Starlight atmospheric refraction navigation method, device and electronic equipment based on ray tracing

Abstract

The present application relates to a starlight atmospheric refraction navigation method, device and electronic equipment based on ray tracing, wherein the method uses the refracted starlight observation quantity obtained by star sensor observation, simulates the transmission process of real starlight in the earth's atmosphere based on ray tracing on the basis of the global atmospheric refraction index field, establishes an iterative algorithm to estimate the refracted apparent height, and locates the spacecraft through the mapping relationship between the apparent height and the spacecraft position. The method can effectively reduce the impact of the global atmospheric spatiotemporal changes on the starlight atmospheric refraction navigation and improve the autonomous navigation accuracy of the spacecraft.

Description

Technical Field

[0001] The present application relates to the field of astronomical navigation technology, and in particular to a starlight atmospheric refraction navigation method, device and electronic equipment based on ray tracing. Background Art

[0002] Autonomous navigation is a key technology for autonomous operation of spacecraft. High-precision autonomous navigation can ensure the reliability of spacecraft operation. Starlight atmospheric refraction navigation technology uses indestructible natural stars as observation information sources, and has the characteristics of good concealment and high autonomy. In starlight atmospheric refraction navigation technology, star sensors observe refracting stars to obtain the refraction information of starlight after passing through the earth's atmosphere, and realize autonomous navigation positioning based on the geometric relationship between the refracted apparent height and the position of the spacecraft.

[0003] The degree of refraction of starlight passing through the Earth's atmosphere is affected by the refractive index in the transmission path, and the atmospheric refractive index is related to the atmospheric density. In general starlight atmospheric refraction navigation methods, the isothermal assumption is often used. According to the USSA 1976 data, an exponential model of atmospheric density increasing with altitude is established, and then an empirical starlight atmospheric refraction model is constructed to obtain the mapping relationship between the refraction angle and the apparent refraction height. Under this mapping relationship, the apparent refraction height is obtained through the observed refraction angle information to achieve spacecraft navigation and positioning solution. However, the empirical starlight atmospheric refraction model fails to take into account the three-dimensional spatiotemporal changes of the global atmosphere. The apparent refraction height calculated using this model has a large error, which seriously affects the accuracy of starlight atmospheric refraction navigation. Summary of the invention

[0004] Based on this, it is necessary to provide a starlight atmospheric refraction navigation method, device and electronic equipment based on ray tracing that can reduce the impact of global atmospheric temporal and spatial variation errors on starlight atmospheric refraction navigation and improve the accuracy of autonomous navigation in response to the above-mentioned technical problems.

[0005] A starlight atmospheric refraction navigation method based on ray tracing, the method comprising:

[0006] The estimated value of the starlight zenith angle is determined based on the refracted starlight information observed by the star sensor and the geometric constraints of the refracted starlight piercing point and the estimated position of the spacecraft.

[0007] The Rodriguez rotation formula is used according to the estimated value of the starlight zenith angle to obtain the unit vector of the vector pointing from the origin to the piercing point of the refracted starlight.

[0008] Calculate the longitude and latitude of the point where the refracted starlight pierces based on the unit vector.

[0009] The unit vector is converted from the geocentric Earth-fixed coordinate system to the northeastern celestial coordinate system according to the longitude and latitude, and the estimated angle between the refracted starlight vector and the east direction in the northeastern celestial coordinate system is obtained.

[0010] According to the longitude and latitude and the estimated angle, the ray tracing method is used to simulate the transmission process of refracted starlight in the global atmospheric refractive index field to obtain the estimated value of the starlight refraction angle and the estimated value of the refracted apparent altitude.

[0011] When the difference between the estimated starlight refraction angle and the actually observed starlight refraction angle is greater than a preset threshold, the starlight zenith angle estimate is updated, and the starlight refraction angle and the refraction apparent altitude are estimated again until the difference is less than the preset threshold, thereby obtaining the refraction apparent altitude measurement.

[0012] Positioning is performed based on the mapping relationship between the refracted apparent altitude measurement value and the spacecraft position.

[0013] In one embodiment, determining the estimated value of the starlight zenith angle based on the refracted starlight information observed by the star sensor and combining the geometric constraints of the refracted starlight puncture point and the estimated position of the spacecraft includes:

[0014] The spacecraft position vector is obtained according to the spacecraft orbital mechanics.

[0015] According to the refracted starlight information observed by the star sensor, the refracted starlight vector is obtained.

[0016] The estimated angle between the spacecraft position vector and the reverse direction of the refracted starlight vector is calculated as:

[0017] ;

[0018] in, is the estimated angle between the spacecraft position vector and the reverse direction of the refracted starlight vector, is the spacecraft position vector, is the refracted starlight vector.

[0019] According to the geometric constraints of the refracted starlight puncture point and the spacecraft position, the estimated value of the starlight zenith angle is:

[0020] ;

[0021] in, is the estimated value of the starlight zenith angle, For the refracted starlight piercing point Height, is the radius of the Earth.

[0022] In one embodiment, the Rodriguez rotation formula is used according to the estimated value of the starlight zenith angle to obtain the unit vector of the vector pointing from the origin to the refracted starlight puncture point:

[0023] ;

[0024] in, is the unit vector from the origin to the point where the refracted starlight pierces. is the estimated value of the starlight zenith angle, is a unit vector, , is the unit vector of starlight before refraction, is the refracted starlight vector, is the identity matrix, is a unit vector The antisymmetric matrix composed of elements, .

[0025] In one embodiment, calculating the longitude and latitude of the refracted starlight puncture point according to the unit vector includes:

[0026] Convert the unit vector to the Earth-centered Earth-fixed coordinate system to obtain the unit vector in the Earth-centered Earth-fixed coordinate system.

[0027] According to the unit vector in the Earth-centered Earth-fixed coordinate system, the longitude and latitude of the refracted starlight puncture point in the WGS84 system are calculated as:

[0028] ;

[0029] in, , are the longitude and latitude of the refracted starlight piercing point, is the radius of curvature of the Earth's circumplex, is the Earth's eccentricity, is a unit vector in the Earth-centered, Earth-fixed coordinate system.

[0030] In one embodiment, converting a unit vector from an Earth-centered Earth-fixed coordinate system to a Northeastern Sky coordinate system according to the longitude and latitude to obtain an estimated angle between the refracted starlight vector and the east direction in the Northeastern Sky coordinate system includes:

[0031] The vector representation of the refracted starlight vector in the northeastern sky coordinate system is:

[0032] ;

[0033] in, is the vector of the refracted starlight vector in the northeastern celestial coordinate system, is the transformation matrix from the northeast celestial coordinate system to the earth-centered earth-fixed coordinate system, is the transformation matrix from the J2000.0 inertial coordinate system to the Earth-centered Earth-fixed coordinate system, , are the longitude and latitude of the refracted starlight piercing point, is the refracted starlight vector.

[0034] According to the x element and y element of the vector of the refracted starlight vector in the northeastern sky coordinate system, the estimated angle between the refracted starlight vector and the east direction in the northeastern sky coordinate system is obtained as follows:

[0035] ;

[0036] in, is the angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system, and are the vectors of the refracted starlight vector in the northeastern sky coordinate system The x element and y element of the .

[0037] In one embodiment, according to the longitude and latitude and the angle estimation value, a ray tracing method is used to simulate the transmission process of refracted starlight in the global atmospheric refractive index field to obtain the estimated value of the starlight refraction angle and the estimated value of the refracted apparent height, including:

[0038] The starlight refraction path is restricted to the starlight refraction plane by the longitude and latitude of the refraction puncture point and the estimated angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system.

[0039] Using the global atmospheric refraction index field and the ray tracing algorithm, the refraction process of starlight in the starlight refraction plane is obtained, and the estimated value of the starlight refraction angle and the estimated value of the true refraction height are obtained.

[0040] According to the estimated true refraction height, the estimated apparent refraction height is determined as:

[0041] ;

[0042] in, is the estimated value of the refracted apparent height, is the estimated true refraction height, is the estimated true refraction height The refractive index at is the radius of the Earth.

[0043] In one embodiment, the update formula of the estimated value of the starlight zenith angle is:

[0044] ;

[0045] in, , , Respectively j +1st, j sequence j -1 updated estimate of the starlight zenith angle, For the j The estimated value of the starlight refraction angle at the iteration, To observe the refraction angle, Representative Iterations do not satisfy the constraints.

[0046] In one embodiment, positioning is performed based on a mapping relationship between a refracted apparent altitude measurement value and a spacecraft position, including:

[0047] A measurement model is established based on the geometric relationship between the refracted apparent altitude measurement value and the spacecraft position.

[0048] The equation of state is established based on the orbital dynamics of the spacecraft.

[0049] The extended Kalman filter algorithm is used for the measurement model and state equation to complete the starlight atmospheric refraction navigation solution.

[0050] A starlight atmospheric refraction navigation device based on ray tracing, the device comprising:

[0051] The starlight zenith angle estimation module is used to determine the estimated value of the starlight zenith angle based on the refracted starlight information observed by the star sensor and the geometric constraints of the refracted starlight puncture point and the estimated position of the spacecraft.

[0052] The module for estimating the angle between the incident starlight vector and the east direction in the northeast celestial coordinate system is used to use the Rodriguez rotation formula according to the estimated value of the starlight zenith angle to obtain the unit vector of the vector pointing from the origin to the refracted starlight piercing point; calculate the longitude and latitude of the refracted starlight piercing point according to the unit vector; and convert the unit vector from the geocentric earth-fixed coordinate system to the northeast celestial coordinate system according to the longitude and latitude to obtain the estimated value of the angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system.

[0053] The module for determining the refracted apparent altitude measurement value is used to simulate the transmission process of refracted starlight in the global atmospheric refraction index field using the ray tracing method according to the longitude and latitude and the estimated angle, and obtain the estimated value of the starlight refraction angle and the estimated value of the refracted apparent altitude; when the difference between the estimated value of the starlight refraction angle and the actually observed starlight refraction angle is greater than a preset threshold, the estimated value of the starlight zenith angle is updated, and the starlight refraction angle and the refracted apparent altitude are continuously estimated until the difference is less than the preset threshold, thereby obtaining the refracted apparent altitude measurement value.

[0054] The starlight atmospheric refraction navigation module based on ray tracing is used to locate the spacecraft based on the mapping relationship between the refraction apparent altitude measurement value and the spacecraft position.

[0055] An electronic device includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0056] The estimated value of the starlight zenith angle is determined based on the refracted starlight information observed by the star sensor and the geometric constraints of the refracted starlight piercing point and the estimated position of the spacecraft.

[0057] The Rodriguez rotation formula is used according to the estimated value of the starlight zenith angle to obtain the unit vector of the vector pointing from the origin to the piercing point of the refracted starlight.

[0058] Calculate the longitude and latitude of the point where the refracted starlight pierces based on the unit vector.

[0059] The unit vector is converted from the geocentric Earth-fixed coordinate system to the northeastern celestial coordinate system according to the longitude and latitude, and the estimated angle between the refracted starlight vector and the east direction in the northeastern celestial coordinate system is obtained.

[0060] According to the longitude and latitude and the estimated angle, the ray tracing method is used to simulate the transmission process of refracted starlight in the global atmospheric refractive index field to obtain the estimated value of the starlight refraction angle and the estimated value of the refracted apparent altitude.

[0061] When the difference between the estimated starlight refraction angle and the actually observed starlight refraction angle is greater than a preset threshold, the starlight zenith angle estimate is updated, and the starlight refraction angle and the refraction apparent altitude are estimated again until the difference is less than the preset threshold, thereby obtaining the refraction apparent altitude measurement.

[0062] Positioning is performed based on the mapping relationship between the refracted apparent altitude measurement value and the spacecraft position.

[0063] The above-mentioned starlight atmospheric refraction navigation method, device and electronic device based on ray tracing use the refracted starlight observation quantity observed by the star sensor, simulate the transmission process of real starlight in the earth's atmosphere based on the global atmospheric refraction index field according to ray tracing, establish an iterative algorithm to estimate the refracted apparent height, and locate the spacecraft through the mapping relationship between the apparent height and the spacecraft position. This method can effectively reduce the impact of the global atmospheric spatiotemporal changes on the starlight atmospheric refraction navigation and improve the autonomous navigation accuracy of the spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a flowchart of a starlight atmospheric refraction navigation method based on ray tracing in one embodiment;

[0065] Figure 2 A flowchart of starlight atmospheric refraction navigation based on ray tracing in one embodiment;

[0066] Figure 3 A schematic diagram of the principle of starlight atmospheric refraction positioning in an embodiment;

[0067] Figure 4FIG. 1 is a starlight atmospheric refraction navigation error based on ray tracing in another embodiment, wherein (a) is a schematic diagram of a simulation result of a total position error, and (b) is a schematic diagram of a simulation result of a total velocity error;

[0068] Figure 5 It is a structural block diagram of a starlight atmospheric refraction navigation device based on ray tracing in one embodiment;

[0069] Figure 6 FIG. 4 is a diagram showing the internal structure of an electronic device in one embodiment. DETAILED DESCRIPTION

[0070] 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.

[0071] In one embodiment, Figure 1 , Figure 2 As shown, a starlight atmospheric refraction navigation method based on ray tracing is provided. Taking a low-orbit spacecraft navigation problem as an example, the method includes the following steps:

[0072] Step 100: Determine the estimated value of the starlight zenith angle based on the refracted starlight information observed by the star sensor and in combination with the geometric constraints of the refracted starlight piercing point and the estimated position of the spacecraft.

[0073] Step 102: Using the Rodriguez rotation formula according to the estimated value of the starlight zenith angle, obtain the unit vector of the vector pointing from the origin to the refracted starlight piercing point.

[0074] Step 104: Calculate the longitude and latitude of the refracted starlight puncture point based on the unit vector.

[0075] Step 106: Convert the unit vector from the Earth-centered Earth-fixed coordinate system to the Northeast Celestial Coordinate System according to the longitude and latitude, and obtain an estimated value of the angle between the refracted starlight vector and the east direction in the Northeast Celestial Coordinate System.

[0076] Step 108: Based on the longitude and latitude and the estimated angle, a ray tracing method is used to simulate the transmission process of refracted starlight in the global atmospheric refractive index field to obtain an estimated starlight refraction angle and an estimated refracted apparent altitude.

[0077] Specifically, through the puncture point Latitude and longitude , With refracted starlight vector Angle with east , limiting the starlight refraction path to the starlight refraction plane. Then, the ERA5 dataset released by the European Center for Medium-Range Weather Forecasts is used to construct the global atmospheric refraction index field. Next, the refraction process of starlight in the starlight refraction plane is obtained by ray tracing, and the estimated value of the starlight refraction angle is obtained. True height estimate with refraction .

[0078] Step 110: When the difference between the estimated starlight refraction angle and the actually observed starlight refraction angle is greater than a preset threshold, the estimated starlight zenith angle is updated, and the starlight refraction angle and the refraction apparent altitude are continuously estimated until the difference is less than the preset threshold, thereby obtaining the refraction apparent altitude measurement value.

[0079] Specifically, determine the estimated value of the starlight refraction angle and observed refraction angle Whether the constraints are satisfied:

[0080] (1)

[0081] in, To set the threshold.

[0082] When the above constraints are not met, it is necessary to repeat the process from step 102 to step 110 until the threshold requirement is met to obtain the refracted apparent height measurement value.

[0083] Step 112: Positioning is performed based on the mapping relationship between the refracted apparent altitude measurement value and the spacecraft position.

[0084] Specifically, a measurement model is established through the geometric relationship between the refraction apparent altitude measurement value and the spacecraft position, the state equation is established using orbital dynamics, and the Kalman filter method is used to solve the starlight atmospheric refraction navigation.

[0085] Schematic diagram of the principle of starlight atmospheric refraction positioning Figure 3 shown.

[0086] In the above-mentioned starlight atmospheric refraction navigation method based on ray tracing, the method uses the refracted starlight observation quantity obtained by star sensor observation, simulates the transmission process of real starlight in the earth's atmosphere based on ray tracing on the basis of the global atmospheric refraction index field, establishes an iterative algorithm to estimate the refracted apparent height, and locates the spacecraft through the mapping relationship between the apparent height and the spacecraft position. This method can effectively reduce the impact of the global atmospheric spatiotemporal changes on starlight atmospheric refraction navigation and improve the autonomous navigation accuracy of the spacecraft.

[0087] (1) Compared with the empirical starlight atmospheric refraction model, this method uses the refraction information observed by star sensors and combines it with the ray tracing method to obtain the refraction angle and apparent refraction height of starlight in the global atmospheric refraction index field, effectively improving the calculation accuracy of the apparent refraction height.

[0088] (2) This method uses the estimated value of the starlight zenith angle The update calculation takes the refraction angle observed by the star sensor as a reference, and establishes a starlight atmospheric refraction navigation process based on the ray tracing method to reduce the impact of the three-dimensional spatiotemporal changes of the global atmosphere on the autonomous navigation solution, thereby ensuring the navigation accuracy of the starlight atmospheric refraction navigation technology.

[0089] In one embodiment, step 100 includes: obtaining a spacecraft position vector according to spacecraft orbital mechanics; obtaining a refracted starlight vector according to refracted starlight information observed by a star sensor; and calculating an estimated angle between the spacecraft position vector and the refracted starlight vector in the reverse direction as:

[0090] (2)

[0091] in, is the estimated angle between the spacecraft position vector and the reverse direction of the refracted starlight vector, is the spacecraft position vector, is the refracted starlight vector.

[0092] According to the geometric constraints of the refracted starlight puncture point and the spacecraft position, the estimated value of the starlight zenith angle is:

[0093] (3)

[0094] in, is the estimated value of the starlight zenith angle, For the refracted starlight piercing point The height of the global atmospheric refractive index field, is the radius of the Earth.

[0095] Specifically, the spacecraft orbital dynamics consider The orbital dynamics are extrapolated by the fourth-order Runge-Kutta method to obtain the spacecraft position vector .

[0096] In one embodiment, step 102 includes: using the Rodriguez rotation formula according to the estimated value of the starlight zenith angle, obtaining the unit vector of the vector pointing from the origin to the refracted starlight puncture point as:

[0097] (4)

[0098] in, is the unit vector from the origin to the point where the refracted starlight pierces. is the estimated value of the starlight zenith angle, is a unit vector, , is the unit vector of starlight before refraction, is the refracted starlight vector, is the identity matrix, is a unit vector The antisymmetric matrix composed of elements, .

[0099] In one embodiment, step 104 includes: converting the unit vector to the Earth-centered Earth-fixed coordinate system to obtain the unit vector in the Earth-centered Earth-fixed coordinate system; and calculating the longitude and latitude of the refracted starlight puncture point in the WGS84 system according to the unit vector in the Earth-centered Earth-fixed coordinate system:

[0100] (5)

[0101] in, , are the longitude and latitude of the refracted starlight piercing point, is the radius of curvature of the Earth's circumplex, is the Earth's eccentricity, is a unit vector in the Earth-centered, Earth-fixed coordinate system.

[0102] Specifically, the unit vector In the Earth-centered Earth-fixed coordinate system:

[0103] (6)

[0104] in, is the transformation matrix from the J2000.0 inertial coordinate system to the Earth-centered Earth-fixed coordinate system, which is accurately calculated by IERS.

[0105] In one embodiment, step 106 includes: the vector representation of the refracted starlight vector in the northeastern sky coordinate system is:

[0106] (7)

[0107] in, is the vector of the refracted starlight vector in the northeastern celestial coordinate system, is the transformation matrix from the northeast celestial coordinate system to the earth-centered earth-fixed coordinate system, is the transformation matrix from the J2000.0 inertial coordinate system to the Earth-centered Earth-fixed coordinate system, , are the longitude and latitude of the refracted starlight piercing point, is the refracted starlight vector.

[0108] According to the x element and y element of the vector of the refracted starlight vector in the northeastern sky coordinate system, the estimated angle between the refracted starlight vector and the east direction in the northeastern sky coordinate system is obtained as follows:

[0109] (8)

[0110] in, is the angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system, and are the vectors of the refracted starlight vector in the northeastern sky coordinate system The x element and y element of the .

[0111] In one embodiment, step 108 includes: limiting the starlight refraction path to the starlight refraction plane by estimating the angle between the longitude and latitude of the refraction puncture point and the refracted starlight vector in the northeast celestial coordinate system and the east direction; using the global atmospheric refraction index field, obtaining the refraction process of the starlight in the starlight refraction plane according to the ray tracing algorithm, and obtaining the estimated value of the starlight refraction angle and the estimated value of the true refraction height; determining the estimated value of the refracted apparent height according to the estimated value of the true refraction height as follows:

[0112] (9)

[0113] in, is the estimated value of the refracted apparent height, is the estimated true refraction height, is the estimated true refraction height The refractive index at is the radius of the Earth.

[0114] In one embodiment, the update formula of the estimated value of the starlight zenith angle is:

[0115] (10)

[0116] in, , , Respectively j +1st, j sequence j -1 updated estimate of the starlight zenith angle, For the j The estimated value of the starlight refraction angle at the iteration, To observe the refraction angle, Representative Iterations do not satisfy the constraints.

[0117] In one embodiment, step 112 includes: establishing a measurement model based on the geometric relationship between the refraction apparent altitude measurement value and the spacecraft position; establishing a state equation based on the orbital dynamics of the spacecraft; and using an extended Kalman filter algorithm to complete the starlight atmospheric refraction navigation solution for the measurement model and the state equation.

[0118] Specifically, a measurement model is established based on the geometric relationship between the refracted apparent height and the spacecraft position. As the state quantity, the state equation is established according to the orbital dynamics. The extended Kalman filter is selected for navigation solution.

[0119] 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.

[0120] In a verification example, the orbital elements of the low-orbit spacecraft are shown in Table 1, and 31 Dec 2023 00:00:00.000 UTCG is used as the simulation start time.

[0121] Table 1 Orbital elements of low-orbit spacecraft

[0122]

[0123] The real orbit of the spacecraft takes into account the non-spherical gravity of the earth, adopts the JGM-3 earth model, and the non-spherical perturbation of the earth takes into account the first 21×21 order band harmonics and field harmonics. At the same time, factors such as solar pressure and atmospheric perturbations are considered.

[0124] The simulation parameters of the star sensor are shown in Table 2.

[0125] Table 2 Star sensor simulation parameters

[0126]

[0127] The simulation results of starlight atmospheric refraction navigation error based on ray tracing are as follows: Figure 4 As shown in the figure, (a) is a schematic diagram of the total position error simulation results, and (b) is a schematic diagram of the total velocity error simulation results. After the filter converges, the error curves of position and velocity do not exceed 3 times the mean square error ( ) curve, the positioning and speed errors are 145.1969m and 0.1433m / s respectively, which effectively ensures the accuracy of starlight atmospheric refraction navigation.

[0128] In one embodiment, Figure 5As shown, a starlight atmospheric refraction navigation device based on ray tracing is provided, comprising: a starlight zenith angle estimation module, an angle estimation module between the shooting starlight vector and the east direction in the northeast celestial coordinate system, a refraction apparent height measurement value determination module and a starlight atmospheric refraction navigation module based on ray tracing, wherein:

[0129] The starlight zenith angle estimation module is used to determine the estimated value of the starlight zenith angle based on the refracted starlight information observed by the star sensor and the geometric constraints of the refracted starlight puncture point and the estimated position of the spacecraft.

[0130] The module for estimating the angle between the incident starlight vector and the east direction in the northeast celestial coordinate system is used to use the Rodriguez rotation formula according to the estimated value of the starlight zenith angle to obtain the unit vector of the vector pointing from the origin to the refracted starlight piercing point; calculate the longitude and latitude of the refracted starlight piercing point according to the unit vector; and convert the unit vector from the geocentric earth-fixed coordinate system to the northeast celestial coordinate system according to the longitude and latitude to obtain the estimated value of the angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system.

[0131] The module for determining the refracted apparent altitude measurement value is used to simulate the transmission process of refracted starlight in the global atmospheric refraction index field using the ray tracing method according to the longitude and latitude and the estimated angle, and obtain the estimated value of the starlight refraction angle and the estimated value of the refracted apparent altitude; when the difference between the estimated value of the starlight refraction angle and the actually observed starlight refraction angle is greater than a preset threshold, the estimated value of the starlight zenith angle is updated, and the starlight refraction angle and the refracted apparent altitude are continuously estimated until the difference is less than the preset threshold, thereby obtaining the refracted apparent altitude measurement value.

[0132] The starlight atmospheric refraction navigation module based on ray tracing is used to perform positioning based on the mapping relationship between the refracted apparent altitude measurement value and the spacecraft position.

[0133] In one embodiment, the starlight zenith angle estimation module is further used to obtain a spacecraft position vector based on spacecraft orbital mechanics; obtain a refracted starlight vector based on refracted starlight information observed by a star sensor; and calculate an estimated value of the angle between the spacecraft position vector and the refracted starlight vector in the opposite direction using formula (2).

[0134] According to the geometric constraints of the refracted starlight piercing point and the spacecraft position, the estimated value of the starlight zenith angle is obtained as shown in formula (3).

[0135] In one embodiment, the module for estimating the angle between the incident starlight vector and the east direction in the northeast celestial coordinate system is also used to obtain the unit vector of the vector pointing from the origin to the refracted starlight piercing point using the Rodriguez rotation formula according to the estimated value of the starlight zenith angle, and the unit vector is shown in formula (4).

[0136] In one embodiment, the module for estimating the angle between the incident starlight vector and the east direction in the northeast celestial coordinate system is also used to convert the unit vector into the geocentric earth-fixed coordinate system to obtain the unit vector in the geocentric earth-fixed coordinate system; based on the unit vector in the geocentric earth-fixed coordinate system, the longitude and latitude of the refracted starlight piercing point in the WGS84 system is calculated using formula (5).

[0137] In one embodiment, in the angle estimation module between the incident starlight vector and the east direction in the northeast celestial coordinate system, the vector representation of the refracted starlight vector in the northeast celestial coordinate system is as shown in formula (7); based on the x element and y element of the vector of the refracted starlight vector in the northeast celestial coordinate system, the estimated angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system is obtained as shown in formula (8).

[0138] In one of the embodiments, the module for determining the refraction apparent altitude measurement value is further used to restrict the starlight refraction path to the starlight refraction plane by using the longitude and latitude at the refraction puncture point and the estimated angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system; using the global atmospheric refraction index field, according to the ray tracing algorithm, the refraction process of the starlight in the starlight refraction plane is obtained to obtain the estimated value of the starlight refraction angle and the estimated value of the refraction true altitude; according to the estimated value of the starlight refraction angle and the estimated value of the refraction true altitude, the estimated value of the refraction apparent altitude is determined, wherein the estimated value of the refraction apparent altitude is as shown in formula (9).

[0139] In one embodiment, the updating formula of the estimated value of the starlight zenith angle is shown in formula (10).

[0140] In one embodiment, step 112 includes: establishing a measurement model based on the geometric relationship between the refraction apparent altitude measurement value and the spacecraft position; establishing a state equation based on the orbital dynamics of the spacecraft; and using an extended Kalman filter algorithm to complete the starlight atmospheric refraction navigation solution for the measurement model and the state equation.

[0141] For the specific definition of the starlight atmospheric refraction navigation device based on ray tracing, please refer to the definition of the starlight atmospheric refraction navigation method based on ray tracing above, which will not be repeated here. Each module in the above-mentioned starlight atmospheric refraction navigation device based on ray tracing 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 of the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules.

[0142] In one embodiment, a computer device is provided. The computer device may be a terminal, and its internal structure diagram may be as follows: Figure 6As shown. The computer device includes a processor, a memory, a network interface, a display screen and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a starlight atmospheric refraction navigation method based on ray tracing is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, or a button, trackball or touchpad set on the computer device housing, or an external keyboard, touchpad or mouse, etc.

[0143] Those skilled in the art will understand that Figure 6 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0144] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps in the above method embodiment when executing the computer program.

[0145] 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.

[0146] 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 starlight atmospheric refraction navigation method based on ray tracing, characterized in that: The method comprises: According to the refracted starlight information observed by the star sensor, combined with the geometric constraints of the refracted starlight puncture point and the estimated position of the spacecraft, the estimated value of the starlight zenith angle is determined; Using the Rodriguez rotation formula according to the estimated value of the starlight zenith angle, a unit vector of a vector pointing from the origin to the refracted starlight puncture point is obtained; Calculate the longitude and latitude of the refracted starlight puncture point according to the unit vector; Converting the unit vector from the Earth-centered Earth-fixed coordinate system to the Northeastern Celestial Coordinate System according to the longitude and latitude to obtain an estimated angle between the refracted starlight vector and the east direction in the Northeastern Celestial Coordinate System; According to the longitude and latitude and the estimated angle, a ray tracing method is used to simulate the transmission process of refracted starlight in the global atmospheric refractive index field to obtain an estimated value of the starlight refraction angle and an estimated value of the refracted apparent height; When the difference between the estimated starlight refraction angle and the actually observed starlight refraction angle is greater than a preset threshold, the estimated starlight zenith angle is updated, and the starlight refraction angle and the refraction apparent height are continuously estimated until the difference is less than the preset threshold, thereby obtaining a refraction apparent height measurement value; Positioning is performed based on the mapping relationship between the refracted apparent altitude measurement value and the spacecraft position.

2. The starlight atmospheric refraction navigation method based on ray tracing according to claim 1, characterized in that: Based on the refracted starlight information observed by the star sensor, combined with the geometric constraints of the refracted starlight puncture point and the estimated position of the spacecraft, the estimated value of the starlight zenith angle is determined, including: The spacecraft position vector is obtained according to the spacecraft orbital mechanics; According to the refracted starlight information observed by the star sensor, the refracted starlight vector is obtained; The estimated angle between the spacecraft position vector and the reverse direction of the refracted starlight vector is calculated as: in, is the estimated value of the angle between the spacecraft position vector and the reverse direction of the refracted starlight unit vector, is the spacecraft position vector, is the refracted starlight vector; According to the geometric constraints of the refracted starlight puncture point and the spacecraft position, the estimated value of the starlight zenith angle is: in, is the estimated value of the starlight zenith angle, For the refracted starlight piercing point Height, is the radius of the Earth.

3. The starlight atmospheric refraction navigation method based on ray tracing according to claim 1, characterized in that: According to the estimated value of the starlight zenith angle, the Rodriguez rotation formula is used to obtain the unit vector of the vector pointing from the origin to the refracted starlight puncture point: in, is the unit vector from the origin to the point where the refracted starlight pierces. is the estimated value of the starlight zenith angle, is a unit vector, , is the unit vector of starlight before refraction, is the refracted starlight vector, is the identity matrix, is a unit vector The antisymmetric matrix composed of elements, .

4. The starlight atmospheric refraction navigation method based on ray tracing according to claim 1, characterized in that: Calculating the longitude and latitude of the refracted starlight puncture point according to the unit vector includes: Convert the unit vector to a geocentric earth-fixed coordinate system to obtain a unit vector in the geocentric earth-fixed coordinate system; According to the unit vector in the Earth-centered Earth-fixed coordinate system, the longitude and latitude of the refracted starlight puncture point in the WGS84 system are calculated as: in, , are the longitude and latitude of the refracted starlight piercing point, is the radius of curvature of the Earth's circumplex, is the Earth's eccentricity, is a unit vector in the Earth-centered, Earth-fixed coordinate system.

5. The starlight atmospheric refraction navigation method based on ray tracing according to claim 1, characterized in that: The unit vector is converted from the Earth-centered Earth-fixed coordinate system to the Northeast Sky coordinate system according to the longitude and latitude to obtain an estimated value of the angle between the refracted starlight vector and the east direction in the Northeast Sky coordinate system, including: The vector representation of the refracted starlight vector in the northeastern sky coordinate system is: in, is the vector of the refracted starlight vector in the northeastern celestial coordinate system, is the transformation matrix from the northeast celestial coordinate system to the earth-centered earth-fixed coordinate system, is the transformation matrix from the J2000.0 inertial coordinate system to the Earth-centered Earth-fixed coordinate system, , are the longitude and latitude of the refracted starlight piercing point, is the refracted starlight vector; According to the x element and y element of the vector of the refracted starlight vector in the northeastern sky coordinate system, the estimated angle between the refracted starlight vector and the east direction in the northeastern sky coordinate system is obtained as follows: in, is the angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system, and are the vectors of the refracted starlight vector in the northeastern sky coordinate system The x element and y element of the .

6. The starlight atmospheric refraction navigation method based on ray tracing according to claim 1, characterized in that: According to the longitude and latitude and the estimated angle, a ray tracing method is used to simulate the transmission process of refracted starlight in the global atmospheric refractive index field to obtain an estimated starlight refraction angle and an estimated refracted apparent height, including: The starlight refraction path is restricted to the starlight refraction plane by the longitude and latitude of the refraction puncture point and the estimated angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system; Using the global atmospheric refraction index field and the ray tracing algorithm, we can obtain the refraction process of starlight in the starlight refraction plane, and get the estimated value of the starlight refraction angle and the estimated value of the true refraction height. According to the estimated true refracted height, the estimated apparent refracted height is determined as: in, is the estimated value of the refracted apparent height, is the estimated true refraction height, is the estimated true refraction height The refractive index at is the radius of the Earth.

7. The starlight atmospheric refraction navigation method based on ray tracing according to claim 1, characterized in that: The update formula for the estimated starlight zenith angle is: in, , , Respectively j +1st time, j sequence j -1 updated estimate of the starlight zenith angle, For the j The estimated value of the starlight refraction angle at the iteration, To observe the refraction angle, Representative Iterations do not satisfy the constraints.

8. The starlight atmospheric refraction navigation method based on ray tracing according to claim 1, characterized in that: Positioning is performed according to the mapping relationship between the refracted apparent altitude measurement value and the spacecraft position, including: Establishing a measurement model based on the geometric relationship between the refracted apparent height measurement value and the spacecraft position; Establish the equation of state based on the orbital dynamics of the spacecraft; The extended Kalman filter algorithm is used for the measurement model and the state equation to complete the starlight atmospheric refraction navigation solution.

9. A starlight atmospheric refraction navigation device based on ray tracing, characterized in that: The device comprises: The starlight zenith angle estimation module is used to determine the estimated value of the starlight zenith angle based on the refracted starlight information observed by the star sensor and the geometric constraints of the refracted starlight puncture point and the estimated position of the spacecraft; The module for estimating the angle between the incident starlight vector and the east direction in the northeast celestial coordinate system is used to obtain the unit vector of the vector pointing from the origin to the refracted starlight puncture point using the Rodriguez rotation formula according to the estimated value of the starlight zenith angle; calculate the longitude and latitude of the refracted starlight puncture point according to the unit vector; convert the unit vector from the geocentric earth-fixed coordinate system to the northeast celestial coordinate system according to the longitude and latitude, and obtain the estimated value of the angle between the refracted starlight vector and the east direction in the northeast celestial coordinate system; A module for determining a refracted apparent altitude measurement value, for simulating the transmission process of refracted starlight in the global atmospheric refractive index field using a ray tracing method according to the longitude and latitude and the estimated angle, to obtain an estimated starlight refraction angle and an estimated refracted apparent altitude value; when the difference between the estimated starlight refraction angle and the actually observed starlight refraction angle is greater than a preset threshold, the estimated starlight zenith angle is updated, and the starlight refraction angle and the refracted apparent altitude are continuously estimated until the difference is less than the preset threshold, thereby obtaining a refracted apparent altitude measurement value; The starlight atmospheric refraction navigation module based on ray tracing is used for positioning according to the mapping relationship between the refraction apparent altitude measurement value and the spacecraft position.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the starlight atmospheric refraction navigation method based on ray tracing described in any one of claims 1 to 8 is implemented.

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