GPS satellite clock error forecasting method based on metabolism GM model

Abstract

The invention discloses a GPS satellite clock error forecasting method based on a metabolism GM model, and belongs to the technical field of satellite navigation and time sequence forecasting. The method comprises the following steps: firstly, acquiring and determining an initial satellite clock error data sequence, secondly, establishing a gray prediction model GM (1, 1) based on the data sequence, calculating a predicted clock error data point at the next moment, then supplementing the newly predicted data point to the tail of the current data sequence, and synchronously removing the oldest data point at the head of the sequence, so as to obtain a predicted clock error data point; and finally, on the basis of the updated data sequence, repeating the iterative process of model establishment, single-step prediction and sequence updating until all forecasting tasks are completed. According to the method, the modeling data is updated in a rolling manner, so that the model can continuously track the newest change trend of the clock error data, error accumulation is effectively inhibited, and the forecasting precision and stability of the GPS satellite clock error are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and time series prediction technology, specifically a GPS satellite clock bias prediction method based on the metabolic GM model. Background Technology

[0002] Global Navigation Satellite Systems (GNSS), such as GPS, have become an indispensable key infrastructure in modern society by providing high-precision positioning, navigation, and timing (PNT) services to users worldwide. The accuracy and stability of the system time directly depend on the performance of the onboard atomic clock. Satellite clock bias is the difference between the time of the onboard atomic clock and the GNSS standard time, and its accurate prediction value is an important prerequisite for realizing high-precision real-time navigation and positioning services.

[0003] International GNSS service organizations such as IGS release post-hoc precision clock bias products, which are highly accurate but have a delay of several hours or even days, making them unsuitable for real-time applications. Therefore, academia and industry have developed various satellite clock bias prediction models in order to predict clock bias changes over a future period using historical data.

[0004] Currently, commonly used satellite clock error prediction models include first-order polynomial models (LPM), second-order polynomial models (QPM), and grey prediction models. Polynomial models (LPM and QPM) are simple in principle and have low computational cost, but their prediction accuracy will decrease significantly as the prediction duration increases due to the fixed model order, making it difficult to fit the complex nonlinear changes of atomic clocks.

[0005] The grey prediction model GM(1,1) has been widely used in satellite clock error prediction due to its advantages such as requiring less modeling data, not being subject to strict requirements on data distribution, and having good short-to-medium-term prediction performance. However, the traditional GM(1,1) model has inherent defects: once the model is established, its parameters are determined by a fixed set of historical data, and all subsequent prediction points are extrapolated based on this fixed set of old information. As the prediction time progresses, new random disturbance factors will continuously enter the system, and the actual trend of clock error data may change locally. The prediction error of the traditional model will continue to accumulate and gradually increase, eventually resulting in a significant reduction in prediction accuracy and reliability.

[0006] Therefore, how to overcome the error accumulation problem caused by the static nature of data in the traditional GM(1,1) model in satellite clock error prediction, and develop a method that can dynamically adapt to data change trends and improve the accuracy and stability of medium and long-term forecasts, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] To address the problems existing in the background technology, this invention proposes a GPS satellite clock bias prediction method based on the metabolic GM model, comprising the following steps: S1. Obtain and determine the initial satellite clock bias data sequence of GPS satellites; S2. Based on the initial satellite clock bias data sequence, establish a grey prediction model GM(1,1); S3. Calculate the predicted clock difference data points for the next time step using the grey prediction model GM(1,1); S4. A new satellite clock bias data sequence is obtained through the sequence metabolism update method, and it is used as the initial satellite clock bias data sequence for the next prediction. S5. Repeat steps S2 to S4 until the clock difference data prediction for the predetermined forecast duration is completed, and the final GPS satellite clock difference prediction sequence is obtained.

[0008] Specifically, step S1 involves selecting a complete, continuous set of data with errors lower than the expected value from the original satellite clock bias data sequence as the initial satellite clock bias data sequence. The initial satellite clock bias data sequence Includes several historical clock difference data points arranged in chronological order: .

[0009] Specifically, step S2 includes: S21. Perform a single accumulation generation process on the initial satellite clock bias data sequence to obtain a single accumulation sequence. The formula for calculating each accumulated data point is as follows: ; in , These are historical clock bias data points in the initial satellite clock bias data sequence. n The number of historical clock difference data points; S22, Based on a single-accumulation sequence Calculate the next nearest mean generation sequence , No. k The nearest data points to the mean The calculation formula is: ; in ; S23. Generating sequences based on nearest neighbor means Construct the first-order linear differential equation of the GM(1,1) model, i.e., the whitening equation: ; in, a The evolution coefficient of the model,b This is the gray action quantity; This can be transformed into the following form by integration: .

[0010] Specifically, step S3 includes: S31. The parameter vector of the grey prediction model GM(1,1) is calculated using the least squares method. Make an estimate: ; in, ; S32, Get initial value The solution to the whitening equation is: ; S33. Obtain the predicted clock difference data point for the next time step by cumulative subtraction and restoration: ; in .

[0011] Specifically, the sequence metabolism update method in step S4 is as follows: the predicted clock bias data points obtained in step S3 are added to the end of the currently used satellite clock bias data sequence, and at the same time, the oldest historical clock bias data point is removed from the beginning of the sequence, thereby generating a new satellite clock bias data sequence.

[0012] In summary, the beneficial technical effects of the present invention are as follows: 1. Strong dynamic adaptability and tracking ability: Through a metabolic mechanism, this invention adds the latest forecast value to the modeling sequence after each forecast step is completed, while removing the oldest historical data points to form a new modeling sequence with equal dimensions. This mechanism enables the grey model to be reconstructed based on the sequence containing the latest information in each iteration, thereby dynamically capturing and tracking the latest trends and local fluctuations of satellite clock bias data over time, overcoming the shortcomings of traditional models that are insensitive to new information due to their reliance on fixed historical data.

[0013] 2. Effective suppression of error accumulation, significantly improving forecast accuracy and stability: Since the model can continuously self-correct and adjust to adapt to the latest data, it effectively avoids systematic bias caused by long-term reliance on outdated data. This significantly suppresses the cumulative effect of forecast errors. Compared with the traditional GM(1,1) model, the forecast error of this invention grows more gradually, and can maintain higher reliability and stability when making medium- and long-term forecasts. Attached Figure Description

[0014] Figure 1This is a flowchart of the method of the present invention; Figure 2 This is a clock bias variation diagram of GPS 06 satellite in an embodiment of the present invention; Figure 3 This is a clock bias variation diagram of GPS16 satellite in an embodiment of the present invention; Figure 4 This is a clock bias variation diagram of GPS23 satellite in an embodiment of the present invention; Figure 5 This is a clock bias variation diagram of GPS 24 satellite in an embodiment of the present invention; Figure 6 This is a clock bias variation diagram of GPS 25 satellite in an embodiment of the present invention; Figure 7 This is a clock bias variation diagram of GPS 30 satellite in an embodiment of the present invention; Figure 8 This is a graph showing the 6-hour satellite clock error prediction change of GPS06 satellite in an embodiment of the present invention. Figure 9 This is a graph showing the 6-hour satellite clock error prediction variation of GPS16 satellite in an embodiment of the present invention. Figure 10 This is a graph showing the 6-hour satellite clock error prediction variation of GPS23 satellite in an embodiment of the present invention. Figure 11 This is a graph showing the 6-hour satellite clock error prediction variation of GPS24 satellite in an embodiment of the present invention. Figure 12 This is a graph showing the 6-hour satellite clock error prediction variation of GPS25 satellite in an embodiment of the present invention. Figure 13 This is a graph showing the 6-hour satellite clock error prediction variation of GPS30 satellite in an embodiment of the present invention. Figure 14 This is a graph showing the changes in the 6-hour average forecast accuracy and stability of each model in the embodiments of this invention. Detailed Implementation

[0015] To make the technical means, creative features, objectives and effects of this invention clearer and easier to understand, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0016] Example This invention uses post-hoc precise satellite clock bias data for day 1 of GPS week 2377, released by the GNSS Analysis Center of Wuhan University, as experimental data. The sampling interval is set to 30 seconds. During this time period, there are 32 satellites in orbit. Clock bias data from six satellites—GPS06, GPS16, GPS23, GPS24, GPS25, and GPS30—were randomly selected for prediction experiments. The specific information is shown in the table below: Table 1. Relevant information about the selected satellites

[0017] The changes in the precise satellite clock bias time series of these six satellites in the first 6 hours of week 2377 are as follows: Figures 2 to 7 As shown, the clock difference time series of GPS06 and GPS25 satellites show a monotonically decreasing trend, while the clock difference time series of GPS16, GPS23, GPS24, and GPS30 satellites show a monotonically increasing trend. These data are highly representative and can verify the method proposed in this invention.

[0018] This invention employs the following method for these six satellites: Figure 1 The GPS satellite clock bias prediction method based on the metabolic GM model shown includes the following steps: S1. Select a complete, continuous set of data with errors lower than expected from the original satellite clock bias data sequence as the initial satellite clock bias data sequence. Initial satellite clock bias data sequence Includes several historical clock difference data points arranged in chronological order: .

[0019] S2. Based on the initial satellite clock bias data sequence, establish a grey prediction model GM(1,1), which specifically includes: S21. Perform a single accumulation generation process on the initial satellite clock bias data sequence to obtain a single accumulation sequence. The formula for calculating each accumulated data point is as follows: ; in , These are historical clock bias data points in the initial satellite clock bias data sequence. n The number of historical clock difference data points; S22, Based on a single-accumulation sequence Calculate the next nearest mean generation sequence , No. k The nearest data points to the mean The calculation formula is: ; in ; S23. Generating sequences based on nearest neighbor means Construct the first-order linear differential equation of the GM(1,1) model, i.e., the whitening equation: ; in, a The evolution coefficient of the model, bThis is the gray action quantity; This can be transformed into the following form by integration: .

[0020] S3. Calculate the predicted clock difference data points for the next time step using the grey prediction model GM(1,1), specifically including: S31. The parameter vector of the grey prediction model GM(1,1) is calculated using the least squares method. Make an estimate: ; in, ; S32, Get initial value The solution to the whitening equation is: ; S33. Obtain the predicted clock difference data point for the next time step by cumulative subtraction and restoration: ; in .

[0021] S4. A new satellite clock bias data sequence is obtained through the sequence metabolism update method, which is used as the initial satellite clock bias data sequence for the next prediction. The sequence metabolism update method is as follows: the predicted clock bias data points obtained in step S3 are added to the end of the currently used satellite clock bias data sequence, and at the same time, the oldest historical clock bias data point is removed from the beginning of the sequence, thereby generating a new satellite clock bias data sequence.

[0022] S5. Repeat steps S2 to S4 until the clock difference data prediction for the predetermined forecast duration is completed, and the final GPS satellite clock difference prediction sequence is obtained.

[0023] Figures 8 to 13 The figure shows a comparison of the forecast error changes for the next 6 hours using satellite clock bias data from the first day of GPS week 2377. This was achieved by establishing LPM, QPM, GM(1,1) models, and the metabolic grey model of this invention. error The root mean square error (RMS) and range were used as statistical measures to analyze and compare the forecast performance of the model. The average forecast accuracy and average forecast stability of the GPS satellite forecast model were evaluated by calculating the average RMS and average range.

[0024] The table below shows the statistical results of satellite clock error prediction for each model: Table 2. Statistical results of satellite clock error prediction (unit: ns)

[0025] The table below shows the average forecast accuracy, stability, and improvement rate of each model over 6 hours: Table 3. Average forecast accuracy, stability, and improvement rate of each model over 6 hours.

[0026] As shown in the table above and appendix Figure 14 As shown, in the 6-hour short-term forecast, the average forecast accuracy of the first-order polynomial model is 0.34 ns, and the average forecast stability is 0.55 ns; the average forecast accuracy of the second-order polynomial model is 1.03 ns, and the average forecast stability is 1.96 ns; the average forecast accuracy of the grey model is 0.28 ns, and the average forecast stability is 0.45 ns; the average forecast accuracy of the metabolic grey model is 0.17 ns, and the average forecast stability is 0.32 ns. The improvement rates of the average forecast accuracy and average forecast stability of the metabolic grey model provided by this invention compared with the first-order polynomial model, the second-order polynomial model, and the grey model are 50.00%, 83.50%, and 39.29%, and 41.82%, 83.67%, and 28.89%, respectively.

[0027] Therefore, this invention provides a GPS satellite clock bias prediction method based on the metabolic GM model. By constructing a closed-loop iterative mechanism of "single-step prediction-sequence update", the new predicted value is added to the end of the data sequence after each prediction step, and the oldest data point is removed simultaneously. This achieves continuous rolling updates of modeling data to the latest information. This invention solves the pain point of traditional gray models, which cannot adapt to new trends due to their reliance on fixed historical data, resulting in the continuous accumulation of prediction errors. It significantly improves the model's ability to track dynamic changes in clock bias data and the accuracy of prediction, effectively suppresses error divergence in long-term predictions, and ultimately provides a high-precision and high-stability real-time satellite clock bias prediction solution for GPS systems, ensuring the reliability of high-precision PNT services.

[0028] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing 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 GPS satellite clock bias prediction method based on a metabolic GM model, characterized in that, Includes the following steps: S1. Obtain and determine the initial satellite clock bias data sequence of GPS satellites; S2. Based on the initial satellite clock bias data sequence, establish a grey prediction model GM(1,1); S3. Calculate the predicted clock difference data points for the next time step using the grey prediction model GM(1,1); S4. A new satellite clock bias data sequence is obtained through the sequence metabolism update method, and it is used as the initial satellite clock bias data sequence for the next prediction. S5. Repeat steps S2 to S4 until the clock difference data prediction for the predetermined forecast duration is completed, and the final GPS satellite clock difference prediction sequence is obtained.

2. The GPS satellite clock bias prediction method based on the metabolic GM model according to claim 1, characterized in that, Step S1 specifically involves selecting a set of complete, continuous data with errors lower than the expected value from the original satellite clock bias data sequence as the initial satellite clock bias data sequence. The initial satellite clock bias data sequence Includes several historical clock difference data points arranged in chronological order: .

3. The GPS satellite clock bias prediction method based on the metabolic GM model according to claim 1, characterized in that, Step S2 specifically includes: S21. Perform a single accumulation generation process on the initial satellite clock bias data sequence to obtain a single accumulation sequence. The formula for calculating each accumulated data point is as follows: ； in , These are historical clock bias data points in the initial satellite clock bias data sequence. n The number of historical clock difference data points; S22, Based on a single-accumulation sequence Calculate the next nearest mean generation sequence , No. k The nearest data points to the mean The calculation formula is: ； in ; S23. Generating sequences based on nearest neighbor means Construct the first-order linear differential equation of the GM(1,1) model, i.e., the whitening equation: ； in, a The evolution coefficient of the model, b This is the gray action quantity; This can be transformed into the following form by integration: 。 4. The GPS satellite clock bias prediction method based on the metabolic GM model according to claim 3, characterized in that, Step S3 specifically includes: S31. The parameter vector of the grey prediction model GM(1,1) is calculated using the least squares method. Make an estimate: ； in, ； S32, Get initial value The solution to the whitening equation is: ； S33. Obtain the predicted clock difference data point for the next time step by cumulative subtraction and restoration: ； in .

5. The GPS satellite clock bias prediction method based on the metabolic GM model according to claim 2, characterized in that, The sequence metabolism update method in step S4 is as follows: the predicted clock bias data points obtained in step S3 are added to the end of the currently used satellite clock bias data sequence, and at the same time, the oldest historical clock bias data point is removed from the beginning of the sequence, thereby generating a new satellite clock bias data sequence.

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