A timing data prediction optimization method and system that introduces dynamic error

Abstract

The application belongs to the technical field of time series data prediction, and particularly relates to a time series data prediction optimization method and system introducing dynamic error. The method comprises the following steps: preprocessing time series data to be processed; inputting the preprocessed data into a prediction model established and trained in advance to obtain preliminary prediction data; comparing the preliminary prediction data with the preprocessed data to obtain a preliminary error; based on the preliminary error, combining historical data of different time lengths, and according to a time decay function, obtaining long-term error and recent error, and through weighted combination, obtaining a corrected prediction value to realize real-time correction of dynamic error. The application firstly applies the dynamic error correction method to time series prediction of satellite telemetry data, realizes real-time correction of prediction error, and significantly improves prediction accuracy.

Description

Technical Field

[0001] This invention belongs to the field of time series data prediction technology, and particularly relates to a time series data prediction optimization method and system that introduces dynamic errors. Background Technology

[0002] Over the past few decades, time series forecasting methods have been widely applied in fields such as anomaly detection, event prediction, power load forecasting, stock market analysis, traffic flow forecasting, and health monitoring. To improve the predictive performance of complex time series data in practical engineering, researchers have continuously innovated and optimized various forecasting methods. However, the inherent complexity of time series data stems from the nonlinearity and non-stationarity of its generation process, as well as noise, multi-scale characteristics, high dimensionality, missing values, and finite observation length. The interaction of these factors makes time series data difficult to model and predict, thus posing a significant challenge to existing analytical methods.

[0003] Traditional statistical models and machine learning algorithms have many limitations in time series forecasting, such as limited ability to extract nonlinear features, insufficient modeling of long-term dependencies, high sensitivity to data noise, and poor flexibility and applicability when handling high-dimensional data. These shortcomings lead to increased prediction errors, reduced accuracy, and impact on the reliability of the models in practical applications. With the rapid development of deep learning technology, its multi-layered neural network structure enables automatic extraction of complex features, significantly improving accuracy and robustness in time series forecasting tasks. In particular, deep learning models such as Recurrent Neural Networks (RNNs) and their variants (e.g., Long Short-Term Memory Networks (LSTM), Graph Neural Networks (GNNs), Generative Adversarial Networks (GANs), and Transformers have demonstrated significant advantages in handling nonlinear relationships and long-term dependencies in time series data. However, deep learning models also suffer from drawbacks such as high computational costs, complexity in model training and tuning, reliance on large-scale data, and poor model interpretability due to their "black box" nature. Current research on time series prediction is mainly developing in two directions. One is to improve and optimize the structure of deep learning models, aiming to improve the model's fit to training data, enhance its expressive power, and promote its adaptive ability by optimizing data processing, model building process, and parameter adjustment strategies.

[0004] Systematic errors often stem from factors such as data bias, the ideality of model assumptions, and the complexity of the external environment. Therefore, another research direction is to improve prediction results from the perspective of error correction. This approach focuses on correcting the model during the prediction process. By introducing residual networks or residual-based optimization algorithms, errors in prediction can be captured and corrected more effectively, thereby improving model accuracy. However, solutions based on error correction tend to rely on specific datasets and application scenarios, which limits their generalization ability under different conditions, leading to unstable performance in new or changing environments. Furthermore, in practical engineering applications driven by both knowledge and data, the impact of historical error information on future predictions varies with the dynamic changes of complex systems. This can cause error correction-based strategies to fail to capture and update error information that changes over time, thus limiting the comprehensiveness and accuracy of the correction effect. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and to propose a time series data prediction optimization method and system that introduces dynamic errors.

[0006] To achieve the above objectives, this invention proposes a time-series data prediction optimization method that introduces dynamic errors, comprising:

[0007] Step 1) Preprocess the time series data to be processed;

[0008] Step 2) Input the preprocessed data into the pre-established and trained prediction model to obtain preliminary prediction data;

[0009] Step 3) Compare the preliminary prediction data with the preprocessed data to obtain the preliminary error;

[0010] Step 4) Based on the initial error, combined with historical data of different time lengths, the long-term error and the recent error are obtained according to the time decay function. By weighted combination, the corrected prediction value is obtained, realizing real-time correction of dynamic error.

[0011] Preferably, step 1) includes:

[0012] Data cleaning includes removing outliers, filling in missing values, and denoising.

[0013] Feature selection is performed on the cleaned data to extract key features.

[0014] Preferably, the prediction model in step 2) is a PatchTST, TimesNet, or iTransformer model.

[0015] Preferably, step 3) includes:

[0016] The actual value y of the preprocessed time series t Compared with the initial predicted value y obtained by the prediction model t The comparison yields a sequence e of differences. t This is the initial error.

[0017] Preferably, the time decay function f(h) in step 4) is exponential, fractional, or Gaussian.

[0018] For exponential forms, the following equation holds:

[0019] f(h)=α -h

[0020] Wherein, the base α is taken as the natural base e, 2 or 3; h represents the duration from the current time t;

[0021] For fractional forms, the following equation must be satisfied:

[0022] f(h) = 1 / 1 + βh

[0023] Where β represents the time decay factor, which determines the decay rate of f(h);

[0024] For Gaussian types, the following equation holds:

[0025]

[0026] Where N is the size of the sliding window and γ is a constant value.

[0027] Preferably, the predicted value corrected in step 4) Satisfy the following formula:

[0028]

[0029] in, Let w be the initial predicted value of the target variable y at time t. i Let represent the weighting factors for long-term error and short-term error, with the sum of the two weighting factors being 1. Here, i = 1 corresponds to the p-duration before time t, which is the long duration m; i = 2 corresponds to the p-duration before time t, which is the short duration n; and y... t-h and t represents the actual value and the preliminary predicted value of the target variable y at time t, respectively. maxerr is the maximum value among the absolute differences between the actual value and the preliminary predicted value at all time points within the time period h.

[0030] Preferred weighting factor w i Satisfy the following formula:

[0031] w i = (1 / n)·e-λi / n n = 2, i = 1, 2 or w2 = 1 - w1, w1 ∈ [0.0, 1.0]

[0032] Where λ is the smoothing factor.

[0033] On the other hand, the present invention also provides a time-series data prediction optimization system that introduces dynamic errors, comprising:

[0034] The preprocessing module is used to preprocess the time series data to be processed;

[0035] The preliminary prediction module is used to input the pre-processed data into the pre-established and trained prediction model to obtain preliminary prediction data.

[0036] The preliminary error output module is used to compare the preliminary prediction data with the preprocessed data to obtain the preliminary error;

[0037] The dynamic correction module is used to obtain long-term error and short-term error based on the initial error and historical data of different time lengths, according to the time decay function. By weighted combination, the corrected prediction value is obtained, realizing real-time dynamic error correction.

[0038] Compared with the prior art, the advantages of the present invention are:

[0039] 1. This invention proposes a prediction optimization method that incorporates dynamic errors. This method adjusts the baseline prediction results in real time and dynamically adjusts the weights of long-term and recent errors on future errors based on multiple time decay functions, making the correction process more flexible and accurate. Correction results show that this method significantly improves prediction accuracy.

[0040] 2. This study is the first to apply a dynamic error correction method to time series forecasting of satellite telemetry data, achieving real-time correction of prediction errors and validating the model's robustness. Combined with deep learning techniques, the method was validated on multiple public datasets, meeting the prediction needs of complex and variable data, and demonstrating its robustness and effectiveness in different scenarios. Attached Figure Description

[0041] Figure 1 Here are some examples of the original data images;

[0042] Figure 2 This is the calculation process for the initial error;

[0043] Figure 3 This is a flowchart of the time series data prediction optimization method that introduces dynamic errors according to the present invention;

[0044] Figure 4 is a visual representation of the corrected values, preliminary predicted values, and true values ​​for the Electricity dataset, Exchange dataset, Weather dataset, and ASOS dataset; where Figure 4(a) shows the baseline prediction model using TimesNet, Figure 4(b) shows the baseline prediction model using PatchTST, and Figure 4(c) shows the baseline prediction model using iTransformer.

[0045] Figure 5 is a scatter plot of the predicted and corrected IA index values ​​for the Electricity, Exchange, Weather, and ASOS datasets; where Figure 5(a) shows the baseline prediction model using TimesNet, Figure 5(b) shows the baseline prediction model using PatchTST, and Figure 5(c) shows the baseline prediction model using iTransformer.

[0046] Figure 6 is a bar chart of all index values ​​before and after DEM optimization; where Figure 6(a) is the MAE index, Figure 6(b) is the MSE index, Figure 6(c) is the MAPE index, Figure 6(d) is the RMSE index, and Figure 6(e) is the SSE index.

[0047] Figure 7 is a radar chart of all index values ​​for all datasets under different optimization strategies. Figure 7(a) is the Electricity dataset, Figure 7(b) is the Exchange dataset, Figure 7(c) is the Weather dataset, and Figure 7(d) is the ASOS dataset. Detailed Implementation

[0048] This invention aims to provide a time series data prediction optimization method. By introducing a dynamic error correction mechanism, errors in the prediction model are corrected in real time, thereby improving the accuracy and generalization performance of time series prediction to meet the needs of aerospace, finance and transportation fields for high-precision and high-stability prediction.

[0049] include:

[0050] Step 1) Preprocess the time series data to be processed;

[0051] Step 2) Input the preprocessed data into the pre-established and trained prediction model to obtain preliminary prediction data;

[0052] Step 3) Compare the preliminary prediction data with the preprocessed data to obtain the preliminary error;

[0053] Step 4) Based on the initial error, combined with historical data of different time lengths, the long-term error and the recent error are obtained according to the time decay function. By weighted combination, the corrected prediction value is obtained, realizing real-time correction of dynamic error.

[0054] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0055] Example 1

[0056] Embodiment 1 of the present invention proposes a time series data prediction optimization method that introduces dynamic errors, comprising:

[0057] 1. Data Preprocessing

[0058] The four datasets selected for this invention are publicly available time-series datasets from different fields: Electricity, Exchange, and Weather, as well as raw telemetry data collected from a Chinese space science satellite. To improve the quality of the raw satellite telemetry data, data cleaning was performed, including removing outliers, filling in missing values, and denoising. Secondly, feature selection was performed on the processed telemetry data to extract key features, which were then used as input for the subsequent prediction model. Some of the raw data are shown below. Figure 1 As shown.

[0059] 2. Benchmark Prediction Model

[0060] To evaluate the performance of our proposed DEM optimization method compared to current benchmark models for time series forecasting, including PatchTST, TimesNet, and iTransformer.

[0061] 3. Dynamic error correction mechanism

[0062] Typically, error sequences are not simply white noise sequences, thus they are considered to contain valuable information that can improve the overall system's predictions. Since the error magnitude and trend at each prediction point are closely related to the error magnitudes and trends at previous prediction points, we can capture and fuse historical information from the error sequence to further investigate how to correct these errors and improve the prediction performance of future characteristic variable states. Furthermore, considering the combined impact of long-term and recent errors on future errors, we can address the issues of dynamically adjusting characteristic variable states and updating predicted values, ultimately improving the overall system's prediction accuracy.

[0063] In-depth analysis of long-term errors allows for better capture of low-frequency information in the data (such as long-term trends and cyclical patterns) and potential systematic biases in the model, thereby maintaining a stable error level and improving the model's long-term predictive ability. In-depth analysis of short-term errors allows for better capture of high-frequency information in the data (such as short-term fluctuations and anomalies), thereby reducing volatility errors and improving the model's immediate predictive ability and accuracy.

[0064] By dynamically fusing the differential impacts of long-term and recent errors on future errors, and considering the combined estimation effects of local and global factors on the outcome state, a DEM method is proposed. This method applies time-dependent weighting to the two error components, dynamically adjusts the system error value, and promptly corrects and updates the target's state prediction value to obtain the final prediction result. The DEM formula is calculated as follows:

[0065]

[0066] in and These are the initial and revised predicted values ​​of the target variable y at time t, respectively. The revision of the prediction result at time t is made using the prediction error values ​​from the preceding p periods. i 'Describes the error e' i Amplitude and its relative trend, y t-h and These represent the actual value and preliminary predicted value of y at time th, respectively. i Let represent the weighting factors for long-term and recent errors, with the sum of the two weighting factors being 1. Here, i = 1 corresponds to a duration p before time t, which is the long duration m; i = 2 corresponds to a duration p before time t, which is the short duration n; and maxerr is the maximum absolute value of the difference between the actual value and the preliminary predicted value across all time points within a duration h. f(h) represents the time decay function, meaning that the influence of historical information errors on the predicted value at time t gradually weakens as time increases. The method in this paper includes corrections for two parts of the error sequence: long-term error with an error information step size of m and recent error with an error information step size of n. i This represents the weighting factor for each of the two error components. Therefore, the proposed error correction method can dynamically utilize historical error sequence information to achieve real-time error correction of the predicted sequence. This optimization strategy effectively solves the problems of time lag, error uniformity, and poor adaptability inherent in traditional methods.

[0067] (1) Initial error sequence e t The calculation of is a sequence formed by the difference between the actual values ​​of the time series and the preliminary predicted values ​​obtained from the benchmark model, such as... Figure 2 As shown.

[0068]

[0069] (2) Dynamic error sequence e t-h Calculation of long-term error e t-m This refers to the difference between predicted and actual values ​​over a long period, reflecting the accumulation of prediction errors by the model over a long time span. Similarly, recent error e t-nThis reflects the model's immediate prediction error over a short time span. As time progresses, the impact of long-term error information on the predicted value at time t gradually weakens. For example... Figure 3 As shown.

[0070]

[0071] (3) Time decay function f(h): exponential, Gaussian, and fractional types. Details are as follows:

[0072] f(h)=α -h

[0073] In the exponential form f(h), α can take the natural base e, 2, 3, etc. In this experiment, α = e, 2 is selected.

[0074] f(h) = 1 / 1 + βh

[0075] In the fractional form f(h), β represents the time decay factor, which determines the decay rate of f(h). In this experiment, β = 0.5, 1, 2 is selected.

[0076]

[0077] In the Gaussian type f(h), N is the sliding window size and γ is a constant value. In this experiment, γ = 1, 2, 3 is selected.

[0078] (4) Weighting factor w i Based on uniform exponential and linear relationships, w i This involves a selective weighting of the impact of long-term and short-term errors on the predicted points. One of the following weighting methods can be used.

[0079]

[0080] Where λ is the smoothing factor, and in this experiment, the exponential weighting factor with λ = 1 and 2 is selected.

[0081] The proposed DEM optimization method is a technique that optimizes the performance of prediction models by fully mining the potentially valuable information contained in the error sequence. This mechanism not only captures instantaneous fluctuations in errors but also identifies systematic biases and trend changes over time, thereby dynamically adjusting model parameters. Specifically, this optimization method gradually corrects prediction errors by fusing local and global estimation results. This correction process utilizes the timely response of local recent information and the robustness of global long-term information to ensure a gradual reduction in prediction errors and to adjust and optimize future predictions in real time, thus significantly improving prediction accuracy and stability. Furthermore, the method of introducing dynamic error optimization into the prediction model can adapt to changes in the model's internal structure, giving the model strong flexibility and anti-interference capabilities, especially when dealing with complex nonlinear and non-stationary time series data.

[0082] Example 2

[0083] Embodiment 2 of the present invention provides a time-series data prediction optimization system that introduces dynamic errors, implemented based on the method of Embodiment 1, including:

[0084] The preprocessing module is used to preprocess the time series data to be processed;

[0085] The preliminary prediction module is used to input the pre-processed data into the pre-established and trained prediction model to obtain preliminary prediction data.

[0086] The preliminary error output module is used to compare the preliminary prediction data with the preprocessed data to obtain the preliminary error;

[0087] The dynamic correction module is used to obtain long-term error and short-term error based on the initial error and historical data of different time lengths, according to the time decay function. By weighted combination, the corrected prediction value is obtained, realizing real-time dynamic error correction.

[0088] Evaluation indicators:

[0089] This invention evaluates results from two aspects. The validity of the results is assessed using evaluation metrics such as MAE, MSE, MAPE, RMSE, and SSE. Furthermore, generalization ability is a crucial indicator of performance, and it is reflected by the consistency index (IA).

[0090] To verify the accuracy, stability, and generalization ability of the proposed DEM optimization method, comparative experiments were conducted on four time series datasets, three baseline models, and six widely used evaluation metrics. Figure 4 shows the original, predicted, and corrected values ​​of the four datasets (Electricity, Exchange, Weather, and ASOS) based on the three baseline prediction models. Figure 4(a) shows the baseline prediction model using TimesNet, Figure 4(b) shows the baseline prediction model using PatchTST, and Figure 4(c) shows the baseline prediction model using iTransformer. Figure 5 presents the IA evaluation results of the predicted and corrected values ​​of the three baseline models on the four datasets. Figure 5(a) shows the baseline prediction model using TimesNet, Figure 5(b) shows the baseline prediction model using PatchTST, and Figure 5(c) shows the baseline prediction model using iTransformer. Figures 6 and 7 show the numerical changes of MAE, MSE, MAPE, RMSE, and SSE on the four datasets before and after optimization using the DEM method. Figure 6(a) shows the MAE indicator, Figure 6(b) shows the MSE indicator, Figure 6(c) shows the MAPE indicator, Figure 6(d) shows the RMSE indicator, and Figure 6(e) shows the SSE indicator; Figure 7(a) shows the Electricity dataset, Figure 7(b) shows the Exchange dataset, Figure 7(c) shows the Weather dataset, and Figure 7(d) shows the ASOS dataset.

[0091] (1) Figure 4 visually illustrates the observed values ​​(blue line), the preliminary predicted values ​​(black line), and the corrected values ​​after DEM optimization (red line). Compared with the baseline model, the DEM-optimized predicted curve shows a significantly improved fit to the actual observed curve. This visual improvement intuitively demonstrates the optimization effect of the DEM method, indicating a significant improvement in prediction accuracy and showcasing the superior performance of this method in optimizing the baseline model.

[0092] (2) Taking one of the graphs in Figure 5(a) as an example, the meaning is: a scatter plot (blue) of the initial predicted value and the true value of the Electricity dataset under the TimesNet baseline prediction model, and a scatter plot (red) of the corrected value and the true value after DEM correction under this baseline prediction model. PreIA: the original IA value under the baseline prediction; ModIA: the IA value after correction under this baseline prediction model.

[0093] As can be observed from Figure 5, the IA values ​​after DEM optimization are generally improved compared to the initial predicted values. For example, the IA values ​​of the Electricity dataset improved by 1.48%, 3.85%, and 0.54%, respectively; while the IA values ​​of the Exchange dataset improved by 22.68%, 2.95%, and 2.89%, respectively. These improvements not only demonstrate the advantages of the DEM method in capturing data patterns and trends but also prove its stability and generalization ability across different tasks.

[0094] (3) Figures 6(a)-6(e) It includes 5 three-dimensional bar charts. Taking Figure 6(a) as an example, it means: the MAE value of each dataset (Electricity, Exchange, Weather and ASOS) under 3 benchmark prediction models (TimesNet, PatchTST and iTransformer) and the DEM optimization method combined with 3 benchmark models.

[0095] Tn stands for TimesNet, Pa stands for PatchTST, and iT stands for iTransformer.

[0096] Tn-Pre: Preliminary value based on the TimesNet baseline prediction model;

[0097] Tn-Mod: The corrected value after combining the TimesNet benchmark prediction model with the DEM method.

[0098] Same as Pa-Pre, iT-Pre, Pa-Mod, and iT-Mod.

[0099] In Figures 6 and 7, the height of the bar charts after DEM optimization shows a comprehensive decrease to varying degrees, while the closed regions in the radar charts become smaller and more concentrated. This indicates that all indicators have improved, and the overall optimization effect is significantly enhanced. This result not only verifies the effectiveness of the DEM method in reducing prediction errors and improving model accuracy, but also demonstrates its robustness and wide applicability across various datasets.

[0100] This invention proposes a time-series data prediction optimization method incorporating Dynamic Error Modification (DEM). This method deeply analyzes the effective information in the error sequence, accurately identifies and captures the dynamic features in the time-series data, thereby optimizing the model's performance across different time series. This method combines historical error information of different lengths: long-term errors capture low-frequency information to maintain error stability, while recent errors capture high-frequency information to reduce fluctuations. By adjusting the time decay function and related parameters, real-time dynamic optimization of the prediction model is achieved. Experimental results show that with a long-term error step size of 24 and a recent error step size of 8, and a distributed and parametric time decay function, the overall prediction accuracy is improved by approximately 12% in different scenarios. This optimization strategy effectively overcomes the problems of time lag, error uniformity, and poor adaptability in traditional methods.

[0101] The DEM optimization method proposed in this invention significantly improves the accuracy and stability of time series forecasting and effectively reduces systematic errors. By enhancing the generalization performance of the prediction model, it becomes applicable to various application scenarios and datasets. This technological breakthrough provides high-precision and high-stability forecasting support for fields such as aerospace, finance, and transportation, promoting the development and application of related technologies.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting and optimizing satellite telemetry time-series data that introduces dynamic errors, comprising: Step 1) Preprocess the collected raw satellite telemetry data; The original satellite telemetry data is time-series data; Step 2) Input the preprocessed data into the pre-established and trained prediction model to obtain preliminary prediction data; Step 3) Compare the preliminary prediction data with the preprocessed data to obtain the preliminary error; Step 4) Based on the initial error, combined with historical data of different time lengths, the long-term error and the recent error are obtained according to the time decay function. By weighted combination, the corrected prediction value is obtained, realizing the real-time correction of the dynamic error of satellite telemetry data.

2. The satellite telemetry time series data prediction and optimization method introducing dynamic errors according to claim 1, characterized in that, Step 1) includes: Data cleaning includes removing outliers, filling in missing values, and denoising. Feature selection is performed on the cleaned data to extract key features.

3. The satellite telemetry time series data prediction and optimization method introducing dynamic errors according to claim 1, characterized in that, The prediction model in step 2) is PatchTST, TimesNet, or iTransformer.

4. The satellite telemetry time series data prediction and optimization method introducing dynamic errors according to claim 1, characterized in that, Step 3) includes: The actual value y of the preprocessed time series t Compared with the preliminary predicted values ​​obtained by the prediction model The comparison yields a sequence e of differences. t This is the initial error.

5. The satellite telemetry time series data prediction and optimization method introducing dynamic errors according to claim 1, characterized in that, The time decay function f(h) in step 4) is exponential, fractional, or Gaussian. For exponential forms, the following equation holds: f(h)=a -h Wherein, the base α is taken as the natural base e, 2 or 3; h represents the duration from the current time t; For fractional forms, the following equation must be satisfied: f(h) = 1 / 1 + βh Where β represents the time decay factor, which determines the decay rate of f(h); For Gaussian types, the following equation holds: Where N is the size of the sliding window and γ is a constant value.

6. The satellite telemetry time series data prediction and optimization method introducing dynamic errors according to claim 5, characterized in that, The corrected predicted value in step 4) Satisfy the following formula: in, Let w be the initial predicted value of the target variable y at time t. i Let represent the weighting factors for long-term error and short-term error, with the sum of the two weighting factors being 1. Here, i = 1 corresponds to the p-duration before time t, which is the long duration m; i = 2 corresponds to the p-duration before time t, which is the short duration n; and y... t-h and t represents the actual value and the preliminary predicted value of the target variable y at time t, respectively. maxerr is the maximum value among the absolute differences between the actual value and the preliminary predicted value at all time points within the time period h.

7. The satellite telemetry time series data prediction and optimization method introducing dynamic errors according to claim 6, characterized in that, Weighting factor w i Satisfy the following formula: w i = (1 / n)·e -λi / n n = 2, i = 1, 2 or w2 = 1 - w1, w1 ∈ [0.0, 1.0] Where λ is the smoothing factor.

8. A satellite telemetry time series data prediction and optimization system that introduces dynamic errors, characterized in that, include: The preprocessing module is used to preprocess the acquired raw satellite telemetry data; The original satellite telemetry data is time-series data; The preliminary prediction module is used to input the pre-processed data into the pre-established and trained prediction model to obtain preliminary prediction data. The preliminary error output module is used to compare the preliminary prediction data with the preprocessed data to obtain the preliminary error; and The dynamic correction module is used to obtain long-term and short-term errors based on the initial error and historical data of different time lengths, according to the time decay function. By weighted combination, the corrected prediction value is obtained, realizing the real-time correction of dynamic errors in satellite telemetry data.

Images