A satellite short-term clock error prediction method integrating time series decomposition and deep learning

Abstract

The present invention relates to a method for predicting short-term satellite clock errors that integrates time series decomposition and deep learning, and belongs to the technical field of satellite clock error prediction. The method comprises: performing first-order difference processing on the historical satellite clock error sequence, and filtering out the outliers in the data according to the Raida criterion, performing time series decomposition on the first-order clock error data, firstly using the adaptive noise complete set empirical mode decomposition algorithm to decompose the first-order clock error sequence to obtain multiple modal components, introducing the permutation entropy algorithm to sort the modal components, and using the t-test algorithm to classify the random terms and periodic terms of the above components and reconstruct them into trend terms, periodic terms and random terms. The reconstructed terms are input into the Transformer model in a channel-independent mode for training, and the required predicted clock error is obtained after the first-order difference processing and superposition of the prediction results of each component. While improving the accuracy and stability of the satellite short-term clock error forecast, the present invention also improves the interpretability of the forecast results.

Description

Technical Field

[0001] The present invention belongs to the technical field of satellite clock error prediction and relates to a satellite short-term clock error prediction method integrating time series decomposition and deep learning. Background Art

[0002] Satellite clock error prediction is a key technology in satellite navigation systems. Accurate clock error prediction directly impacts navigation positioning accuracy. Satellite clock error is the time deviation between the satellite clock and a reference clock, and is affected by a variety of complex factors, including satellite clock drift, orbital environment disturbances, and internal system noise. As navigation applications increasingly demand higher positioning accuracy, achieving high-precision short-term prediction of satellite clock error has become a key research topic in navigation systems.

[0003] Traditional satellite clock error prediction methods primarily rely on physical and statistical models, such as those based on Kalman filtering and ARMA (autoregressive moving average). However, these methods exhibit limitations when dealing with complex time series characteristics and multiple noises. In particular, when dealing with long-term dependencies, nonlinear changes, and non-stationary sequences, the prediction accuracy often fails to meet the requirements of high-precision navigation systems. Furthermore, satellite clock error data often contains complex components such as trends, periodicity, and random fluctuations. Traditional methods struggle to effectively distinguish and extract these time series components, leading to biased forecasts.

[0004] In recent years, the rapid development of artificial intelligence technology, especially the breakthrough progress of deep learning technology in the field of time series data processing, has provided new solutions for satellite clock error prediction. Deep learning models, especially Transformer and Long Short-Term Memory (LSTM) networks, have powerful time series modeling capabilities and can capture long-term and short-term dependencies and nonlinear characteristics in the data. However, relying solely on deep learning models to directly model raw clock error data may face problems such as data noise and interference from complex time series features, resulting in a decline in model performance. Therefore, combining traditional time series decomposition methods with deep learning technology, using time series decomposition methods to extract trend, cycle, and random components in the data, and then using deep learning models for modeling and prediction, can improve the accuracy and robustness of satellite clock error prediction while preserving the time series characteristics of the data. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for predicting short-term satellite clock errors that integrates time series decomposition and deep learning. By combining the time series decomposition method with deep learning models such as Transformer, it is possible to more accurately capture the multi-level features contained in satellite clock error data and significantly improve the accuracy of clock error prediction. The advantage of this method is that it combines the fine-grained decomposition capability of traditional time series analysis with the powerful time series modeling capability of deep learning models, making up for the limitation that a single model is difficult to simultaneously handle complex time series features and global dependencies.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention provides a method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning, comprising the following steps:

[0008] Step 1: Perform a primary difference on the original clock error data, use the Raida criterion to filter out outliers from the differential data, and use linear interpolation to fill in the outlier filter areas to obtain the primary difference data to be decomposed;

[0009] Step 2: To extract the fluctuation characteristics of the clock error data, the data is decomposed using the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) algorithm to obtain multiple modal components and residual components. The irredecomposable residual component is used as the trend term.

[0010] Step 3: Use the permutation entropy algorithm to sort the complexity of the above multiple modal components, and then use the t-test method to divide the periodic component and random component, and reconstruct the periodic term and residual term. The random component superposition becomes the random term, and the periodic component superposition becomes the periodic term;

[0011] Step 4: Input the trend term, period term, and residual term into the Transformer model in a channel-independent manner for training and prediction, and finally obtain the first-order difference prediction results of each item;

[0012] Step 5: Superimpose the first-order difference prediction results of each item, and perform reverse difference on the superimposed first-order difference prediction results to obtain the final clock error prediction result.

[0013] Furthermore, the specific method of filtering out outliers and filling in the data in step 1 includes:

[0014] For the sequence x(t) after the original clock error data is first differenced, its mean μ and standard deviation σ are calculated. The outlier judgment threshold τ=3σ is set using the Raida criterion. If |x(t)-μ|>τ, the clock error value at this time point is an outlier. Assuming that the time point is t i , the corresponding difference sequence value is x(t i), then use two adjacent normal data points x(t i-1 ) and x(t i+1 ) is estimated and filled in according to the following formula, where To fill the value:

[0015]

[0016] Furthermore, in step 2, the decomposition process of the CEEMDAN algorithm includes:

[0017] Step 2.1: Add a set of white noise ε(t) with a sum of mean 0 to the clock error sequence x(t) to be decomposed in step 1. The sequence after adding the qth set of white noise is:

[0018] x q (t)=x(t)+ε q (t), q=1,2,…,N

[0019] Step 2.2, for x q (t) Perform empirical mode decomposition (EMD) to decompose the N groups of decomposed signals IMF1 q (t) is obtained by arithmetic averaging to obtain the first-order intrinsic mode component IMF1(t), which is expressed as:

[0020]

[0021] The residual component r after removing the first-order eigenmodal component of x(t) s1 (t) can be expressed as:

[0022] r s1 (t) = x(t) - IMF1(t)

[0023] If we continue to add white noise with a mean sum of 0 to the residual component, the second modal component IMF2(t) can be expressed as:

[0024]

[0025] The residual component r after the second EMD decomposition s2 (t) can be expressed as:

[0026] r s2 (t) = r s1 (t)-IMF2(t)

[0027] Step 2.3, repeat the above steps until the residual component r sK (t) can no longer be decomposed by EMD, then all CEEMDAN steps are completed, and the number of modal components obtained is K. The signal of x(t) after CEEMDAN decomposition can be expressed as:

[0028]

[0029] The residual component after the CEEMDAN algorithm is decomposed cannot be decomposed any further, indicating that the residual component has become relatively stable. At this time, the residual component r sK (t) is the trend term X(t) of the clock error sequence trend .

[0030] Furthermore, in step 3, the entropy value calculation process includes:

[0031] The entropy calculation process first involves the decomposition of the modal components (IMF 1～K ) is standardized to eliminate the dimensional influence between different components and ensure that each component has the same comparison benchmark; then, the permutation entropy algorithm is applied to calculate the entropy value of each standardized modal component. The algorithm counts the number of occurrences of permutations and combinations of data values ​​at different time points and calculates their probability distribution. Then, the entropy value is calculated based on the probability distribution to quantify the time series complexity and uncertainty of each modal component; finally, the modal components are sorted according to the calculated entropy value to identify and distinguish the random components and periodic components in the signal.

[0032] Furthermore, in step 3, the permutation entropy algorithm is used to sort the complexity of the above modal components, and then the t-test method is used to divide the periodic component and the random component. Based on this, the trend term, periodic term and random term are reconstructed. The reconstruction process includes:

[0033] The permutation entropy algorithm is used to calculate and arrange the entropy values ​​of each modal component decomposed by CEEMDAN in step 2, and the change characteristics of each component are divided and reconstructed according to the t-test algorithm. Specifically, the modal components processed by the permutation entropy algorithm are arranged according to the principle of entropy reduction. Assuming that the component starts from the i-th modal component, a t-test is performed on these i-th components. When the t-test statistic is significantly different from 0, it is used as the critical condition for the periodic component and the random component. The first i-1 modal components are random components, and the remaining modal components starting from item i are periodic components. The sum of the random components in the original sequence decomposition signal is regarded as a random term, and the sum of the periodic components is regarded as a periodic term. The residual component in step 2 is regarded as a trend term. At this point, the reconstruction of the characteristic components is completed.

[0034] Furthermore, the process of inputting each reconstruction item in step 4 into the Transformer in a channel-independent manner includes:

[0035] The trend term, periodic term, and random term reconstructed in step 3 are respectively input into the deep learning model Transformer for training based on the principle of channel independence, and the model is used to predict the required short-term first-order difference data. The input layer of the Transformer adopts a multi-head self-attention mechanism, which can capture the time-varying characteristics and global dependencies of each time series. The encoder-decoder architecture is used to extract features and perform sequence modeling on the input reconstructed terms. Compared with traditional RNN or LSTM networks, the Transformer abandons the recursive structure and can effectively capture the long-term dependencies in the sequence on a global scale. It also has higher computational parallelism and stability. After the above model training is completed, short-term predictions are made for the trend term, periodic term, and random term to obtain the predicted first-order difference of clock error for each term.

[0036] The beneficial effects of the present invention are:

[0037] 1. This paper utilizes a time series decomposition method to effectively remove noise and irregular fluctuations from the data, significantly enhancing the model's stability when processing complex, non-stationary data. Even when clock error data fluctuates dramatically, the model maintains high prediction accuracy and exhibits strong robustness.

[0038] 2. By combining time series decomposition methods with deep learning models, this paper decomposes complex satellite clock error data into distinct components, such as trend, periodic, and random terms. These components are then modeled to capture their respective time series characteristics, thereby improving forecast accuracy. Compared to directly modeling the raw data, the decomposed data possesses clearer characteristics, resulting in more accurate forecasts.

[0039] 3. This invention can flexibly handle the multi-layered features of satellite clock error data, capturing long-term trends while also identifying periodic fluctuations and random noise. This gives the model greater generalization capabilities, enabling it to perform well across various time series forecasting tasks and demonstrates strong generalization.

[0040] 4. This invention uses time series decomposition to break down complex raw clock error data into trends, cycles, and random terms with clear physical meaning. The independent prediction results for each component provide a clear and intuitive explanation, helping to understand the model's prediction process and enhancing the credibility of the forecast results. Furthermore, the decomposed components correspond to actual physical processes, providing a theoretical basis for the analysis and prediction of satellite clock errors.

[0041] Other advantages, objects, and features of the present invention will be described in part in the following description and, in part, will be apparent to those skilled in the art upon examination of the following description or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below with reference to the accompanying drawings, in which:

[0043] Figure 1 This is an overall flow chart of a satellite short-term clock error prediction method that integrates time series decomposition and deep learning provided by the present invention;

[0044] Figure 2 A satellite short-term clock error prediction method that integrates time series decomposition and deep learning provided by the present invention performs screening and replacement of outliers in a satellite clock error sequence within a certain time period;

[0045] Figure 3 This is a diagram showing the effect of performing signal decomposition using CEEMDAN on satellite clock error data using a satellite short-term clock error prediction method that integrates time series decomposition and deep learning, as provided by the present invention.

[0046] Figure 4 This is a diagram showing the recognition and reconstruction effect of a satellite short-term clock error prediction method that integrates time series decomposition and deep learning provided by the present invention on certain satellite clock error data. DETAILED DESCRIPTION

[0047] The following describes the embodiments of the present invention by means of specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0048] Among them, the accompanying drawings are only for illustrative purposes and represent only schematic diagrams rather than actual pictures, and should not be understood as limiting the present invention. In order to better illustrate the embodiments of the present invention, some parts of the accompanying drawings may be omitted, enlarged or reduced, and do not represent the dimensions of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions may be omitted in the accompanying drawings.

[0049] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "back", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0050] The flowchart of the satellite short-term clock error prediction method constructed by the present invention that integrates time series decomposition and deep learning is as follows: Figure 1 By combining signal decomposition technology with a deep learning model, the present invention provides a method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning. This method can effectively extract multi-level time series features from satellite clock error data and significantly improve the prediction accuracy and stability. The method specifically includes the following steps:

[0051] Step 1: Perform a difference on the original clock error data and use the Raida criterion to filter out abnormal values ​​from the differenced data, such as Figure 2 As shown, the linear interpolation method is used to fill in the outlier screening areas to obtain the clock error first difference data to be decomposed.

[0052] Specifically, for the sequence x(t) after the original clock error data is subjected to a difference, its mean μ and standard deviation σ are calculated. Using the triple standard deviation principle, the outlier judgment threshold τ = 3σ is set. If |x(t)-μ|>τ, the clock error value at this time point is an outlier. Assuming that the time point is t i , the corresponding difference sequence value is x(t i ), then use two adjacent normal data points x(t i-1 ) and x(t i+1 ) is estimated and filled in according to the following formula, where To fill the value:

[0053]

[0054] Step 2: To extract the fluctuation characteristics of clock error data, the CEEMDAN algorithm is used to decompose the above data to obtain multiple modal components and residual components. The residual component cannot be decomposed any further and can be directly regarded as a trend item, such as Figure 3 As shown in IMF9.

[0055] Specifically, step 2 can be divided into the following three specific steps:

[0056] Step 2.1: Add a set of white noise ε(t) with a sum of mean 0 to the clock error sequence x(t) to be decomposed in step 1. The sequence after adding the qth set of white noise is:

[0057] x q (t)=x(t)+ε q (t), q=1,2,…,N

[0058] Step 2.2, for x q (t) Perform empirical mode decomposition (EMD) to decompose the N groups of decomposed signals IMF1 q (t) is obtained by arithmetic averaging to obtain the first-order intrinsic mode component IMF1(t), which is expressed as:

[0059]

[0060] The residual component r after removing the first-order eigenmodal component of x(t) s1 (t) can be expressed as:

[0061] r s1 (t) = x(t) - IMF1(t)

[0062] If we continue to add white noise with a mean sum of 0 to the residual component, the second modal component IMF2(t) can be expressed as:

[0063]

[0064] The residual component r after the second EMD decomposition s2 (t) can be expressed as:

[0065] r s2 (t) = r s1 (t)-IMF2(t)

[0066] Step 2.3, repeat the above steps until the residual component r sK (t) can no longer be decomposed by EMD, then all CEEMDAN steps are completed, and the number of modal components obtained is K. The signal of x(t) after CEEMDAN decomposition can be expressed as:

[0067]

[0068] The residual component after the CEEMDAN algorithm is decomposed cannot be decomposed any further, indicating that the residual component has become relatively stable. At this time, the residual component r sK (t) is regarded as the trend term X(t) of the clock error sequence trend .

[0069] Step 3: Use the permutation entropy algorithm to sort the complexity of the above multiple modal components, and then use the t-test method to divide the periodic component and random component, and reconstruct the trend term, periodic term and residual term. Among them, the random component superposition becomes the random term, the periodic component superposition becomes the periodic term, and the permutation entropy value is significantly lower than the periodic component as the trend term, such as Figure 4 shown.

[0070] The Permutation Entropy (PE) algorithm is a method for measuring the complexity and irregularity of time series. The larger the entropy value, the greater the complexity of the time series. Compared to algorithms such as fuzzy entropy, the Permutation Entropy algorithm introduces the concept of permutation when calculating the complexity between reconstructed subsequences. The specific steps are as follows:

[0071] 1. The K modal components decomposed above are reconstructed into a phase space with an embedding dimension of M. The length of each modal component is S, and the number of subsequences after phase space reconstruction is L. Then the spatial matrix A generated by the subsequence of each modal component is q It can be expressed as:

[0072]

[0073] Where t is the time delay in the reconstruction process, N is the sequence length of the modal component, L = S-(M-1)t≤M!

[0074] 2. Arrange the elements of the subsequence in the reconstruction matrix of the K modal components in ascending order, and the index of each element after sorting constitutes a set of symbol sequences a L , it can be expressed as:

[0075]

[0076] 3. The M-dimensional phase space is fully permuted according to the above index values ​​to obtain M! symbol sequences. Then, the number of times each permutation corresponding to the L reconstruction components appears in the M! full permutation is counted. k , then the probability of occurrence of the reconstructed component P l for:

[0077]

[0078] 4. Permutation entropy calculated using probability of occurrence:

[0079]

[0080] When all reconstructed components have equal probability of occurrence, the permutation entropy is the largest, which is recorded as PE max , then the normalized permutation entropy for:

[0081]

[0082] According to the definition of entropy, the greater the modal classification entropy, the higher the complexity of the signal, and vice versa.

[0083] The permutation entropy algorithm can quantify the complexity of the decomposed signal, but the frequency domain characteristics of the decomposed signal are still not obvious, so the prediction results lack interpretability when making subsequent predictions. To solve the above problems, this paper introduces a t-test method to analyze and classify each characteristic component.

[0084] The t-test algorithm is a statistical method used to analyze whether there are significant differences between multiple groups in the data. It is generally applicable to data with small sample sizes. In EMD decomposition, the upper and lower envelopes of the IMF components are locally symmetrical about the horizontal axis, and the upper and lower envelopes are formed by connecting multiple signal peak points. For the random components in the IMF, due to their drastic changes and the large number of peak points, their IMF component data is basically symmetrical, and the data mean tends to 0. Conversely, for the periodic IMF components, due to their stable changes, the number of peak points is small, and the envelope changes are smooth. This makes their IMF component data asymmetrical with the horizontal axis, and the data mean does not approach 0.

[0085] The residual component after the CEEMDAN algorithm is decomposed cannot be decomposed any further. sK (t) is the trend term X(t) of the clock error sequence trend After being processed by the permutation entropy algorithm, the modal components are arranged according to the principle of entropy reduction. Assuming that the periodic component starts from the i-th modal component, it is only necessary to start from the first item and perform a t-test on the first i-1 components and the i-th component. When the t-test statistic is significantly different from 0, it is used as the critical condition for distinguishing between random items and periodic items. The t-test algorithm formula is as follows:

[0086]

[0087] in is the mean entropy of the first i indicators, σ i is the entropy standard deviation of the first i modal components, n is the sample size of i, and the test statistic t is assumed to follow a t-distribution with n degrees of freedom when μ = 0. When the t-test statistic is significantly different from 0, the first i-1 modal components are identified as random components, and the remaining modal components starting from item i are identified as periodic components. Then the random term X(t) of the original sequence is residual It is regarded as the sum of random components in the decomposed signal, and the sum of periodic components is regarded as the periodic term X(t) period , so far all feature components have been reconstructed.

[0088] Step 4: Input the trend term, period term, and residual term into the Transformer model in a channel-independent manner for training and prediction, and finally obtain the first-order difference prediction results of each item.

[0089] The trend term, cycle term, and random term are taken as three independent input channels to form the multi-channel input format of the model. For each time step, a three-dimensional input vector is constructed, and the input matrix shape is [batch_size, sequence_length, 3], where 3 corresponds to the three channels (trend, cycle, random). In the Transformer, there are four main structures, namely the input embedding layer (Input Embedding), the positional encoding layer (Positional Encoding), the multi-head self-attention mechanism layer (Multi-Head Self-Attention) and the feed-forward network layer (Feed-Forward Network). The input shape is [batch_size, sequence_length, embedding_dim], where embedding_dim is the dimensional expansion of the trend, cycle, and random terms. The input of each time step consists of three items and is processed through embedding and positional encoding. The trained Transformer model is used to predict future time steps to obtain the first-difference prediction results for the forecast period of each input channel (trend, cycle, random) and

[0090] Step 5: Superimpose the first-order difference prediction results of each item, and perform reverse difference on the superimposed first-order difference prediction results to obtain the final clock error prediction result.

[0091] Assume that the first difference prediction result of the trend item in the forecast period is The first difference prediction result of the periodic term is The first difference prediction result of the random term is Then the first epoch clock error that needs to be predicted is:

[0092]

[0093] Assume that the last historical clock error data in the training set is C history (end), then the predicted clock error C of the first predicted epoch is predict (1) is:

[0094]

[0095] And so on, all the forecast clock error values ​​needed subsequently are obtained.

[0096] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions, which should all be included in the scope of the claims of the present invention.

Claims

1. A method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning, characterized by: The following steps are involved: Step 1: Perform a primary difference on the original clock error data, use the Raida criterion to filter out outliers from the differential data, and use linear interpolation to fill in the outlier filter areas to obtain the primary difference data to be decomposed; Step 2: To extract the fluctuation characteristics of the clock error data, the adaptive noise complete ensemble empirical mode decomposition (CEEMDAN) algorithm is used to decompose the data to obtain multiple modal components and residual components, of which the irredecomposable residual component is used as the trend term. Step 3: Use the permutation entropy algorithm to sort the complexity of the above multiple modal components, then use the t-test method to divide the periodic component and random component, and reconstruct the periodic term and residual term; the random component superposition becomes the random term, and the periodic component superposition becomes the periodic term; Step 4: Input the trend term, period term, and residual term into the Transformer model in a channel-independent manner for training and prediction, and finally obtain the first-order difference prediction results of each item; Step 5: Superimpose the first-order difference prediction results of each item, and perform reverse difference on the superimposed first-order difference prediction results to obtain the final clock error prediction result.

2. The method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning according to claim 1, characterized in that: In step 1, the specific method of screening out outliers and filling in the gaps includes: For the sequence x(t) after the original clock error data is first differenced, its mean μ and standard deviation σ are calculated. The outlier judgment threshold τ=3σ is set using the Raida criterion. If |x(t)-μ|>τ, the clock error value at this time point is an outlier. Assuming that the time point is t i , the corresponding difference sequence value is x(t i ), then use two adjacent normal data points x(t i-1 ) and x(t i+1 ) is estimated and filled in according to the following formula, where To fill the value:

3. The method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning according to claim 2, characterized in that: In step 2, the CEEMDAN algorithm decomposition process includes: Step 2.1: Add a set of white noise ε(t) with a sum of mean 0 to the clock error sequence x(t) to be decomposed in step 1. The sequence after adding the qth set of white noise is: x q (t)=x(t)+ε q (t),q=1,2,…,N Step 2.2, for x q (t) Perform empirical mode decomposition (EMD) to decompose the N groups of decomposed signals IMF1 q (t) is obtained by arithmetic averaging to obtain the first-order intrinsic mode component IMF1(t), which is expressed as: The residual component r after removing the first-order eigenmodal component of x(t) s1 (t) is expressed as: r s1 (t)=x(t)-IMF1(t) Continue to add white noise with a mean sum of 0 to the residual component, then the second modal component IMF2(t) is expressed as: The residual component r after the second EMD decomposition s2 (t) is expressed as: r s2 (t)=r s1 (t)-IMF2(t) Step 2.3, repeat the above steps until the residual component r sK If (t) can no longer be decomposed by EMD, all CEEMDAN steps are completed. At this time, the number of modal components obtained is K. The signal after x(t) decomposed by CEEMDAN is expressed as: The residual component after the CEEMDAN algorithm is decomposed cannot be decomposed any further, indicating that the residual component has become relatively stable. At this time, the residual component r sK (t) is the trend term X(t) of the clock error sequence trend .

4. The method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning according to claim 3 is characterized in that: In step 3, the entropy value calculation process includes: The entropy calculation process first involves the IMF of each modal component obtained by CEEMDAN decomposition. 1～K Standardization is performed to eliminate the impact of dimensions between different components and ensure that each component has the same comparison benchmark; then, the permutation entropy algorithm is applied to calculate the entropy value of each standardized modal component. The algorithm counts the number of occurrences of permutations and combinations of data values ​​at different time points and calculates their probability distribution. Then, the entropy value is calculated based on the probability distribution to quantify the time series complexity and uncertainty of each modal component; finally, the modal components are sorted according to the calculated entropy value to identify and distinguish between random components and periodic components in the signal.

5. The method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning according to claim 4, characterized in that: In step 3, the reconstruction process includes: The permutation entropy algorithm is used to decompose the IMF of each modal component decomposed by CEEMDAN in step 2. 1～K The entropy value is calculated and arranged, and the change characteristics of each component are divided and reconstructed according to the t-test algorithm. Specifically, the modal components processed by the permutation entropy algorithm are arranged according to the principle of entropy reduction. Assuming that the component starts from the i-th modal component, a t-test is performed on these i-th components. When the t-test statistic is significantly different from 0, it is used as the critical condition for the periodic component and the random component. The first i-1 modal components are random components, and the remaining modal components starting from the i-th item are periodic components. The sum of the random components in the original sequence decomposition signal is regarded as a random term, and the sum of the periodic components is regarded as a periodic term. The residual component in step 2 is used as a trend term. At this point, the reconstruction of the characteristic component is completed.

6. The method for predicting satellite short-term clock errors by integrating time series decomposition and deep learning according to claim 1, characterized in that: In step 4, the process of inputting each reconstruction item into the Transformer in a channel-independent manner includes: The trend term, periodic term and random term reconstructed in step 3 are respectively input into the deep learning model Transformer for training based on the principle of channel independence, and the model is used to predict the required first-order difference data; the input layer of the Transformer adopts a multi-head self-attention mechanism to capture the time-varying features and global dependencies of each time series, and performs feature extraction and sequence modeling on the input reconstructed terms through the encoder-decoder architecture; after the model training is completed, the data to be predicted is input into the above-mentioned trained model to obtain the required forecast clock error.

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