Low-earth-orbit satellite-borne clock forecasting method, device and equipment and storage medium

Abstract

The invention provides a low-earth-orbit satellite-borne clock forecasting method, device and equipment and a storage medium. Relates to the field of low-orbit satellite positioning navigation time service. The method comprises the following steps: performing trend separation on the basis of original satellite-borne clock error data to obtain a trend term and a periodic residual sequence, and normalizing the trend term and the periodic residual sequence; a Fourier analysis network is constructed, the Fourier analysis network comprises an input layer, a plurality of Fourier analysis layers and an output layer, the input layer is used for converting the input normalized periodic residual error sequence into an input sequence, and the plurality of Fourier analysis layers are stacked to establish a mapping relation from the input sequence to periodic prediction output; outputting a predicted value of a future moment based on the input sequence, and superposing the predicted value and a trend term of the future moment by an output layer to obtain a clock skew predicted value; according to the method, the number of cycles or the frequency value does not need to be preset, the problem of omission or misjudgment possibly caused by manual setting of cycle items is eliminated, and the modeling capability of the periodic fluctuation of the satellite-borne clock is 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 predicting onboard clocks for low-Earth orbit satellites. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) provide ground users with high-precision and low-cost Positioning, Navigation, and Timing (PNT) services. However, traditional GNSS systems, primarily based on medium- and high-Earth orbit (MEO) satellites, have inherent limitations in signal strength, coverage, and robustness, making it difficult to meet the increasingly stringent technical requirements for positioning, navigation, and timing accuracy, integrity, and convergence time in autonomous navigation and high-security scenarios. In recent years, with the rapid development of satellite miniaturization, mass production, and low-cost payload launch technologies, the deployment of Low Earth Orbit (LEO) constellations has entered a phase of rapid growth, bringing new opportunities for high-precision and high-reliability positioning, navigation, and timing services. LEO satellites, located in low Earth orbit (LEO) at altitudes of 400 to 1500 kilometers, possess inherent advantages over MEO satellites, such as stronger signal power, higher spatial coverage density, and faster geometric change rates. These advantages can significantly enhance PNT service availability, anti-interference and anti-spoofing capabilities, and effectively shorten positioning convergence time.

[0003] As the time and frequency reference for low-Earth orbit (LEO) satellites, onboard clocks play a crucial role in supporting high-precision orbit determination for GNSS payloads and ranging signal generation for navigation payloads. Due to engineering constraints such as size, weight, and power consumption, LEO satellites are typically equipped with ultra-stable crystal oscillators, temperature-controlled crystal oscillators, or chip-scale atomic clocks as time-keeping devices. Compared to the high-performance atomic clocks used in navigation satellites, these clock devices exhibit significantly poorer short-term frequency stability, typically... to The performance drop is more than an order of magnitude, resulting in a decrease in stability. On medium- to long-term scales, this performance gap is even more pronounced, manifesting as stronger random noise and a significant frequency drift trend. Furthermore, LEO satellites undergo high-speed periodic motion in low Earth orbit, making their onboard clocks more susceptible to external factors such as relativistic effects, payload voltage fluctuations, and temperature changes caused by the thermal control system. These disturbances lead to abnormal clock fluctuations, accelerating the error accumulation process and posing a more severe challenge to LEO onboard clock prediction.

[0004] Currently, most satellite clock prediction methods employ traditional numerical models with polynomial superposition of periodic terms. The optimal polynomial and periodic term coefficients are estimated using least-squares estimation, and the model is then used for subsequent satellite clock predictions. However, this traditional method has significant drawbacks: 1) Insufficient modeling of periodic components: Existing methods primarily extract periodic terms through subjective observation or spectral analysis, only modeling a limited number of major periodic terms. The presence of residual periodic terms significantly reduces prediction accuracy. 2) Limited utilization of historical information: Traditional methods model based on only half a day or less of data, failing to fully explore and utilize longer-term historical observation data. 3) Traditional models struggle to handle nonlinear and non-stationary characteristics: LEO satellite satellite clocks are more affected by orbital dynamics and the space environment, exhibiting stronger nonlinear and non-stationary characteristics. Traditional modeling methods are poorly adapted to these characteristics, resulting in limited prediction stability and accuracy. Summary of the Invention

[0005] This application provides a method, apparatus, device, and storage medium for predicting onboard clocks for low-Earth orbit satellites. The aim is to effectively extract and model the periodic and nonlinear components of onboard clock errors from a large amount of historical data using neural networks, thereby improving the accuracy and stability of clock prediction. Specifically, this application first separates the linear trend term and periodic term in the clock error using polynomial fitting, and then uses a Fourier analysis network to extract and analytically model the periodic characteristics of the onboard clock error. The Fourier Analysis Network (FAN) combines broad applicability with efficient modeling of periodic terms. Unlike traditional methods that rely on pre-setting the order and period of the periodic term, the FAN network directly learns the underlying periodic structure from the data, enabling it to adapt to a wide range of periodic components and noise patterns. After predicting the periodic error, it is combined with the pre-extracted trend term to achieve accurate prediction of the onboard clock error.

[0006] Firstly, this application provides a method for predicting the onboard clock of a low-Earth orbit satellite, including: Based on the original onboard clock error data, trend separation is performed to obtain the trend term and the periodic residual sequence, and the periodic residual sequence is normalized to obtain the normalized periodic residual sequence. A Fourier analysis network is constructed, comprising an input layer, multiple Fourier analysis layers, and an output layer. The input layer transforms the normalized periodic residual sequence into multiple time-target pairs as input sequences. The multiple Fourier analysis layers are stacked to establish a mapping relationship from the input sequences to the periodic prediction output, and output the predicted value for future times based on the input sequences. Each Fourier analysis layer includes at least one neuron, which embeds a sine function, a cosine function, and a sigmoid function. The output layer superimposes the predicted value with the trend term for future times to obtain the clock deviation prediction value. The Fourier analysis network is trained using supervised learning, and the onboard clock prediction for low-Earth orbit satellites is realized based on the trained Fourier analysis network.

[0007] In one possible design, based on the original onboard clock error data, trend separation is performed using the following formula to obtain the trend term and the periodic residual sequence: ; ; In the formula, Indicates the trend term. The fitting coefficients are obtained through least squares fitting. This indicates the order of the fitted polynomial. k Index representing the order of a polynomial It is a periodic residual sequence. For trend items, t For time variables, The original onboard clock error data for the target low-Earth orbit satellite; The periodic residual sequence is normalized using the following formula to obtain the normalized periodic residual sequence: ; In the formula, For a normalized periodic residual sequence, and These represent the sample mean and standard deviation of the original onboard clock error data, respectively.

[0008] In one possible design, a sliding window mechanism is used at the input layer to transform the normalized residual sequence into multiple time-target pairs using the following formula. : ; ; In the formula, For the output window length, To predict the time step, , and The first , No. and the The normalized residual value of the step, , and The first , No. and the The normalized residual value of the step, The normalized residual vector corresponding to the input time window contains The observation information of a continuous time step.

[0009] In one possible design, the data flow of a single neuron in the Fourier analysis layer is as follows: ; right Decoupling is performed in the following manner: ; In the formula, The basic drift vector is used to fit the non-periodic offset of the residuals. It is an angular frequency matrix, where each row represents an independent learned frequency component. The input features are mapped to the corresponding frequency space through product mapping. The Fourier coefficient matrix is ​​responsible for linearly combining the results of sine and cosine transformations to obtain the amplitude and phase information of the periodic components. This indicates that the feature vectors are concatenated column by column. This represents the normalized residual sequence corresponding to the input time series window. This represents the mapping function of a single-layer Fourier network.

[0010] In one possible design, the multiple Fourier analysis layers are stacked using the following formula: ; In the formula, The mapping function representing a multilayer Fourier network. , and Representing the first layer and the second layer respectively M -1st floor and the M Layer Fourier analysis layer, x This represents the normalized residual sequence corresponding to the input time series window.

[0011] right After decoupling, the following formula is obtained: ; in, These are the learnable parameters of the cosine and sine functions in the neuron. and These are the learnable parameters of the sigmoid function in the neuron.

[0012] In one possible design, the clock skew prediction is obtained by superimposing the predicted value with a trend term for future times, including: Based on the predicted value, the predicted value in the original units can be recovered using the following formula. : ; In the formula, For predicted values, and These are the sample mean and standard deviation of the original spaceborne clock error data, respectively. Based on the data within the input window of the input layer, a new polynomial fitting is performed to predict future times. Trend component : ; In the formula, Denotes the coefficients of a linear polynomial. This indicates the order of the fitted polynomial. k An index indicating the order of a polynomial; Will and The clock deviation prediction value is obtained by superimposing the values.

[0013] In one possible design, when training the Fourier analysis network using supervised learning, the training objective is to minimize the root mean square error loss function between the predicted residual and the true residual; wherein the root mean square error loss function is expressed as: ; In the formula, This represents the root mean square error. and These represent the predicted onboard clock residual and the actual onboard clock residual, respectively. i Indicates the index of the prediction time step. h This indicates the prediction step size.

[0014] Secondly, this application provides a low-Earth orbit satellite onboard clock prediction device, the device comprising: The data preprocessing module is configured to perform trend separation based on the original onboard clock error data to obtain a trend term and a periodic residual sequence, and to normalize the periodic residual sequence to obtain a normalized periodic residual sequence. The network construction module is configured to construct a Fourier analysis network. The Fourier analysis network includes an input layer, multiple Fourier analysis layers, and an output layer. The input layer transforms the normalized periodic residual sequence into multiple time-target pairs as input sequences. The multiple Fourier analysis layers are stacked to establish a mapping relationship from the input sequences to the periodic predicted output, and output predicted values ​​for future times based on the input sequences. Each Fourier analysis layer includes at least one neuron, which embeds a sine function, a cosine function, and a sigmoid function. The output layer superimposes the predicted values ​​with a trend term for future times to obtain a clock deviation prediction value. The network training module is configured to train the Fourier analysis network using supervised learning, and to realize low-Earth orbit satellite onboard clock prediction based on the trained Fourier analysis network.

[0015] 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 perform the low-Earth orbit satellite onboard clock prediction method as described in the first aspect and various possible designs of the first aspect.

[0016] 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 low-Earth orbit satellite onboard clock prediction method described in the first aspect and various possible designs of the first aspect.

[0017] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the low-Earth orbit satellite onboard clock prediction method as described in the first aspect and various possible designs of the first aspect.

[0018] The low-Earth orbit satellite onboard clock prediction method, apparatus, equipment, and storage medium provided in this application have at least the following beneficial effects: (1) Significantly enhanced periodic modeling capability, adapting to complex periodic structures at multiple scales: The Fourier analysis network model proposed in this application deeply integrates the Fourier series modeling idea and data-driven mechanism in the form of a neural network. Its periodic extraction capability breaks through the limitation of traditional models that can only subjectively select a small number of major periods. FAN extracts multi-scale periodic features layer by layer through a multi-layer stacked structure, supporting joint modeling of strong periodicity, weak periodicity and alternating frequency components. By training a learnable angular frequency parameter matrix, this application can automatically extract the optimal frequency combination from historical data without pre-setting the number of periods or frequency values, eliminating the omission or misjudgment problems that may be caused by manually setting periodic terms, and significantly improving the modeling capability of periodic fluctuations of spaceborne clocks.

[0019] (2) Make full use of long-term historical data to achieve more stable and accurate modeling: The FAN network in this application is based on a neural network architecture, which has good data throughput and fitting capabilities. It can process historical observation data spanning multiple days or even multiple cycles, thereby learning the variation law of the satellite clock more comprehensively. Through the structure of combining trend term separation and residual modeling, the decoupled prediction of trend and cycle is realized, which enhances the generalization ability in complex non-stationary backgrounds.

[0020] (3) The model structure is simple and efficient, and easy to deploy and integrate into engineering: The FAN model proposed in this application adopts an explicit periodic modeling structure based on sine and cosine functions. The network structure is clear, the number of parameters is small, and the computational complexity is low. It can be efficiently deployed even in resource-constrained spaceborne or ground-embedded systems, meeting the engineering application requirements of real-time performance and lightweight design, and is easy to promote and use in large-scale constellation systems or edge computing nodes. 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 flowchart illustrating a low-Earth orbit satellite onboard clock prediction method provided in this application embodiment; Figure 2 A framework diagram of the Fourier analysis network provided in the embodiments of this application; Figure 3 A diagram of the neuron structure of the Fourier analysis network provided in the embodiments of this application; Figure 4 This is a structural diagram of the low-Earth orbit satellite-borne clock prediction device 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 concept of this application to those skilled in the art through reference to particular 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 now be described with reference to the accompanying drawings.

[0028] This application provides a method for predicting onboard clocks for low-Earth orbit satellites. It fully integrates time-domain trend modeling and frequency-domain periodic feature extraction techniques, employing a multi-layer Fourier analysis network to perform deep learning and prediction on the complex periodic perturbation structure in the onboard clock error sequence. The process is as follows: Figure 1 As shown, the specific implementation steps include the following S100-S300.

[0029] S100: Based on the original onboard clock error data, trend separation is performed to obtain the trend term and periodic residual sequence, and the periodic residual sequence is normalized to obtain the normalized periodic residual sequence.

[0030] The purpose of step S100 is to process the raw onboard clock error data and separate the trend term. The onboard clock error sequence can typically be obtained synchronously during precise orbit determination, with a typical sampling interval of 10 seconds to 5 minutes. In this embodiment, the raw onboard clock error data of the target low-Earth orbit satellite is obtained from a precise low-Earth orbit satellite clock error product, denoted as... Based on the physical mechanism of clock error formation, It typically includes three main components: linear drift trend, multi-scale periodic perturbations, and various noises.

[0031] To isolate the periodic perturbation term so that the network can focus on learning later, in some embodiments, a trend separation method is introduced in step S100, using multinomial fitting techniques to model the original sequence. Trend term Represented as: ; In the formula, This indicates the order of the fitted polynomial, which is empirically set to 2 to 3 to balance fitting accuracy and model complexity. The fitting coefficients are obtained through least squares fitting. k Index representing the order of a polynomial t It is a time variable.

[0032] By removing the trend term from the original data, a periodic residual sequence is obtained. .

[0033] ; Since clock skew scales may differ across satellites, missions, or time periods, data normalization is necessary to improve model training stability and generalization ability. Normalization employs the standard deviation scaling method: calculating the sample mean of the original sequence (original onboard clock error data). with standard deviation And convert all clock values ​​to dimensionless form: ; In the formula, It is a normalized periodic residual sequence.

[0034] In some embodiments, considering that data interruptions or jumps may occur during satellite missions due to attitude switching, signal blockage, or lack of visibility at ground stations, this embodiment adopts the following processing before and after standardization: 1) Outlier removal: using three times the standard deviation ( 1) Method to detect and remove outliers; 2) Missing value interpolation: local linear interpolation is used to fill in a small number of missing samples.

[0035] S200: Construct a Fourier analysis network; wherein, the Fourier analysis network includes an input layer, multiple Fourier analysis layers, and an output layer. The input layer is used to transform the normalized periodic residual sequence of the input into multiple time-target pairs as input sequences. Multiple Fourier analysis layers are stacked to establish a mapping relationship from the input sequence to the periodic prediction output, and output the predicted value of future time based on the input sequence. The Fourier analysis layer includes at least one neuron, and the neuron embeds a sine function, a cosine function, and a sigmoid function. The output layer is used to superimpose the predicted value with the trend term of the future time to obtain the clock deviation prediction value.

[0036] This application innovatively designs a Fourier analysis network (FAN) with periodic awareness capability. Its core idea is to embed sine and cosine basis functions into neurons, enabling the network to automatically extract periodic components at different scales. This structure combines traditional Fourier series expansion theory with modern deep learning techniques, overcoming the shortcomings of traditional frequency domain analysis methods, such as fixed frequencies and lack of adaptive learning capabilities.

[0037] like Figure 2 As shown, the Fourier analysis network includes an input layer, multiple Fourier analysis layers, a fully connected layer, and an output layer. Figure 2 The method for polynomial fitting of low-Earth orbit satellite clock errors is described in step S100 above and will not be repeated here. The residual term obtained by polynomial fitting is a normalized periodic residual sequence, and the linear trend term is the trend term for future times. After the residual term is processed by the Fourier analysis layer, it is fed to the output layer through the fully connected layer. The linear trend term is directly fed to the output layer. The output layer superimposes the Fourier analysis layer processing result and the linear trend term to obtain the final clock deviation prediction value.

[0038] Specifically: In the input layer, a sliding window mechanism is used to transform the normalized residual sequence into multiple time-target pairs. Used for supervised learning: ; ; in, For the output window length, To predict the time step, the specific value is selected based on task requirements and the model's generalization ability. , and The first , No. and the The normalized residual value of the step, , and The first , No. and the The normalized residual value of the step, The normalized residual vector corresponding to the input time window contains The observation information of a continuous time step.

[0039] In the Fourier analysis layer, the residual time series obtained from the output layer (consisting of multiple time-target pairs) The sequence (composed of the data) is input into multiple Fourier analysis layers. Each Fourier analysis layer consists of several neurons. The neuronal structure of a Fourier analysis layer is as follows: Figure 3 As shown, it is based on the classic Fourier series expansion theory and uses three activation functions—sine (Sin activation function), cosine (Cos activation function), and sigmoid (Sigmoid activation function)—to directly embed periodicity into the neural network model. The physical implementation of a single neuron is shown below: ; right Decoupling is performed in the following manner: ; in, The basic drift vector is used to fit the non-periodic offset of the residuals. It is an angular frequency matrix, where each row represents an independent learned frequency component. The input features are mapped to the corresponding frequency space through product mapping. The Fourier coefficient matrix is ​​responsible for linearly combining the results of sine and cosine transformations to obtain the amplitude and phase information of the periodic components. This indicates that the feature vectors are concatenated column by column. This represents the normalized residual sequence corresponding to the input time series window. This represents the mapping function of a single-layer Fourier network.

[0040] This structure essentially learns the appropriate periodic frequency and amplitude for the data through parameterized sine and cosine transforms, unlike the fixed frequency and untrainable limitations of traditional Fourier transforms. While single-layer FAN networks can fit certain periodic components, they struggle to capture complex periodic behaviors involving multiple scales, frequencies, and nonlinear superposition. Therefore, this invention constructs a deep Fourier analysis network through a multi-layer stacked FAN design: ; In the formula, each layer (i=1,2,3) The structure (M, where M is the total number of layers) is a single-layer FAN network (i.e., a single Fourier analysis layer), capable of extracting periodic features and performing nonlinear mapping. This represents the mapping function of a multilayer Fourier network.

[0041] right After decoupling, the following formula is obtained: ; in, These are the learnable parameters of the cosine and sine functions in the neuron. and The sigmoid function in neurons Learnable parameters.

[0042] After the input features undergo multiple nonlinear transformations and periodic mappings, the model can decompose the different frequency components contained in the residual sequence layer by layer, realizing multi-scale periodic modeling from low-frequency dominant periodicity to high-frequency weak periodicity. This hierarchical design enhances the model's ability to fit nonlinear periodic signals and effectively avoids the underfitting problem of shallow models for complex periodic signals.

[0043] The fully connected layer is used to output the predicted values ​​obtained from multiple Fourier analysis layers to the output layer. The output layer then superimposes the predicted values ​​with the trend terms for future time periods to obtain the clock skew prediction value.

[0044] S300: The Fourier analysis network is trained using supervised learning, and the onboard clock prediction of low-Earth orbit satellites is realized based on the trained Fourier analysis network.

[0045] This application employs supervised learning to train the FAN network. The training objective is to minimize the root mean square error (RMSE) loss function between the predicted residuals and the true residuals, defined as: ; In the formula, and These represent the predicted onboard clock residual and the actual onboard clock residual, respectively. i Indicates the index of the prediction time step. h This indicates the prediction step size.

[0046] An exemplary training process includes: 1) Input processing: The input is historical residual data within a sliding window; 2) Forward propagation: Extracting periodic features layer by layer through the FAN network; 3) Backpropagation and optimization: Use the Adam optimizer to perform joint iterative updates on the same parameters; 4) Frequency self-learning: During the training process, the angular frequency matrix automatically learns and fits the adaptive frequency distribution, avoiding the drawbacks of manual frequency setting and parameter tuning in traditional methods. 5) Validation set early stopping mechanism: An early stopping strategy is introduced to avoid overfitting.

[0047] Through multiple iterations, the model gradually establishes a mapping relationship from the input sequence to the periodic predicted output and automatically focuses on the main periodic components.

[0048] Trend-cycle fusion and final prediction output: After training the Fourier analysis network, a practical inference process is implemented to predict the onboard clock error at any future time. The predicted values ​​are generated using the outputs of multiple Fourier analysis layers. The periodic disturbance term is represented by the inverse normalization process, which recovers the predicted value in the original unit. : ; Based on the data within the input window, a new polynomial fitting is performed to predict future times. Trend components: ; In the formula, Represents the coefficients of a linear polynomial.

[0049] By superimposing the trend and the periodic residual, the final predicted clock bias value is obtained: ; In the formula, This is the final predicted clock skew value.

[0050] The above approach achieves decoupled prediction of trends and cycles, enhancing the robustness and generalization ability of predictions in complex and non-stationary environments.

[0051] This application also provides a low-Earth orbit satellite onboard clock prediction device, such as... Figure 4 As shown, the low-Earth orbit satellite onboard clock prediction device includes: The data preprocessing module 401 is configured to perform trend separation based on the original satellite clock error data to obtain a trend term and a periodic residual sequence, and to normalize the periodic residual sequence to obtain a normalized periodic residual sequence. Network construction module 402 is configured to construct a Fourier analysis network; wherein, the Fourier analysis network includes an input layer, multiple Fourier analysis layers, and an output layer. The input layer is used to transform the input normalized periodic residual sequence into multiple time-target pairs as input sequences. The multiple Fourier analysis layers are stacked to establish a mapping relationship from the input sequence to the periodic prediction output, and output the predicted value of future time based on the input sequence. Each Fourier analysis layer includes at least one neuron, and the neuron embeds a sine function, a cosine function, and a sigmoid function. The output layer is used to superimpose the predicted value with the trend term of the future time to obtain the clock deviation prediction value. The network training module 403 is configured to train the Fourier analysis network using supervised learning, and to realize low-orbit satellite onboard clock prediction based on the trained Fourier analysis network.

[0052] In some embodiments, the data preprocessing module is further configured to perform trend separation based on the original onboard clock error data using the following formula to obtain a trend term and a periodic residual sequence: ; ; In the formula, Indicates the trend term. The fitting coefficients are obtained through least squares fitting. This indicates the order of the fitted polynomial. k Index representing the order of a polynomial It is a periodic residual sequence. For trend items, t For time variables, The original onboard clock error data for the target low-Earth orbit satellite; The periodic residual sequence is normalized using the following formula to obtain the normalized periodic residual sequence: ; In the formula, For a normalized periodic residual sequence, and These represent the sample mean and standard deviation of the original onboard clock error data, respectively.

[0053] In some embodiments, a sliding window mechanism is used in the input layer to transform the normalized residual sequence into multiple time-target pairs using the following formula. : ; ; In the formula, For the output window length, To predict the time step, , and The first , No. and the The normalized residual value of the step, , and The first , No. and the The normalized residual value of the step, The normalized residual vector corresponding to the input time window contains The observation information of a continuous time step.

[0054] In some embodiments, the data flow of a single neuron in the Fourier analysis layer is as follows: ; In the formula, The basic drift vector is used to fit the non-periodic offset of the residuals. It is an angular frequency matrix, where each row represents an independent learned frequency component. The input features are mapped to the corresponding frequency space through product mapping. The Fourier coefficient matrix is ​​responsible for linearly combining the results of sine and cosine transformations to obtain the amplitude and phase information of the periodic components. This indicates that the feature vectors are concatenated column by column. This represents the normalized residual sequence corresponding to the input time series window. This represents the mapping function of a single-layer Fourier network.

[0055] In some embodiments, the plurality of Fourier analysis layers are stacked using the following formula: ; In the formula, The mapping function representing a multilayer Fourier network. , and Representing the first layer and the second layer respectively M -1st floor and the M Layer Fourier analysis layer, x This represents the normalized residual sequence corresponding to the input time series window.

[0056] In some embodiments, the clock deviation prediction value is obtained by superimposing the predicted value with a trend term for future times. Based on the predicted value, the predicted value in the original units can be recovered using the following formula. : ; In the formula, For predicted values, and These are the sample mean and standard deviation of the original spaceborne clock error data, respectively. Based on the data within the input window of the input layer, a new polynomial fitting is performed to predict future times. Trend component : ; In the formula, Denotes the coefficients of a linear polynomial. This indicates the order of the fitted polynomial. k An index indicating the order of a polynomial; Will and The clock deviation prediction value is obtained by superimposing the values.

[0057] In some embodiments, when training the Fourier analysis network using supervised learning, the training objective is to minimize the root mean square error loss function between the predicted residual and the true residual; wherein, the root mean square error loss function is expressed as: ; In the formula, This represents the root mean square error. and These represent the predicted onboard clock residual and the actual onboard clock residual, respectively. i Indicates the index of the prediction time step. h This indicates the prediction step size.

[0058] 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.

[0059] 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.

[0060] 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.

[0061] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0062] 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 low-Earth orbit satellite onboard clock prediction method described above.

[0063] 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 low-orbit satellite onboard clock prediction method in the above embodiments.

[0064] 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.

[0065] 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.

[0066] 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.

[0067] 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.

[0068] 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.

[0069] 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.

[0070] 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.

[0071] 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.

[0072] 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.

[0073] 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.

[0074] 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 low earth orbit satellite on-board clock prediction method, characterized in that, The method comprises: Based on the original satellite-borne clock error data, trend separation is performed to obtain a trend item and a periodic residual sequence, and the periodic residual sequence is normalized to obtain a normalized periodic residual sequence; A Fourier analysis network is constructed; wherein the Fourier analysis network comprises an input layer, a plurality of Fourier analysis layers, and an output layer, the input layer is used to convert the input normalized periodic residual sequence into a plurality of time-target pairs as input sequences, the plurality of Fourier analysis layers are stacked to establish a mapping relationship from the input sequences to a periodic prediction output, and based on the input sequences, a predicted value at a future time is output, the Fourier analysis layer comprises at least one neuron, the neuron is embedded with a sine function, a cosine function and a Sigmoid function, and the output layer is used to superimpose the predicted value and the trend item at the future time to obtain a clock bias prediction value; The Fourier analysis network is trained in a supervised learning manner, and low-orbit satellite-borne clock prediction is realized based on the trained Fourier analysis network.

2. The low Earth orbit satellite on-board clock prediction method of claim 1, wherein, Based on the original satellite-borne clock error data, trend separation is performed by the following formula to obtain a trend item and a periodic residual sequence: ； ； wherein denotes a trend term, is a fitting coefficient, obtained by least square fitting, denotes the order of the fitting polynomial, k denotes an index of the order of the polynomial, is a periodic residual series, is a trend term, t is a time variable, is raw on-board clock error data of the target LEO satellite; The periodic residual sequence is normalized by the following formula to obtain a normalized periodic residual sequence: ； wherein is the normalized periodic residual sequence, and are the sample mean and standard deviation of the raw spaceborne clock error data, respectively.

3. The low Earth orbit satellite on-board clock prediction method of claim 1, wherein, At the input layer, a sliding window mechanism is adopted to transform the normalized residual series into multiple time-target pairs by the following equation : ； ； In the formula, For the output window length, To predict the time step, , and The first , No. and the The normalized residual value of the step, , and The first , No. and the The normalized residual value of the step, The normalized residual vector corresponding to the input time window contains The observation information of a continuous time step.

4. The low Earth orbit satellite on-board clock prediction method of claim 3, wherein, The data flow of a single neuron in the Fourier analysis layer is as follows: ； wherein, is the base drift vector, which is used to fit the non-periodic shift of the residual, is the angular frequency matrix, each row of which represents an independent learned frequency component, mapping the input features to the corresponding frequency space through the product; is the Fourier coefficient matrix, which is responsible for linear combination of the results of sine, cosine transformation to obtain the amplitude and phase information of the periodic component; denotes the concatenation of feature vectors by column, denotes the normalized residual sequence corresponding to the input time series window, denotes the mapping function of the single-layer Fourier network.

5. The low Earth orbit satellite on-board clock prediction method of claim 1, wherein, The plurality of Fourier analysis layers are stacked by the following formula: ； wherein represents the mapping function of the multi-layer Fourier network, , and represent the first, the M -1thand the M thlayer Fourier analysis layer, respectively, x represents the normalized residual sequence corresponding to the input time series window.

6. The low Earth orbit satellite on-board clock prediction method of claim 1, wherein, The way of superimposing the predicted value and the trend item at the future time to obtain a clock bias prediction value comprises: Based on the predicted value, the predicted value in the original unit is recovered by the following formula : ； wherein is the predicted value, and are the sample mean and standard deviation of the raw space-borne clock error data, respectively. Based on the data in the input layer input window, re-perform polynomial fitting to predict the trend component at future time :​ ； wherein represents a linear polynomial coefficient, represents an order of the fitting polynomial, k represents an index of the polynomial order; The clock bias prediction value is obtained by superimposing and stacking.

7. The low Earth orbit satellite on-board clock prediction method of claim 1, wherein, When the Fourier analysis network is trained in a supervised learning manner, the root mean square error loss function between the predicted residual and the true residual is minimized as the training target; wherein the root mean square error loss function is represented as: ； wherein denotes the root mean square error, and are the predicted and actual on-board clock residuals, respectively, i denotes the index of the prediction time step, h denotes the prediction step size.

8. A low earth orbit satellite on-board clock prediction apparatus, characterized by, The device comprises: A data preprocessing module configured to, based on original satellite-borne clock error data, perform trend separation to obtain a trend item and a periodic residual sequence, and normalize the periodic residual sequence to obtain a normalized periodic residual sequence; A network construction module configured to construct a Fourier analysis network; wherein the Fourier analysis network comprises an input layer, a plurality of Fourier analysis layers, and an output layer, the input layer is used to convert the input normalized periodic residual sequence into a plurality of time-target pairs as input sequences, the plurality of Fourier analysis layers are stacked to establish a mapping relationship from the input sequences to a periodic prediction output, and based on the input sequences, a predicted value at a future time is output, the Fourier analysis layer comprises at least one neuron, the neuron is embedded with a sine function, a cosine function and a Sigmoid function, and the output layer is used to superimpose the predicted value and the trend item at the future time to obtain a clock bias prediction value; A network training module configured to train the Fourier analysis network in a supervised learning manner, and realize low-orbit satellite-borne clock prediction based on the trained Fourier analysis network.

9. An electronic device, comprising: It comprises: A processor and a memory connected in communication with the processor; The memory stores computer execution instructions; The processor executes computer-executed instructions stored in the memory to implement the low-orbit satellite on-board clock prediction method according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executed instructions, and the computer-executed instructions are executed by the processor to implement the low-orbit satellite on-board clock prediction method according to any one of claims 1-7.

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