Satellite clock error prediction method and system based on ordinary differential equation neural network

Abstract

The application provides a satellite clock error prediction method and system based on a neural network of ordinary differential equations, comprising: preprocessing satellite original clock error observation data; constructing a physically embedded neural dynamic model, the physically embedded neural dynamic model comprising a deterministic term composed of a quadratic polynomial physical model and a random compensation term composed of a deep residual model; performing model evolution and training on the physically embedded neural dynamic model based on adaptive step integration, performing forward calculation using a preset numerical solver, updating gradients using an adjoint state equation, obtaining updated neural network weights, and obtaining a trained ordinary differential equation neural network model; and performing prediction derivation in a preset extrapolation time interval, and outputting discrete clock error prediction values corresponding to any time stamp. The application abstracts satellite clock error evolution as a restricted continuous dynamic process, and uses a Neural ODE to establish a mapping from discrete observation to continuous physical trajectory.

Description

Technical Field

[0001] This invention relates to the field of satellite technology, and in particular to a satellite clock error prediction method and system based on ordinary differential equation neural networks. Background Technology

[0002] In the field of satellite navigation, high-precision satellite clock error prediction is the key to achieving real-time precision positioning.

[0003] Currently, the mainstream prediction methods include: (1) Physical statistical models: such as quadratic polynomial models and grey prediction models, which mainly extrapolate by fitting the time evolution trend of clock difference.

[0004] (2) Discrete time series models: such as long short-term memory networks and recurrent neural networks, which use neural networks to learn the nonlinear variation law of clock error sequences.

[0005] The shortcomings of existing technology: (1) Discretization bottleneck of physical evolution process: Traditional neural networks regard clock difference as discrete time series points, which cannot truly restore the nature of the continuous evolution of the physical state of atomic clock over time, resulting in the lack of physical interpretability of the model.

[0006] (2) Poor adaptability of non-equidistant sampling: GNSS observation data often have inconsistent sampling intervals due to receiver environmental disturbances or loss of lock. Existing discrete models must perform complex interpolation preprocessing when processing such non-equidistant data, which introduces additional human error.

[0007] (3) Large cumulative error in long-term prediction: Multinomial models are difficult to capture complex random noise (such as random walk frequency noise), while ordinary neural networks lack continuous time constraints in multi-step inference, and the prediction accuracy diverges rapidly with time. Summary of the Invention

[0008] This invention provides a satellite clock bias prediction method and system based on ordinary differential equation neural networks to address the shortcomings of existing technologies. By modeling the clock bias evolution process as a continuous dynamic system, robust prediction is achieved under irregular sampling scenarios, and physical information constraints are used to improve the stability of medium- and long-term predictions.

[0009] In a first aspect, the present invention provides a satellite clock error prediction method based on ordinary differential equation neural networks, comprising: Acquire raw satellite clock bias observation data and preprocess the raw satellite clock bias observation data; A physical embedded neurodynamic model is constructed, which includes deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model. The physical embedded neural dynamics model is subjected to model evolution and training based on adaptive step-size integral. A preset numerical solver is used for forward calculation, and the gradient is updated using the adjoint state equation to obtain the updated neural network weights, thus obtaining the trained ordinary differential equation neural network model. Based on the trained ordinary differential equation neural network model, a prediction extrapolation is performed for a preset time interval, and the discrete clock difference prediction value corresponding to any timestamp is output.

[0010] According to the satellite clock bias prediction method based on ordinary differential equation neural networks provided by the present invention, before acquiring raw satellite clock bias observation data and preprocessing the raw satellite clock bias observation data, the method further includes: Construct a state-space model and determine The state vector of the satellite clock difference at time is ,in Indicates the clock difference value. Indicates clock speed; State vector The rate of change over time is determined by a composite derivative neural network. Decide:

[0011] in This represents the weights of the neural network.

[0012] According to the present invention, a satellite clock bias prediction method based on ordinary differential equation neural networks is provided, which acquires raw satellite clock bias observation data and preprocesses the raw satellite clock bias observation data, including: Obtain the raw clock bias observation sequence of any satellite via real-time stream from the monitoring station or the IGS product FTP server. It is divided into training set and validation set. Indicates the epochal time of the astronomical calendar. This represents the satellite clock difference value corresponding to the epoch time; Extract the first valid epoch from the original clock error observation sequence clock phase as The initial frequency deviation is obtained by the difference between preceding and following epochs. , forming the initial value vector .

[0013] According to the satellite clock error prediction method based on ordinary differential equation neural networks provided by the present invention, a physical embedded neural dynamics model is constructed. The physical embedded neural dynamics model includes deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model, including: The deterministic term Based on a quadratic polynomial physical model:

[0014] By differentiating the quadratic polynomial physical model, the state vector is derived. Deterministic rate of change:

[0015] The random compensation item A three-layer residual neural network, ResNet, is used to calculate the current time step. and state vector For input; The final derivative field output is determined as follows: The number of neurons in the hidden layer of the network is determined, and the Tanh function is used as the activation function to ensure the continuous smoothness of the clock error trajectory on the second derivative.

[0016] According to the present invention, a satellite clock error prediction method based on ordinary differential equation neural networks is provided. The method involves performing model evolution and training on the physical embedded neural dynamics model based on adaptive step-size integration, using a preset numerical solver for forward computation, updating the gradient using the adjoint state equation, obtaining updated neural network weights, and ultimately obtaining a trained ordinary differential equation neural network model. The method includes: An initial value is given by a numerical solver with adaptive step size control. For any discrete observation point The state estimate is obtained through integration. :

[0017] Obtain the adjoint state equation:

[0018] in As a companion variable; State estimate By comparing the actual satellite clock errors at the corresponding times, a loss function is constructed, and the adjoint state equation is used to... Towards Inverse integration is used to obtain the gradient and update the neural network weights. ; Repeat the iteration until the preset number of training iterations is reached, and when the rate of change of the loss function is less than the rate of change threshold, stop training and output the trained ordinary differential equation neural network model.

[0019] According to the present invention, a satellite clock bias prediction method based on ordinary differential equation neural network is provided. Based on the trained ordinary differential equation neural network model, prediction extrapolation is performed over a preset time interval, and the discrete clock bias prediction value corresponding to any timestamp is output, including: Starting from the latest precise observation status, determine the preset extrapolation time interval; The trained ordinary differential equation neural network model is continuously deduced, and the integrator outputs a continuous clock difference curve on the time axis. Extract discrete clock difference prediction values ​​from any timestamp on the clock difference curve according to actual needs.

[0020] Secondly, the present invention also provides a satellite clock error prediction system based on ordinary differential equation neural networks, comprising: The acquisition module is used to acquire raw satellite clock bias observation data and preprocess the raw satellite clock bias observation data. A construction module is used to construct a physical embedded neurodynamic model, which includes deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model. The training module is used to perform model evolution and training on the physical embedded neural dynamics model based on adaptive step-size integral. It uses a preset numerical solver for forward calculation, uses the adjoint state equation for gradient update, obtains updated neural network weights, and obtains a trained ordinary differential equation neural network model. The extrapolation module is used to perform prediction extrapolation for a preset time interval based on the trained ordinary differential equation neural network model, and output the discrete clock difference prediction value corresponding to any timestamp.

[0021] Thirdly, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the satellite clock error prediction method based on ordinary differential equation neural networks as described above.

[0022] Fourthly, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the satellite clock error prediction method based on ordinary differential equation neural networks as described above.

[0023] The satellite clock error prediction method and system based on ordinary differential equation neural networks provided by this invention have the following beneficial effects: (1) Data sampling flexibility: It can directly process clock difference data with any sampling rate (such as 1s, 30s or random intervals) without preprocessing interpolation, thus preserving the most original clock difference characteristics; (2) Physical consistency and prediction stability: The prediction trajectory generated by Neural ODE is naturally smooth and constrained by the physical trend term, showing higher reliability than traditional discrete networks in medium- and long-term predictions (more than 24 hours); (3) High efficiency of computing resources: Using the adjoint method, it exhibits constant memory usage when processing large-scale historical clock difference data, making it suitable for integration into high-performance GNSS data processing centers. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0025] Figure 1 This is a flowchart illustrating the satellite clock error prediction method based on ordinary differential equation neural networks provided by the present invention. Figure 2 This is a schematic diagram of the satellite clock error prediction system based on ordinary differential equation neural network provided by the present invention; Figure 3 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0027] Figure 1 This is a flowchart illustrating the satellite clock error prediction method based on ordinary differential equation neural networks provided in this embodiment of the invention, as shown below. Figure 1 As shown, it includes: Step 100: Obtain raw satellite clock bias observation data and preprocess the raw satellite clock bias observation data; Step 200: Construct a physical embedded neurodynamic model, which includes deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model. Step 300: Perform model evolution and training based on adaptive step-size integral on the physical embedded neural dynamics model, use a preset numerical solver for forward calculation, use the adjoint state equation for gradient update, obtain the updated neural network weights, and obtain the trained ordinary differential equation neural network model. Step 400: Based on the trained ordinary differential equation neural network model, perform prediction and deduction for a preset extrapolation time interval, and output the discrete clock difference prediction value corresponding to any timestamp.

[0028] It is understood that the embodiments of the present invention employ an ODE derivative field modeling method based on the continuity of clock error physical evolution, utilizing a neural network to learn the instantaneous frequency offset (derivative field) of satellite clock error, thereby achieving dynamic fitting of the continuous evolution process of atomic clocks; it also employs a hybrid modeling technique that integrates physical priors and neural dynamics, integrating quadratic polynomial parameters as a basic benchmark in the derivative terms of differential equations, and using a neural network for residual compensation; it adopts a continuous loss calculation and optimization strategy based on irregular sampling points, utilizing an ODE integrator to perform forward inference at irregular time sampling points, and combining it with the adjoint state method for parameter updating training process; and it utilizes numerical solver error control for prediction confidence assessment, transforming the adaptive step size or truncation error in the solver integration process into the prediction confidence interval output.

[0029] Specifically, this invention abstracts the evolution of satellite clock bias into a constrained continuous dynamic process and uses NeuralODE to establish a mapping from discrete observations to continuous physical trajectories.

[0030] The first step is the construction of the state space for continuous clock difference dynamics: This invention no longer treats clock error prediction as a simple regression task, but rather establishes it within a state-space model. Definitions The state vector of the satellite clock difference at time is ,in This represents the phase deviation (clock error value). This represents the frequency deviation (clock speed). The rate of change of this state over time (i.e., the first derivative) is represented by a composite derivative neural network. Decide:

[0031] in Represents the weights of the neural network; Through this ordinary differential equation, the present invention transforms the originally discrete clock error sequence into an integrable and differentiable evolution trajectory on a continuous time axis.

[0032] Then, we build a hybrid derivative architecture inspired by physical information: To ensure that the output of the neural network conforms to the inherent physical characteristics of atomic clocks (such as high stability and linear frequency drift), this invention explicitly embeds a physical prior model in the derivative layer. Derivative function It consists of two parts: a deterministic term and a stochastic compensation term. (1) Deterministic trend derivative based on physical model ( ): Based on the classic quadratic polynomial physical model: .

[0033] By differentiating this physical model, the deterministic rate of change of the state variables is derived:

[0034] This element, serving as the "base color" of the derivative field, ensures that the model can lock onto the main physical orientation of the satellite clock in long-term extrapolation predictions, avoiding the divergence risk common in purely data-driven models.

[0035] (2) Stochastic dynamic compensation term based on neural network ( ): This paper utilizes deep residual networks to fit small, nonlinear frequency perturbations caused by variations in the space environment (temperature fluctuations, relativistic residuals) and internal noise of the atomic clock (such as random walk frequency noise). This is presented as... The high-frequency correction captures dynamic change characteristics that traditional physical models cannot characterize.

[0036] (3) Association logic: The final derivative field output is This mechanism achieves deep fusion of physical and neural data at the first derivative level, enabling the model to maintain physical consistency while exhibiting strong robustness to complex noise.

[0037] Finally, there is the accompanying sensitivity training and numerical solution mechanism: This invention achieves model parameters through numerical solution and continuous gradient propagation. Optimal learning: (1) Solving layer: Introduce a numerical solver with adaptive step size control (such as Adaptive Runge-Kutta45). Given initial values... Then, for any discrete observation point (Regardless of whether the intervals are equal), obtain the state estimate through integration:

[0038] This method natively supports irregular sampled data, completely solving the distortion problem caused by interpolation preprocessing in existing technologies.

[0039] (2) Optimization layer (adjoint sensitivity method): In order to accurately train the network under extremely long sequences, this invention does not use the traditional discrete backpropagation, but introduces an adjoint state equation:

[0040] in This is the accompanying variable. By solving this accompanying ODE, rigorous propagation of the gradient along the continuous time axis is achieved. This mechanism mathematically ensures that the model can learn the global dynamics of clock bias evolution, significantly improving the long-term extrapolation accuracy for windows of 24 hours and above.

[0041] Based on the above embodiments, this invention takes the GPS satellite on-orbit clock error prediction task as an example to explain in detail the specific implementation steps of this invention.

[0042] Step S1: Acquisition and Precise Preprocessing of Raw Observation Data Constructing the dataset: Obtain the raw clock bias observation sequence of a satellite through real-time streaming from monitoring stations or the IGS product FTP server. , Indicates the epochal time of the astronomical calendar. This represents the satellite clock difference value corresponding to the epoch time, and is divided into training set and validation set.

[0043] State initialization: Extract the first valid epoch of the sequence clock phase as The initial frequency deviation is obtained by the difference between preceding and following epochs. , forming the initial value vector .

[0044] Step S2: Construct a physically embedded neurodynamic model Define the derivative field architecture: construct the composite derivative function as described above. Among them, the deterministic part The coefficients of the prefitted quadratic polynomial Real-time calculation; random compensation component A three-layer residual neural network (ResNet) is used to calculate the current time step. and state For input.

[0045] Parameter configuration: Set the number of neurons in the hidden layer of the network (e.g., 64 or 128), and select the Tanh function as the activation function to ensure the continuous smoothness of the clock error change trajectory on the second derivative.

[0046] Step S3: Model Evolution and Training Based on Adaptive Step Size Integral Forward calculation: An adaptive Runge-Kutta integrator (e.g., dopri5) is invoked. The integrator dynamically adjusts the calculation step size based on the drastic change in clock bias. At the observation timestamp At this point, the predicted state is calculated through numerical integration. .

[0047] Gradient update: Compare the predicted value with the actual satellite clock error at the corresponding time in step S1 to construct a loss function. Utilize the adjoint state equation from... Towards Inverse integration is used to obtain the gradient and update the neural network weights. .

[0048] Convergence criterion: Repeat the iteration until the rate of change of the loss function is less than 1 / 2 in 10 consecutive training iterations. .

[0049] Step S4: Clock difference long-term extrapolation prediction output Starting from the latest precise observations, an extrapolation time interval (e.g., the next 24 or 48 hours) is set, and the trained Neural ODE model performs continuous extrapolation. The integrator will output a continuous clock difference curve on the time axis, and discrete predicted values ​​can be extracted at any timestamp (e.g., every 30 seconds or every 1 hour) according to actual needs.

[0050] To demonstrate the optimality of this embodiment, three consecutive days of data from a GPS rubidium atomic clock satellite were selected for verification and compared with traditional models: Scenario 1: Processing Irregular Sampling Data In a scenario where data loss is artificially simulated (data loss rate of 20%), traditional LSTM models fail to predict due to interruption of discrete step size, while this invention maintains prediction accuracy within 1.2ns through a continuous integration mechanism.

[0051] Scenario 2: 24-hour long-term extrapolation accuracy Quadratic polynomial model (QP): The error increases quadratically with time, and the 24-hour forecast error RMS is approximately 4.5 ns; This invention (Neural ODE) achieves a 24-hour forecast error RMS of only 0.8 ns by embedding a physical trend term and correcting frequency drift at the derivative level, which is an improvement of approximately 82% compared to the QP model.

[0052] It is understood that the present invention has extremely strong robustness when processing non-equal interval observation data and can effectively fit the random evolution law of atomic clocks, which is significantly better than the existing technology.

[0053] The satellite clock error prediction system based on ordinary differential equation neural network provided by the present invention is described below. The satellite clock error prediction system based on ordinary differential equation neural network described below can be referred to in correspondence with the satellite clock error prediction method based on ordinary differential equation neural network described above.

[0054] Figure 2 This is a schematic diagram of the satellite clock error prediction system based on ordinary differential equation neural networks provided in an embodiment of the present invention, as shown below. Figure 2 As shown, it includes: acquisition module 21, construction module 22, training module 23, and inference module 24, wherein: The acquisition module 21 is used to acquire raw satellite clock error observation data and preprocess the raw satellite clock error observation data; the construction module 22 is used to construct a physical embedded neural dynamics model, which includes deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model; the training module 23 is used to perform model evolution and training on the physical embedded neural dynamics model based on adaptive step-size integral, using a preset numerical solver for forward solving, using the adjoint state equation for gradient updating, obtaining updated neural network weights, and obtaining a trained ordinary differential equation neural network model; the deduction module 24 is used to perform prediction deduction based on the trained ordinary differential equation neural network model for a preset extrapolation time interval, and output the discrete clock error prediction value corresponding to any timestamp.

[0055] Figure 3 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 3As shown, the electronic device may include: a processor 310, a communication interface 320, a memory 330, and a communication bus 340, wherein the processor 310, the communication interface 320, and the memory 330 communicate with each other through the communication bus 340. The processor 310 can call logic instructions in the memory 330 to execute a satellite clock error prediction method based on ordinary differential equation neural networks. This method includes: acquiring raw satellite clock error observation data; preprocessing the raw satellite clock error observation data; constructing a physically embedded neural dynamics model, the physically embedded neural dynamics model including deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model; performing model evolution and training on the physically embedded neural dynamics model based on adaptive step-size integrals, using a preset numerical solver for forward computation, updating the gradient using the adjoint state equation, obtaining updated neural network weights, and obtaining a trained ordinary differential equation neural network model; performing prediction extrapolation over a preset time interval based on the trained ordinary differential equation neural network model, and outputting discrete clock error prediction values ​​corresponding to any timestamp.

[0056] Furthermore, the logical instructions in the aforementioned memory 330 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0057] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the satellite clock error prediction method based on ordinary differential equation neural networks provided by the above methods. The method includes: acquiring raw satellite clock error observation data and preprocessing the raw satellite clock error observation data; constructing a physical embedded neural dynamics model, which includes deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model; performing model evolution and training on the physical embedded neural dynamics model based on adaptive step-size integral, performing forward solving using a preset numerical solver, updating the gradient using the adjoint state equation, obtaining updated neural network weights, and obtaining a trained ordinary differential equation neural network model; and performing prediction extrapolation for a preset extrapolation time interval based on the trained ordinary differential equation neural network model, and outputting discrete clock error prediction values ​​corresponding to any timestamp.

[0058] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the satellite clock error prediction method based on ordinary differential equation neural networks provided by the above methods. The method includes: acquiring raw satellite clock error observation data and preprocessing the raw satellite clock error observation data; constructing a physical embedded neural dynamics model, the physical embedded neural dynamics model including deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model; performing model evolution and training on the physical embedded neural dynamics model based on adaptive step-size integral, performing forward solving using a preset numerical solver, updating the gradient using the adjoint state equation, obtaining updated neural network weights, and obtaining a trained ordinary differential equation neural network model; performing prediction extrapolation over a preset extrapolation time interval based on the trained ordinary differential equation neural network model, and outputting discrete clock error prediction values ​​corresponding to arbitrary timestamps.

[0059] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units 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 achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0060] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0061] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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 of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A satellite clock error prediction method based on ordinary differential equation neural networks, characterized in that, include: Acquire raw satellite clock bias observation data and preprocess the raw satellite clock bias observation data; A physically embedded neurodynamic model is constructed, comprising deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model, including: The deterministic term Based on a quadratic polynomial physical model: By differentiating the quadratic polynomial physical model, the state vector is derived. Deterministic rate of change: The random compensation item A three-layer residual neural network, ResNet, is used to calculate the current time step. and state vector For input; The final derivative field output is determined as follows: The number of neurons in the hidden layer of the network is determined, and the Tanh function is used as the activation function to ensure the continuous smoothness of the clock error trajectory on the second derivative. The physical embedded neural dynamics model is subjected to model evolution and training based on adaptive step-size integral. A preset numerical solver is used for forward calculation, and the gradient is updated using the adjoint state equation to obtain the updated neural network weights, thus obtaining the trained ordinary differential equation neural network model. Based on the trained ordinary differential equation neural network model, a prediction extrapolation is performed for a preset time interval, and the discrete clock difference prediction value corresponding to any timestamp is output.

2. The satellite clock error prediction method based on ordinary differential equation neural networks according to claim 1, characterized in that, Before acquiring raw satellite clock bias observation data and preprocessing the raw satellite clock bias observation data, the process also includes: Construct a state-space model and determine The state vector of the satellite clock difference at time is ,in Indicates the clock difference value. Indicates clock speed; State vector The rate of change over time is determined by a composite derivative neural network. Decide: in This represents the weights of the neural network.

3. The satellite clock error prediction method based on ordinary differential equation neural networks according to claim 2, characterized in that, Acquire raw satellite clock bias observation data and preprocess the raw satellite clock bias observation data, including: Obtain the raw clock bias observation sequence of any satellite via real-time stream from the monitoring station or the IGS product FTP server. It is divided into training set and validation set. Indicates the epochal time of the astronomical calendar. This represents the satellite clock difference value corresponding to the epoch time; Extract the first valid epoch from the original clock error observation sequence clock phase as The initial frequency deviation is obtained by the difference between preceding and following epochs. , forming the initial value vector .

4. The satellite clock error prediction method based on ordinary differential equation neural networks according to claim 1, characterized in that, The physical embedded neural dynamics model is subjected to model evolution and training based on adaptive step-size integral. A preset numerical solver is used for forward computation, and the adjoint state equation is used for gradient update to obtain updated neural network weights, resulting in a trained ordinary differential equation neural network model, including: An initial value is given by a numerical solver with adaptive step size control. For any discrete observation point The state estimate is obtained through integration. : Obtain the adjoint state equation: in As a companion variable; State estimate By comparing the actual satellite clock errors at the corresponding times, a loss function is constructed, and the adjoint state equation is used to... Towards Inverse integration is used to obtain the gradient and update the neural network weights. ; Repeat the iteration until the preset number of training iterations is reached, and when the rate of change of the loss function is less than the rate of change threshold, stop training and output the trained ordinary differential equation neural network model.

5. The satellite clock error prediction method based on ordinary differential equation neural networks according to claim 1, characterized in that, Based on the trained ordinary differential equation neural network model, a prediction extrapolation is performed for a preset time interval, outputting a discrete clock difference prediction value corresponding to any timestamp, including: Starting from the latest precise observation status, determine the preset extrapolation time interval; The trained ordinary differential equation neural network model is continuously deduced, and the integrator outputs a continuous clock difference curve on the time axis. Extract discrete clock difference prediction values ​​from any timestamp on the clock difference curve according to actual needs.

6. A satellite clock error prediction system based on ordinary differential equation neural networks, based on the satellite clock error prediction method based on ordinary differential equation neural networks according to any one of claims 1 to 5, characterized in that, include: The acquisition module is used to acquire raw satellite clock bias observation data and preprocess the raw satellite clock bias observation data. A construction module is used to construct a physical embedded neurodynamic model, which includes deterministic terms composed of a quadratic polynomial physical model and stochastic compensation terms composed of a deep residual model. The training module is used to perform model evolution and training on the physical embedded neural dynamics model based on adaptive step-size integral. It uses a preset numerical solver for forward calculation, uses the adjoint state equation for gradient update, obtains updated neural network weights, and obtains a trained ordinary differential equation neural network model. The extrapolation module is used to perform prediction extrapolation for a preset time interval based on the trained ordinary differential equation neural network model, and output the discrete clock difference prediction value corresponding to any timestamp.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the satellite clock error prediction method based on ordinary differential equation neural networks as described in any one of claims 1 to 5.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the satellite clock error prediction method based on ordinary differential equation neural networks as described in any one of claims 1 to 5.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the satellite clock error prediction method based on ordinary differential equation neural networks as described in any one of claims 1 to 5.

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