Low-orbit satellite-oriented satellite-borne clock modeling and simulation method, device and equipment and storage medium

Abstract

The invention provides a low earth orbit satellite-oriented satellite-borne clock modeling and simulation method, device and equipment and a storage medium, and relates to the technical field of low earth orbit satellite positioning navigation time service. The method comprises the following steps: acquiring and preprocessing satellite-borne clock skew data, and extracting a long-term trend term to obtain a residual signal; on the basis of the residual signals, modeling is carried out on various intrinsic noises of the lightweight clock by adopting a three-state random process; constructing a periodic term including South Atlantic Ocean abnormal region irradiation driving and power spectral density extraction and a multi-source environment driving term of relativistic correction; integrating a trend term, an intrinsic noise model and an environment driving term, and establishing a comprehensive clock error dynamic model; after the model is discretized, a high-fidelity clock skew sequence is generated through time recursion iteration. According to the invention, clock long-term drift, intrinsic noise and in-orbit environment disturbance can be depicted at the same time, and the authenticity and efficiency of low-orbit constellation-level clock simulation are remarkably improved.

Description

Technical Field

[0001] This application relates to the field of low-Earth orbit satellite positioning, navigation and timing technology, and in particular to a method, apparatus, equipment and storage medium for modeling and simulating onboard clocks for low-Earth orbit satellites. Background Technology

[0002] In recent years, with the continuous growth of global demand for high-precision spatiotemporal services, the strategic importance of low-Earth orbit (LEO) satellite constellations in navigation, positioning, and timing has rapidly increased, gradually becoming an important component of the integrated air-space-ground information network. As the core time and frequency reference in LEO satellite systems, onboard clocks play a fundamental supporting role in inter-satellite link synchronization, satellite-to-ground link scheduling, ranging and orbit determination, and the construction of a unified time reference for the constellation. However, the on-orbit operational data of LEO onboard clocks is usually considered key technical data by the constellation operators and is often not publicly disclosed for security and commercial reasons. This makes it difficult for external research institutions to obtain high-precision, long-term on-orbit clock observation data, hindering large-scale system performance analysis and simulation verification at the constellation level. Furthermore, LEO satellites operate under low altitude, high speed, and drastically changing environmental conditions, and are affected by various factors such as temperature fluctuations, cumulative radiation, power supply disturbances, and attitude changes. Their clock error characteristics differ significantly from those tested in ground-based laboratory environments. Since the on-orbit environment is difficult to fully replicate under ground conditions, relying solely on laboratory tests is insufficient to accurately assess the actual operational characteristics of LEO onboard clocks. Therefore, in order to conduct overall performance research and system-level scheme demonstration of LEO constellations, it is urgent to construct a clock error model that can reflect the real operating environment of LEO and carry out corresponding simulations to ensure the scientificity and reliability of constellation design and performance evaluation.

[0003] Existing research on spaceborne clock modeling and simulation primarily relies on the time-frequency theory of traditional navigation satellites and ground-based atomic clocks. Within a stochastic process framework, state variables such as phase, frequency, and frequency drift are constructed, and clock error models are formed by superimposing typical noise components such as white phase noise, white frequency noise, and random walk frequency noise. Common methods include generating clock deviation sequences using continuous or discrete three-state stochastic process equations, and then tuning the noise power spectral density parameters based on stability indices such as Allan variance and Hadamard variance to simulate the statistical characteristics of the target clock. Furthermore, some studies utilize laboratory test data or on-orbit measured samples to empirically fit clock noise models, constructing empirical error models suitable for specific atomic clock models for long-term stability analysis and engineering performance verification of spaceborne clocks.

[0004] However, existing clock simulation methods have the following significant problems when applied to the simulation of clocks on low-Earth orbit (LEO) satellites in orbit: 1) Insufficient characterization of the error characteristics of LEO satellite-borne clocks: Most methods follow the noise assumptions of medium- and high-Earth orbit (MEO) or ground-based atomic clocks, while LEO satellites generally use lightweight clocks, whose noise intensity, drift characteristics, and stability differ significantly from traditional clocks, making it difficult to reconstruct the true intrinsic error characteristics; 2) Lack of modeling mechanisms for the impact of the LEO operating environment: Factors such as the non-uniform Earth's gravitational field, geomagnetic field anomalies, temperature cycles, cumulative radiation, power supply disturbances, and attitude changes in the LEO environment directly drive the clock's internal clock. The clock generates significant multi-scale periodic errors, but most simulation methods treat the clock as operating under ideal stable conditions and do not explicitly incorporate environmental driving terms into the model framework. As a result, the simulation sequence cannot reflect the actual external disturbance effects on orbit, nor can it characterize the coupling relationship between environmental factors and clock state. The authenticity and credibility of the simulation results are limited. 3) Insufficient simulation efficiency and scalability: Some methods rely on complex solutions, which have high computational costs and are not suitable for multi-star, long-term or large-scale scenarios. At the same time, the parameter reusability is poor and the model adaptability is weak, making it difficult to meet the efficiency and scalability requirements of low-orbit constellation-level simulation platforms. Summary of the Invention

[0005] This application provides a method, apparatus, device, and storage medium for modeling and simulating onboard clocks for low-Earth orbit (LEO) satellites. The aim is to simultaneously characterize the linear variation trend, intrinsic noise characteristics, and on-orbit environmental disturbance effects of LEO onboard clocks, generating a high-fidelity clock deviation sequence that reflects real-world LEO operating conditions. Specifically, this application introduces a noise modeling mechanism suitable for lightweight onboard clocks based on traditional linear polynomial models, and constructs multi-source environmental driving terms such as Earth's gravitational field and magnetic field, temperature, irradiance, power supply, and attitude, thus forming a unified modeling framework coupling clock errors and the orbital environment. Furthermore, this application employs an efficient discretized state update and parameterized driving method to achieve rapid and stable simulation of multi-satellite, long-term sequences. It allows for flexible configuration of model parameters for different constellation configurations, better meeting the practical needs of LEO constellation-level system analysis, performance evaluation, and scheme demonstration.

[0006] Firstly, this application provides a method for modeling and simulating onboard clocks for low-Earth orbit satellites, including: The onboard clock deviation data of the target low-Earth orbit satellite is acquired. Outlier removal, missing point interpolation, and data continuity checks are performed on the data in sequence to obtain a preprocessed clock deviation sequence. A polynomial model is used to model the long-term drift trend of the preprocessed clock deviation sequence to obtain a clock trend term. The clock trend term is removed from the preprocessed clock deviation sequence to obtain the residual signal. Based on the residual signal, the intrinsic noise of the lightweight spaceborne clock is modeled to obtain the intrinsic noise model. We construct a multi-source environmental driving term, including an irradiation driving term caused by the South Atlantic anomaly, other periodic environmental driving terms extracted through power spectral density analysis, and a relativistic correction term considering the Earth's oblateness effect. Based on the aforementioned clock trend term, intrinsic noise model, and multi-source environmental driving term, a comprehensive clock error dynamic model is established. The comprehensive clock error dynamic model is discretized using a fixed sampling interval and iteratively updated using a time recursion method. Based on the phase, frequency, and frequency drift of the previous moment, the environmental driving quantity and intrinsic noise disturbance of the current simulation step are superimposed to generate a low-Earth orbit satellite clock deviation sequence that simultaneously includes long-term drift, intrinsic noise, and environmental disturbance.

[0007] In one possible design, the clock trend term is represented as: ; in, Let the order of the trend polynomial be . Index of the order of the trend polynomial; coefficients Obtained through least squares fitting; For clock trend items; The residual signal is represented as follows: ; in, For residual signals, This is the preprocessed clock offset sequence.

[0008] In one possible design, the intrinsic noise of the lightweight spaceborne clock is modeled based on the residual signal, including: Set the clock state vector as follows: ; in, This is the clock state vector. For clock phase deviation, To normalize the frequency deviation, This is frequency drift; Considering five types of intrinsic noise sources—phase white noise, frequency white noise, flicker frequency noise, random walk frequency noise, and random walk frequency drift noise—construct a system of continuous-time stochastic differential equations: ; in, This is the phase white noise driving quantity; This is the frequency-driven white noise quantity; This is the noise driving quantity at the flicker frequency; This is the frequency noise driving factor for random walks; This is the driving force of the random walk frequency drift noise. Phase deviation versus time The first derivative (phase change rate); Normalized frequency deviation versus time The first derivative; Frequency drift versus time The first derivative; The above process can be expressed as a vector-form continuous-time state equation: ; ; in, State vector The first derivative with respect to time; It is a continuous-time state transition matrix (system matrix). It is a continuous-time process noise vector (composed of various intrinsic noise driving quantities). Let the five noise sources be independent, with a mean of 0 and a variance of . Gaussian white noise process: ; in, It follows a Gaussian distribution; Five noise intensity parameters; In the frequency domain, frequency deviation The power spectral density is represented as the superposition of five types of noise: ; Among them, coefficient and One-to-one correspondence; For frequency variables (unit: Hz); By sampling interval Δt Discretizing the continuous-time state equation in vector form yields the discrete state equation of the intrinsic noise model: ; in, This is the discrete-time state transition matrix. , e It is a natural constant; Given a discrete Gaussian noise vector, its covariance matrix is... The noise intensity parameters are calculated using a continuous-discrete covariance transformation. and The first The and the first A state vector for each discrete epoch.

[0009] In one possible design, the multi-source environment driver is represented as: ; in, This indicates the radiation-driven term caused by the South Atlantic anomaly. This indicates other periodic environmental drivers extracted through power spectral density analysis, comprehensively reflecting the equivalent effects of factors such as temperature cycling, background irradiance, and power fluctuations. This represents the relativistic correction term that takes into account the effect of Earth's oblateness J2. The irradiation-driven term induced by the South Atlantic anomaly was determined using the following method. : Using the World Magnetic Field Model Calculate the total intensity of the satellite's geomagnetic field at each epoch. : ; Where pos represents the coordinates of the low-orbit satellite; For the first The time corresponding to each discrete epoch; Compare the magnetic field strength output by WMM with the SAA (South Atlantic Anomaly) threshold: ; in, Indicators for identifying the South Atlantic anomaly; Constructing the irradiation-driven term caused by the South Atlantic anomaly : ; in, These are radiation-sensitive parameters based on observational calibration.

[0010] In one possible design, it is determined as follows: : Numerical integration of relativistic effects: ; in, This is the cumulative amount of clock error correction caused by relativistic effects; These are Earth's standard gravitational parameters; It is the speed of light in a vacuum; The distance from the satellite to the Earth's center; The semi-major axis of the Earth's reference ellipsoid or the equivalent equatorial radius; The current time; The magnitude of the satellite's speed; This represents the component of the satellite's position along the Earth's rotation axis; Extract only The portion that changes over time serves as a driver of other periodic environments: ; in This is the trend term after removing the second-order polynomial.

[0011] In one possible design, it is determined as follows: : The quadratic polynomial trend term is removed sequentially from the original clock error sequence. and The environment-dominated residual sequence was obtained. ; right Perform Discrete Fourier Transform to calculate the power spectral density. Several significant spectral peak frequencies were identified on the spectral lines. ; For each significant frequency component, estimate the corresponding amplitude. With phase ,Sure : ; in, For frequency component index; The total number of significant frequency components; For the first The amplitude of each frequency component; For the first The frequency of each frequency component; For the first The time corresponding to each discrete epoch; For the first The phase of each frequency component.

[0012] In one possible design, the integrated clock error dynamic model is represented as: ; in, State vector The first derivative with respect to time; This is a continuous-time state transition matrix (system matrix). This is the clock state vector; This is a control matrix used to control environmental driving terms. Mapped to the corresponding components of the state equation; This is the noise matrix.

[0013] Secondly, this application provides a spaceborne clock modeling and simulation device for low-Earth orbit satellites, the device comprising: The data preprocessing module is configured to acquire the onboard clock deviation data of the target low-orbit satellite, and sequentially perform outlier removal, missing point interpolation, and data continuity checks on the data to obtain a preprocessed clock deviation sequence. A polynomial model is used to model the long-term drift trend of the preprocessed clock deviation sequence to obtain a clock trend term. The clock trend term is removed from the preprocessed clock deviation sequence to obtain a residual signal. The intrinsic noise modeling module is configured to model the intrinsic noise of the lightweight spaceborne clock based on the residual signal, and obtain the intrinsic noise model. The multi-source driving term construction module is configured to construct multi-source environmental driving terms, including irradiation driving terms caused by the South Atlantic anomaly, other periodic environmental driving terms extracted by power spectral density analysis, and relativistic correction terms considering the Earth's oblateness effect. The discretization simulation module is configured to establish a comprehensive clock error dynamic model based on the clock trend term, intrinsic noise model, and multi-source environmental driving term. The comprehensive clock error dynamic model is discretized using a fixed sampling interval and iteratively updated through a time recursion method. Based on the phase, frequency, and frequency drift of the previous moment, the environmental driving quantity and intrinsic noise disturbance of the current simulation step are superimposed to generate a low-Earth orbit satellite clock deviation sequence that simultaneously includes long-term drift, intrinsic noise, and environmental disturbance.

[0014] Thirdly, embodiments of this application provide an electronic device, including: at least one processor and a memory; the memory stores computer execution instructions; the at least one processor executes the computer execution instructions stored in the memory, causing the at least one processor to execute the onboard clock modeling and simulation method for low-Earth orbit satellites as described in the first aspect and various possible designs of the first aspect.

[0015] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the onboard clock modeling and simulation method for low-Earth orbit satellites as described in the first aspect and various possible designs of the first aspect.

[0016] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the onboard clock modeling and simulation method for low-Earth orbit satellites as described in the first aspect and various possible designs of the first aspect.

[0017] The method, apparatus, equipment, and storage medium for modeling and simulating onboard clocks for low-Earth orbit satellites provided in this application have at least the following beneficial effects: (1) Modeling capability that better matches the intrinsic characteristics of low-Earth orbit lightweight satellite clocks: This application introduces five types of intrinsic noise sources under the framework of three-state stochastic processes: phase white noise, frequency white noise, flicker frequency noise, random walk frequency noise and random walk frequency drift noise. The Gauss-Newton fitting method is used to calibrate the noise parameters, so that the stability performance of the simulated clock at different time scales is more consistent with the actual low-Earth orbit satellite clock, which significantly improves the authenticity and precision of intrinsic error modeling.

[0018] (2) Explicit characterization of the impact of the low-Earth orbit environment on clock error: This application adds a multi-source environment driving term to the clock dynamics equation, identifies the SAA region and constructs the irradiation driving through the world magnetic field model, uses power spectral density analysis to uniformly extract weak periodic disturbances such as temperature cycle, background irradiation, and power fluctuation, and explicitly adds a relativistic correction that considers the J2 oblateness of the Earth, so that the generated clock deviation sequence can reproduce the 12-hour dominant cycle and typical structures such as the first and second orbital cycles, which greatly improves the simulation results' accuracy in reproducing the on-orbit behavior.

[0019] (3) High simulation efficiency and easy to extend to constellation-level clock simulation applications: This application stores the parameterized results of trend, noise, and environmental terms as a low-orbit clock feature library, which can be combined as needed to generate different types of simulation clocks, realizing rapid model reuse and flexible adaptation. This mechanism has high computational efficiency and can be easily extended to multi-star and constellation-level scenarios, meeting the needs of system-level performance analysis and scheme demonstration.

[0020] (4) High-fidelity system evaluation can still be carried out in the absence of publicly available on-orbit data: Based on limited measured data of low-orbit clocks, this application constructs a representative error model, which can provide high-fidelity simulation input for external research institutions and system design departments when on-orbit data is not publicly available or difficult to obtain, supporting low-orbit constellation design and performance evaluation, and has significant engineering application value. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0022] Figure 1 A technical schematic diagram of a method for modeling and simulating onboard clocks for low-Earth orbit satellites provided in this application embodiment; Figure 2 A flowchart illustrating a method for modeling and simulating onboard clocks for low-Earth orbit satellites, provided in this application embodiment; Figure 3 This is a structural diagram of a satellite clock modeling and simulation device for low-Earth orbit satellites provided in an embodiment of this application.

[0023] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concepts of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0024] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0025] The collection, storage, use, processing, transmission, provision, and disclosure of financial data or user data involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0026] It should be noted that in the embodiments of this application, 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.

[0027] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described below with reference to the accompanying drawings.

[0028] This application provides a method for modeling and simulating onboard clocks for low-Earth orbit (LEO) satellites. It fully considers the intrinsic noise characteristics of lightweight onboard clocks and the disturbances caused by the complex operating environment of LEO. By constructing a unified model framework that integrates linear drift, random noise, and environmental driving terms, it achieves high-fidelity simulation of LEO onboard clock errors. The overall process is shown in the attached figure. Figure 1 As shown, this method takes the measured low-orbit satellite clock error as the initial input, first decomposes it into three core components: linear trend term, periodic term, and random noise term, and then performs feature analysis and parameter extraction for each component.

[0029] For the linear trend term, a trend term extraction (polynomial fitting) method is used to process it, and three types of characteristic quantities that characterize the long-term change law of the clock, namely phase offset, frequency offset and frequency drift, are separated from the measured clock error, so as to clearly characterize the long-term drift characteristics of the clock.

[0030] For the periodic term, relying on the technical means of periodic term decomposition (power spectral density analysis), the periodic characteristics corresponding to various environmental disturbances during the operation of low-Earth orbit satellites are analyzed. Specifically, it covers multi-dimensional environmental driving factors such as South Atlantic anomaly, relativistic effects, voltage changes, and temperature changes, and fully covers the disturbance effect of the complex low-Earth orbit operating environment on the clock.

[0031] For the random noise term, the intrinsic noise parameters are calibrated by power-law noise intensity estimation (Gauss-Newton method), accurately obtaining the intrinsic noise components of the lightweight spaceborne clock, such as phase white noise, frequency white noise, flicker frequency noise, random walk frequency noise, and random drift frequency noise, and fully matching its noise characteristics.

[0032] Subsequently, the phase shift, frequency shift, and frequency drift obtained from the linear trend term analysis, the environmental disturbance features such as the South Atlantic anomaly and relativistic effects obtained from the periodic term decomposition, and various power-law noise components estimated from the random noise term are all integrated into the low-Earth orbit satellite clock feature library to complete the systematic extraction and storage of clock bias-related features.

[0033] When conducting clock simulation, the required parameters such as clock type, stability, accuracy, and orbit characteristics are first input through the simulation configuration module. Then, based on the low-Earth orbit satellite clock feature library, component extraction and combination operations are performed to fuse linear trend terms, environmental disturbance terms, and random noise terms as needed. Finally, the simulated clock error sequence is output, thereby completing the high-fidelity simulation of low-Earth orbit satellite clock errors.

[0034] Specifically, such as Figure 2 As shown, the modeling and simulation method for onboard clocks for low-Earth orbit satellites includes the following steps S10-S40.

[0035] S10: Acquire the onboard clock deviation data of the target low-orbit satellite, and sequentially perform outlier removal, missing point interpolation, and data continuity checks on the data to obtain a preprocessed clock deviation sequence; use a polynomial model to model the long-term drift trend of the preprocessed clock deviation sequence to obtain the clock trend term, and remove the clock trend term from the preprocessed clock deviation sequence to obtain the residual signal.

[0036] Step S10 is used to process the raw onboard clock error data and model the trend term. This embodiment first acquires the onboard clock deviation data of the target low-Earth orbit satellite. The raw clock data typically originates from precise orbit determination or onboard ranging equipment, and is characterized by high sampling frequency and a large time span. To ensure the stability and interpretability of subsequent modeling, this embodiment performs the following data processing: (1) Outlier removal: using a method based on The outlier detection method of the criteria removes abrupt changes caused by attitude changes, link switching, occlusion, or instrument transient anomalies; (2) Missing point interpolation: Local linear interpolation or neighborhood average interpolation methods are used to fill in short-term missing data; (3) Data continuity check: ensure that subsequent modeling can be based on the complete time series.

[0037] Based on the error characteristics of lightweight clocks, the original clock deviation sequence It can be decomposed into three components: linear drift trend, intrinsic noise disturbance, and periodic error caused by environmental factors. To characterize long-term variation, this embodiment uses a polynomial model to represent the clock trend term: ; in, The order of the trend polynomial is typically 1 to 3; the coefficients are... The trend term was obtained through least squares fitting. This trend term reflects the long-term evolution of the onboard clock over time, laying the foundation for the baseline layer of subsequent error formation.

[0038] The trend term is removed from the original sequence to obtain the residual signal: ; in, For residual signals, This is the preprocessed clock offset sequence.

[0039] S20: Based on the residual signal, the intrinsic noise of the lightweight spaceborne clock is modeled to obtain the intrinsic noise model.

[0040] The purpose of step S20 is to model the intrinsic noise of a lightweight spaceborne clock: Low-Earth orbit satellites typically carry lightweight clocks that are small in size and low in power consumption, and their noise characteristics are significantly different from those of traditional medium- and high-Earth orbit atomic clocks. In order to realistically describe its spontaneously generated random errors, this embodiment uses a three-state stochastic process model to uniformly model phase deviation, frequency deviation, and frequency drift, while comprehensively considering five main intrinsic noise sources: phase white noise, frequency white noise, flicker frequency noise, random walk frequency noise, and random walk frequency drift noise.

[0041] In this modeling framework, the clock state vector is set as follows: ; in, For clock phase deviation, To normalize the frequency deviation, This is frequency drift.

[0042] To accurately reproduce the random characteristics of the onboard clock, this embodiment considers five main intrinsic noise sources simultaneously: phase white noise, frequency white noise, flicker frequency noise, random walk frequency noise, and random walk frequency drift noise. These are then injected into the differential equations of the three states mentioned above, forming the following set of continuous-time stochastic differential equations: ; in, The white phase noise (WPM) driving force directly acts on the phase differential equation, corresponding to the Allan variance. Slope segment; The white frequency noise (WFM) driving factor acts on the frequency bias equation and corresponds to the Allan variance. Slope segment; The flicker frequency noise (FFM) driving factor acts on the frequency deviation equation and corresponds to an approximation in the Allan variance. Flat section; The random walk frequency noise (RWFM) acts on the frequency bias equation, and its integral effect causes the frequency to exhibit random walk characteristics, corresponding to the Allan variance. Slope segment; The random walk frequency drift (RWFD) noise driver acts on the frequency drift equation, making It exhibits a random walk, corresponding to drift uncertainty over a longer time scale; Phase deviation versus time The first derivative (phase change rate); Normalized frequency deviation versus time The first derivative; Frequency drift versus time The first derivative.

[0043] From a vector perspective, the above process can be written as a continuous-time state equation in vector form: ; in, ; in, State vector The first derivative with respect to time; It is a continuous-time state transition matrix (system matrix). It is a continuous-time process noise vector (composed of various intrinsic noise driving quantities).

[0044] Let the five noise sources be independent, with a mean of 0 and a variance of . Gaussian white noise process: ; in, It follows a Gaussian distribution; There are five noise intensity parameters.

[0045] In the frequency domain, the frequency deviation The power spectral density can be expressed as the superposition of five types of noise: ; in, coefficient and One-to-one correspondence; For frequency variables (unit: Hz).

[0046] In the simulation implementation, this embodiment applies the above continuous-time state equation according to the sampling interval. Discretization yields: ; in, This is the discrete-time state transition matrix. , e It is a natural constant; Given a discrete Gaussian noise vector, its covariance matrix is... The noise intensity parameters are calculated using a continuous-discrete covariance transformation. and The first The and the first The state vector of each discrete epoch. By adjusting these five parameters, the Allan variance of the simulated clock is made to vary at different average times. The measurement results or index curves of the target low-orbit satellite clock are matched to ensure that the three-state model can simultaneously take into account the combined effects of five types of intrinsic noise sources.

[0047] S30: Construct multi-source environmental drivers, including irradiation drivers caused by the South Atlantic anomaly, other periodic environmental drivers extracted through power spectral density analysis, and relativistic corrections that take into account the Earth's oblateness effect.

[0048] The purpose of step S30 is to model the low-Earth orbit (LEO) environment driving factors. To accurately simulate the non-stationary disturbances of the LEO satellite's onboard clock in the real space environment, this embodiment introduces multi-source environmental driving factors based on intrinsic noise modeling. These include South Atlantic Anomaly (SAA) irradiance disturbances, geomagnetic field weakening effects, temperature cycling, power fluctuations, and relativistic corrections caused by the Earth's oblateness (J2). These disturbances are injected into the frequency deviation or frequency drift state in a parameterized form, achieving the coupling of clock error and orbital environment.

[0049] ; in, This indicates the radiation-driven term caused by the South Atlantic anomaly. This indicates other periodic environmental drivers extracted through power spectral density analysis (comprehensively reflecting the equivalent effects of factors such as temperature cycling, background irradiance, and power fluctuations). This represents the relativistic correction term that takes into account the effect of Earth's oblateness J2. For the first The time corresponding to each discrete epoch.

[0050] (1) South Atlantic Anomaly (SAA) Irradiation Driver: The SAA region is the weakest geomagnetic field in space. Due to the reduced magnetic shielding ability, high-energy particles can penetrate deep into the Earth's surface, resulting in a significantly enhanced radiation dose for low-Earth orbit satellites crossing the SAA. This embodiment uses the World Magnetic Model (WMM) to calculate the total geomagnetic field strength of the satellite at each epoch: ; Where pos represents the coordinates of the low-orbit satellite.

[0051] Compare the magnetic field strength output by WMM with the SAA decision threshold: ; in, This is a marker for identifying the South Atlantic anomaly, with a value of 0 or 1.

[0052] Based on measured results (e.g., GRACE-C / GRACE-D), once a satellite enters the SAA (Satellite Area Array), its instantaneous clock frequency drops abruptly, resulting in a significant 12-hour periodic disturbance in the phase deviation. To model this effect, this embodiment constructs an SAA driving term: ; in For observation-calibrated radiation-sensitive parameters (2) Relativistic driving terms considering the Earth's J2 oblateness effect: LEO satellites have high velocities and low orbits, making their clock deviations susceptible to changes in Earth's gravitational potential and velocity. In particular, the J2 oblateness term introduces relativistic errors once per orbital period and twice per orbital period. This embodiment uses numerical integration to address the relativistic effects: ; in, This is the cumulative amount of clock error correction caused by relativistic effects; The standard gravitational parameters for Earth; It is the speed of light in a vacuum; The distance from the satellite to the Earth's center; The semi-major axis of the Earth's reference ellipsoid or the equivalent equatorial radius; The current time; The magnitude of the satellite's speed; This represents the component of the satellite's position along the Earth's rotation axis.

[0053] This embodiment only extracts the portion that changes over time as an assimilable periodic perturbation: ; in To remove the trend term after the second-order polynomial. The relativistic perturbation peak-to-peak value can reach approximately 3 ns, and should be explicitly modeled in high-precision clock simulations.

[0054] (3) In addition to the aforementioned dominant periodic term, the onboard clock of a low-Earth orbit satellite is also affected by a variety of environmental factors such as temperature cycling, background irradiance, and power bus fluctuations. These factors often manifest as weak periodic disturbances with multiple frequencies superimposed in the time domain, making it difficult to model their mechanisms individually. To avoid introducing too many empirical parameters, this embodiment adopts the idea of ​​unified modeling using power spectral density analysis, treating it as an equivalent periodic driving term. The specific steps are as follows: A) By sequentially removing the quadratic polynomial trend term, relativistic correction term, and SAA-dominated periodic term from the original clock error sequence, an environment-dominated residual sequence is obtained. ; B) Perform Discrete Fourier Transform to calculate the power spectral density. Several significant spectral peak frequencies were identified on the spectral lines. ; C) For each significant frequency component, estimate the corresponding amplitude. With phase This allows for the construction of an equivalent harmonic superposition model, and further determination of... : ; in, For frequency component index; The total number of significant frequency components; For the first The amplitude of each frequency component; For the first The frequency of each frequency component; For the first The time corresponding to each discrete epoch; For the first The phase of each frequency component. The corresponding period typically falls near the orbital period and its integer multiples, comprehensively reflecting the combined effects of multiple environmental factors such as temperature-driven, background irradiance, and power supply disturbances on the clock. This embodiment extracts these periodic components uniformly through power spectral density, avoiding separate modeling for each type of environmental factor, thereby simplifying parameter configuration and improving model scalability.

[0055] S40: Based on the clock trend term, intrinsic noise model, and multi-source environmental driving term, a comprehensive clock error dynamic model is established; the comprehensive clock error dynamic model is discretized using a fixed sampling interval and iteratively updated through time recursion. Based on the phase, frequency, and frequency drift of the previous moment, the environmental driving quantity and intrinsic noise disturbance of the current simulation step are superimposed to generate a low-Earth orbit satellite clock deviation sequence that simultaneously includes long-term drift, intrinsic noise, and environmental disturbance.

[0056] The purpose of step S40 is to achieve unified state equation construction and discretization simulation: After constructing the trend term, intrinsic noise term and low-Earth orbit environment driving term, this embodiment integrates the three into a continuous-discrete stochastic state equation framework and generates a high-fidelity low-Earth orbit satellite clock deviation sequence through iterative update.

[0057] Based on a three-state clock dynamics framework, clock phase, frequency, and frequency drift are treated as dynamic state variables of the system. In this framework: the trend term describes the long-term frequency drift and gradual offset of the clock; the intrinsic noise term generates random noise behavior consistent with actual spaceborne clocks, including phase white noise, frequency white noise, flicker frequency noise, random walk frequency noise, and random walk frequency drift noise; the environmental driving term injects external factors such as SAA irradiation disturbances, thermal cycling, power supply fluctuations, and relativistic effects into the model as explicit driving quantities. By combining these three types of factors, this embodiment establishes a comprehensive clock error dynamic model capable of simultaneously describing long-term drift, random noise, and external disturbances. ; in, State vector The first derivative with respect to time; This is a continuous-time state transition matrix (system matrix). This is the clock state vector; This is a control matrix used to control environmental driving terms. Mapped to the corresponding components of the state equation; This is the noise matrix.

[0058] To enable numerical simulation on a computer, this embodiment discretizes the continuous dynamic model using a fixed sampling interval. The discretized form resembles a time recursive relationship, where the clock state at each time step is derived from the state of the previous time step, with corresponding environmental driving quantities and random noise terms superimposed during the calculation process. In specific implementation: the phase, frequency, and frequency drift of the previous moment are naturally propagated to the next moment through the state update formula; the dominant periodic term of SAA, the equivalent periodic term extracted from the power spectral density, and the time-varying part of relativistic effects are added to the model as external drivers in each simulation step; random perturbations from the five types of intrinsic noise are injected into each discrete time step, ensuring that the simulation results are statistically consistent with the real spaceborne clock. Through this time-step-by-time update method, this embodiment can efficiently generate long-term, high-fidelity clock error sequences while maintaining good physical meaning and interpretability.

[0059] This application also provides a spaceborne clock modeling and simulation device for low-Earth orbit satellites, such as... Figure 3 As shown, the onboard clock modeling and simulation device for low-Earth orbit satellites includes: The data preprocessing module 301 is configured to acquire the onboard clock deviation data of the target low-orbit satellite, perform outlier removal, missing point interpolation, and data continuity check on the data in sequence to obtain a preprocessed clock deviation sequence; use a polynomial model to model the long-term drift trend of the preprocessed clock deviation sequence to obtain a clock trend term, and remove the clock trend term from the preprocessed clock deviation sequence to obtain a residual signal; Intrinsic noise modeling module 302 is configured to model the intrinsic noise of the lightweight spaceborne clock based on the residual signal to obtain an intrinsic noise model. The multi-source driving term construction module 303 is configured to construct multi-source environmental driving terms, including irradiation driving terms caused by the South Atlantic anomaly, other periodic environmental driving terms extracted by power spectral density analysis, and relativistic correction terms considering the Earth's oblateness effect. The discretization simulation module 304 is configured to establish a comprehensive clock error dynamic model based on the clock trend term, intrinsic noise model, and multi-source environmental driving term; the comprehensive clock error dynamic model is discretized using a fixed sampling interval and iteratively updated through a time recursion method. Based on the phase, frequency, and frequency drift of the previous moment, the environmental driving quantity and intrinsic noise disturbance of the current simulation step are superimposed to generate a low-Earth orbit satellite clock deviation sequence that simultaneously includes long-term drift, intrinsic noise, and environmental disturbance.

[0060] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0061] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0062] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between database access devices and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0063] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0064] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the above-described method for modeling and simulating onboard clocks for low-Earth orbit satellites.

[0065] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the onboard clock modeling and simulation method for low-Earth orbit satellites described in the above embodiments.

[0066] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or modules, and may be electrical, mechanical, or other forms.

[0067] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0068] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0069] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0070] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as execution by a hardware processor, or execution by a combination of hardware and software modules within the processor.

[0071] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0072] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0073] The aforementioned storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium that can be accessed by a general-purpose or special-purpose computer.

[0074] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0075] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for modeling and simulating onboard clocks for low-Earth orbit satellites, characterized in that, The method includes: The onboard clock deviation data of the target low-Earth orbit satellite is acquired. Outlier removal, missing point interpolation, and data continuity checks are performed on the data in sequence to obtain a preprocessed clock deviation sequence. A polynomial model is used to model the long-term drift trend of the preprocessed clock deviation sequence to obtain a clock trend term. The clock trend term is removed from the preprocessed clock deviation sequence to obtain the residual signal. Based on the residual signal, the intrinsic noise of the lightweight spaceborne clock is modeled to obtain the intrinsic noise model. We construct a multi-source environmental driving term, including an irradiation driving term caused by the South Atlantic anomaly, other periodic environmental driving terms extracted through power spectral density analysis, and a relativistic correction term considering the Earth's oblateness effect. Based on the aforementioned clock trend term, intrinsic noise model, and multi-source environmental driving term, a comprehensive clock error dynamic model is established. The comprehensive clock error dynamic model is discretized using a fixed sampling interval and iteratively updated using a time recursion method. Based on the phase, frequency, and frequency drift of the previous moment, the environmental driving quantity and intrinsic noise disturbance of the current simulation step are superimposed to generate a low-Earth orbit satellite clock deviation sequence that simultaneously includes long-term drift, intrinsic noise, and environmental disturbance.

2. The method for modeling and simulating onboard clocks for low-Earth orbit satellites according to claim 1, characterized in that, The clock trend term is represented as follows: ； in, Let the order of the trend polynomial be . Index of the order of the trend polynomial; coefficients Obtained through least squares fitting; For clock trend items; The residual signal is represented as follows: ； in, For residual signals, This is the preprocessed clock offset sequence.

3. The method for modeling and simulating onboard clocks for low-Earth orbit satellites according to claim 1, characterized in that, Based on the residual signal, the intrinsic noise of the lightweight spaceborne clock is modeled, including: Set the clock state vector as follows: ； in, For clock state vector, For clock phase deviation, To normalize the frequency deviation, This is frequency drift; Considering five types of intrinsic noise sources—phase white noise, frequency white noise, flicker frequency noise, random walk frequency noise, and random walk frequency drift noise—construct a system of continuous-time stochastic differential equations: ； in, This is the phase white noise driving quantity; This is the frequency-driven white noise quantity; This is the noise driving quantity at the flicker frequency; This is the frequency noise driving factor for random walks; This is the driving force of the random walk frequency drift noise. Phase deviation versus time The first derivative of; Normalized frequency deviation versus time The first derivative; Frequency drift versus time The first derivative; The above process can be expressed as a vector-form continuous-time state equation: ； ； in, State vector The first derivative with respect to time; It is a continuous-time state transition matrix; This is the noise vector for a continuous-time process; Let the five noise sources be independent, with a mean of 0 and a variance of . Gaussian white noise process: ； in, It follows a Gaussian distribution; Five noise intensity parameters; In the frequency domain, frequency deviation The power spectral density is represented as the superposition of five types of noise: ； Among them, coefficient and One-to-one correspondence; For frequency variables; By sampling interval Δt Discretizing the continuous-time state equation in vector form yields the discrete state equation of the intrinsic noise model: ； in, This is the discrete-time state transition matrix. , e It is a natural constant; Given a discrete Gaussian noise vector, its covariance matrix is... The noise intensity parameters are calculated using a continuous-discrete covariance transformation. and The first The and the first A state vector for each discrete epoch.

4. The method for modeling and simulating onboard clocks for low-Earth orbit satellites according to claim 1, characterized in that, The multi-source environment driving term is represented as follows: ； in, This represents the radiation-driven term caused by the South Atlantic anomaly. This represents other periodic environmental drivers extracted through power spectral density analysis, comprehensively reflecting the equivalent effects of factors such as temperature cycling, background irradiance, and power fluctuations. This represents the relativistic correction term that takes into account the effect of Earth's oblateness J2. The irradiation-driven term induced by the South Atlantic anomaly was determined using the following method. : Using the World Magnetic Field Model Calculate the total intensity of the satellite's geomagnetic field at each epoch. : ； Where pos represents the coordinates of the low-orbit satellite; For the first The time corresponding to each discrete epoch; Compare the magnetic field strength output by WMM with the SAA (South Atlantic Anomaly) threshold: ； in, Indicators for identifying the South Atlantic anomaly; Constructing the irradiation-driven term caused by the South Atlantic anomaly : ； in, These are radiation-sensitive parameters based on observational calibration.

5. The method for modeling and simulating onboard clocks for low-Earth orbit satellites according to claim 4, characterized in that, Determined in the following manner : Numerical integration of relativistic effects: ； in, This is the cumulative amount of clock error correction caused by relativistic effects; These are Earth's standard gravitational parameters; It is the speed of light in a vacuum. The distance from the satellite to the Earth's center; The semi-major axis of the Earth's reference ellipsoid or the equivalent equatorial radius; The current time; The magnitude of the satellite's speed; This represents the component of the satellite's position along the Earth's rotation axis; Extract only The portion that changes over time serves as a driver of other periodic environments: ； in This is the trend term after removing the second-order polynomial.

6. The method for modeling and simulating onboard clocks for low-Earth orbit satellites according to claim 4, characterized in that, Determined in the following manner : The quadratic polynomial trend term is removed sequentially from the original clock error sequence. and The environment-dominated residual sequence was obtained. ; right Perform Discrete Fourier Transform to calculate the power spectral density. Several significant spectral peak frequencies were identified on the spectral lines. ; For each significant frequency component, estimate the corresponding amplitude. With phase ,Sure : ； in, For frequency component index; The total number of significant frequency components; For the first The amplitude of each frequency component; For the first The frequency of each frequency component; For the first The time corresponding to each discrete epoch; For the first The phase of each frequency component.

7. The method for modeling and simulating onboard clocks for low-Earth orbit satellites according to claim 1, characterized in that, The integrated clock error dynamic model is expressed as follows: ； in, State vector The first derivative with respect to time; It is a continuous-time state transition matrix (system matrix). This is the clock state vector; This is a control matrix used to control environmental driving terms. Mapped to the corresponding components of the state equation; This is the noise matrix.

8. A modeling and simulation device for onboard clocks of low-Earth orbit satellites, characterized in that, The device includes: The data preprocessing module is configured to acquire the onboard clock deviation data of the target low-orbit satellite, and sequentially perform outlier removal, missing point interpolation, and data continuity checks on the data to obtain a preprocessed clock deviation sequence. A polynomial model is used to model the long-term drift trend of the preprocessed clock deviation sequence to obtain a clock trend term. The clock trend term is removed from the preprocessed clock deviation sequence to obtain a residual signal. The intrinsic noise modeling module is configured to model the intrinsic noise of the lightweight spaceborne clock based on the residual signal, and obtain the intrinsic noise model. The multi-source driving term construction module is configured to construct multi-source environmental driving terms, including irradiation driving terms caused by the South Atlantic anomaly, other periodic environmental driving terms extracted by power spectral density analysis, and relativistic correction terms considering the Earth's oblateness effect. The discretization simulation module is configured to establish a comprehensive clock error dynamic model based on the clock trend term, intrinsic noise model, and multi-source environmental driving term. The comprehensive clock error dynamic model is discretized using a fixed sampling interval and iteratively updated through a time recursion method. Based on the phase, frequency, and frequency drift of the previous moment, the environmental driving quantity and intrinsic noise disturbance of the current simulation step are superimposed to generate a low-Earth orbit satellite clock deviation sequence that simultaneously includes long-term drift, intrinsic noise, and environmental disturbance.

9. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes the computer execution instructions stored in the memory to implement the onboard clock modeling and simulation method for low-Earth orbit satellites as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the onboard clock modeling and simulation method for low-Earth orbit satellites as described in any one of claims 1-7.

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