential equations in three-dimensional space, which consumes a lot of computing resources. Moreover, each ray is solved independently. When the number of rays is huge (such as tens of thousands), the demand for computing resources grows exponentially. Especially in dynamic scenes (such as moving signal sources and changing atmospheric environments), it is necessary to frequently recalculate all ray paths, which is time-consuming and difficult to meet the needs of real-time or near-real-time application scenarios.

[0007] Compared to 3D ray tracing, 2D ray tracing significantly improves efficiency, but it uses a ray coordinate system, namely a local polar coordinate system with the ray's origin as the origin. r , i There are serious adaptation problems when calculating second-order atmospheric state statistics. Constructing atmospheric delay correction models for radio signals often requires second-order atmospheric state statistics, such as the variance-covariance function of refractive index and horizontal / vertical correlation lengths. Since atmospheric physical parameters are usually defined and measured in a global or regional coordinate system with the geocentric reference, their second-order statistics are essentially based on the geocentric reference. Therefore, existing second-order atmospheric state statistical models and methods (such as Kolmogorov turbulent energy spectrum) also mostly choose the geocentric reference for ease of calculation. However, the moving ray coordinate system used in current two-dimensional ray tracing makes it difficult to directly introduce and efficiently calculate second-order atmospheric statistical characteristics with the geocentric coordinate reference. Furthermore, transforming statistics from the geocentric coordinate system to the moving ray coordinate system requires complex and frequent coordinate transformations, introducing additional errors and computational overhead, increasing algorithm complexity. Summary of the Invention

[0008] The core technical problem this invention aims to solve is how to establish an "intermediate" method between traditional three-dimensional full-space ray tracing (three-dimensional ray tracing) and local ray coordinate system tracing (two-dimensional ray tracing). This method should possess low complexity, high computational efficiency, and real-time performance, while overcoming the shortcomings of existing two-dimensional ray tracing hierarchical recursive methods that do not consider the physical characteristics of continuous refractive index changes and are difficult to directly calculate and obtain second-order atmospheric state statistical information. It should also be compatible with atmospheric statistical physical models based on a geocentric reference frame. Thus, this invention provides a novel two-dimensional ray tracing method that can simultaneously meet the requirements of large-scale, real-time / quasi-real-time ray tracing and the acquisition of second-order atmospheric statistical characteristics.

[0009] The above-mentioned technical problems of the present invention are mainly solved by the following technical solutions: A two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates includes: Obtain the geographical location parameters of the launch point, including at least the radial distance of the launch point relative to the Earth's center; and obtain the refractive index distribution data on the vertical profile of the atmosphere; Construct a geocentric polar coordinate system with the Earth's center as the pole, and use the radial distance and the angle between the Earth's center and the pole as coordinate axes; define the instantaneous exit angle of the ray, and establish the representation of the ray's initial state in the geocentric polar coordinate system; Using refractive index distribution data, the atmosphere is divided into several continuous layers in the radial direction, and each layer is assigned a function or interpolation table of refractive index variation with radial distance. In the geocentric polar coordinate system, the ray propagation differential equation is solved iteratively by continuous numerical integration starting from the emission point. In each iteration, the refractive index and its radial gradient are calculated based on the radial distance and instantaneous exit angle of the current point, combined with the refractive index data. The radial distance, geocentric angle and exit angle are then updated to generate a sequence of ray path points. Establish an analytical mapping relationship between the geocentric polar coordinate system and the specified output coordinate system, and transform the ray path point sequence to the specified output coordinate system; The converted ray propagation path data is output to calculate the atmospheric propagation delay or refraction correction of radio signals.

[0010] Moreover, the differential equation for ray propagation is in differential form with the distance from the Earth's center and the angle between the Earth's centers as variables.

[0011] Furthermore, the continuous numerical integration employs the Runge-Kutta method or a variant thereof.

[0012] Moreover, the refractive index distribution data comes from at least one of the following sources: Measured profile of refractive index distribution obtained by a radiosonde; Refractive index distribution profile output by numerical weather prediction model; An empirical exponential function fitting profile is constructed based on the surface refractive index collected in real time by local sensors.

[0013] Moreover, the analytical mapping relationship is a closed-form transformation relationship that does not require iterative solution.

[0014] Furthermore, the specified output coordinate system is at least one of the following: ray coordinate system, geocentric polar coordinate system, or Cartesian coordinate system.

[0015] Moreover, it can be used in at least one of the following scenarios: tropospheric delay modeling for space geodesy, radar coverage analysis, communication link diagnosis, or atmospheric turbulence effect assessment.

[0016] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the two-dimensional ray tracing method for radio atmospheric propagation based on the geocentric polar coordinate system as described above.

[0017] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the two-dimensional ray tracing method for radio atmospheric propagation based on the geocentric polar coordinate system as described above.

[0018] On the other hand, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the two-dimensional ray tracing method for radio atmospheric propagation based on the geocentric polar coordinate system as described above.

[0019] Compared with existing technologies, the two-dimensional ray tracing method for atmospheric propagation of radio signals based on geocentric polar coordinates proposed in this invention has the following advantages: 1) Significantly reduces computational complexity, meeting the needs of real-time / near real-time applications. This invention only applies to the geocentric polar coordinate system (r, x Ray tracing is performed in a two-dimensional plane, avoiding the need for simultaneous integration in three-dimensional space in three-dimensional ray tracing. At the same time, it retains the advantages of low complexity and high efficiency of two-dimensional ray tracing methods. Compared to three-dimensional ray tracing methods, the computational cost is reduced by an order of magnitude, supporting rapid calculation of large-scale ray groups (e.g., thousands to tens of thousands of rays). 2) It can directly and efficiently calculate second-order atmospheric state statistics. Existing two-dimensional ray tracing uses a local ray coordinate system with the ray originating from the ray's starting point (…). r , iThe current coordinate system is inconsistent with the commonly used reference system for expressing atmospheric physical parameters (the geocentric reference system), which leads to complex coordinate transformations and approximations when calculating second-order statistics. This invention directly adopts the geocentric polar coordinate system as the tracking coordinate system. This coordinate system is more compatible with the reference system of the spherical surface layering model of the great balloon and global or regional atmospheric statistical models, making the calculation of second-order statistical information (such as the spatial covariance of refractive index, correlation length, etc.) simple and efficient.

[0020] 3) Provides concise coordinate system transformation relationships. This invention can simultaneously solve for ray coordinate systems ( r , i ) and geocentric polar coordinate system ( r , x The ray path under the geocentric polar coordinate system was established. r , x The analytical transformation relationship between the geocentric reference meteorological data and the Cartesian coordinate system (x, z) is presented. This transformation relationship does not require iterative solution, is concise and efficient, and has extremely high flexibility and compatibility in calling meteorological data with the geocentric reference and outputting observation parameters in the station-centric coordinate system. It avoids the loss of numerical accuracy that may be caused by frequent switching between multiple local coordinate systems in traditional methods. Attached Figure Description

[0021] Figure 1 This is a schematic diagram illustrating the principle of existing 3D ray tracing technology.

[0022] Figure 2 This is a schematic diagram illustrating the principle of existing two-dimensional ray tracing technology.

[0023] Figure 3 This is a schematic diagram of the two-dimensional ray tracing principle based on the geocentric polar coordinate system of this invention.

[0024] Figure 4 This is a schematic diagram illustrating the transformation of the ray path from the geocentric polar coordinate system to the Cartesian rectangular coordinate system according to the present invention. Detailed Implementation

[0025] The following will further explain the concept, specific structure and technical effects of the present invention in conjunction with the accompanying drawings and embodiments, so as to fully understand the purpose, features and effects of the present invention.

[0026] Example 1: This invention notes that existing 3D ray tracing methods require simultaneously solving for the three components of the ray's position and the three components of its propagation direction in a 3D Cartesian or spherical coordinate system, where the ray path can be arbitrarily curved in 3D space. While offering the highest computational accuracy, these methods suffer from high computational complexity, demanding significant computational resources and consuming considerable time. They are typically used in high-precision offline simulations with complex terrain and significant atmospheric horizontal gradients, but cannot meet the real-time requirements of dynamic environments. This invention proposes to constrain the ray within a great circle plane determined by the geocenter, the emission point, and the initial propagation direction, based on the assumption of a spherically layered atmosphere. This requires only solving for the ray in the geocentric polar coordinate system (…). r , x This method solves for two state variables in a single step, fundamentally reducing a three-dimensional problem to a two-dimensional one. In this case, only a one-dimensional refractive index profile is needed for ray tracing, reducing the computational cost per step by more than an order of magnitude compared to three-dimensional ray tracing. Under the same ray density and propagation distance, the overall computation time of this method is typically only 1% to 5% of that of the three-dimensional method, meeting the requirements for real-time or near-real-time large-scale ray swarm solutions. It is suitable for dynamically changing and resource-constrained platforms such as vehicle-mounted, airborne, and shipborne systems.

[0027] Furthermore, existing two-dimensional ray tracing methods based on spherically layered atmospheric models often employ a layered recursive approach. This method is essentially a discrete geometrical optics approximation, dividing the atmosphere radially into several discrete thin layers, with the refractive index within each layer considered constant. This invention differs from the aforementioned layered recursive approach by directly establishing a continuous differential equation for ray propagation in a geocentric polar coordinate system. Based on the assumption of a spherically layered atmosphere, this invention derives a system of differential equations with the distance from the Earth's center and the angle between the Earth's centers as state variables. Numerical integration is used to continuously solve the differential equations, with each integration step based on the refractive index and its gradient at the current point, resulting in a smooth and continuous ray path. Technically, this method better reflects the continuous variation of refractive index in the actual atmosphere, eliminates the need for pre-dividing the atmosphere into layers, and allows for adaptive adjustment of the step size, reducing computational redundancy while maintaining accuracy.

[0028] This embodiment provides a two-dimensional ray tracing method for atmospheric propagation of radio signals based on a geocentric polar coordinate system, comprising the following steps: Data acquisition steps: Obtain the geographical location parameters of the radio signal transmission point, including at least the radial distance of the transmission point relative to the Earth's center; and obtain the refractive index distribution data on the vertical profile of the atmosphere (which can be collected in real time by radiosonde, numerical weather prediction model or local sensor).

[0029] In one possible implementation, the refractive index distribution data comes from at least one of the following: a measured refractive index distribution profile obtained by a radiosonde, a refractive index distribution profile output by a numerical weather prediction model, and an empirical exponential function fitting profile of the surface refractive index based on real-time data collected by local sensors.

[0030] Coordinate system construction steps: With the Earth's center as the pole, construct a geocentric polar coordinate system to describe the ray propagation trajectory. This coordinate system uses the radial distance (distance from the Earth's center) and the angle between the Earth's center and the Earth's center as coordinate axes. Define the instantaneous exit angle of the ray (i.e., the angle between the ray direction and the local horizontal plane) in this coordinate system, and establish the representation of the ray's initial state (emission point position, initial exit angle) in the geocentric polar coordinate system.

[0031] Atmospheric stratification and parameterization steps: Using the acquired refractive index distribution data, the atmosphere is divided into several continuous layers in the radial direction (from the Earth's center). Each layer is assigned a continuous function or discrete interpolation table of refractive index variation with altitude, so that the refractive index value and its radial gradient can be quickly obtained based on the current radial distance during ray tracing.

[0032] Ray path recursion steps: In the geocentric polar coordinate system, starting from the emission point, the ray propagation differential equation is solved iteratively using continuous numerical integration (such as the Runge-Kutta method). In each iteration, based on the radial distance and instantaneous exit angle of the current point, the refractive index and radial gradient are calculated in conjunction with the atmospheric stratification parameterization data. The ray position (radial distance, geocentric angle) and exit angle are then updated, thereby progressively generating a sequence of ray path points. During the recursive process, the first-order integral of the atmospheric refractive index can be accumulated along the path simultaneously (used to calculate the propagation delay).

[0033] In one possible embodiment, the ray propagation differential equation is expressed as a distance from the Earth's center. r Angle with the Earth's center x It is the differential form of the variable.

[0034] In one possible embodiment, the continuous numerical integration in the ray path recursion step employs the Runge-Kutta method or a variant thereof.

[0035] The solution to the ray propagation equation of this invention is not limited to numerical integration methods. It can also be achieved by using a layered recursive method based on Snell's conservation, which divides the atmosphere into radial layers and calculates the changes in the ray elevation angle and the geocentric angle layer by layer.

[0036] The ray tracing direction of this invention is not limited to forward tracing from the emission point to the receiving point. As an equivalent alternative, a reverse ray tracing method can be used, that is, starting from the receiving point, solving the ray path in reverse to the emission point, and then reversing the reverse path to obtain the forward path. This scheme is also based on the geocentric polar coordinate system and does not change the core features of this invention.

[0037] Coordinate mapping steps: Establish the analytical mapping relationship between the geocentric polar coordinate system and the specified output coordinate system (e.g., geographic coordinate system or Cartesian coordinate system), and transform the calculated ray path point sequence to the specified output coordinate system.

[0038] The specified output coordinate system is a ray coordinate system. Geocentric polar coordinate system Or a Cartesian coordinate system (x, y, z).

[0039] Output steps: Output the converted ray propagation path data, which can be used to calculate the atmospheric propagation delay and refraction correction of radio signals, or to calculate second-order statistical information (such as the spatial covariance of refractive index, correlation length, etc.).

[0040] The above solution includes the following three key improvements: (1) Select the geocentric polar coordinate system as the main coordinate system for two-dimensional ray tracing. The ray coordinate system used in traditional two-dimensional ray tracing ( r , i Replace with geocentric polar coordinates. r , x ).

[0041] In one alternative embodiment, the geocentric polar coordinate system described in this invention ( r , x The coordinate system can be replaced by the geocentric rectangular coordinate system (ECEF). There is an analytical transformation relationship between the two, and the ray always lies within the plane of the great circle (i.e., the attached plane). Figure 4 The geometric constraints of the plane containing the yz coordinate axes in the model are used to perform equivalent two-dimensional ray tracing.

[0042] (2) Construct the ray propagation equation in the geocentric polar coordinate system to form a complete two-dimensional ray tracing process based on the geocentric polar coordinate system. Based on the spherical layered atmospheric model and Snell's law, in the geocentric polar coordinate system ( r , x The derivation and solution are re-derived and solved in ) x The differential equation for ray propagation with differential variables.

[0043] (3) Simultaneous calculation of ray paths in both ray coordinate system and geocentric polar coordinate system, and establishment of a concise coordinate transformation formula between Cartesian coordinate system.

[0044] The above scheme can be applied to at least one scenario in space geodesy (such as GNSS / VLBI) tropospheric delay modeling, radar coverage analysis, communication link diagnosis, and atmospheric turbulence effect assessment.

[0045] Example 2 This invention provides a two-dimensional ray tracing method for radio atmospheric propagation based on a geocentric polar coordinate system. The specific process includes the following steps: Step 1. Data Acquisition Temperature is read from meteorological reanalysis data or radiosonde measurements. T ,humidity qair pressure P The atmospheric refractive index at each altitude is calculated using the following empirical formula, with a profile ranging from 0 to 80 km. N : (1) In the formula, R d and R w These are the gas constants for dry air and water vapor, respectively. P w The partial pressure of water vapor is generally calculated using the following formula: (2) Then, the physical refractive index is obtained through conversion. The refractive index data is stored as a refractive index array for later use. Simultaneously, the geographical parameters of the launch point are determined, specifically the radial distance from the geocenter of the launch point. r 0.

[0046] Step 2. Coordinate System Construction Establish a geocentric polar coordinate system with the Earth's center as the origin. , This is the distance between the Earth's centers (radial distance). The angle between the Earth's centers and the Earth's core. Consider the great circle plane containing the emission point: this plane is defined by the Earth's center, the emission point, and the initial ray direction (…). i 0 ，α 0) Determined, among which i 0 represents the initial ray emission elevation angle. α 0 represents the initial azimuth angle of the emitted ray (clockwise relative to true north). In the geocentric polar coordinate system, the initial state is represented as: (3) At the point of emission, the ray is at the starting point of the geocentric polar coordinate system, therefore the geocentric angle is... The radial distance is equal to the distance from the center of the Earth to the launch point. The direction of the emitted ray changes from the initial emission angle. The decision is made. These three parameters together constitute the initial conditions for ray tracing, and are the starting values ​​for subsequent numerical integration to solve the differential equation system (16).

[0047] Step 3. Atmospheric Stratification and Parameterization In a preferred embodiment, the radial distance is from r 0 to r The 0+80 km interval is divided into multiple layers (e.g., setting the number of layers). k (800 layers, each layer approximately 100 m thick), with radial distances from each layer to the node. r 0, r 1, ...,r k Based on the refractive index array obtained in step 1, exponential interpolation is performed to obtain the corresponding refractive index. n ( r k The refractive index at that point was calculated using the central difference method. Radial gradient: (4) Assuming the refractive index depends only on the radial height, the derivative of the refractive index with respect to the radial height can be written in partial derivative form: (5) Step 4. Ray path Assuming the atmosphere is vertically stratified and has a spherically symmetrical structure, and considering that the Earth's local shape is approximately a regular sphere, the refractive index... n It can be expressed as radial height r function n ( r ( )): (6) In the formula, s represents the distance the signal travels along the ray path.

[0048] Following the propagation path of radio signals through the Earth's atmosphere, according to Snell's law under the assumption of spherical symmetry, we have: (7) In the formula, const represents a conserved quantity that remains unchanged along the entire ray path, i.e., the invariant of Snell's law in a spherically layered atmosphere; r 0, r 1, ..., r k These represent the radial heights at the intersections of the rays with each atmospheric layer. i k This represents the emission angle of the ray corresponding to each layer. Taking a single radio signal ray as an example, see attached... Figure 3 As shown, consider the radio signal emitted from point A on the ground. The distance between point A and the Earth's center point O is... r Based on the atmospheric stratification assumption, the ray propagation path can be viewed as the differential of the height of the signal ray as it passes through each atmospheric layer along its propagation direction. dr At that time, the differential of the corresponding propagation distance ds The integral. The ray originates from point A and reaches the next altitude layer. r+dr At puncture point B, in the local horizontal coordinate system between points A and B, the signal emission angle (i.e., the angle between the signal emission direction and the local vertical direction) can be expressed as follows: i and i + dth express, dth Let A be the change in the angle of emission between points A and B. The geocentric angle between the two points in their local vertical directions can be expressed as: dx .

[0049] According to the Law of Sines, in the appendix Figure 3 triangle In ABO, there are (8) By transforming the two items on the left, we can obtain: (9) Expanding and simplifying equation (9), we obtain the rate of change of the geocentric distance with respect to the geocentric angle: (10) Similarly, by transforming the two terms on the right side of equation (8), we can obtain the rate of change of the propagation distance with respect to the geocentric angle: (11) Snell's law under the assumption of spherical symmetry (Equation (7)) can be simply written as: (12) Angles between the two sides and the Earth's center x Differentiating, we have: (13) Substituting equation (5) into equation (13) yields (14) Substituting equation (10) into equation (14), we get: (15) The simultaneous equations (10), (11), and (15) can construct a system of two-dimensional ray tracing differential equations based on the geocentric polar coordinate system: (16) The classical fourth-order Runge-Kutta method is used to integrate the two-dimensional ray tracing differential equation (Equation (16)). Given the initial conditions (Equation (3)), the refractive index and refractive index gradient at the corresponding point of each numerical iteration are obtained from step 3. The state increment, including the geocentric distance increment, is calculated and accumulated. Δr Increment of the geocentric angle Right Increment of the exit angle Dth Distance increment Δs Update the current ray propagation path position and record the new path points obtained in each iteration.

[0050] When the radial distance exceeds the preset maximum value, the numerical iteration is terminated, and the radio signal in the ray coordinate system can be solved simultaneously. and geocentric polar coordinate system The atmospheric propagation path below.

[0051] Step 5. Coordinate Mapping Based on the solution results of the two-dimensional ray tracing differential equation in step 4, the following formula can be used. (17) Directly convert the path point sequence from the geocentric polar coordinate system to the commonly used station-centric Cartesian coordinate system (see appendix). Figure 4 The transformation relationship is a closed-form analytical expression. During calculation, the radial distance and geocentric angle of each path point are directly substituted into the above formula. The corresponding Cartesian coordinates can be obtained in one step without iterative approximation, thus avoiding the computational overhead and accumulated errors that may be introduced by numerical iteration.

[0052] Step 6. Output Results Output the sequence of coordinates of the ray path points in the specified coordinate system and the total ray propagation distance. s .

[0053] Example 3 A two-dimensional ray tracing system for radio atmospheric propagation based on a geocentric polar coordinate system includes: (1) Data acquisition module: used to acquire the geographical location parameters of the radio signal transmission point and the refractive index distribution data on the vertical profile of the atmosphere; (2) Coordinate system construction module: used to construct a geocentric polar coordinate system with the geocenter as the pole, and to define the instantaneous exit angle of the ray in the coordinate system; (3) Atmospheric parameterization module: used to divide the atmosphere into several continuous layers in the radial direction, and to establish a continuous function or interpolation table for the refractive index of each layer as a function of radial distance; (4) Ray recursion module: used to iteratively solve the ray propagation differential equation in the geocentric polar coordinate system by continuous numerical integration, update the radial distance, geocentric angle and exit angle of the ray, and generate the ray path point sequence; (5) Coordinate mapping module: used to establish the analytical mapping relationship between the geocentric polar coordinate system and the specified output coordinate system, and to transform the path point sequence to the specified output coordinate system; (6) Output module: used to output the converted ray propagation path data and its cumulative amount.

[0054] To facilitate understanding of the technical effects of this invention, the following experimental data is provided: To illustrate the technical advantages of this invention compared to existing radio signal atmospheric propagation ray tracing techniques, two sets of comparative tests were conducted to quantitatively evaluate its efficiency and accuracy. The tests used typical mid-latitude atmospheric refractive index field data provided by the ERA5 product, selecting three typical elevation angles (5°, 30°, and 80°). At each elevation angle, 120 azimuth angles were randomly generated (uniformly distributed from 0° to 360°). Three methods were applied—three-dimensional ray tracing, two-dimensional layered recursive ray tracing, and the method of this invention—to trace each ray to an altitude of 80 km. The three-dimensional ray tracing employed Runge-Kutta integration with an integration step size of 10 m. The two-dimensional layered recursive ray tracing divided the atmosphere into 100 layers, with each layer's thickness increasing from 50 m to 500 m. Test 1 involved independently tracing each ray and recording the average ray tracing time (in milliseconds) for the three methods to evaluate computational efficiency. Test 2 used the 3D ray tracing results as a reference to calculate the atmospheric refractive index integral (also known as tropospheric oblique path delay in GNSS data processing) along the ray path. The integral values ​​calculated by the 2D layered recursive ray tracing method were compared with those obtained by the method of this invention to evaluate the accuracy of the ray tracing results. All tests were executed on a unified hardware platform (Intel Core i7-12700K CPU 2.2 GHz; 16 GB RAM) using a single thread. The test results are summarized below: Table 1. Statistical table of computational efficiency of three ray tracing methods

[0055] Table 2. Statistical table of calculation accuracy for three ray tracing methods

[0056] As shown in Table 1, compared with 3D ray tracing, the computation time of this invention is reduced by about an order of magnitude, demonstrating a significant improvement in computational efficiency. Compared with conventional 2D recursion, the computation time of this invention is reduced by about 25% at low elevation angles (5°) and by about 9% at high elevation angles (80°). The computational efficiency advantage of this invention is more pronounced at low elevation angles (scenarios with long atmospheric paths and multiple layers). Table 2 shows that, at different elevation angles, the MAE and RMSE of this invention are superior to the conventional 2D recursion method, with an accuracy improvement of 15% to 25%. At low elevation angles (5°), the long atmospheric paths and the cumulative error effect of layered recursion are more significant, making the relative advantage of this invention more prominent. At high elevation angles, both errors are smaller, and the advantage of this invention is not as significant as in low elevation angle scenarios. Therefore, this invention provides a 2D ray tracing method that balances computational efficiency and accuracy, simultaneously meeting the requirements of large-scale, real-time / near-real-time ray tracing.

[0057] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0058] The following describes the two-dimensional ray tracing electronic device for radio atmospheric propagation based on the geocentric polar coordinate system provided by the present invention. The two-dimensional ray tracing electronic device for radio atmospheric propagation based on the geocentric polar coordinate system described below can be referred to in correspondence with the two-dimensional ray tracing method for radio atmospheric propagation based on the geocentric polar coordinate system described above.

[0059] The electronic device may include a processor, a communications interface, memory, and a communication bus. The processor, communications interface, and memory communicate with each other via the communication bus. The processor can call logical instructions from the memory to execute a two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates, primarily including the software processing portion described above.

[0060] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0061] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the software processing part of the two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates provided by the above methods.

[0062] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the software processing portion of the two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates provided by the above methods.

[0063] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0064] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A two-dimensional ray tracing method for radio atmospheric propagation based on a geocentric polar coordinate system, characterized in that, include: Obtain the geographical location parameters of the launch point, including at least the radial distance of the launch point relative to the Earth's center; And obtain the refractive index distribution data on the vertical profile of the atmosphere; Construct a geocentric polar coordinate system with the Earth's center as the pole, and use the radial distance and the angle between the Earth's center and the pole as coordinate axes; define the instantaneous exit angle of the ray, and establish the representation of the ray's initial state in the geocentric polar coordinate system; Using refractive index distribution data, the atmosphere is divided into several continuous layers in the radial direction, and each layer is assigned a function or interpolation table of refractive index variation with radial distance. In the geocentric polar coordinate system, the ray propagation differential equation is solved iteratively by continuous numerical integration starting from the emission point. In each iteration, the refractive index and its radial gradient are calculated based on the radial distance and instantaneous exit angle of the current point, combined with the refractive index data. The radial distance, geocentric angle and exit angle are then updated to generate a sequence of ray path points. Establish an analytical mapping relationship between the geocentric polar coordinate system and the specified output coordinate system, and transform the ray path point sequence to the specified output coordinate system; The converted ray propagation path data is output to calculate the atmospheric propagation delay or refraction correction of radio signals.

2. The two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates according to claim 1, characterized in that: The differential equation for ray propagation is expressed in a differential form with the distance from the Earth's center and the angle between the Earth's centers as variables.

3. The two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates according to claim 1, characterized in that: The continuous numerical integration employs the Runge-Kutta method or a variation thereof.

4. The two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates according to claim 1, characterized in that: The refractive index distribution data comes from at least one of the following sources. Measured profile of refractive index distribution obtained by a radiosonde; Refractive index distribution profile output by numerical weather prediction model; An empirical exponential function fitting profile is constructed based on the surface refractive index collected in real time by local sensors.

5. The two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates according to claim 1, characterized in that: The analytical mapping relationship is a closed-form transformation relationship that does not require iterative solution.

6. The two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates according to claim 1, characterized in that: The specified output coordinate system is at least one of the following: ray coordinate system, geocentric polar coordinate system, or Cartesian coordinate system.

7. The two-dimensional ray tracing method for radio atmospheric propagation based on geocentric polar coordinates according to claim 1, characterized in that: It is used for at least one of the following scenarios: tropospheric delay modeling in space geodesy, radar coverage analysis, communication link diagnosis, or atmospheric turbulence effect assessment.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, it implements the two-dimensional ray tracing method for radio atmospheric propagation based on the geocentric polar coordinate system as described in any one of claims 1 to 7.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the two-dimensional ray tracing method for radio atmospheric propagation based on the geocentric polar coordinate system as described in any one of claims 1 to 7.

10. A computer program product, comprising a computer program, characterized in that: When the computer program is executed by the processor, it implements the two-dimensional ray tracing method for radio atmospheric propagation based on the geocentric polar coordinate system as described in any one of claims 1 to 7.

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