Starlight refraction simulation method and device considering three-dimensional refraction index distribution characteristics

Abstract

The invention relates to a starlight refraction simulation method and device considering three-dimensional refraction index distribution characteristics, and the method comprises the steps: constructing a global atmospheric refraction index field through a global reanalysis data set at the current time according to the simulation scene time of a starlight atmospheric refraction navigation ground simulation system; calculating a refraction index at an interested interpolation point in starlight path updating and a refraction index gradient of the interested interpolation point in starlight path updating; calculating an update path of the starlight refraction model based on the three-dimensional eikonal equation by adopting a numerical calculation method; and calculating a starlight refraction angle in starlight path updating according to a tangent method in a starlight refraction process. According to the method, simplification of a starlight refraction process by a two-dimensional system is avoided, and the starlight refraction process in a three-dimensional space is simulated with high precision; the distribution characteristics of the three-dimensional refractive index are considered, the influence of the refractive index gradients in latitude, longitude and radial directions on the starlight refraction process is simulated in a high-precision manner, and the geometric characteristics of the three-dimensional path in the starlight refraction process are reflected in a high-precision manner.

Description

Technical Field

[0001] The present application relates to the field of celestial navigation technology, and in particular to a method and device for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics. Background Art

[0002] Starlight refraction refers to the process in which the direction of light propagation is deflected when light from a star passes through the Earth's atmosphere due to changes in the atmospheric refractive index in the atmosphere. This phenomenon causes the apparent position of a star observed by the spacecraft to be slightly higher than its actual position in space. In the ground simulation of the starlight atmospheric refraction navigation system, this refraction process needs to be simulated with high precision. The spacecraft uses the simulated high-precision starlight refraction angle information as the observation value to achieve subsequent navigation solutions.

[0003] Usually, in the ground simulation of the starlight atmospheric refraction navigation system, the refraction process of starlight passing through the atmosphere is simplified, and the three-dimensional refraction process is simplified to a two-dimensional system. At the same time, only the change of meteorological data in altitude is considered, and it is assumed that it is independent of time, longitude and latitude. Therefore, it is difficult to ensure high-precision starlight refraction simulation results. Summary of the invention

[0004] Based on this, it is necessary to provide a starlight refraction simulation method and device that takes into account the three-dimensional refraction index distribution characteristics and can ensure that the simulation accuracy of refraction information such as starlight refraction angle meets the requirements of starlight atmospheric refraction navigation scenarios in order to address the above technical problems.

[0005] A method for simulating starlight refraction taking into account three-dimensional refractive index distribution characteristics, the method comprising: Step S1: According to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system, a global atmospheric refraction index field is constructed through the global reanalysis dataset of the current time.

[0006] Step S2: Calculate the refractive index at the interpolation point of interest in the starlight path update based on the global atmospheric refractive index field.

[0007] Step S3: Calculate the refractive index gradients in latitude, longitude and radial directions at the interpolation point of interest in the starlight path update according to the refractive index at the interpolation point of interest.

[0008] Step S4: construct a starlight refraction path model based on the three-dimensional Eikonal equation, and use a numerical calculation method to calculate the update path of the starlight refraction model based on the three-dimensional Eikonal equation.

[0009] Step S5: Calculate the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process.

[0010] A starlight refraction simulation device taking into account three-dimensional refractive index distribution characteristics, the device comprising: The global atmospheric refraction index field construction module is used to construct the global atmospheric refraction index field according to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system through the global reanalysis dataset of the current time.

[0011] The refractive index calculation module at the interpolation point of interest is used to calculate the refractive index at the interpolation point of interest in the starlight path update according to the global atmospheric refractive index field.

[0012] The refractive index gradient calculation module is used to calculate the refractive index gradient in the latitude, longitude and radial directions at the interpolation point of interest in the starlight path update according to the refractive index at the interpolation point of interest.

[0013] The starlight refraction model path update module based on the three-dimensional Eikonal equation is used to construct a starlight refraction path model based on the three-dimensional Eikonal equation, and uses numerical calculation methods to calculate the update path of the starlight refraction model based on the three-dimensional Eikonal equation.

[0014] The starlight refraction angle calculation module in the starlight path update is used to calculate the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process.

[0015] The above-mentioned method and device for simulating starlight refraction taking into account the three-dimensional refraction index distribution characteristics include: constructing a global atmospheric refraction index field according to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system through the global reanalysis data set of the current time; calculating the refraction index at the interpolation point of interest in the starlight path update; then calculating the refraction index gradient of the interpolation point of interest in the starlight path update; using a numerical calculation method to calculate the update path of the starlight refraction model based on the three-dimensional eikonal equation; and calculating the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process. This method avoids the simplification of the starlight refraction process by the two-dimensional system, and can simulate the starlight refraction process in three-dimensional space with high precision; considering the three-dimensional refraction index distribution characteristics, the influence of the refraction index gradient in latitude, longitude and radial on the starlight refraction process is simulated with high precision, and the three-dimensional path geometric characteristics in the starlight refraction process are reflected with high precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A schematic diagram of a flow chart of a method for simulating starlight refraction taking into account three-dimensional refractive index distribution characteristics in one embodiment; Figure 2 A flow chart of a method for simulating starlight refraction taking into account three-dimensional refractive index distribution characteristics in one embodiment; Figure 3The result of a starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in one embodiment is as follows: a schematic diagram of the change in the radial distance of the starlight path from the center of the earth; Figure 4 The result of a starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in one embodiment is as follows: a schematic diagram of the latitude variation of the starlight path; Figure 5 The result of a starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in one embodiment: a schematic diagram of the longitude variation of the starlight path; Figure 6 The result of the starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in one embodiment: a schematic diagram of the change of the first partial differential component; Figure 7 The result of the starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in one embodiment: a schematic diagram of the change of the second partial differential component; Figure 8 The result of the starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in one embodiment: a schematic diagram of the change of the third partial differential component; Fig. 9 The result of a starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in one embodiment: a schematic diagram of the radial gradient change of the refractive index; Fig.10 Result of a starlight refraction simulation method taking into account the three-dimensional refractive index distribution characteristics in one embodiment: a schematic diagram of the change of the refraction angle during the starlight path update. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0018] In one embodiment, Figure 1 , Figure 2 As shown, a method for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics is provided, and the method comprises the following steps: Step S1: According to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system, a global atmospheric refraction index field is constructed through the global reanalysis dataset of the current time.

[0019] Specifically, according to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system, a global atmospheric refraction index field is constructed through a global three-dimensional atmospheric data set or other measured global three-dimensional atmospheric parameters.

[0020] According to the fifth-generation global atmospheric reanalysis dataset released by the European Weather Forecast Centre, meteorological data at an altitude of 18km-84km were selected for processing, with a horizontal resolution of 0.75°×0.75° and a vertical resolution of 20m, for a total of 3301 layers, thus obtaining the global atmospheric refractive index field at the current simulation moment.

[0021] Step S2: Calculate the refractive index at the interpolation point of interest in the starlight path update based on the global atmospheric refractive index field.

[0022] Step S3: Calculate the refractive index gradients in latitude, longitude and radial directions at the interpolation point of interest in the starlight path update according to the refractive index at the interpolation point of interest.

[0023] Step S4: construct a starlight refraction path model based on the three-dimensional Eikonal equation, and use a numerical calculation method to calculate the update path of the starlight refraction model based on the three-dimensional Eikonal equation.

[0024] Step S5: Calculate the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process.

[0025] In the above-mentioned starlight refraction simulation method considering the three-dimensional refraction index distribution characteristics, the method includes: constructing a global atmospheric refraction index field according to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system through the global reanalysis data set of the current time; calculating the refraction index at the interpolation point of interest in the starlight path update; then calculating the refraction index gradient of the interpolation point of interest in the starlight path update; using a numerical calculation method to calculate the update path of the starlight refraction model based on the three-dimensional eikonal equation; and calculating the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process. This method avoids the simplification of the starlight refraction process by the two-dimensional system, and can simulate the starlight refraction process in three-dimensional space with high precision; considering the three-dimensional refraction index distribution characteristics, it simulates the influence of the refraction index gradient in latitude, longitude and radial on the starlight refraction process with high precision, and reflects the three-dimensional path geometric characteristics in the starlight refraction process with high precision.

[0026] In one embodiment, step S2 includes: calculating the refractive index at the interpolation point of interest in the starlight path update according to the global atmospheric refractive index field; wherein the expression of the refractive index at the interpolation point of interest is: ; The expression for the refractive index of the underlying layer near the interpolation point of interest is: ; in, is the refractive index at the interpolation point of interest, is the refractive index of the lower layer near the interpolation point of interest, The layer is the lower layer adjacent to the interpolation point of interest. and Respectively Layer and The radial distance of the layer from the center of the Earth, is the global atmospheric refractive index grid number near the interpolation point of interest; ; , , , are the radial distance, latitude, and longitude from the center of the earth at the interpolation point of interest, respectively. , are the grid numbers of the global atmospheric refractive index near the interpolation point of interest. The latitude and longitude of , are the grid numbers of the global atmospheric refractive index near the interpolation point of interest. The latitude and longitude of the location.

[0027] Specifically, if The layer is the lower layer adjacent to the interpolation point of interest. At this time, the radial distance of this layer from the center of the earth is , then the refractive index of the lower layer near the interpolation point of interest is This is shown in the expression for the refractive index of the underlying layer adjacent to the interpolation point of interest above.

[0028] Assume that in Layer and The refractive index between layers is in exponential form, so the refractive index at the interpolation point of interest is This is shown in the expression for the refractive index at the interpolation point of interest above.

[0029] In one embodiment, step S3 includes: calculating the refractive index gradient of the interpolation point of interest in the latitudinal direction in the starlight path update according to the refractive index at the interpolation point of interest; the expression of the refractive index gradient of the interpolation point of interest in the latitudinal direction in the starlight path update is: ; in, is the refractive index gradient in the latitude direction of the interpolation point of interest in the starlight path update, , , are the radial distance, latitude, and longitude from the center of the earth at the interpolation point of interest, respectively. , Respectively Layer and The radial distance of the layer from the center of the Earth, and are the radial distance and latitude of the starlight refraction point from the center of the earth during the numerical update process, is the refractive index function.

[0030] According to the refractive index at the interpolation point of interest, the refractive index gradient of the interpolation point of interest in the longitude direction in the starlight path update is calculated; wherein, the expression of the refractive index gradient of the interpolation point of interest in the longitude direction in the starlight path update is: ; in, is the refractive index gradient in the longitude direction of the interpolation point of interest in the starlight path update, It is the longitude of the starlight refraction point from the center of the earth during the value update process.

[0031] According to the refractive index at the interpolation point of interest, the refractive index gradient of the interpolation point of interest in the starlight path update in the radial direction is calculated; wherein, the expression of the refractive index gradient of the interpolation point of interest in the starlight path update in the radial direction is: ; in, It is the refractive index gradient in the radial direction at the interpolation point of interest in the starlight path update.

[0032] In one embodiment, step S4 includes: constructing a starlight refraction path model based on a three-dimensional eikonal equation as follows: ; in, is the length of the arc along the ray path, , and They are The partial differential components in the radial, latitudinal and longitudinal directions, is the light path length, , and are the radial distance, latitude and longitude of the starlight refraction point from the center of the earth during the numerical update process, It is the refraction index at the starlight refraction point during the value update process.

[0033] Define the state vector , the starlight refraction path model based on the three-dimensional eikonal equation is converted into the first-order derivative of the state vector (i.e. ), the starlight refraction path is numerically updated using the fourth-order Runge-Kutta method; wherein, the update of the refraction index related variables during the update process is calculated according to step S2 and step S3. As a preferred embodiment: the update step length is given as .

[0034] In one embodiment, step S5 includes: establishing a spherical coordinate system; the tangent vector of the starlight direction in the spherical coordinate system The expression is: ; in, is the tangent vector of the starlight direction in the spherical coordinate system, is the length of the arc along the ray path, , and They are the radial distance, latitude and longitude of the starlight refraction point from the center of the earth during the numerical update process; Convert the tangent vector of the starlight direction in the spherical coordinate system to the Cartesian rectangular coordinate system; the expression of the tangent vector of the starlight direction in the Cartesian rectangular coordinate system is: ; The three-dimensional component expression of the tangent vector in the direction of starlight in the Cartesian rectangular coordinate system is: ; in, is the tangent vector of the starlight direction in the Cartesian rectangular coordinate system, are the three-dimensional components of the tangent vector of the starlight direction in the Cartesian rectangular coordinate system, , and are the radial distance, latitude and longitude of the starlight refraction point from the center of the earth during the numerical update process.

[0035] In the During the update process, the angle change of the tangent vector of the starlight direction in the Cartesian rectangular coordinate system is used as the change of the starlight refraction angle; the change of the starlight refraction angle in each starlight path update process is summed to obtain the starlight refraction angle in the starlight path update.

[0036] Specifically, the starlight refraction angle in the starlight path update ,in The number of times the starlight path is updated.

[0037] In one embodiment, the expression of the change in the starlight refraction angle in the Cartesian rectangular coordinate system is: ; in, is the change in the starlight refraction angle in the Cartesian rectangular coordinate system, is the inverse tangent function, and Respectively Second and The tangent vector of the starlight direction in Cartesian coordinates during the update of the timestamp.

[0038] The starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics is used. Figure 2 shown.

[0039] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0040] In a simulation embodiment, the latitude of the starlight incident puncture point is 60.1° N, the longitude is 169.4° W, the azimuth relative to the north is 172.088°, and the incident zenith angle is 97.8264° as an implementation scenario of the ground navigation simulation system, and 31 Dec 2023 00:00:00.000 UTCG is used as the navigation simulation time. The simulation results of the starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics are shown in FIG. Figures 3 to 10 As shown, Figure 3 This is a schematic diagram of the change in radial distance between the starlight path and the center of the earth. Figure 4 This is a schematic diagram of the latitude changes of the starlight path. Figure 5 This is a schematic diagram of the longitude changes of the starlight path. Figure 6 is a schematic diagram of the change of the first partial differential component, Figure 7 is a schematic diagram of the change of the second partial differential component, Figure 8 is a schematic diagram of the change of the third partial differential component, Fig. 9 Schematic diagram of radial gradient change of refractive index. Fig.10 Schematic diagram of the change in refraction angle during starlight path update.

[0041] In one embodiment, a starlight refraction simulation device considering the three-dimensional refractive index distribution characteristics is provided, comprising: a global atmospheric refractive index field construction module, a refractive index calculation module at an interpolation point of interest, a refractive index gradient calculation module, a starlight refraction model path update module based on a three-dimensional eikonal equation, and a starlight refraction angle calculation module in the starlight path update, wherein: The global atmospheric refraction index field construction module is used to construct the global atmospheric refraction index field according to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system through the global reanalysis dataset of the current time.

[0042] The refractive index calculation module at the interpolation point of interest is used to calculate the refractive index at the interpolation point of interest in the starlight path update according to the global atmospheric refractive index field.

[0043] The refractive index gradient calculation module is used to calculate the refractive index gradient in the latitude, longitude and radial directions at the interpolation point of interest in the starlight path update according to the refractive index at the interpolation point of interest.

[0044] The starlight refraction model path update module based on the three-dimensional Eikonal equation is used to construct a starlight refraction path model based on the three-dimensional Eikonal equation, and uses numerical calculation methods to calculate the update path of the starlight refraction model based on the three-dimensional Eikonal equation.

[0045] The starlight refraction angle calculation module in the starlight path update is used to calculate the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process.

[0046] In one of the embodiments, the refractive index calculation module at the interpolation point of interest is further used to calculate the refractive index at the interpolation point of interest in the starlight path update based on the global atmospheric refractive index field and using the expression of the refractive index at the interpolation point of interest in the starlight path update.

[0047] In one of the embodiments, the refractive index gradient calculation module is further used to calculate the refractive index gradient of the interpolation point of interest in the latitudinal direction in the starlight path update according to the refractive index at the interpolation point of interest, using the expression of the refractive index gradient of the interpolation point of interest in the latitudinal direction in the starlight path update; calculate the refractive index gradient of the interpolation point of interest in the longitude direction in the starlight path update according to the refractive index at the interpolation point of interest; calculate the refractive index gradient of the interpolation point of interest in the radial direction in the starlight path update according to the refractive index at the interpolation point of interest, using the expression of the refractive index gradient of the interpolation point of interest in the radial direction in the starlight path update.

[0048] In one embodiment, the starlight refraction model path update module based on the three-dimensional eikonal equation is also used to construct a starlight refraction path model based on the three-dimensional eikonal equation as shown in the starlight refraction path model expression based on the three-dimensional eikonal equation above; define the state vector , converting the starlight refraction path model based on the three-dimensional Eikonal equation into In the form of a fourth-order Runge-Kutta method, the starlight refraction path is numerically updated; wherein, during the updating process, the update of the refractive index related variables is calculated according to step S2 and step S3.

[0049] In one of the embodiments, the starlight refraction angle calculation module in the starlight path update is also used to establish a spherical coordinate system; the tangent vector of the starlight direction in the spherical coordinate system is as shown in the expression of the tangent vector of the starlight direction in the spherical coordinate system. The starlight tangent t in the spherical coordinate system is converted to the Cartesian rectangular coordinate system, wherein the tangent vector of the starlight direction in the Cartesian rectangular coordinate system and the tangent vector and three-dimensional component of the starlight direction in the Cartesian rectangular coordinate system are as shown in the expression of the tangent vector of the starlight direction in the Cartesian rectangular coordinate system and the expression of the three-dimensional component of the tangent vector of the starlight direction in the Cartesian rectangular coordinate system; in the i-th update process, the angle change of the tangent vector of the starlight direction in the Cartesian rectangular coordinate system is used as the starlight refraction angle change, and the starlight refraction angle change in each starlight path update process is summed to obtain the starlight refraction angle in the starlight path update.

[0050] In one of the embodiments, the change amount of the starlight refraction angle in the starlight refraction angle calculation module in the light path update is as shown in the expression of the starlight refraction angle change amount mentioned above.

[0051] The specific definition of the starlight refraction simulation device considering the three-dimensional refractive index distribution characteristics can be referred to the definition of the starlight refraction simulation method considering the three-dimensional refractive index distribution characteristics in the above text, and will not be repeated here. Each module in the above-mentioned starlight refraction simulation device considering the three-dimensional refractive index distribution characteristics can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory in the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0052] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0053] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics, characterized in that: The method comprises: Step S1: constructing a global atmospheric refraction index field through a global reanalysis data set at the current time according to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system; Step S2: Calculate the refractive index at the interpolation point of interest in the starlight path update according to the global atmospheric refractive index field; Step S3: Calculate the refractive index gradients at the interpolation point of interest in the latitude, longitude and radial directions in the starlight path update according to the refractive index at the interpolation point of interest; Step S4: constructing a starlight refraction path model based on the three-dimensional eikonal equation, and using a numerical calculation method to calculate an update path of the starlight refraction model based on the three-dimensional eikonal equation; Step S5: Calculate the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process.

2. The method for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics according to claim 1, characterized in that: Step S2 includes: calculating the refractive index at the interpolation point of interest in the starlight path update according to the global atmospheric refractive index field as: ； ； in, is the refractive index at the interpolation point of interest, is the refractive index of the underlying layer near the interpolation point of interest, The layer is the lower layer that is adjacent to the interpolation point of interest. and Respectively Layer and The radial distance of the layer from the center of the Earth, is the global atmospheric refractive index grid number near the interpolation point of interest; ; , , and are the radial distance, latitude and longitude from the center of the earth at the interpolation point of interest, respectively. and are the grid numbers of the global atmospheric refractive index near the interpolation point of interest. The latitude and longitude of and are the grid numbers of the global atmospheric refractive index near the interpolation point of interest. The latitude and longitude of is the refractive index function.

3. The method for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics according to claim 1, characterized in that: Step S3 includes: according to the refractive index at the interpolation point of interest, calculating the refractive index gradient of the interpolation point of interest in the starlight path update in the latitude direction as: ； in, is the refractive index gradient in the latitude direction of the interpolation point of interest in the starlight path update, , , are the radial distance, latitude, and longitude from the center of the earth at the interpolation point of interest, respectively. , Respectively Layer and The radial distance of the layer from the center of the Earth, and are the radial distance and latitude of the starlight refraction point from the center of the earth during the numerical update process, is the refractive index function; According to the refractive index at the interpolation point of interest, the refractive index gradient of the interpolation point of interest in the longitude direction in the starlight path update is calculated as: ； in, is the refractive index gradient in the longitude direction of the interpolation point of interest in the starlight path update, It is the longitude of the starlight refraction point from the center of the earth during the value update process; According to the refractive index at the interpolation point of interest, the refractive index gradient of the interpolation point of interest in the radial direction in the starlight path update is calculated as: ； in, It is the refractive index gradient in the radial direction at the interpolation point of interest in the starlight path update.

4. The method for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics according to claim 1, characterized in that: Step S4 includes: constructing a starlight refraction path model based on a three-dimensional eikonal equation: ； in, is the length of the arc along the ray path, , and They are The partial differential components in the radial, latitudinal and longitude directions, is the light path length, , and are the radial distance, latitude and longitude of the starlight refraction point from the center of the earth during the numerical update process, is the refractive index function; Define the state vector , the starlight refraction path model based on the three-dimensional eikonal equation is converted into the form of the first-order derivative of the state vector, and the starlight refraction path is numerically updated using the fourth-order Runge-Kutta method; wherein, the update of the refractive index related variables during the updating process is calculated according to step S2 and step S3.

5. The method for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics according to claim 1, characterized in that: Step S5 includes: establishing a spherical coordinate system; the tangent vector of the starlight direction in the spherical coordinate system is: ； in, is the tangent vector of the starlight direction in the spherical coordinate system, is the length of the arc along the ray path, , and They are the radial distance, latitude and longitude of the starlight refraction point from the center of the earth during the numerical update process; Convert the tangent vector of the starlight direction in the spherical coordinate system to the Cartesian rectangular coordinate system; the tangent vector of the starlight direction in the Cartesian rectangular coordinate system is: ； ； in, is the tangent vector of the starlight direction in the Cartesian rectangular coordinate system, are the three-dimensional components of the tangent vector to the starlight direction in the Cartesian rectangular coordinate system; In the In the first updating process, the angle change of the tangent vector of the starlight direction in the Cartesian rectangular coordinate system is taken as the change of the starlight refraction angle; The changes in the starlight refraction angle during each starlight path update are summed to obtain the starlight refraction angle in the starlight path update.

6. The method for simulating starlight refraction taking into account the three-dimensional refractive index distribution characteristics according to claim 5, characterized in that: The change in the starlight refraction angle in the Cartesian rectangular coordinate system is: ； in, is the change in the starlight refraction angle, is the inverse tangent function, and Respectively Second and The tangent vector of the starlight direction in Cartesian coordinates during the update of the timestamp.

7. A starlight refraction simulation device taking into account the three-dimensional refractive index distribution characteristics, characterized in that: The device comprises: The global atmospheric refraction index field construction module is used to construct the global atmospheric refraction index field according to the simulation scene time of the starlight atmospheric refraction navigation ground simulation system and the global reanalysis data set of the current time; A refractive index calculation module at an interpolation point of interest, used to calculate the refractive index at an interpolation point of interest in starlight path updating according to the global atmospheric refractive index field; A refractive index gradient calculation module, used to calculate the refractive index gradient at the interpolation point of interest in the starlight path update in the latitude, longitude and radial directions according to the refractive index at the interpolation point of interest; A starlight refraction model path update module based on three-dimensional Eikonal equations is used to construct a starlight refraction path model based on three-dimensional Eikonal equations and to calculate the update path of the starlight refraction model based on three-dimensional Eikonal equations by using numerical calculation methods; The starlight refraction angle calculation module in the starlight path update is used to calculate the starlight refraction angle in the starlight path update according to the tangent method in the starlight refraction process.

8. The starlight refraction simulation device taking into account the three-dimensional refractive index distribution characteristics according to claim 7, characterized in that: The refractive index calculation module at the interpolation point of interest is also used to calculate the refractive index at the interpolation point of interest in the starlight path update according to the global atmospheric refractive index field: ； ； in, is the refractive index at the interpolation point of interest, is the refractive index of the lower layer near the interpolation point of interest, The layer is the lower layer that is adjacent to the interpolation point of interest. and Respectively Layer and The radial distance of the layer from the center of the Earth, is the global atmospheric refractive index grid number near the interpolation point of interest; ; , , and are the radial distance, latitude and longitude from the center of the earth at the interpolation point of interest, respectively. and are the grid numbers of the global atmospheric refractive index near the interpolation point of interest. The latitude and longitude of and are the grid numbers of the global atmospheric refractive index near the interpolation point of interest. The latitude and longitude of the location.

9. The starlight refraction simulation device taking into account the three-dimensional refractive index distribution characteristics according to claim 7, characterized in that: The refractive index gradient calculation module is further used to calculate the refractive index gradient of the interpolation point of interest in the latitude direction in the starlight path update according to the refractive index at the interpolation point of interest: ； in, is the refractive index gradient in the latitude direction of the interpolation point of interest in the starlight path update, and Respectively Layer and The radial distance of the layer from the center of the Earth, , and are the radial distance, latitude and longitude from the center of the earth at the interpolation point of interest, respectively. and They are the radial distance and latitude of the starlight refraction point from the center of the earth during the numerical update process; According to the refractive index at the interpolation point of interest, the refractive index gradient of the interpolation point of interest in the longitude direction in the starlight path update is calculated as: ； in, is the refractive index gradient in the longitude direction of the interpolation point of interest in the starlight path update, and They are respectively the radial distance and longitude of the starlight refraction point from the center of the earth during the numerical update process; According to the refractive index at the interpolation point of interest, the refractive index gradient of the interpolation point of interest in the radial direction in the starlight path update is calculated as: ； in, It is the refractive index gradient in the radial direction at the interpolation point of interest in the starlight path update.

10. The starlight refraction simulation device taking into account the three-dimensional refractive index distribution characteristics according to claim 7, characterized in that: The starlight refraction model path update module based on the three-dimensional Eikonal equation is also used to construct the starlight refraction path model based on the three-dimensional Eikonal equation: ； in, is the length of the arc along the ray path; , and They are Partial differential components in radial, latitudinal and longitudinal directions; is the light path length, , , They are the radial distance, latitude, and longitude of the starlight refraction point from the center of the earth during the numerical update process. It is the refraction index at the starlight refraction point during the value update process; Define the state vector , the starlight refraction path model based on the three-dimensional eikonal equation is converted into the form of the first-order derivative of the state vector, and the starlight refraction path is numerically updated using the fourth-order Runge-Kutta method; wherein, the update of the refractive index related variables during the updating process is calculated according to step S2 and step S3.

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