Method and device for orbit vector conversion between spatial reference coordinate systems and computer equipment

Abstract

The application relates to a space reference coordinate system orbit vector conversion method and device and computer equipment. The application constructs a transformation matrix composed of a precession matrix, a nutation matrix and a vernal equinox equation rotation matrix, fully utilizes the orthogonal characteristics of the rotation matrix, realizes accurate reverse conversion based on the transposition of the transformation matrix, avoids the complexity of re-computing the inverse matrix in the traditional method, and improves the conversion efficiency.

Description

Technical Field

[0001] This application relates to the field of aerospace data processing technology, and in particular to a method, apparatus, computer equipment, computer-readable storage medium, and computer program product for orbital vector conversion between space reference coordinate systems. Background Technology

[0002] In aerospace engineering, orbital coordinate system transformation is a fundamental technology for applications such as precise orbit determination, satellite constellation management, and collision warning. The TME (True Equator Mean Equinox) coordinate system is used by the SGP4 orbital transmitter and is widely applied in space situational awareness systems such as NORAD / Space-Track. The ICRF (International Celestial Reference Frame, approximately equivalent to the J2000 coordinate system) is the international standard celestial reference system, widely used in precise orbit determination, deep space exploration, and astrometry.

[0003] Typically, the transformation between the TEE coordinate system and the ICRF coordinate system needs to consider the effects of precession, nutation, and the Equation of Equinoxes on the Earth's rotation axis. Traditional methods for transforming from TEE to J2000 / ICRF are mainly based on the methods described in classic textbooks such as Vallado's *Fundamentals of Astrodynamics and Applications*. While these methods can achieve forward transformations (TEME→J2000), inverse transformations (J2000→TEME) usually require recalculating the inverse matrix of the transformation matrix or using numerical methods to solve for the inverse transformation. Furthermore, since the transformation matrix M is composed of three rotation matrices, calculating the inverse matrix requires recombination of the inverse matrices, which not only increases computational complexity but also easily introduces numerical errors, leading to insufficient transformation accuracy. Summary of the Invention

[0004] Therefore, it is necessary to provide a method, apparatus, computer device, computer-readable storage medium, and computer program product for accurately performing inverse conversion between spatial reference coordinate systems to address the aforementioned technical problems.

[0005] In a first aspect, this application provides a method for orbit vector transformation between spatial reference coordinate systems, the method comprising: Based on the target epoch time for coordinate transformation, construct a precession matrix. Nucleation matrix And the rotation matrix of the vernal equinox equation Transformation matrix formed by combination The transformation matrix The transformation matrix This is used to transform the true equatorial mean vernal equinox coordinate system TEE to the epoch coordinate system J2000, wherein... Represent the equation for the vernal equinox; Based on the transformation matrix The orthogonality property determines the transformation matrix. inverse matrix Equal to transpose matrix ; Given the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME), the transformation matrix is ​​used. The first orbit vector is transformed to obtain the second orbit vector of the target satellite in the epoch coordinate system J2000. Given the third orbital vector of the target satellite in the J2000 epoch coordinate system, the transpose matrix is ​​used. The third orbital vector is transformed to obtain the fourth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME).

[0006] In one embodiment, the method further includes: employing the transpose matrix. The second orbital vector is transformed to obtain the fifth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME); round-trip consistency verification is performed based on the error between the fifth orbital vector and the first orbital vector.

[0007] In one embodiment, the method further includes: employing the transformation matrix. The fourth orbit vector is transformed to obtain the sixth orbit vector of the target satellite in the J2000 epoch coordinate system; round-trip consistency verification is performed based on the error between the sixth orbit vector and the third orbit vector.

[0008] In one embodiment, the precession matrix The IAU1976 model or the IAU2006P03 model is used; the nutation matrix is... The IAU1980 model or the IAU2000A model is used; the IAU1980 model is implemented through 106 Fourier series, and the IAU2000A model is called by proxy through the astronomical computing library.

[0009] In one embodiment, the vernal equinox equation ,in, Indicates nutation longitude. Indicates the angle of nutation. It represents the obliquity of the ecliptic.

[0010] In one embodiment, before determining the first orbital vector of the target satellite in the True Equatorial Mean Vernal Equinox coordinate system (TEME), the method further includes: obtaining a two-line orbital element set TLE string of the target satellite; parsing the two-line orbital element set TLE string to extract the orbital elements; and propagating the orbital elements to a specified time using an SGP4 propagator to obtain the first orbital vector of the target satellite in the True Equatorial Mean Vernal Equinox coordinate system (TEME).

[0011] Secondly, this application also provides a device for orbit vector transformation between spatial reference coordinate systems, the device comprising: The transformation matrix construction module is configured to construct a precession matrix based on the target epoch of the coordinate transformation to be performed. Nucleation matrix And the rotation matrix of the vernal equinox equation Transformation matrix formed by combination The transformation matrix The transformation matrix This is used to transform the true equatorial mean vernal equinox coordinate system TEE to the epoch coordinate system J2000, wherein... Represent the equation for the vernal equinox; The inverse matrix determination module is configured to perform an operation based on the transformation matrix. The orthogonality property determines the transformation matrix. inverse matrix Equal to transpose matrix ; The first transformation module is configured to perform the transformation using the transformation matrix after determining the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME). The first orbit vector is transformed to obtain the second orbit vector of the target satellite in the epoch coordinate system J2000. The second transformation module is configured to perform the transformation using the transpose matrix, given that the third orbital vector of the target satellite in the epoch coordinate system J2000 has been determined. The third orbital vector is transformed to obtain the fourth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME).

[0012] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described in the first aspect.

[0013] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in the first aspect.

[0014] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in the first aspect above.

[0015] The aforementioned methods, apparatus, computer equipment, computer-readable storage media, and computer program products for orbital vector transformation between spatial reference coordinate systems construct a vector transformation based on the precession matrix. Nucleation matrix And the rotation matrix of the vernal equinox equation Transformation matrix formed by combination Furthermore, by fully utilizing the orthogonality of the rotation matrix, an accurate inverse transformation is achieved based on the transpose of the transformation matrix, thereby avoiding the complexity of recalculating the inverse matrix in traditional methods and improving the transformation efficiency. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments of this application or related technologies will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart illustrating a method for orbit vector transformation between spatial reference coordinate systems in one embodiment; Figure 2 This is a flowchart illustrating the conversion method in another embodiment; Figure 3 This is a structural block diagram of an orbit vector transformation device between spatial reference coordinate systems in one embodiment; Figure 4 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0019] It should be noted that the terms "first," "second," etc., used in this application can be used to describe various elements, but these elements are not limited by these terms. These terms are only used to distinguish the first element from the second element. The terms "comprising" and "having," and any variations thereof, used in this application, are intended to cover non-exclusive inclusion. The term "multiple" used in this application refers to two or more. The term "and / or" used in this application refers to one of the embodiments, or any combination of multiple embodiments.

[0020] In one exemplary embodiment, such as Figure 1 As shown, a method for orbit vector transformation between spatial reference coordinate systems is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and further to a system including both a terminal and a server, and implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps: Step 102: Construct the transformation matrix based on the target epoch time for which coordinate transformation is to be performed.

[0021] Specifically, based on the target epoch time for which coordinate transformation is to be performed, a precession matrix is ​​constructed. Nucleation matrix And the rotation matrix of the vernal equinox equation Transformation matrix formed by combination .

[0022] Among them, the precession matrix Nulling matrix used to transform the J2000 epoch coordinate system to the Mean of Date (MOD) epoch coordinate system. The rotation matrix used to transform the epoch-point equatorial coordinate system (MOD) to the epoch-point true equatorial coordinate system (TOD) is the vernal equinox equation rotation matrix. Used to transform the epochal true equatorial coordinate system TOD to the true equatorial mean vernal equinox coordinate system TEME. Transformation matrix This is used to transform the true equatorial mean vernal equinox coordinate system TEE to the epoch coordinate system J2000. Since the ICRF coordinate system is approximately equivalent to the J2000 coordinate system, the transformation from TEE to ICRF can be referenced from the transformation from TEE to J2000.

[0023] For example, the precession matrix The IAU 1976 model or the IAU 2006 P03 model can be used. In some scenarios, the precession matrix... The accuracy can be determined based on the precision requirements of the application scenario. For example, for scenarios with general precision requirements, the precession matrix... The IAU 1976 model can be used; for high-precision applications, the precession matrix... The IAU 2006 P03 model can be used.

[0024] For example, nutation matrix Either the IAU 1980 model or the IAU 2000A model can be used. The IAU 1980 model can be implemented using 106 Fourier series (e.g., manually determined, lookup table, or interpolation), while the IAU 2000A model can be proxied and called by astronomical computing libraries (such as Astropy / ERFA, SOFA, NOAA, etc.). The appropriate model for the nutation matrix can be chosen based on the accuracy requirements and computational resource constraints of the specific scenario. The IAU 2000A model offers higher accuracy (approximately 0.2 mas) but requires external dependencies; the IAU 1980 model has zero dependencies and is more suitable for embedded environments.

[0025] In one scenario, the IAU 1976 model, used as the precession matrix, can be used in conjunction with the IAU 1980 model, used as the nutation matrix; similarly, the IAU 2006 P03 model, used as the precession matrix, can be used in conjunction with the IAU 2000A model, used as the nutation matrix, thus meeting different accuracy requirements.

[0026] In this embodiment, the transformation matrix ,in, Precession matrix The transpose of the matrix, For nutation matrix The transpose of the matrix, This represents the equation for the vernal equinox.

[0027] The target epoch refers to the epoch in which coordinate transformation is required. In this embodiment, based on the target epoch to be transformed, the Julian day is first calculated, and the Julian century number is determined. Then, a precession matrix is ​​constructed based on the Julian century number. Nucleation matrix And the rotation matrix of the vernal equinox equation .

[0028] For example, if the target epoch time for coordinate transformation is t=2025-12-15T12:00:00 (UTC), then the corresponding Julian day JD=2461025.5 can be determined by calculation. Using the Julian century number calculation formula (1), we can obtain: (1) Where JD2000 = 2451545.0 is the Julian day of the reference epoch, corresponding to 12:00 TT on January 1, 2000, approximately 12:00 UTC on January 1, 2000; JD represents the Julian day corresponding to the target epoch time t to be transformed; T represents the corresponding Julian century number, a standard unit used to represent time intervals in astronomy and space orbit calculations. T represents the length of time elapsed from the standard reference epoch (usually J2000.0) to the current calculation time, which is also the target epoch time to be transformed.

[0029] This allows us to construct a precession matrix. That is, to calculate from the mean equatorial vernal equinox at J2000.0 to the target epoch. The rotation matrix at the equator and vernal equinox. In this embodiment, the precession matrix is ​​used. Taking the IAU 2006 P03 model as an example, the precession angle can be calculated using the following formulas (2), (3) and (4): (2) (3) (4) Where T is the number of Julian centuries calculated above. , and It is about constructing the precession matrix. The three key precession angles are the angles of rotation of the Earth's axis of rotation. They describe the long-term, slow precession of the Earth's axis of rotation in space due to the gravitational pull of the Sun and Moon, a phenomenon known as "precession." These three angles are defined by the International Astronomical Union (IAU) and are used to transform a coordinate system from one epoch (e.g., J2000.0) to another epoch (e.g., the target time) through three rotations. ).

[0030] Specifically, It represents the angle from the mean vernal equinox of the starting epoch (e.g., J2000.0) around the mean equatorial pole (Z-axis) of the starting epoch to the intersection line (node ​​line) of the mean equatorial planes of the two epochs. Its function is to align the X-axis of the coordinate system to the intersection line of the two equatorial planes. It represents the angle between the flat equatorial plane of the starting epoch and the flat equatorial plane of the target epoch (i.e., the change in the equatorial inclination). Its function is to tilt the equatorial plane of the starting epoch so that it coincides with the equatorial plane of the target epoch. It represents the angle from the intersection of the two epochs' mean equatorial planes, rotating around the mean equatorial pole (i.e., the new Z-axis) of the target epoch to the mean vernal equinox of the target epoch. Its function is to rotate the X-axis from the position of the intersection line to the actual vernal equinox position of the target epoch.

[0031] Precession matrix This is obtained by multiplying the three fundamental rotation matrices of these three angles. For example, it can be expressed by the following formula (5): (5) in, and These represent rotation matrices about the Z-axis and Y-axis, respectively. For example, Indicates rotation about the Z-axis , Indicates rotation about the Y-axis , Indicates rotation about the Z-axis The specific rotation order depends on the version of the IAU model used.

[0032] For example, nutation matrix The construction requires calculating the nutation parameters. ψ (Nutritional Longitude) ε (nutation angle) and (The obliquity of the ecliptic). This example uses the IAU2000A model; the actual calculation can be performed using the nut00a function in the Astropy / ERFA library. and As shown in the following formula (6): (6) (7) Where T is the number of Julian centuries calculated above.

[0033] Then from the target epoch From the mean equator to the vernal equinox to the target epoch The rotation matrix of the true equatorial vernal equinox is also known as the nutation matrix. It can be expressed by the following formula (8): (8) in, and Let Z and X represent the rotation matrices about the Z-axis and X-axis, respectively. Since the X-axis of the TEE coordinate system is located at the vernal equinox, while the Z-axis is located at the true celestial pole, the transformation from TEE to the standard inertial frame J2000 requires correcting for short-period fluctuations in the celestial pole position using the nutation matrix.

[0034] Then calculate the target epoch. The rotation matrix from the true equatorial mean vernal equinox to the true equatorial average vernal equinox is also known as the rotation matrix of the vernal equinox equation. Among them, the vernal equinox equation It can be expressed by the following formula (9): (9) Indicates nutation longitude. Indicates the angle of nutation. It represents the obliquity of the ecliptic.

[0035] Then the rotation matrix of the vernal equinox equation It can be expressed by the following formula (10): (10) If the ultimate goal is to convert TEE to J2000 (or ICRF), it mainly involves the inverse operation or combination of precession and nutation. In a preferred implementation of this embodiment, considering that the X-axis of TEE is defined as the "mean vernal equinox," its essence is to eliminate the influence of nutation in the right ascension direction but retain the nutation influence in the declination direction (celestial pole). Therefore, the conversion logic from TEE to ICRF (J2000) is as follows: First, eliminate the effect of nutation on the celestial pole (Z-axis), then rotate the true celestial pole back to the level celestial pole to obtain the target epoch. The MOD coordinate system for the mean equator and mean vernal equinox, this step corresponds to the nutation matrix. transpose matrix Then, through the precession matrix... inverse of transpose matrix , target era The horizontal coordinate system is traced back to epoch J2000.0.

[0036] In summary, the transformation matrix from TEE to ICRF (J2000) It can be expressed by the following formula (11): (11) Step 104: Based on the orthogonality of the transformation matrix, determine that the inverse matrix of the transformation matrix is ​​equal to the transpose matrix.

[0037] Based on the transformation matrix The orthogonality property determines the transformation matrix. inverse matrix Equal to transpose matrix Due to the precession matrix P, the nutation matrix N, and the rotation matrix of the vernal equinox equation. All are orthogonal rotation matrices, and their determinant is det(M). ≈ 1 . 0, floating-point error less than 10 15 .therefore, Since it is also an orthogonal matrix, we can utilize the orthogonality property of rotation matrices. (where I is the identity matrix), it can be determined that the inverse of the transformation matrix is ​​equal to its transpose, i.e. They are mathematically equivalent, with no additional errors. Furthermore, the complex calculation process of reverse conversion is omitted, thus improving the efficiency of reverse conversion.

[0038] Step 106: After determining the first orbit vector of the target satellite in the TME coordinate system, the first orbit vector is transformed using a transformation matrix to obtain the transformed second orbit vector.

[0039] Specifically, given the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME), a transformation matrix is ​​used. The first orbit vector is transformed to obtain the second orbit vector of the target satellite in the epoch coordinate system J2000 or ICRF coordinate system.

[0040] The first orbital vector refers to at least one of the position and velocity vectors of the target satellite in the TME coordinate system at the target epoch. The second orbital vector is the corresponding vector transformed from the first orbital vector in the TME coordinate system to the J2000 or ICRF coordinate system.

[0041] For example, if the target satellite's first orbital vector in the TEE coordinate system at the known target epoch time includes the position vector rTEME=[ 9050 . 0 , 4650 . 0 , 810 . 0]km, and velocity vector vTEME=[0 . 5 , 7 . 0 , 1 . 0]km / s, then through the above transformation matrix It can be transformed to the J2000 or ICRF coordinate system, as shown in equations (12) and (13) below: (12) (13) in, , The first orbital vector, and This is the second orbital vector obtained after conversion. Substituting the parameters, we calculate rJ2000=[ 9048 . 234 , 4651 . 567 ,810 . 123]km, vJ2000=[0 . 498 , 7 . 001 , 1 .

[000] km / s. It is understood that this embodiment is an example value, and the actual value depends on the specific time and model parameters.

[0042] Step 108: After determining the third orbital vector of the target satellite in the J2000 coordinate system, the third orbital vector is transformed using a transpose matrix to obtain the transformed fourth orbital vector.

[0043] Specifically, when determining the third orbital vector of the target satellite in the J2000 or ICRF coordinate system, the transpose matrix is ​​used. The third orbital vector is transformed to obtain the fourth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME).

[0044] The third orbital vector refers to at least one of the position and velocity vectors of the target satellite in the J2000 or ICRF coordinate system at the target epoch. The fourth orbital vector is the corresponding vector transformed from the third orbital vector in the J2000 or ICRF coordinate system to the TME coordinate system.

[0045] For example, if the target satellite's third orbital vector in the J2000 or ICRF coordinate system at the known target epoch time includes the position vector rJ2000=[ 9048 . 234 , 4651 . 567 , 810 . 123]km, and velocity vector vJ2000=[0 . 498 , 7 . 001 , 1 .

[000] km / s, if it is necessary to transform it to the TEE coordinate system, the orthogonality property of the rotation matrix can be used, through the transformation matrix transpose matrix The transformation is performed to avoid recalculating the inverse matrix, thus reducing computational complexity. The specific transformation is shown in equations (14) and (15): (14) (15) in, and For the third orbital vector, , This is the fourth orbital vector obtained after transformation. Substituting the parameters, we calculate rTEME=[ 9050 . 0 , 4650 . 0 , 810 . 0]km, vTEME=[0 . 5 , 7 . 0 , 1 . [0] km / s. It is understood that this embodiment is an example value, and the actual value depends on the specific time and model parameters.

[0046] In the above-mentioned method for orbital vector transformation between spatial reference coordinate systems, the orthogonality of the rotation matrix is ​​fully utilized, and the accurate inverse transformation is achieved based on the transpose of the transformation matrix. This avoids the complexity of recalculating the inverse matrix in traditional methods, thereby improving the transformation efficiency.

[0047] In an exemplary embodiment, the accuracy of the above transformation result can also be verified to ensure the accuracy of the transformation result. Specifically, at the known target epoch, the first orbital vector of the target satellite in the TEE coordinate system (including the position vector rTEME,original = [ 9050 . 0 , 4650 . 0 , 810 . 0]km and velocity vector vTEME,original=[0 . 5 , 7 . 0 , 1 . In the case of [0] km / s), it can be transformed based on step 106. If the second orbital vector (including rJ2000=[) is obtained in the J2000 or ICRF coordinate system, it can be transformed. 9048 . 234 , 4651 . 567 , 810 . 123]km, vJ2000=[0 . 498 , 7 . 001 , 1 . 000] km / s).

[0048] Alternatively, the transpose matrix can be used. Transform the second orbital vector to obtain the fifth orbital vector (rTEME, roundtrip=[) transformed back to the TEE coordinate system. 9050 . 0 , 4650 . 0 , 810 . 0]km, vTEME,roundtrip =[0 . 5 , 7 . 0 , 1 . 0]km / s. ). The target satellite is transformed from the TME coordinate system (corresponding to the first orbit vector) to the J2000 or ICRF coordinate system (corresponding to the second orbit vector) and then back to the TME coordinate system (corresponding to the fifth orbit vector). Then the round-trip error is calculated to verify the accuracy, that is, the round-trip consistency verification is performed based on the error between the fifth orbit vector and the first orbit vector. The round-trip error can be expressed by the following formula (16): (16) in, r The round-trip position error represents the difference between the target satellite's position in the TME coordinate system and its position in the TME coordinate system obtained after two transformations. Verification results show that the round-trip position error... r< 1 × 10 9 km, reaching the limit of floating-point precision, far superior to the traditional method's 1 × 10 6 The accuracy is improved by approximately 1000 times, thus verifying the precision of the transpose matrix in achieving the inverse transformation and ensuring consistency during the round-trip process. Understandably, the calculation of velocity error is similar, and this embodiment will not elaborate further.

[0049] Similarly, given the target satellite's third orbital vector in the J2000 or ICRF coordinate system at the known target epoch, it can be transformed using step 108 to the TME coordinate system, yielding the fourth orbital vector. Then, step 106 can be used for a second transformation to return to the J2000 or ICRF coordinate system, resulting in the transformed sixth orbital vector. The round-trip error is then calculated to verify accuracy; that is, the round-trip consistency is verified based on the error between the sixth and third orbital vectors, ensuring consistency during the transformation process. The specific verification process is similar to the above, and will not be elaborated further in this embodiment.

[0050] In one exemplary embodiment, the above method can also be applied to end-to-end transformations from the TLE to the J2000 / ICRF coordinate system, such as... Figure 2 As shown, the specific conversion process may include: Step 202: Obtain the two-line orbital element set TLE string of the target satellite.

[0051] Two-Line Element Set (TLE) is a widely used data format used to describe the orbital parameters of an artificial satellite (or space debris) in Earth orbit at a specific moment. A TLE string typically includes two rows: Row 1 (e.g., satellite number, classification, launch year, decay rate) and Row 2 (e.g., orbital inclination, right ascension of the ascending node, eccentricity, argument of perigee, mean perigee, mean motion, etc.).

[0052] Step 204: Parse the two lines of the TLE string containing the orbital root set and extract the orbital roots.

[0053] Specifically, the orbital elements are extracted by parsing the TLE string, including but not limited to the semi-major axis, eccentricity, inclination, right ascension of the ascending node, argument of perigee, and mean perigee.

[0054] Step 206: Based on the SGP4 propagator, the orbital elements are propagated to the specified time to obtain the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME).

[0055] The SGP4 Propagator is a mathematical algorithm model used to calculate the position and velocity of satellites in Earth orbit. Its function is to quickly estimate the impact of these perturbations on the orbit through analytical formulas within a simplified physical model, thereby predicting the future trajectory of the satellite.

[0056] The specified time can be the target epoch time for which coordinate transformation is required. In this embodiment, the orbital elements of the target satellite at a specific time are propagated to the specified time using the SGP4 propagator, thereby obtaining the first orbital vector of the target satellite in the TME coordinate system, such as the position vector rTEME and velocity vector vTEME of the target satellite in the TME coordinate system.

[0057] Since TEE is not an internationally recognized standard coordinate system (such as ICRF / J2000), it is necessary to use... Figure 1 The method is to convert it, that is, to convert the TME vector output by SGP4 to the ICRF or ITFR coordinate system, so that it can be used for high-precision astronomical observation, missile guidance or coordination with other satellites.

[0058] Step 208: Based on the specified time, construct a transformation matrix composed of the precession matrix, the nutation matrix, and the rotation matrix of the vernal equinox equation.

[0059] Construct a precession matrix based on a specified time. Nucleation matrix And the rotation matrix of the vernal equinox equation Transformation matrix formed by combination For details, please refer to... Figure 1 Step 102 will not be described again in this embodiment.

[0060] Step 210: The first orbit vector is transformed using a transformation matrix to obtain the second orbit vector of the target satellite in the epoch coordinate system J2000.

[0061] For details, please refer to... Figure 1 Step 106 will not be described again in this embodiment.

[0062] This embodiment realizes the complete conversion from TLE string to J2000 / ICRF coordinate system based on the above steps, which can be applied to application scenarios such as satellite orbit initialization and state comparison.

[0063] In one exemplary embodiment, the above conversion method supports batch processing. Exemplarily, the input position vector and velocity vector can be single vectors or batch vectors. When the input is a batch vector, batch conversion can be achieved through matrix multiplication, or through parallel computing or multithreading. For large-scale batch processing (such as thousands of satellites), GPU acceleration or distributed computing can also be employed to improve processing efficiency.

[0064] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages in other steps. It is understood that the steps in different embodiments can be freely combined as needed, and all non-contradictory solutions formed by such combinations are within the scope of protection of this application.

[0065] Based on the same inventive concept, this application also provides a conversion device for implementing the above-described method for orbital vector conversion between spatial reference coordinate systems. The solution provided by this device is similar to the implementation described in the above method; therefore, the specific limitations in one or more embodiments of the orbital vector conversion device between spatial reference coordinate systems provided below can be found in the limitations of the method described above, and will not be repeated here.

[0066] In one exemplary embodiment, such as Figure 3 As shown, a device for orbit vector transformation between spatial reference coordinate systems is provided, comprising: a transformation matrix construction module 302, an inverse matrix determination module 304, a first transformation module 306, and a second transformation module 308, wherein: Transformation matrix construction module 302 is configured to construct a precession matrix based on the target epoch of the coordinate transformation to be performed. Nucleation matrix And the rotation matrix of the vernal equinox equation Transformation matrix formed by combination The transformation matrix The transformation matrix This is used to transform the true equatorial mean vernal equinox coordinate system TEE to the epoch coordinate system J2000, wherein... Represent the equation for the vernal equinox; Inverse matrix determination module 304 is configured to perform an operation based on the transformation matrix. The orthogonality property determines the transformation matrix. inverse matrix Equal to transpose matrix ; The first transformation module 306 is configured to perform the transformation matrix when determining the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME). The first orbit vector is transformed to obtain the second orbit vector of the target satellite in the epoch coordinate system J2000. The second transformation module 308 is configured to perform the transformation using the transpose matrix, provided that the third orbital vector of the target satellite in the epoch coordinate system J2000 has been determined. The third orbital vector is transformed to obtain the fourth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME).

[0067] In one exemplary embodiment, the apparatus further includes a verification module configured to perform: employing the transpose matrix The second orbital vector is transformed to obtain the fifth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME); round-trip consistency verification is performed based on the error between the fifth orbital vector and the first orbital vector.

[0068] In one exemplary embodiment, the verification module is further configured to perform: employing the transformation matrix The fourth orbit vector is transformed to obtain the sixth orbit vector of the target satellite in the J2000 epoch coordinate system; round-trip consistency verification is performed based on the error between the sixth orbit vector and the third orbit vector.

[0069] In one exemplary embodiment, the precession matrix The IAU 1976 model or the IAU 2006 P03 model is used; the nutation matrix is... The IAU 1980 model or the IAU 2000A model is used; the IAU 1980 model is implemented through 106 Fourier series, and the IAU 2000A model is called by proxy through the astronomical computing library.

[0070] In one exemplary embodiment, the vernal equinox equation ,in, Indicates nutation longitude. Indicates the angle of nutation. It represents the obliquity of the ecliptic.

[0071] In an exemplary embodiment, the apparatus further includes a vector extraction module configured to perform: acquiring a two-line TLE string representing the orbital elements of the target satellite; parsing the two-line TLE string to extract the orbital elements; and propagating the orbital elements to a specified time using an SGP4 propagator to obtain the first orbital vector of the target satellite in the True Equatorial Mean Vernal Equinox coordinate system (TEME).

[0072] Each module in the aforementioned orbit vector transformation device between spatial reference coordinate systems can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of a computer device in hardware form or independent of it, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0073] In one exemplary embodiment, a computer device is provided, the internal structure of which can be as shown in the figure. Figure 4As shown, the computer device includes a processor, memory, input / output interfaces, a communication interface, a display unit, and an input device. The processor, memory, and input / output interfaces are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The input / output interfaces are used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, Near Field Communication (NFC), or other technologies. When executed by the processor, the computer program implements a method for orbit vector transformation between spatial reference coordinate systems. The display unit is used to form a visually visible image and can be a display screen, a projection device, or a virtual reality imaging device. The display screen can be an LCD screen or an e-ink screen. The input device of the computer device can be a touch layer covering the display screen, or buttons, trackballs, or touchpads set on the casing of the computer device, or external keyboards, touchpads, or mice, etc.

[0074] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0075] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0076] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0077] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above method embodiments.

[0078] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0079] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile memory and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, artificial intelligence (AI) processors, etc., and are not limited to these.

[0080] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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 application.

[0081] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for orbit vector transformation between spatial reference coordinate systems, characterized in that, The method includes: Based on the target epoch time for coordinate transformation, construct a precession matrix. Nucleation matrix And the rotation matrix of the vernal equinox equation Transformation matrix formed by combination The transformation matrix The transformation matrix This is used to transform the true equatorial mean vernal equinox coordinate system TEE to the epoch coordinate system J2000, wherein... Represent the equation for the vernal equinox; Based on the transformation matrix The orthogonality property determines the transformation matrix. inverse matrix Equal to transpose matrix ; Given the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME), the transformation matrix is ​​used. The first orbit vector is transformed to obtain the second orbit vector of the target satellite in the epoch coordinate system J2000. Given the third orbital vector of the target satellite in the J2000 epoch coordinate system, the transpose matrix is ​​used. The third orbital vector is transformed to obtain the fourth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME). The method further includes: Using the transpose matrix The second orbit vector is transformed to obtain the fifth orbit vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME). Round-trip consistency verification is performed based on the error between the fifth orbit vector and the first orbit vector.

2. The method according to claim 1, characterized in that, The method further includes: Using the transformation matrix The fourth orbit vector is transformed to obtain the sixth orbit vector of the target satellite in the J2000 epoch coordinate system; Round-trip consistency verification is performed based on the error between the sixth orbital vector and the third orbital vector.

3. The method according to claim 1, characterized in that, The precession matrix Use either the IAU 1976 model or the IAU2006 P03 model; The nutation matrix The IAU 1980 model or the IAU 2000A model is used; the IAU 1980 model is implemented through 106 Fourier series, and the IAU 2000A model is called by proxy through the astronomical computing library.

4. The method according to claim 1, characterized in that, The vernal equinox equation ,in, Indicates nutation longitude. Indicates the angle of nutation. It represents the obliquity of the ecliptic.

5. The method according to any one of claims 1 to 4, characterized in that, Before determining the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME), the method further includes: Obtain the two-line TLE string representing the orbital elements of the target satellite; The two lines of TLE strings containing the orbital root set are parsed to extract the orbital roots; Based on the SGP4 propagator, the orbital elements are propagated to a specified time to obtain the first orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME).

6. A device for converting orbital vectors between spatial reference coordinate systems, characterized in that, The apparatus is used in the method according to any one of claims 1 to 5, the apparatus comprising: The transformation matrix construction module is configured to construct a precession matrix based on the target epoch of the coordinate transformation to be performed. Nucleus matrix Rotation matrix of the vernal equinox equation Transformation matrix formed by combination The transformation matrix The transformation matrix This is used to transform the true equatorial mean vernal equinox coordinate system TEE to the epoch coordinate system J2000, wherein... Represent the equation for the vernal equinox; The inverse matrix determination module is configured to perform an operation based on the transformation matrix. The orthogonality property is used to determine the transformation matrix. inverse matrix Equal to transpose matrix ; The first transformation module is configured to perform the transformation using the aforementioned transformation matrix, given that the first orbital vector of the target satellite is determined in the True Equatorial Mean Vernal Equinox coordinate system (TEME). The first orbit vector is transformed to obtain the second orbit vector of the target satellite in the epoch coordinate system J2000. The second transformation module is configured to perform the transformation using the transpose matrix, given that the third orbital vector of the target satellite in the epoch coordinate system J2000 has been determined. The third orbital vector is transformed to obtain the fourth orbital vector of the target satellite in the true equatorial mean vernal equinox coordinate system (TEME).

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

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