Low earth orbit satellite dynamics model processing method and apparatus based on spectral analysis

Abstract

The present specification provides a low-orbit satellite dynamics model processing method and device based on spectrum analysis. By using a target prior model about target force perturbation, combined with target measurement data of a target satellite, target acceleration data of the target satellite is determined; then according to the target acceleration data, corresponding target spectrum analysis results are obtained through spectrum analysis; and according to the target spectrum analysis results, a target orbit dynamics model of the target satellite about the target force perturbation is obtained through refined modeling; and then according to the target orbit dynamics model, running orbit parameters of the target satellite are determined. By obtaining and performing spectrum analysis on the target acceleration data of the target satellite, and reconstructing the target orbit dynamics model according to the spectrum analysis results, model errors existing in the prior model can be compensated in a targeted manner, a relatively high-precision orbit dynamics model is obtained, and then the orbit accuracy during precise orbit determination of the low-orbit satellite can be improved.

Description

Technical Field

[0001] This manual belongs to the field of satellite navigation and positioning technology, and in particular relates to a method and apparatus for processing low-orbit satellite dynamic models based on spectrum analysis. Background Technology

[0002] Currently, low-Earth orbit (LEO) satellites have become a crucial infrastructure in global communications, navigation enhancement, and environmental remote sensing monitoring. The orbital accuracy of LEO satellites directly impacts the application level of the satellite platform. Centimeter-level precise orbit determination for LEO satellites typically requires the construction and reliance on accurate dynamic models. However, constructing dynamic models based on existing methods, especially those involving non-conservative force perturbations, relies on the satellite's flight attitude, the physical radiation properties of its surface materials, and the geometric models of the satellite body and solar panels. Furthermore, with the decay and aging of satellite surface materials, shifts in the satellite's center of mass, and electromagnetic interference from the space environment, model accuracy can easily deteriorate and become distorted, thus affecting the orbital accuracy during precise orbit determination.

[0003] There is currently no effective solution to the above problems. Summary of the Invention

[0004] This specification provides a method and apparatus for processing low-Earth orbit satellite dynamics models based on spectrum analysis. It can specifically compensate for model errors existing in prior models, and reconstruct a relatively accurate orbit dynamics model using spectrum analysis results. This allows for precise satellite orbit determination based on the orbit dynamics model, reducing data errors during orbit determination.

[0005] This specification provides a method for processing low-Earth orbit satellite dynamics models based on spectrum analysis, including:

[0006] Acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation;

[0007] Based on the target measurement data and the target prior model of the target satellite, a set of target acceleration data for the target satellite is determined;

[0008] Based on the target acceleration data set, the target spectrum analysis results are obtained through spectrum analysis;

[0009] Based on the target spectrum analysis results, a target orbit dynamics model of the target satellite with respect to target force perturbations is constructed;

[0010] Based on the target orbit dynamics model, the orbital parameters of the target satellite are determined.

[0011] In one embodiment, acquiring target measurement data of a target satellite includes:

[0012] The target satellite's onboard GNSS receiver receives measurement data from navigation satellites based on multiple frequency points, which is then used as the target satellite's target measurement data.

[0013] In one embodiment, the target force includes: conservative forces and / or non-conservative forces; wherein the conservative forces include one or more of the following: Earth's gravity, the gravitational pull of large celestial bodies, and tidal loads; and the non-conservative forces include one or more of the following: atmospheric drag, solar radiation pressure, and Earth's radiation pressure.

[0014] In one embodiment, based on the target measurement data and the target prior model of the target satellite, a set of target acceleration data for the target satellite is determined, including:

[0015] Based on the target measurement data of the target satellite, observation constraints are constructed;

[0016] By using the observation constraints, the target prior model is adjusted to obtain the corresponding target intermediate model;

[0017] Based on a preset sampling frequency, the target measurement data is processed using a target intermediate model to obtain a target acceleration data set for the target satellite; wherein, the target acceleration data set includes satellite acceleration data in the tangential, normal, and radial directions along the satellite orbital system, and the time interval between two adjacent satellite acceleration data is equal to a preset time interval.

[0018] In one embodiment, observation constraints are constructed based on the target measurement data of the target satellite, including:

[0019] Based on the target measurement data of the target satellite, obtain the pseudorange and phase observation values ​​of the target satellite regarding the GNSS navigation signal at multiple frequency points;

[0020] Based on the pseudorange and phase observations of the target satellite with respect to GNSS navigation signals at multiple frequency points, the pseudorange and carrier phase observations of the target satellite based on dual-frequency ionosphere-free conditions are calculated.

[0021] Based on the pseudorange and carrier phase observations of the target satellite using dual-frequency ionosphere-free methods, corresponding observation constraints are constructed.

[0022] In one embodiment, when the multiple frequency points include a first frequency point and a second frequency point, the step of calculating the pseudorange and carrier phase observations of the target satellite based on the pseudorange and phase observations of the target satellite with respect to the GNSS navigation signal at the multiple frequency points includes:

[0023] The pseudorange and carrier phase observations of the target satellite based on the dual-frequency ionosphere are calculated using the following formula:

[0024]

[0025] in, The frequency of the first frequency point, The frequency of the second frequency point, S represents the navigation satellite. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal S at the first frequency point. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal S at the second frequency point. The target satellite's carrier phase observation value for the GNSS navigation signal S at the first frequency point. The target satellite's carrier phase observations of the GNSS navigation signal S at the second frequency point. The target satellite's pseudorange observations are based on dual-frequency, ionosphere-free measurements. The target satellite's carrier phase observations are based on dual-frequency, ionosphere-free carrier phase measurements.

[0026] In one embodiment, obtaining the target spectrum analysis result based on the target acceleration data set through spectrum analysis includes:

[0027] Based on the target acceleration data set, a fast Fourier transform is performed to obtain the corresponding target function;

[0028] Based on the objective function, the target spectrum analysis result is determined by at least obtaining the power spectrum of the objective function through spectrum analysis.

[0029] In one embodiment, based on the target spectrum analysis results, a target orbital dynamics model of the target satellite with respect to target force perturbations is constructed, including:

[0030] Based on the target spectrum analysis results, key features were determined;

[0031] Based on the key features, by setting the corresponding constant terms, periodic acceleration, and perturbation frequency of the periodic acceleration, the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system are determined respectively.

[0032] By combining the acceleration relationships in the tangential, normal, and radial directions of the target satellite based on the orbital system, a target orbit dynamic model of the target satellite with respect to target force perturbations is constructed.

[0033] In one embodiment, the target orbital dynamics model includes:

[0034]

[0035]

[0036]

[0037] in, The radial acceleration of the target satellite based on its orbital system. The acceleration of the target satellite in the normal direction based on its orbital frame. The tangential acceleration of the target satellite based on its orbital system. The acceleration constant in the radial direction, Let be the acceleration constant in the normal direction. Let be the acceleration constant in the tangential direction. The radial acceleration sine coefficient, The radial acceleration cosine coefficient, The coefficient of the sine wave of acceleration in the normal direction. The cosine coefficient of acceleration in the normal direction. The tangential acceleration sine coefficient is... Here, is the tangential acceleration cosine coefficient, k is the perturbation frequency, f is the target satellite's orbital angle, and E is a preset coefficient.

[0038] In one embodiment, when the target force is a non-conservative force, the target orbital dynamics model is the orbital dynamics model of the target satellite with respect to the perturbation of the non-conservative force;

[0039] The method further includes:

[0040] Obtain a priori model of conservative force perturbation;

[0041] By combining a priori models of conservative force perturbations with target orbit dynamics models, the orbital parameters of the target satellite are determined.

[0042] This specification also provides a method for processing low-Earth orbit satellite dynamics models based on spectrum analysis, including:

[0043] Acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation;

[0044] Based on the target measurement data and the target prior model of the target satellite, a set of target acceleration data for the target satellite is determined;

[0045] Based on the target acceleration data set, the target spectrum analysis results are obtained through spectrum analysis;

[0046] Based on the target spectrum analysis results, a target orbit dynamics model of the target satellite with respect to the target force perturbation is constructed.

[0047] This specification also provides a low-Earth orbit satellite dynamics model processing device based on spectrum analysis, including:

[0048] The acquisition module is used to acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation;

[0049] The first determining module is used to determine a set of target acceleration data about the target satellite based on the target measurement data and the target prior model of the target satellite.

[0050] The spectrum analysis module is used to obtain the target spectrum analysis results based on the target acceleration data set through spectrum analysis.

[0051] The module is used to construct a target orbital dynamics model of the target satellite with respect to target force perturbations based on the target spectrum analysis results;

[0052] The second determining module is used to determine the orbital parameters of the target satellite based on the target orbit dynamics model.

[0053] This specification also provides an electronic device, including a processor and a memory for storing processor-executable instructions, wherein the processor executes the instructions to implement the relevant steps of the low-Earth orbit satellite dynamics model processing method based on spectrum analysis.

[0054] This specification also provides a computer-readable storage medium storing computer instructions that, when executed by a processor, implement the steps of the low-Earth orbit satellite dynamics model processing method based on spectrum analysis.

[0055] This specification also provides a computer program product comprising a computer program that, when executed by a processor, implements the steps of the low-Earth orbit satellite dynamics model processing method based on spectrum analysis.

[0056] Based on the spectrum analysis-based method and apparatus for processing low-Earth orbit satellite dynamics models provided in this specification, the target acceleration data set of the target satellite can be determined first using a prior model of the target force perturbation combined with the target measurement data of the target satellite. Then, based on the target acceleration data set, spectrum analysis is performed to obtain the corresponding target spectrum analysis results. Based on these results, the target orbit dynamics model of the target satellite with respect to the target force perturbation is reconstructed. Finally, the orbital parameters of the target satellite are determined based on this target orbit dynamics model. By acquiring and performing spectrum analysis on the target acceleration data set of the target satellite, and reconstructing the target orbit dynamics model based on the spectrum analysis results, model errors in the prior model can be specifically compensated for, resulting in a relatively high-precision orbit dynamics model. This allows for accurate satellite orbit determination based on the orbit dynamics model, effectively reducing data errors during orbit determination and improving the orbital accuracy during precise orbit determination of low-Earth orbit satellites. Attached Figure Description

[0057] To more clearly illustrate the embodiments of this specification, the accompanying drawings used in the embodiments will be briefly introduced below. The drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 This is a flowchart illustrating a method for processing low-Earth orbit satellite dynamics models based on spectrum analysis, provided in one embodiment of this specification.

[0059] Figure 2 This is a schematic diagram of an embodiment of determining a target acceleration data set by applying the low-Earth orbit satellite dynamics model processing method based on spectrum analysis provided in the embodiments of this specification in a scenario example;

[0060] Figure 3 This is a schematic diagram illustrating an embodiment of constructing a target orbit dynamics model using the low-Earth orbit satellite dynamics model processing method based on spectrum analysis provided in the embodiments of this specification, in a scenario example.

[0061] Figure 4 This is a flowchart illustrating a low-Earth orbit satellite dynamics model processing method based on spectrum analysis, provided in another embodiment of this specification.

[0062] Figure 5 This is a schematic diagram of the structural composition of an electronic device provided in one embodiment of this specification;

[0063] Figure 6 This is a schematic diagram of the structural composition of a low-orbit satellite dynamics model processing device based on spectrum analysis, provided in one embodiment of this specification.

[0064] Figure 7 This is a schematic diagram of an embodiment of applying the low-Earth orbit satellite dynamics model processing method based on spectrum analysis provided in this specification to perform spectrum analysis in a scenario example. Detailed Implementation

[0065] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0066] It should be noted that the information and data related to users involved in the embodiments of this specification are all information and data authorized by the user or fully authorized by the relevant parties. Furthermore, the collection, storage, use, processing, transmission, provision, disclosure, and application of the relevant data all comply with relevant laws, regulations, and standards, and necessary confidentiality measures have been taken. They do not violate public order and good morals, and corresponding operation entry points are provided for users or relevant parties to choose to authorize or refuse.

[0067] It should also be noted that in the embodiments of this specification, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0068] See Figure 1 As shown in the embodiments of this specification, a method for processing low-Earth orbit satellite dynamic models based on spectrum analysis is provided. Specifically, this method may include the following:

[0069] S101: Acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation;

[0070] S102: Based on the target measurement data and the target prior model of the target satellite, determine the target acceleration data set of the target satellite;

[0071] S103: Based on the target acceleration data set, obtain the target spectrum analysis results through spectrum analysis;

[0072] S104: Based on the target spectrum analysis results, a target orbit dynamics model of the target satellite with respect to the target force perturbation is constructed;

[0073] S105: Based on the target orbit dynamics model, determine the orbital parameters of the target satellite.

[0074] Specifically, the target satellites mentioned above can include low-Earth orbit (LEO) satellites. These LEO satellites can be satellites with altitudes between 200 and 2000 km, and can be used as spaceborne platforms in high-precision Earth observation systems, with wide applications in fields such as environmental remote sensing monitoring, space environment detection, satellite gravity measurement, and communication and navigation.

[0075] Specifically, low-Earth orbit satellites are often affected by both conservative forces (such as Earth's gravitational field, tidal load, many-body perturbations, and relativistic effects) and non-conservative forces (such as solar radiation pressure, atmospheric drag, and Earth's radiation pressure) during their motion. Therefore, the orbital dynamics model for these perturbations directly affects the accuracy and quality of satellite orbit determination.

[0076] The aforementioned target force can be specifically understood as the perturbation force of interest related to the motion of the target satellite. Specifically, the target force can include both conservative and non-conservative forces.

[0077] Specifically, the aforementioned target force may include a single conservative force, a single non-conservative force, or a combination of multiple different conservative forces, multiple different non-conservative forces, or different conservative and non-conservative forces.

[0078] The aforementioned prior model of the target can be understood as an existing physical dynamic model corresponding to the target force.

[0079] Specifically, prior models corresponding to conservative forces typically exhibit relatively high model accuracy and good performance. Conversely, prior models corresponding to non-conservative forces generally have relatively low accuracy and poor performance, thus affecting subsequent satellite orbit determination. Accordingly, the dynamic model used for non-conservative forces is crucial for the accuracy and quality of satellite orbit determination. The aforementioned target forces can include at least non-conservative forces.

[0080] The aforementioned target measurement data can be specifically understood as orbital motion data of the target satellite obtained based on measurements taken by navigation satellites.

[0081] The above target spectrum analysis results can reflect the spectral characteristics of the target satellite's motion acceleration under the perturbation of the target force.

[0082] The aforementioned target orbit dynamics model can be understood as a reconstructed orbit dynamics model based on the spectral analysis results of the target satellite's acceleration data, which differs from the prior model.

[0083] The aforementioned trajectory parameters may include at least one of the following: position, speed, trajectory shape, etc. It should be noted that the trajectory parameters listed above are merely illustrative. In actual implementation, depending on the specific circumstances and processing requirements, the aforementioned trajectory parameters may also include other types of parameters. This specification does not limit this.

[0084] In practice, firstly, while acquiring target measurement data from the target satellite, a priori model corresponding to the target force can be determined from a pre-set priori model library based on the target force of interest. This priori model serves as the target priori model. The pre-set priori model library can store multiple priori models, each corresponding to at least one perturbation force.

[0085] Next, based on a preset sampling frequency (or sampling theorem), by combining the target measurement data of the target satellite and the target prior model, a target acceleration data set (e.g., a target acceleration sequence) containing residual acceleration information not absorbed by the target prior model can be obtained.

[0086] Furthermore, based on the aforementioned target acceleration data set, a fast Fourier transform can be performed to convert the relatively discrete target acceleration data set from the time domain to the frequency domain. Then, in the frequency domain, spectral analysis can be performed to identify the spectral characteristics related to the target satellite's influence by the target force perturbation, thus obtaining the corresponding target spectral analysis results. Based on these target spectral results, the tangential acceleration relationship, normal acceleration relationship, and radial acceleration relationship of the target satellite based on the sine and cosine fundamental models can be constructed and combined to reconstruct a target orbital dynamics model of the target satellite with respect to the target force perturbation that meets the requirements.

[0087] Specifically, when constructing the target orbit dynamics model of the target satellite with respect to the target force perturbation based on the target spectrum analysis results, the corresponding target acceleration spectrum characteristics are obtained based on the target spectrum analysis results; wherein, the target acceleration spectrum characteristics include at least: periodic signals and constant signals related to the orbital period of the low-Earth orbit satellite; the target orbit dynamics model is constructed based on the target acceleration spectrum characteristics.

[0088] Specifically, based on the target spectrum analysis results, information such as the magnitude of the main periodic acceleration, perturbation frequency, and the magnitude of the constant acceleration (less than one orbital period) can be obtained from the amplitude power spectrum. Then, based on the aforementioned constant acceleration magnitude, periodic acceleration magnitude, and perturbation frequency, a constant acceleration term for the modeled low-Earth orbit satellite, along with the corresponding periodic acceleration at the perturbation frequency, can be added. An acceleration time series can be input, and through spectrum analysis, power spectrum analysis results for the orbital tangential, normal, and radial axes can be obtained. For example, refer to... Figure 7As shown; then, based on the short-period signal in the 0-CPR (circle-per-revolution) interval and the periodic signal above 1CPR, the reconstructed acceleration combination model is obtained and determined using relevant features. Specifically, it can be expressed as a constant + periodic combination. The perturbation frequency CPR signal of the periodic signal can be determined by the power spectrum, and thus the refined complete dynamic model, i.e., the target orbit dynamic model, can be obtained.

[0089] By employing the above methods, high-precision, unmodeled acceleration information can be obtained using spaceborne millimeter-level observation constraints. Periodic acceleration information related to the satellite's orbital period can be extracted from the chaotic residual acceleration information, and the acceleration can be transformed from the time domain to the frequency domain. This provides accurate model error distribution characteristics for low-Earth orbit satellite dynamics modeling. Based on these error distribution characteristics, an acceleration model that conforms to the satellite's actual perturbation characteristics can be used for modeling, thereby achieving high-precision low-Earth orbit satellite dynamics modeling and providing model support for precise orbit determination and orbit prediction.

[0090] Finally, by utilizing the target orbit dynamics model and combining it with other relevant data, the target satellite's orbital parameters can be determined, enabling high-precision and high-quality orbit determination.

[0091] Specifically, the orbital parameters of the target satellite can be determined by iteratively solving the target orbit dynamics model based on the target satellite's target measurement data and target acceleration data set, thus achieving orbit determination of the target satellite.

[0092] Based on the above embodiments, a prior model of the target force perturbation can be used first, combined with target measurement data of the target satellite, to determine the target satellite's target acceleration data set, absorbing residual acceleration information not fully modeled in the prior model. Then, based on the target acceleration data set, spectral analysis is performed to obtain target spectral analysis results that reflect the actual perturbation effect of the target force on the target satellite's motion. Based on these spectral analysis results, the target satellite's acceleration model is reconstructed, resulting in a target orbital dynamics model that meets the requirements regarding the target force perturbation. Finally, the target satellite's orbital parameters can be determined based on this target orbital dynamics model. By performing spectral analysis on the target acceleration data set and reconstructing the target orbital dynamics model based on the spectral analysis results, model errors in the prior model can be specifically compensated for, resulting in a relatively high-precision orbital dynamics model. This allows for accurate satellite orbit determination based on the orbital dynamics model, reducing processing errors during orbit determination.

[0093] In some embodiments, acquiring the target measurement data of the target satellite may specifically include the following:

[0094] The target satellite's onboard GNSS receiver receives measurement data from navigation satellites based on multiple frequency points, which is then used as the target satellite's target measurement data.

[0095] Specifically, the aforementioned Global Navigation Satellite System (GNSS) can refer to an airborne radio navigation and positioning system that can provide users with all-weather 3D coordinates, velocity, and time information at any location on the Earth's surface or in near-Earth space.

[0096] In some cases, during implementation, target measurement data of the target satellite can also be obtained through a Doppler Orbitography and Radio Positioning Integrated by Satellite (DORIS) receiver or Satellite laser ranging (SLR). Alternatively, a GNSS receiver can be used in conjunction with one or more of the above methods to obtain target measurement data of the target satellite.

[0097] In some embodiments, the target force may specifically include: conservative forces and / or non-conservative forces; wherein, the conservative forces may specifically include one or more of the following: Earth's gravity, the gravitational pull of large celestial bodies, tidal loads, etc.; the non-conservative forces may specifically include one or more of the following: atmospheric drag, solar radiation pressure, Earth's radiation pressure, etc. The aforementioned gravitational pull of large celestial bodies may specifically include the gravitational pull of large celestial bodies such as the Sun and Moon.

[0098] Specifically, the aforementioned conservative force can be understood as a force whose magnitude and direction are determined solely by the satellite's position in space, and whose work only alters the conversion between the satellite's potential and kinetic energy, while maintaining the conservation of total mechanical energy.

[0099] The aforementioned non-conservative forces can be understood as forces whose magnitude and direction are related to the satellite's motion state (e.g., velocity) or surrounding environment (e.g., atmosphere, radiation, etc.), and which cause the satellite's mechanical energy to be lost or increased when work is done.

[0100] Specifically, the aforementioned tidal loads can include: solid tides, ocean tides, atmospheric tides, and polar tides.

[0101] Furthermore, the aforementioned conservative forces can also include lunar gravity, general relativistic effects, and many-body perturbations. The aforementioned non-conservative forces can also include active forces (e.g., rocket thrust).

[0102] Of course, it should be noted that the conservative and non-conservative forces listed above are only illustrative. In actual implementation, depending on the specific circumstances and processing requirements, the aforementioned conservative and non-conservative forces may also include other types of forces. This specification does not limit this.

[0103] In some embodiments, see Figure 2 As shown, the above-mentioned target acceleration data set for the target satellite is determined based on the target measurement data and the target prior model. In specific implementation, it may include the following:

[0104] S2-1: Construct observation constraints based on the target measurement data of the target satellite;

[0105] S2-2: Using the observation constraints, adjust the target prior model to obtain the corresponding target intermediate model;

[0106] S2-3: Based on a preset sampling frequency, the target measurement data is processed using a target intermediate model to obtain a target acceleration data set for the target satellite; wherein, the target acceleration data set includes multiple satellite acceleration data arranged in sequence, and the time interval between two adjacent satellite acceleration data is equal to a preset time interval.

[0107] Specifically, the aforementioned observation constraints can be based on dual-frequency, ionosphere-free constraints.

[0108] The aforementioned dual-frequency ionosphere-free combination specifically refers to a key technology used in global navigation satellite systems to eliminate ionospheric delay errors. By simultaneously receiving signals of two different frequencies transmitted by satellites, and utilizing the correlation between ionospheric delay and signal frequency, the positioning result after eliminating the influence of the ionosphere can be calculated.

[0109] The preset time interval is determined based on the preset sampling frequency. Specifically, the preset time interval can be 5 minutes, 10 minutes, etc. The preset sampling frequency can be determined based on the sampling theorem.

[0110] Specifically, if a preset time interval of 10 minutes is used to collect and utilize corresponding acceleration data to estimate the residual error in satellite orbit determination, taking the orbital cycle (94-110 minutes) of a low-Earth orbit satellite with an altitude of 500-1000 kilometers as an example, perturbation frequency signals within a maximum range of 5-CPR (circle-per-revolution) can be obtained according to the sampling theorem. This allows for the acquisition of a target acceleration data set that meets the requirements.

[0111] In practice, the on-orbit data of the target satellite can be obtained based on the target measurement data of the target satellite. At the same time, related data such as GNSS orbit and clock bias data, defined parameters, and orbit determination auxiliary data can be obtained. Then, based on the observation constraints, and in combination with the on-orbit data and related data of the target satellite, the target prior model can be adjusted to obtain the corresponding target intermediate model.

[0112] Based on the above embodiments, firstly, by using the observation constraint based on dual-frequency ionosphere as a constraint condition, the target prior model is adjusted and corrected to obtain a target intermediate model with relatively higher accuracy; furthermore, by processing the target measurement data using the target intermediate model according to the preset sampling frequency, the high-frequency residual error of the target prior model during orbit determination can be estimated by calculating and using the acceleration data at the corresponding time interval, thereby obtaining a target acceleration data set of the target satellite that meets the requirements.

[0113] In some embodiments, constructing observation constraints based on the target measurement data of the target satellite may include the following:

[0114] S11: Based on the target measurement data of the target satellite, obtain the pseudorange and phase observation values ​​of the target satellite regarding the GNSS navigation signal at multiple frequency points;

[0115] S12: Based on the pseudorange and phase observations of the target satellite with respect to GNSS navigation signals at multiple frequency points, calculate the pseudorange and carrier phase observations of the target satellite based on dual-frequency ionosphere-free signals;

[0116] S13: Based on the pseudorange and carrier phase observations of the target satellite using dual-frequency ionosphere-free methods, construct the corresponding observation constraints.

[0117] Among these multiple frequency points, at least two are different frequency points.

[0118] The aforementioned GNSS navigation signals can specifically originate from navigation systems. These navigation systems can include satellite-based BeiDou navigation systems, as well as Global Positioning System (GPS) and other suitable global satellite navigation systems such as the European Union's Galileo.

[0119] In specific implementation, when multiple frequency points include two frequency points: a first frequency point and a second frequency point, the step of calculating the pseudorange and carrier phase observations of the target satellite based on the pseudorange and phase observations of the target satellite with respect to the GNSS navigation signal at multiple frequency points includes:

[0120] Using a short-frequency acceleration model, the pseudorange and carrier phase observations of the target satellite based on dual-frequency ionosphere-free conditions are calculated according to the following formula:

[0121]

[0122] in, The frequency of the first frequency point, The frequency of the second frequency point, S represents the navigation satellite. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal S at the first frequency point. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal S at the second frequency point. The target satellite's carrier phase observation value for the GNSS navigation signal S at the first frequency point. The target satellite's carrier phase observations of the GNSS navigation signal S at the second frequency point. The target satellite's pseudorange observations are based on dual-frequency, ionosphere-free measurements. The target satellite's carrier phase observations are based on dual-frequency, ionosphere-free carrier phase measurements.

[0123] Based on the above embodiments, target measurement data can be used to construct observation constraints for target satellites based on dual-frequency ionosphere-free technology, which have good effects.

[0124] In some embodiments, the above-mentioned method of obtaining target spectrum analysis results based on the target acceleration data set through spectrum analysis may include the following:

[0125] S21: Perform a fast Fourier transform based on the target acceleration data set to obtain the corresponding target function;

[0126] S22: Based on the objective function, through spectrum analysis, at least obtain and determine the target spectrum analysis result based on the power spectrum of the objective function.

[0127] The target spectrum analysis results include at least the power spectrum. Furthermore, depending on the specific circumstances and processing requirements, the target spectrum analysis results may also include information such as phase spectrum amplitude and amplitude spectrum.

[0128] It should be noted that, considering the power spectrum is the self-multiplication of the time-domain amplitude of each harmonic frequency, it can clearly represent the main frequency signals in the harmonics. Therefore, when applied to the acceleration model, it can intuitively reflect the principal periodic acceleration forms in the tangential, normal, and radial directions within the orbital system. Thus, the target spectrum analysis results used here must include at least the power spectrum.

[0129] In practice, the relatively discrete target acceleration data set based on the time domain can be converted into a non-periodic continuous signal in the frequency domain, i.e., the objective function, by using the Fast Fourier Transform. Then, the target spectrum analysis results that can be used for model reconstruction can be obtained by performing spectrum analysis on the objective function in the frequency domain.

[0130] Specifically, a set of constant acceleration models using 5 / 10 min intervals can be added to the tangential, normal, and radial axes of the low-Earth orbit (LEO) satellite to absorb the unmodeled acceleration residual information from the LEO satellite's orbit determination process. Then, the three-axis acceleration time series of the LEO satellite can be converted from the time-domain acceleration information to the frequency acceleration power spectrum using Fast Fourier Transform (FFT). Based on the acceleration power spectrum obtained from the FFT, the amplitude and perturbation frequency of the main periodic signals of the LEO satellite in the tangential, normal, and radial axes can be obtained. This information can be used as a pre-input for reconstructing the dynamic model (i.e., the target orbit dynamic model).

[0131] Specifically, the target acceleration spectrum characteristics can be obtained based on the target spectrum analysis results; wherein, the target spectrum characteristics include at least: periodic signals and constant signals related to the orbital period of the low-Earth orbit satellite; and a target orbit dynamics model is constructed based on the target acceleration spectrum characteristics.

[0132] In some embodiments, see Figure 3 As shown above, based on the target spectrum analysis results, a target orbital dynamics model of the target satellite with respect to target force perturbations is constructed. In specific implementation, this model may include the following:

[0133] S3-1: Based on the target spectrum analysis results, key features are determined;

[0134] S3-2: Based on the key features, by setting the corresponding constant terms, periodic acceleration, and the perturbation frequency of the periodic acceleration, the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system are determined respectively.

[0135] S3-3: Combining the acceleration relationships in the tangential, normal, and radial directions of the target satellite based on the orbital system, a target orbit dynamics model of the target satellite with respect to target force perturbation is constructed.

[0136] In practice, firstly, based on the target spectrum analysis results, the frequencies of a predetermined number of harmonics with the largest amplitude can be selected as perturbation frequencies in the target orbit dynamics model to be reconstructed; at the same time, based on the target spectrum analysis results, the changes in the data values ​​of the aforementioned predetermined number of harmonics are analyzed, and then, combined with the perturbation mechanism of the target force of interest, the influence coefficient and basic action amount of the target force on the target satellite are determined as the key features.

[0137] Furthermore, based on the aforementioned key characteristics, the acceleration relationships of the target satellite in the tangential direction, the normal direction, and the radial direction based on the orbital system can be reconstructed respectively; and by combining the above acceleration relationships in different directions, the target orbit dynamics model of the target satellite with respect to the target force perturbation can be obtained.

[0138] Among them, the acceleration relationships in the tangential direction, normal direction, and radial direction of the target satellite based on the orbital system can be obtained by modifying the basic sine and cosine model.

[0139] Accordingly, in specific implementation, based on a preset configuration strategy, the aforementioned key features can be utilized to determine the sine coefficients, cosine coefficients, and acceleration constants in the corresponding sine and cosine models of the target satellite's acceleration relationships in the tangential, normal, and radial directions based on the orbital system. This allows for the determination of the target satellite's acceleration relationships in the tangential, normal, and radial directions based on the orbital system. The preset configuration strategy can be determined in advance through clustering learning of a large amount of historical sample data.

[0140] In practice, after determining the perturbation frequency, the perturbation frequency can also be used to evaluate the error magnitude of the target prior model and the systematic error related to the orbit period during orbit determination.

[0141] Based on the above embodiments, the frequency domain-based spectrum analysis results can be fully utilized to construct and combine the radial, normal, and tangential acceleration relationships, thereby obtaining a target orbit dynamics model that can more realistically reflect the perturbation effect of the target force on the target satellite.

[0142] In some embodiments, based on the above approach, the target orbit dynamics model may include the following form:

[0143]

[0144]

[0145]

[0146] in, The radial acceleration of the target satellite based on its orbital system. The acceleration of the target satellite in the normal direction based on its orbital frame. The tangential acceleration of the target satellite based on its orbital system. The acceleration constant in the radial direction, Let be the acceleration constant in the normal direction. Let be the acceleration constant in the tangential direction. The radial acceleration sine coefficient, The radial acceleration cosine coefficient, The coefficient of the sine wave of acceleration in the normal direction. The cosine coefficient of acceleration in the normal direction. The tangential acceleration sine coefficient is... Here, is the tangential acceleration cosine coefficient, k is the perturbation frequency, f is the target satellite's orbital angle, and E is a preset coefficient.

[0147] In this context, the subscript R represents radial direction, the subscript T represents normal direction, and the subscript N represents tangential direction.

[0148] In practice, the aforementioned preset coefficients can be determined by obtaining and using the transformation matrix from the satellite coordinate system to the inertial coordinate system.

[0149] In practice, the initial values ​​of the radial acceleration sine coefficient, radial acceleration cosine coefficient, normal acceleration sine coefficient, normal acceleration cosine coefficient, tangential acceleration sine coefficient, and tangential acceleration cosine coefficient can be determined first based on the target satellite's target measurement data. These initial values ​​are then substituted into the target orbit dynamics model. The target orbit dynamics model is then used to perform multiple iterative solutions to determine the target satellite's orbit. During these multiple iterative solutions, the data values ​​of the radial acceleration sine coefficient, radial acceleration cosine coefficient, normal acceleration sine coefficient, normal acceleration cosine coefficient, and tangential acceleration sine coefficient are continuously updated. This process continues until the iterations are complete, at which point the final values ​​of these coefficients can be determined.

[0150] In some embodiments, when the target force is a non-conservative force, the target orbital dynamics model can be the orbital dynamics model of the target satellite with respect to the perturbation of the non-conservative force;

[0151] Accordingly, in specific implementations, the method may also include the following:

[0152] S31: Obtain a priori model of conservative force perturbation;

[0153] S32: By combining the prior model of conservative force perturbation and the target orbit dynamics model, the orbital parameters of the target satellite are determined.

[0154] In practice, since the prior model for conservative force perturbations already possesses relatively high model accuracy, it is not necessary to reconstruct the dynamic model for conservative forces; instead, only the dynamic model for non-conservative forces needs to be reconstructed. Accordingly, the aforementioned target forces can include only non-conservative forces. Therefore, the prior model for conservative force perturbations can be directly used, combined with the reconstructed dynamic model for non-conservative forces (i.e., the target orbit dynamic model), to determine the target satellite's orbital parameters, achieving precise orbit determination.

[0155] In some cases, during implementation, multiple prior models regarding conservative force perturbations can be tested using measurement data from the target satellite. Based on the test results, valid and invalid models are selected from these prior models. The conservative force corresponding to the invalid model is then determined and denoted as the specified conservative force. At this point, a new dynamic model needs to be constructed for both the specified and non-conservative forces. Correspondingly, the target force can include both the specified and non-conservative forces. Then, the valid models from the multiple prior models regarding conservative force perturbations can be directly used, combined with the reconstructed target orbit dynamic model for both the specified and non-conservative forces, to achieve accurate orbit determination of the target satellite.

[0156] As can be seen from the above, the low-Earth orbit satellite dynamics model processing method based on spectrum analysis provided in the embodiments of this specification can first utilize a prior model of the target force perturbation, combined with the target measurement data of the target satellite, to determine the target acceleration data set of the target satellite; then, based on the target acceleration data set, obtain the corresponding target spectrum analysis results through spectrum analysis; and reconstruct the target orbit dynamics model of the target satellite with respect to the target force perturbation based on the target spectrum analysis results; and determine the orbital parameters of the target satellite based on the target orbit dynamics model. By performing spectrum analysis on the target acceleration data set and reconstructing the target orbit dynamics model based on the spectrum analysis results, the model errors existing in the prior model can be compensated in a targeted manner, resulting in a relatively accurate orbit dynamics model. This allows for precise satellite orbit determination based on the orbit dynamics model, reducing data errors during orbit determination.

[0157] See Figure 4 As shown in the embodiments of this specification, another method for processing low-Earth orbit satellite dynamic models based on spectrum analysis is also provided. Specifically, this method may include the following:

[0158] S401: Acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation;

[0159] S402: Based on the target measurement data and the target prior model of the target satellite, determine the target acceleration data set of the target satellite;

[0160] S403: Based on the target acceleration data set, obtain the target spectrum analysis results through spectrum analysis;

[0161] S404: Based on the target spectrum analysis results, a target orbit dynamics model of the target satellite with respect to the target force perturbation is constructed.

[0162] The aforementioned target force may include conservative forces and / or non-conservative forces.

[0163] Based on the above embodiments, by performing spectral analysis on the target acceleration data set and reconstructing the target orbital dynamics model according to the spectral analysis results, it is possible to specifically compensate for the model errors existing in the prior model and obtain a relatively accurate orbital dynamics model.

[0164] This specification provides an electronic device through its embodiments. (See attached document.) Figure 5 As shown. The electronic device includes a network communication port 501, a processor 502, and a memory 503. These structures are connected by internal cables so that they can perform specific data interaction.

[0165] Specifically, the network communication port 501 can be used to acquire target measurement data of the target satellite, as well as a priori model of the target force perturbation.

[0166] Specifically, the processor 502 can be used to determine a target acceleration data set for the target satellite based on the target measurement data and the target prior model; to obtain a target spectrum analysis result through spectrum analysis based on the target acceleration data set; to construct a target orbit dynamics model of the target satellite with respect to target force perturbation based on the target spectrum analysis result; and to determine the orbital parameters of the target satellite based on the target orbit dynamics model.

[0167] The memory 503 can be used to store the corresponding instruction program and related intermediate data.

[0168] Based on the above method, the relevant structural performance of electronic equipment can be effectively utilized to improve the data processing speed of electronic equipment and efficiently realize the data processing for satellite orbit determination.

[0169] In this embodiment, the network communication port 501 can be a virtual port bound to different communication protocols, thereby enabling the sending or receiving of different data. For example, the network communication port can be a port responsible for web data communication, a port responsible for FTP data communication, or a port responsible for email data communication. Furthermore, the network communication port can also be a physical communication interface or communication chip. For example, it can be a wireless mobile network communication chip, such as GSM or CDMA; it can also be a Wi-Fi chip; or it can be a Bluetooth chip.

[0170] In this embodiment, the processor 502 can be implemented in any suitable manner. For example, the processor can take the form of a microprocessor or processor and a computer-readable medium storing computer-readable program code (e.g., software or firmware) executable by the (micro)processor, logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers, and embedded microcontrollers, etc. This specification is not limiting.

[0171] In this embodiment, the memory 503 may include multiple layers. In a digital system, anything that can store binary data can be a memory. In an integrated circuit, a circuit with storage function but no physical form is also called a memory, such as RAM, FIFO, etc. In a system, a storage device with a physical form is also called a memory, such as a memory stick, TF card, etc.

[0172] This specification also provides a computer-readable storage medium based on the above-described method for processing low-Earth orbit satellite dynamics models based on spectral analysis. The computer-readable storage medium stores computer program instructions that, when executed, implement the following: acquiring target measurement data of the target satellite and a priori model of the target force perturbation; determining a target acceleration data set of the target satellite based on the target measurement data and the priori model; obtaining target spectral analysis results based on the target acceleration data set through spectral analysis; constructing a target orbital dynamics model of the target satellite regarding target force perturbation based on the target spectral analysis results; and determining the orbital parameters of the target satellite based on the target orbital dynamics model.

[0173] In this embodiment, the storage medium includes, but is not limited to, Random Access Memory (RAM), Read-Only Memory (ROM), Cache, Hard Disk Drive (HDD), or Memory Card. The memory can be used to store computer program instructions. The network communication unit can be an interface configured according to standards specified in the communication protocol for network connection communication.

[0174] In this embodiment, the specific functions and effects implemented by the program instructions stored in the computer-readable storage medium can be explained in comparison with other embodiments, and will not be repeated here.

[0175] This specification also provides a computer program product, comprising at least a computer program that, when executed by a processor, implements the following method steps: acquiring target measurement data of a target satellite and a target prior model regarding target force perturbation; determining a target acceleration data set of the target satellite based on the target measurement data and the target prior model; obtaining a target spectrum analysis result through spectrum analysis based on the target acceleration data set; constructing a target orbital dynamics model of the target satellite regarding target force perturbation based on the target spectrum analysis result; and determining the orbital parameters of the target satellite based on the target orbital dynamics model.

[0176] See Figure 6 As shown in the embodiments of this specification, a low-Earth orbit satellite dynamics model processing device based on spectrum analysis is also provided. This device may specifically include the following structural modules:

[0177] The acquisition module 601 can be used to acquire target measurement data of the target satellite, as well as a priori model of the target force perturbation;

[0178] The first determining module 602 can be specifically used to determine the target acceleration data set of the target satellite based on the target measurement data and the target prior model of the target satellite;

[0179] The spectrum analysis module 603 can be specifically used to obtain the target spectrum analysis result based on the target acceleration data set through spectrum analysis;

[0180] Module 604 can be used to construct a target orbit dynamics model of the target satellite with respect to target force perturbations based on the target spectrum analysis results.

[0181] The second determining module 605 can be used to determine the orbital parameters of the target satellite based on the target orbit dynamics model.

[0182] In some embodiments, when the acquisition module 601 is specifically implemented, the target measurement data of the target satellite can be acquired in the following manner: the target satellite's onboard GNSS receiver receives measurement data of the navigation satellite based on multiple frequency points, which is then used as the target measurement data of the target satellite.

[0183] In some embodiments, the target force may specifically include: conservative forces and / or non-conservative forces; wherein, the conservative forces include one or more of the following: Earth's gravity, the gravitational pull of large celestial bodies, tidal loads, etc.; the non-conservative forces include one or more of the following: atmospheric drag, solar radiation pressure, Earth's radiation pressure, etc.

[0184] In some embodiments, when the first determining module 602 is specifically implemented, it can determine the target acceleration data set of the target satellite based on the target measurement data and the target prior model of the target satellite in the following manner: constructing observation constraints based on the target measurement data of the target satellite; adjusting the target prior model using the observation constraints to obtain a corresponding target intermediate model; processing the target measurement data using the target intermediate model based on a preset sampling frequency to obtain the target acceleration data set of the target satellite; wherein, the target acceleration data set includes multiple satellite acceleration data arranged in sequence, and the time interval between two adjacent satellite acceleration data is equal to a preset time interval.

[0185] In some embodiments, when the first determining module 602 is specifically implemented, it can construct observation constraints based on the target measurement data of the target satellite in the following manner: based on the target measurement data of the target satellite, obtain the pseudorange and phase observation values ​​of the target satellite with respect to the GNSS navigation signal at multiple frequency points; based on the pseudorange and phase observation values ​​of the target satellite with respect to the GNSS navigation signal at multiple frequency points, calculate the pseudorange and carrier phase observation values ​​of the target satellite based on the dual-frequency ionosphere-free pseudorange and carrier phase observation values ​​of the target satellite; and construct corresponding observation constraints based on the pseudorange and carrier phase observation values ​​of the target satellite based on the dual-frequency ionosphere-free pseudorange and carrier phase observation values.

[0186] In some embodiments, when multiple frequency points include a first frequency point and a second frequency point, the first determining module 602 described above can calculate the pseudorange and carrier phase observations of the target satellite based on the dual-frequency ionosphere according to the following formula:

[0187]

[0188] in, The frequency of the first frequency point, The frequency of the second frequency point, The pseudorange observation value of the target satellite with respect to the GNSS navigation signal at the first frequency point. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal at the second frequency point. The target satellite's carrier phase observations of the GNSS navigation signal at the first frequency point. The target satellite's carrier phase observations of the GNSS navigation signal at the second frequency point. The target satellite's pseudorange observations are based on dual-frequency, ionosphere-free measurements. The target satellite's carrier phase observations are based on dual-frequency, ionosphere-free carrier phase measurements.

[0189] In some embodiments, when the spectrum analysis module 603 is specifically implemented, the target spectrum analysis result can be obtained by performing spectrum analysis on the target acceleration data set in the following manner: performing a fast Fourier transform on the target acceleration data set to obtain the corresponding objective function; and determining the target spectrum analysis result by performing spectrum analysis on the objective function, at least obtaining the power spectrum of the objective function.

[0190] In some embodiments, when the above-mentioned construction module 604 is specifically implemented, the target orbit dynamics model of the target satellite with respect to the target force perturbation can be constructed according to the target spectrum analysis results in the following manner: Based on the target spectrum analysis results, key features are determined; based on the key features, by setting corresponding constant terms, periodic acceleration, and the perturbation frequency of periodic acceleration, the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system are determined respectively; the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system are combined to construct the target orbit dynamics model of the target satellite with respect to the target force perturbation.

[0191] In some embodiments, the target orbit dynamics model may specifically include the following formula:

[0192]

[0193]

[0194]

[0195] in, The radial acceleration of the target satellite based on its orbital system. The acceleration of the target satellite in the normal direction based on its orbital frame. The tangential acceleration of the target satellite based on its orbital system. The acceleration constant in the radial direction, Let be the acceleration constant in the normal direction. Let be the acceleration constant in the tangential direction. The radial acceleration sine coefficient, The radial acceleration cosine coefficient, The coefficient of the sine wave of acceleration in the normal direction. The cosine coefficient of acceleration in the normal direction. The tangential acceleration sine coefficient is... Here, is the tangential acceleration cosine coefficient, k is the perturbation frequency, f is the target satellite's orbital angle, and E is a preset coefficient.

[0196] In some embodiments, when the target force is a non-conservative force, the target orbital dynamics model is the orbital dynamics model of the target satellite with respect to the perturbation of the non-conservative force;

[0197] Accordingly, in specific implementations, the device can also be used to: obtain a priori models of conservative force perturbations; and jointly use the priori models of conservative force perturbations and the target orbit dynamics model to determine the orbital parameters of the target satellite.

[0198] It should be noted that the units, devices, or modules described in the above embodiments can be implemented by computer chips or physical entities, or by products with certain functions. For ease of description, the above devices are described by dividing them into various modules according to their functions. Of course, in implementing this specification, the functions of each module can be implemented in one or more software and / or hardware, or the module that implements the same function can be implemented by a combination of multiple sub-modules or sub-units, etc. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and there may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection between the devices or units shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0199] As can be seen from the above, the low-orbit satellite dynamics model processing device based on spectrum analysis provided in the embodiments of this specification can perform spectrum analysis on the target acceleration data set and reconstruct the target orbit dynamics model based on the spectrum analysis results. This can specifically compensate for the model errors existing in the prior model, obtain a relatively accurate orbit dynamics model, and then accurately realize satellite orbit determination based on the orbit dynamics model, reducing the processing errors during orbit determination.

[0200] In a specific scenario example, the spectrum analysis-based low-Earth orbit (LEO) satellite dynamics modeling method provided in this specification can be applied to perform LEO satellite dynamics modeling. The specific implementation process may include the following:

[0201] In this scenario example, considering that current low-Earth orbit satellites achieve centimeter-level accuracy orbit determination through various space geodetic methods such as spaceborne GNSS (Global Navigation Satellite System) receivers, DORIS (Doppler Orbitography and Radio Positioning Integrated by Satellite) receivers, and satellite laser ranging (SLR) technology, the parameter estimation algorithm employs filtering and batch least squares based on real-time and post-event models. An accurate satellite dynamics model is a crucial prerequisite and guarantee for precise satellite orbit determination.

[0202] Furthermore, the conservative force perturbations experienced by low-Earth orbit (LEO) satellites include Earth's gravitational field, tidal load, many-body perturbations, and relativistic effects, while non-conservative force perturbations include solar radiation pressure, atmospheric drag, and Earth's radiation pressure. With advancements in related technologies, the accuracy of existing Earth gravitational field and tidal load models has been significantly improved. Satellite conservative force perturbations can be described using high-precision model values. Therefore, the accuracy of non-conservative force models related to the satellite surface has become a major factor limiting the precise orbit determination of LEO satellites.

[0203] Existing non-conservative force modeling methods rely heavily on the satellite's prior physical models and structure. Their dynamic models are directly related to the satellite's geometry, surface materials, attitude changes, and operating speed, including solar radiation pressure, Earth radiation pressure, and atmospheric drag. These models also require the introduction of external auxiliary products such as surface radiation data, geomagnetic data, and solar activity indices during the modeling process.

[0204] Because non-conservative force models rely on prior satellite information and external auxiliary products, their accuracy deteriorates due to satellite surface material decay and aging, as well as electromagnetic interference from the space environment. To address the shortcomings of current methods for modeling the dynamics of low-Earth orbit (LEO) satellites, this invention proposes a dynamic modeling method based on spectrum analysis. For large-scale LEO satellite constellations, this method offers a high-precision and easy-to-operate approach that can significantly improve satellite application capabilities.

[0205] In this scenario example, to address the aforementioned problems and their root causes, we can consider first utilizing carrier phase observations (e.g., target measurement data) acquired by the onboard GNSS receiver of a low-Earth orbit satellite (e.g., the target satellite) to construct a dual-frequency, ionosphere-free combination with millimeter-level precision. Then, we can use prior constant acceleration data (e.g., target acceleration data sets) obtained in 5 / 10-minute intervals to absorb residual acceleration information not fully modeled by the LEO satellite during precise orbit determination. Finally, we can employ a fast Fourier transform to convert the discrete acceleration values ​​from the time domain to the frequency domain, reconstruct the satellite acceleration model based on the satellite acceleration spectrum analysis results, and establish a high-precision orbital dynamics model (e.g., the target orbital dynamics model) that conforms to the actual perturbations of the satellite. In specific implementation, this can include the following steps.

[0206] S1: Using high-precision dual-frequency ionospheric observations in orbit, and employing a short-frequency acceleration model, the dynamic errors of the unmodeled low-Earth orbit satellite in precise orbit determination are obtained.

[0207] First, the LEO satellite's onboard GNSS receiver receives pseudorange and phase observations from the navigation satellite S at different frequencies. The dual-frequency pseudorange and carrier phase observations without an ionosphere can be obtained using the following formula.

[0208]

[0209] in, The frequency of the first frequency point, The frequency of the second frequency point, The pseudorange observation value of the target satellite with respect to the GNSS navigation signal at the first frequency point. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal at the second frequency point. The target satellite's carrier phase observations of the GNSS navigation signal at the first frequency point. The target satellite's carrier phase observations of the GNSS navigation signal at the second frequency point. The target satellite's pseudorange observations are based on dual-frequency, ionosphere-free measurements. The target satellite's carrier phase observations are based on dual-frequency, ionosphere-free carrier phase measurements.

[0210] Specifically, for pseudorange and phase observations, accuracy indices of 1 m and 0.01 m are used as prior constraint weight ratios for parameter estimation of LEO satellite precise orbit determination.

[0211] Secondly, before adding a set of piecewise constant accelerations every 5 / 10 minutes, a high-precision background geophysical model is needed to describe most of the perturbations experienced by the low-Earth orbit satellite. This includes considering conservative force perturbations (higher-order terms of the Earth's gravitational field are sufficient for high accuracy, depending on the satellite's orbital altitude), tidal loads (including solid tides, ocean tides, atmospheric tides, and polar tides), many-body perturbations (compensated), and relativistic corrections; and non-conservative force perturbations (solar radiation pressure, Earth's radiation pressure, and atmospheric drag are considered, though these can be ignored at orbital altitudes above 1000 km). Based on a priori background field model (e.g., a target prior model), on-orbit data is used to estimate the residual errors in the prior dynamic model.

[0212] Specifically, based on relevant prior models, the piecewise acceleration models of radial, tangential, and normal directions in the low Earth orbit satellite system can be expressed in the following form:

[0213]

[0214] Where E represents the transformation matrix from the orbital frame to the inertial frame. , and These are the initial accelerations to be estimated in the radial, orbital plane normal, and tangential directions, respectively, with initial values ​​of zero. This pseudo-random parameter estimation is easily achieved in the precise orbit determination process by forming linear combination integral partial derivatives with respect to the initial state. When using the Fast Fourier Transform to convert discrete time-domain signals into frequency-domain signals, the sampling theorem applies, meaning the sampling frequency must be at least twice the highest frequency component. If we estimate the residual error in precise orbit determination using accelerations at 10-minute intervals, taking the orbital period of a low-Earth orbit satellite with an altitude of 500-1000 km as an example (94-110 minutes), the perturbation frequency signal within a maximum range of 5-CPR (circle-per-revolution) can be obtained according to the sampling theorem.

[0215] S2: Use Fourier transform to extract the spectral characteristics of satellite perturbation acceleration.

[0216] Obtaining high-frequency residual acceleration estimates under the current dynamic strategy is beneficial for studying and analyzing the variation law of satellite perturbation error in orbit. The spectral analysis of acceleration uses Fast Fourier Transform to transform the acceleration time series into a non-periodic continuous signal in the frequency domain, and then analyzes its spectral characteristics to find the satellite's perturbation frequency. The specific implementation method can refer to the following formula: any periodic signal x(t) existing in the time domain, regardless of its amplitude variation, can be converted into the sum of sine and cosine signals with a varying pattern.

[0217]

[0218] In the formula, It is a component of the constant term signal. and It is the amplitude of the sine and cosine signals. These are the signal frequencies, specifically, k is the harmonic order. ω is the angular frequency.

[0219] Furthermore, the above formula can be converted into its corresponding complex form, as shown below:

[0220]

[0221] In the formula, , where j is the imaginary unit. The principle of periodic signal decomposition, under certain constraints, states that if a periodic function can be composed of a fundamental harmonic and its integer multiples of the fundamental harmonic, then the phase and amplitude of the signal's frequency components can be represented by Fourier series. Under the premise of satisfying the sampling theorem, after Fourier transform, the power spectrum, phase spectrum amplitude, and amplitude spectrum of a periodic signal can be obtained. Here, we select the power spectrum, which is of interest, for analysis. The power spectrum reflects the self-multiplication of the time-domain amplitude of each harmonic frequency, clearly representing the main frequency signals in the harmonics. Correspondingly, in the acceleration model, it can intuitively reflect the main periodic acceleration forms in the tangential, normal, and radial directions within the orbital system. Using the above transformation to extract the main perturbation frequencies of satellite perturbation acceleration information, we can effectively evaluate the error magnitude of the prior dynamic model and the systematic errors related to the orbital period. Secondly, based on the frequency characteristics of acceleration, we can establish an optimized combined acceleration model for verification during low-Earth orbit satellite reprocessing. For details, please refer to... Figure 7 The figure shows the original acceleration sequences of the satellite in the tangential, normal, and radial directions, and the acceleration power spectrum results obtained in the three directions after using the fast Fourier transform. Figure 7 In the figure, the vertical axis represents the amplitude of the acceleration signal, with units of 1000 m / s. The horizontal axis represents the frequency of the acceleration signal perturbation, in Hz.

[0222] S3: Based on the frequency analysis results, determine the optimal acceleration combination model.

[0223] When simplified dynamics orbit determination is used for low-Earth orbit (LEO) satellites, the differences in orbit determination strategies mainly lie in the observation model and the prior dynamics model. Conservative force perturbations can be described by a general, high-precision deterministic model; therefore, errors in non-conservative force models related to the LEO satellite surface are the primary source of error. For example, using a more accurate panel macroscopic model or a simplified spherical model in the satellite geometry model will affect the residual acceleration estimation results in precise LEO satellite orbit determination. To obtain complete residual error information from the prior dynamics model, the scale parameters related to the solar radiation pressure and atmospheric drag models can be fixed, considering only high-frequency piecewise acceleration models.

[0224] Based on the spectral analysis results of the acceleration, and considering the influence of perturbation terms related to the orbital period of the low-Earth orbit satellite, the combined acceleration model (e.g., the target orbit dynamics model) is shown below:

[0225]

[0226]

[0227]

[0228] in, The radial acceleration of the target satellite based on its orbital system. The acceleration of the target satellite in the normal direction based on its orbital frame. The tangential acceleration of the target satellite based on its orbital system. The acceleration constant in the radial direction, Let be the acceleration constant in the normal direction. Let be the acceleration constant in the tangential direction. The radial acceleration sine coefficient, The radial acceleration cosine coefficient, The coefficient of the sine wave of acceleration in the normal direction. The cosine coefficient of acceleration in the normal direction. The tangential acceleration sine coefficient is... Here, is the tangential acceleration cosine coefficient, k is the perturbation frequency, f is the target satellite's orbital angle, and E is a preset coefficient.

[0229] The specific configuration strategy is based on the satellite's non-conservative force-perturbed acceleration spectrum analysis results, determining the satellite's main perturbation frequencies and constant term estimates. When there are perturbation signals with non-zero mean values, these are usually considered as uncompensated constant biases in the atmospheric drag and light pressure perturbation models. Piecewise constant acceleration terms are typically set in the tangential direction (atmospheric drag compensation) or the normal direction (light pressure perturbation compensation), and perturbation frequencies with higher contribution rates are combined with constant terms to participate in precise orbit determination.

[0230] The above scenario examples validate the low-Earth orbit (LEO) satellite dynamics model processing method based on spectrum analysis provided in this specification. For large-scale LEO satellite constellations, this method achieves high-precision dynamic modeling of LEO satellites without relying on prior satellite information, utilizing short-frequency acceleration and fast Fourier transform. Compared to existing physical analysis models related to satellite surface forces, such as atmospheric drag and radiation pressure models, which are highly dependent on satellite geometry, surface materials, and flight attitude, this invention effectively extracts residual error terms from the perturbation model of LEO satellites under the constraints of onboard GNSS data. It constructs a dynamic model that conforms to the actual perturbations of satellites using on-orbit data, enabling refined modeling of LEO satellites with different mission payloads and effectively improving the orbital quality of LEO satellites.

[0231] While this specification provides the steps of operation for the methods described in the embodiments or flowcharts, more or fewer steps may be included based on conventional or non-inventive means. The order of steps listed in the embodiments is merely one possible order of execution among many steps and does not represent the only possible order. In actual device or client product execution, the methods shown in the embodiments or drawings may be executed sequentially or in parallel (e.g., in a parallel processor or multi-threaded processing environment, or even a distributed data processing environment). The terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, product, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, product, or apparatus. Without further limitations, the presence of other identical or equivalent elements in a process, method, product, or apparatus that includes said elements is not excluded. The terms "first," "second," etc., are used to denote names and do not indicate any particular order.

[0232] Those skilled in the art will also know that, besides implementing the controller using purely computer-readable program code, the same functions can be achieved by logically programming the method steps, making the controller function as logic gates, switches, application-specific integrated circuits (ASICs), programmable logic controllers (PLCs), and embedded microcontrollers. Therefore, such a controller can be considered a hardware component, and the devices within it used to implement various functions can also be considered structures within that hardware component. Alternatively, the devices used to implement various functions can be considered as both software modules implementing the method and structures within a hardware component.

[0233] This specification can be described in the general context of computer-executable instructions that are executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, classes, etc., that perform a specific task or implement a specific abstract data type. This specification can also be practiced in distributed computing environments, where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer-readable storage media, including storage devices.

[0234] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that this specification can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions of this specification can essentially be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, mobile terminal, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments of this specification.

[0235] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. This specification can be used in numerous general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable electronic devices, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.

[0236] Although this specification has been described by way of examples, those skilled in the art will recognize that many variations and modifications are possible without departing from the spirit of this specification, and it is intended that the appended claims cover such variations and modifications without departing from the spirit of this specification.

Claims

1. A method for processing low-Earth orbit satellite dynamics models based on spectrum analysis, characterized in that, include: Acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation; Based on the target measurement data and the target prior model of the target satellite, a set of target acceleration data for the target satellite is determined; Based on the target acceleration data set, the target spectrum analysis results are obtained through spectrum analysis; Based on the target spectrum analysis results, a target orbit dynamics model of the target satellite with respect to target force perturbations is constructed; Based on the target orbit dynamics model, the orbital parameters of the target satellite are determined, including: determining key features based on the target spectrum analysis results; Based on key features, by setting corresponding constant terms, periodic acceleration, and the perturbation frequency of periodic acceleration, the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system are determined respectively. By combining the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system, a target orbit dynamics model of the target satellite with respect to target force perturbation is constructed.

2. The method according to claim 1, characterized in that, The acquisition of target measurement data of the target satellite includes: The target satellite's onboard GNSS receiver receives measurement data from navigation satellites based on multiple frequency points, which is then used as the target satellite's target measurement data.

3. The method according to claim 1, characterized in that, The target force includes: conservative forces and / or non-conservative forces; wherein, the conservative forces include one or more of the following: Earth's gravity, the gravitational pull of large celestial bodies, and tidal loads; the non-conservative forces include one or more of the following: atmospheric drag, solar radiation pressure, and Earth's radiation pressure.

4. The method according to claim 1, characterized in that, The step of determining a set of target acceleration data for the target satellite based on the target measurement data and the target prior model includes: Based on the target measurement data of the target satellite, observation constraints are constructed; By using the observation constraints, the target prior model is adjusted to obtain the corresponding target intermediate model; Based on a preset sampling frequency, the target measurement data is processed using a target intermediate model to obtain a target acceleration data set for the target satellite; wherein, the target acceleration data set includes satellite acceleration data in the tangential, normal, and radial directions along the satellite orbital system, and the time interval between two adjacent satellite acceleration data is equal to a preset time interval.

5. The method according to claim 4, characterized in that, The step of constructing observation constraints based on the target measurement data of the target satellite includes: Based on the target measurement data of the target satellite, obtain the pseudorange and phase observation values ​​of the target satellite regarding the GNSS navigation signal at multiple frequency points; Based on the pseudorange and phase observations of the target satellite with respect to GNSS navigation signals at multiple frequency points, the pseudorange and carrier phase observations of the target satellite based on dual-frequency ionosphere-free conditions are calculated. Based on the pseudorange and carrier phase observations of the target satellite using dual-frequency ionosphere-free methods, corresponding observation constraints are constructed.

6. The method according to claim 5, characterized in that, When multiple frequency points include a first frequency point and a second frequency point, the step of calculating the pseudorange and carrier phase observations of the target satellite based on dual-frequency ionosphere-free pseudorange and carrier phase observations of the target satellite with respect to GNSS navigation signals at multiple frequency points includes: The pseudorange and carrier phase observations of the target satellite based on the dual-frequency ionosphere are calculated using the following formula: in, The frequency of the first frequency point, The frequency of the second frequency point, S represents the navigation satellite. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal S at the first frequency point. The pseudorange observation value of the target satellite with respect to the GNSS navigation signal S at the second frequency point. The target satellite's carrier phase observation value for the GNSS navigation signal S at the first frequency point. The target satellite's carrier phase observations of the GNSS navigation signal S at the second frequency point. The target satellite's pseudorange observations are based on dual-frequency, ionosphere-free measurements. The target satellite's carrier phase observations are based on dual-frequency, ionosphere-free carrier phase measurements.

7. The method according to claim 1, characterized in that, The step of obtaining the target spectrum analysis result through spectrum analysis based on the target acceleration data set includes: Based on the target acceleration data set, a fast Fourier transform is performed to obtain the corresponding target function; Based on the objective function, the target spectrum analysis result is determined by at least obtaining the power spectrum of the objective function through spectrum analysis.

8. The method according to claim 1, characterized in that, The target orbit dynamics model includes: in, The radial acceleration of the target satellite based on its orbital system. The acceleration of the target satellite in the normal direction based on its orbital frame. The tangential acceleration of the target satellite based on its orbital system. The acceleration constant in the radial direction, Let be the acceleration constant in the normal direction. Let be the acceleration constant in the tangential direction. The radial acceleration sine coefficient, The radial acceleration cosine coefficient, The coefficient of the sine wave of acceleration in the normal direction. The cosine coefficient of acceleration in the normal direction. The tangential acceleration sine coefficient is... Here, is the tangential acceleration cosine coefficient, k is the perturbation frequency, f is the target satellite's orbital angle, and E is a preset coefficient.

9. The method according to claim 1, characterized in that, When the target force is a non-conservative force, the target orbital dynamics model is the orbital dynamics model of the target satellite with respect to the perturbation of the non-conservative force; The method further includes: Obtain a priori model of conservative force perturbation; By combining a priori models of conservative force perturbations with target orbit dynamics models, the orbital parameters of the target satellite are determined.

10. A method for processing low-Earth orbit satellite dynamics models based on spectrum analysis, characterized in that, include: Acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation; Based on the target measurement data and the target prior model of the target satellite, a set of target acceleration data for the target satellite is determined; Based on the target acceleration data set, the target spectrum analysis results are obtained through spectrum analysis; Based on the target spectrum analysis results, a target orbit dynamics model of the target satellite with respect to target force perturbation is constructed, including: determining key features based on the target spectrum analysis results; Based on key features, by setting corresponding constant terms, periodic acceleration, and the perturbation frequency of periodic acceleration, the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system are determined respectively. By combining the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system, a target orbit dynamics model of the target satellite with respect to target force perturbation is constructed.

11. A low-Earth orbit satellite dynamics model processing device based on spectrum analysis, characterized in that, include: The acquisition module is used to acquire target measurement data from the target satellite, as well as a priori model of the target force perturbation; The first determining module is used to determine a set of target acceleration data about the target satellite based on the target measurement data and the target prior model of the target satellite. The spectrum analysis module is used to obtain the target spectrum analysis results based on the target acceleration data set through spectrum analysis. The module is used to construct a target orbital dynamics model of the target satellite with respect to target force perturbations based on the target spectrum analysis results; The second determining module is used to determine the orbital parameters of the target satellite based on the target orbit dynamics model. Specifically, the second determining module is used to determine key features based on the target spectrum analysis results; Based on key features, by setting corresponding constant terms, periodic acceleration, and the perturbation frequency of periodic acceleration, the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system are determined respectively. By combining the acceleration relationships of the target satellite in the tangential direction, normal direction, and radial direction based on the orbital system, a target orbit dynamics model of the target satellite with respect to target force perturbation is constructed.

12. An electronic device, characterized in that, It includes a processor and a memory for storing processor-executable instructions, wherein the processor, when executing the instructions, implements the steps of the method according to any one of claims 1 to 10.

13. A computer-readable storage medium, characterized in that, It stores computer instructions that, when executed by a processor, implement the steps of the method according to any one of claims 1 to 10.

14. A computer program product, characterized in that, It includes a computer program that, when executed by a processor, implements the steps of the method according to any one of claims 1 to 10.

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