Satellite short-term clock error forecasting method fusing time sequence decomposition and deep learning

Abstract

The invention relates to a satellite short-term clock error forecasting method fusing time sequence decomposition and deep learning, and belongs to the technical field of satellite clock error forecasting. The method comprises the steps of performing primary difference processing on a satellite historical clock error sequence, screening out abnormal values existing in data according to a Raida criterion, performing time sequence decomposition on clock error primary difference data, firstly, decomposing the clock error primary difference sequence by adopting an adaptive noise complete set empirical mode decomposition algorithm to obtain a plurality of mode components, and performing time sequence decomposition on the plurality of mode components; a permutation entropy algorithm is introduced to sort modal components, and a t check algorithm is used to classify random items and periodic items of the components and reconstruct the components into trend items, periodic items and random items. And inputting the reconstruction item into a Transform model in a channel independent mode for training, and obtaining the clock error required to be forecasted after inverse primary difference processing and superposition of component prediction results. According to the method, the precision and the stability of satellite short-term clock correction forecasting are improved, and meanwhile, the interpretability of a forecasting result is also improved.

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 one of the key technologies in satellite navigation systems. Accurate clock error prediction directly affects the accuracy of navigation positioning. Satellite clock error is the time deviation between the satellite clock and the reference clock, which is affected by many complex factors, such as satellite clock drift, orbital environment disturbances, and system internal noise. As navigation applications continue to increase the positioning accuracy requirements, how to achieve high-precision short-term prediction of satellite clock errors has become an important research topic in navigation systems.

[0003] Traditional satellite clock error prediction methods mainly rely on physical models and statistical models, such as methods based on Kalman filtering and ARMA (autoregressive moving average model). However, these methods have certain limitations when dealing with complex time series characteristics and multiple noises, especially when dealing with long-term dependencies, nonlinear changes and non-stationary sequences. The prediction accuracy often cannot meet the needs of high-precision navigation systems. In addition, satellite clock error data often contain multiple complex components such as trends, periodicity and random fluctuations. Traditional methods are difficult to effectively distinguish and extract these time series components with different characteristics, which leads to deviations in prediction results.

[0004] In recent years, with the rapid development of artificial intelligence technology, especially the breakthrough progress of deep learning technology in the field of time series data processing, new solutions have been provided for satellite clock error prediction. Deep learning models, especially Transformer, long short-term memory network (LSTM), etc., have powerful time series modeling capabilities and can capture long-term and short-term dependencies and nonlinear characteristics in the data. However, simply relying on deep learning models to directly model the original clock error data may face problems such as data noise and interference from complex time series features, resulting in a decrease in model performance. Therefore, combining the traditional time series decomposition method with deep learning technology, using the time series decomposition method 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 retaining 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 satellite short-term clock error prediction method 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 the satellite clock error data and significantly improve the accuracy of the 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 satellite short-term clock error prediction method 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 locations to obtain the primary difference clock error data to be decomposed;

[0009] Step 2: In order to extract the fluctuation characteristics of the clock error data, the above data are decomposed using the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm to obtain multiple modal components and residual components, among which the irreversible 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 the random component, and reconstruct the periodic term and the residual term. The random component is superimposed to become the random term, and the periodic component is superimposed to become 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, 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 step 1 includes:

[0014] For the sequence x(t) after the original clock error data is differentiated once, its mean μ and standard deviation σ are calculated, and 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 group of white noise ε(t) with a sum of means equal to 0 to the clock error sequence x(t) to be decomposed in step 1. The sequence after adding the qth group of white noise is:

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

[0019] Step 2.2: 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] x(t) is the residual component after removing the first-order eigenmode component. s1 (t) can be expressed as:

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

[0023] Continue to add white noise with a mean sum of 0 to the residual component, then 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. 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 each modal component (IMF 1～K ) is standardized 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 values ​​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, and based on this, they are reconstructed into trend terms, periodic terms and random terms. 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 the i-th component. When the t-test statistic is significantly different from 0, it is used as the critical condition of 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. Then 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, and the reconstruction of the characteristic component is completed.

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

[0035] For the trend item, period item and random item reconstructed in step 3, they 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 Transformer adopts a multi-head self-attention mechanism, which can capture the time-varying characteristics and global dependencies of each time series, and perform feature extraction and sequence modeling on the input reconstructed items through the encoder-decoder architecture. Compared with the traditional RNN or LSTM network, Transformer abandons the recursive structure, can effectively capture the long-term dependencies in the sequence on a global scale, and has higher computational parallelism and stability. After the above model training is completed, short-term predictions are made for the trend item, period item and random item respectively to obtain the predicted value of the first-order difference of the clock error of each item.

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

[0037] 1. The present invention uses the time series decomposition method to effectively remove noise and irregular fluctuations in the data, significantly enhancing the stability of the model when processing complex and non-stationary data. Even when the clock error data fluctuates drastically, the model can maintain a high prediction accuracy and has strong robustness.

[0038] 2. By combining the time series decomposition method with the deep learning model, the present invention can decompose the complex satellite clock error data into different components such as trend terms, periodic terms and random terms, and model their respective time series characteristics, thereby improving the accuracy of the forecast. Compared with directly modeling the original data, the decomposed data has clearer features, making the prediction results more accurate.

[0039] 3. The present invention can flexibly deal with the multi-level features in satellite clock error data, and can not only capture long-term trend changes, but also identify periodic fluctuations and random noise. This makes the model more generalizable and can perform well in different types of time series forecasting tasks, with strong generalization.

[0040] 4. The present invention decomposes the complex raw clock error data into trends, cycles and random items with clear physical meanings through time series decomposition. The independent prediction results of each component can provide a clear and intuitive explanation, help understand the prediction process of the model, and enhance the credibility of the forecast results. At the same time, the decomposed components correspond to the actual physical process, providing a theoretical basis for the analysis and prediction of satellite clock errors.

[0041] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can 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 in conjunction with the accompanying drawings, wherein:

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

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

[0045] Figure 3 The effect diagram of signal decomposition of CEEMDAN on certain satellite clock difference data by using a satellite short-term clock difference prediction method integrating time series decomposition and deep learning 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 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 only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

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

[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 the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position 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 integrating time series decomposition and deep learning constructed by the present invention is as follows: Figure 1 By combining signal decomposition technology with a deep learning model, the present invention provides a satellite short-term clock error prediction method that integrates time series decomposition and deep learning. This method can effectively extract multi-level time series features in satellite clock error data and significantly improve the prediction accuracy and prediction stability. Specifically, it includes the following steps:

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

[0052] Specifically, for the sequence x(t) after the original clock error data is differentiated once, 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 group of white noise ε(t) with a sum of means equal to 0 to the clock error sequence x(t) to be decomposed in step 1. The sequence after adding the qth group of white noise is:

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

[0058] Step 2.2: 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] x(t) is the residual component after removing the first-order eigenmode component. s1 (t) can be expressed as:

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

[0062] Continue to add white noise with a mean sum of 0 to the residual component, then 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. 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. The random component superposition becomes the random term, the periodic component superposition is 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 to measure the complexity and irregularity of a time series. The larger the entropy value, the higher the complexity of the time series. When calculating the complexity between reconstructed subsequences, the permutation entropy algorithm introduces the idea of ​​permutation compared to algorithms such as fuzzy entropy. 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 space 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, and L=S-(M-1)t≤M!

[0074] 2. Arrange the elements in the subsequence of 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 arranged according to the above index values ​​to obtain M! symbol sequences. Then, the number of times each arrangement corresponding to the L reconstruction components appears in the M! full arrangement is counted. k , then the probability of occurrence of the reconstructed component is 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, denoted as PE max , then the normalized permutation entropy for:

[0081]

[0082] According to the definition of entropy, the larger the modal classification arrangement 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. In order 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 suitable for data with a small sample size. In the EMD decomposition, the upper and lower envelopes of the IMF component are locally symmetrical about the horizontal axis, and the upper and lower envelopes are connected by multiple signal peak points. For the random component in the IMF, due to its drastic changes and the large number of peak points, its IMF component data is basically symmetrical, and the data mean tends to 0. On the contrary, for the periodic IMF component, due to its stable changes, the small number of peak points, and the smoother envelope changes, the IMF component data is not symmetrical with the horizontal axis, so the data mean does not approach 0.

[0085] The residual component after the CEEMDAN algorithm decomposes cannot be decomposed any further. sK (t) is the trend term X(t) of the clock error sequence trend The modal components processed by the permutation entropy algorithm 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 terms and periodic terms. 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 obey the 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 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 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 by embedding and position encoding. The trained Transformer model is used to predict future time steps to obtain the first-difference prediction results for the forecast time period of each input channel (trend, cycle, random) and

[0090] Step 5: Superimpose the first-order difference prediction results, 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 term within 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 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 solution of the present invention rather than to limit it. 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 solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. A satellite short-term clock error prediction method 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 locations to obtain the primary difference clock error data to be decomposed; Step 2: In order to extract the fluctuation characteristics of the clock error data, the above data are decomposed using the adaptive noise complete set empirical mode decomposition (CEEMDAN) algorithm to obtain multiple modal components and residual components, among which the irreversible 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, and then use the t-test method to divide the periodic component and the random component, and reconstruct the periodic term and the residual term; the random component is superimposed to become the random term, and the periodic component is superimposed as 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, and perform reverse difference on the superimposed first-order difference prediction results to obtain the final clock error prediction result.

2. According to claim 1, a satellite short-term clock error prediction method integrating time series decomposition and deep learning is characterized in that: In step 1, the specific method of screening out outliers and filling in the outliers includes: For the sequence x(t) after the original clock error data is differentiated once, its mean μ and standard deviation σ are calculated, and 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. According to claim 2, a satellite short-term clock error prediction method integrating time series decomposition and deep learning is characterized in that: In step 2, the CEEMDAN algorithm decomposition process includes: Step 2.1: Add a group of white noise ε(t) with a sum of means equal to 0 to the clock error sequence x(t) to be decomposed in step 1. The sequence after adding the qth group of white noise is: x q (t)=x(t)+ε q (t),q=1,2,…,N Step 2.2: 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: x(t) is the residual component after removing the first-order eigenmode component. 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 (t) can no longer be decomposed by EMD, then all steps of CEEMDAN are completed, and the number of modal components obtained is K. The signal of x(t) after CEEMDAN decomposition 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. sK (t) is the trend term X(t) of the clock error sequence trend .

4. According to claim 3, a satellite short-term clock error prediction method integrating time series decomposition and deep learning 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 the random components and periodic components in the signal.

5. According to claim 4, a method for predicting satellite short-term clock errors integrating time series decomposition and deep learning is characterized in that: In step 3, the reconstruction process includes: The permutation entropy algorithm is used to analyze 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 the i-th component. 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 satellite short-term clock error prediction method integrating time series decomposition and deep learning according to claim 1 is 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 Transformer adopts a multi-head self-attention mechanism to capture the time-varying characteristics and global dependencies of each time series, and performs feature extraction and sequence modeling on the input reconstructed term 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 difference.

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