A satellite real-time clock difference prediction method based on VMD-LSTM model

Abstract

The present invention relates to a satellite real-time clock difference prediction method based on a VMD-LSTM model. The method comprises the following steps: receiving satellite real-time clock difference data and performing first-order difference processing on the data to obtain jump data and the epoch where the data is located, and compensating all original clock difference data before the next jump data; judging gross errors from the jump-compensated satellite real-time clock difference data, and compensating for the gross errors in the satellite real-time clock difference data; decomposing the satellite real-time clock difference data using a VMD method to obtain various modal component data; standardizing the various modal component data obtained by the decomposition; dividing the various modal component data obtained by the standardization process into a training set and a validation set using a sliding window method, and establishing and training a VMD-LSTM model; inputting the obtained standardized various modal component data into the VMD-LSTM model, and performing recovery processing on the output data to obtain a final clock difference prediction result.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation technology, and in particular to a satellite real-time clock difference prediction method based on a VMD-LSTM model. Background Art

[0002] The Global Navigation Satellite System (GNSS) has powerful functions such as navigation, positioning, and timing, and is an important means to help realize the informatization and modernization of transportation. High-precision satellite real-time clock difference products are a necessary condition for realizing Real Time Precise Point Positioning (RT-PPP) technology. Currently, the clock difference data that can be applied to RT-PPP mainly include ultra-fast clock difference products and real-time services (RTS) provided by the International Global Navigation Satellite System Service (IGS). Ultra-fast clock difference products rely on the construction of high-precision clock difference prediction models. The products have high stability but poor accuracy. The RTS service is mainly provided by institutions such as the IGS Real-time Data Center and Analysis Center, which use hundreds of real-time tracking stations distributed around the world to calculate precise clock error products in real time and broadcast them to global users in the RTCM-SSR format. It has high accuracy, but because it relies on the network for real-time broadcasting, unstable network conditions on the mobile user side can lead to data loss and connection interruption during real-time transmission. In this case, the satellite real-time clock error forecast value must be used to ensure data continuity, ensure continuous high-precision positioning of RT-PPP, and meet the positioning reliability requirements.

[0003] To improve the reliability of RT-PPP, scholars at home and abroad have proposed a variety of clock error prediction models, including quadratic polynomial models, gray models, spectral analysis models, Kalman filter models, and autoregressive moving average models. These models primarily model the trend and periodic terms of satellite real-time clock errors and exhibit certain limitations in handling the nonlinear characteristics of clock errors. Compared to traditional clock error prediction models, artificial neural networks are more effective in expressing nonlinear characteristics. The long short-term memory (LSTM) network can effectively process the nonlinear sequence of satellite real-time clock error data, achieving better prediction accuracy. However, due to the complex and unstable physical characteristics of onboard atomic clocks, when using LSTM models for satellite real-time clock error prediction, the fitting residuals contain various colored noises in addition to white noise, which the LSTM model itself cannot fully fit.

[0004] Therefore, the satellite real-time clock difference data used in RT-PPP is easily affected by the network status and may have data interruption problems. Because the satellite real-time clock difference data contains a variety of colored noise characteristics, the clock difference data prediction model using LSTM is difficult to fully fit the various colored noises. These defects lead to low satellite real-time clock difference prediction accuracy in the case of data interruption, affecting positioning accuracy. Summary of the Invention

[0005] To address the above problems, the present invention proposes a satellite real-time clock difference prediction method based on the VMD-LSTM model, comprising:

[0006] Step S1) Receive satellite real-time clock difference data and perform first-order difference processing on it, use the gross error detection method of the MAD method to obtain the jump data and the epoch where it is located, and compensate all the original clock error data before the next jump data;

[0007] Step S2) determining gross error data from the satellite real-time clock difference data after jump compensation and obtaining its location, and compensating the gross error data in the satellite real-time clock difference data using a cubic spline interpolation method;

[0008] Step S3) using the VMD method to decompose the satellite real-time clock difference data obtained in step S2 to obtain various modal component data;

[0009] Step S4) standardizing the various modal component data of the decomposed satellite real-time clock difference data;

[0010] Step S5) using a sliding window method to divide the normalized modal component data into a training set and a validation set, and establishing and training a VMD-LSTM prediction model;

[0011] Step S6) The received satellite real-time clock difference data is processed in steps S1-4 to obtain standardized various modal component data, which is input into the VMD-LSTM prediction model. The output data is denormalized to restore the various modal component data, and then the various modal component data are inversely differentiated to obtain the final clock difference prediction result.

[0012] The beneficial effects of the present invention are:

[0013] The present invention provides a satellite real-time clock difference prediction method based on the VMD-LSTM model. This method adopts the idea of ​​first decomposing and then modeling and predicting the satellite real-time clock difference data. The VMD method is used to decompose the preprocessed satellite real-time clock difference data, obtain various modal components of the satellite real-time clock difference data of different frequencies, construct a VMD-LSTM prediction model, and predict the modal components of the decomposed satellite real-time clock difference data. The clock difference prediction method provided by the present invention solves the problems of poor model fitting effect and low prediction accuracy caused by the presence of various colored noises in the satellite real-time clock difference data. It can achieve high-precision prediction of breakpoints in the satellite real-time clock difference data, ensuring continuous high-precision positioning and higher reliability requirements in RT-PPP application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 The present invention provides a flow chart of a satellite real-time clock difference prediction method based on the VMD-LSTM model. DETAILED DESCRIPTION

[0015] The present invention proposes a method for forecasting satellite real-time clock difference data by first decomposing the satellite real-time clock difference data using VMD, then using LSTM model to forecast the decomposed satellite real-time clock difference data, and finally synthesizing the forecast values ​​of each mode to forecast the satellite real-time clock difference data. This method can effectively deal with the RT-PPP positioning continuity and reliability problems caused by data interruption in RTS service. Figure 1 , the technical solution of the present invention is further specifically described.

[0016] refer to Figure 1 The present invention proposes a satellite real-time clock difference prediction method based on the VMD-LSTM model, which specifically includes:

[0017] Step S1) Receive satellite real-time clock difference data and perform first-order difference processing on it, use the gross error detection method of the MAD method to obtain the jump data and the epoch where it is located, and compensate all the original clock difference data before the next jump data.

[0018] The mobile terminal receives satellite real-time clock difference data and performs first-order difference analysis on the data to eliminate the trend term in the clock difference data. A gross error detection method using the MAD (median absolute deviation) method is then used. The median of the first-order difference data is first calculated, and 10 times the median is set as the detection threshold. First-order difference data that exceeds the detection threshold are considered to be transition data. The transition location in the first-order difference data is marked, and the epoch at the marked location plus 1 is the epoch in the original clock difference sequence data where the transition data is located. A set of satellite real-time clock difference data may contain multiple data transitions, and each data point corresponding to a moment is called an epoch. A set of satellite real-time clock difference data may contain transition data in multiple epochs. A linear polynomial is used to fit the clock difference data for the 10 epochs before the transition to predict the clock difference data for the epoch containing the transition data. The difference between the actual received clock difference data and the predicted clock difference data is used as the compensation value. This compensation is applied to all original clock difference data before the next transition, where the compensation value is subtracted from the original clock difference data. If the number of clock error data between two jump data does not reach 10 epochs of clock error data, all the clock error data before the two data jumps are used for fitting, and so on, until the linear polynomial is used to fit the clock error data of at least 10 epochs.

[0019] Step S2) The gross error data is determined from the satellite real-time clock difference data after jump compensation and its location is obtained, and the gross error data in the satellite real-time clock difference data is compensated using a cubic spline interpolation method.

[0020] In the satellite real-time clock difference data after jump compensation obtained by step S1, in the gross error detection method using the MAD (median absolute deviation) method, the gross error detection threshold is set to 3, and the data exceeding the gross error detection threshold in the satellite real-time clock difference data after jump compensation is considered to be gross error data. The location of the gross error data is determined, and the cubic spline interpolation method is used to compensate for the gross error data.

[0021] The specific method is: for a set of clock difference data {y1,y2,...,y n}, n is the number of data, construct a set of data points {(x1,y1),(x2,y2),...,(x i ,y i ),...,(x n ,y n )}, where {x1,x2,...,x n} is divided into {1, 2, 3, ..., n} according to the number of clock error data, then the cubic spline interpolation (Spline interpolation for short) formula is:

[0022] S i (x) = a i +bi (xx i )+c i (xx i ) 2 +d i (xx i ) 3 (1)

[0023] In formula (1), S i (x) is the interpolation result, a i is a constant term, b i is the coefficient of the first term, c i is the coefficient of the quadratic term, d i is the coefficient of the cubic term.

[0024] When the basic difference condition is met: S i (x i )=y i and S i (x i+1 )=y i+1 , and the smoothness condition is: the first-order derivative S i '(x i+1 )=S i ' +1 (x i+1 ) and the second-order derivative S i "(x i+1 )=S i " +1 (x i+1 ) is used to derive formula (1) and calculate the constant term a i and the other three coefficients b i ,c i ,d i The value of a i ,b i ,c i ,d i The value of is brought into formula (1), and the interpolation result S at the location of the gross error data can be calculated. i (x).

[0025] After compensating for the gross error data, clean clock error data is obtained to ensure the accuracy of model fitting.

[0026] Step S3) Using the VMD method, the satellite real-time clock difference data processed in step S2 is decomposed to obtain various modal component data.

[0027] The variational mode decomposition (VMD) method is an efficient signal decomposition method. It decomposes time series data into various modal components (Intrinsic Mode Functions, IMF) of different frequencies through an optimization process. It can effectively extract the local time-frequency characteristics of time series data and achieve efficient signal decomposition.

[0028] The VMD method is used to decompose the clean clock error data obtained after compensating the gross error data in step S2 to obtain various modal components. For a set of clean first-order difference clock error data f(t) = {t1, t2, ..., t n-1}, where the number of original satellite real-time clock difference data is n, the number of data obtained after the first-order difference is n-1, and t is the data obtained after the first-order difference. The expression formula is:

[0029]

[0030] In formula (2), min is the objective function of the first constraint, st is the constraint condition of the objective function, t is the data obtained after the first-order difference, K is the number of modal decompositions, {u k} represents the kth modal component of the decomposed satellite real-time clock difference, {ω k} represents the center frequency of the kth modal component, δ(t) is the Dirac function, and “*” represents the convolution process.

[0031] Introducing the Lagrangian function λ(t) and the penalty factor α, the optimal solution of the variational problem is:

[0032]

[0033] Alternately find the optimal iterative u k n+1 、ω k n+1 and λ n+1 Until the convergence condition is reached, that is, the change between two iterations is less than the set threshold. Here the threshold is set to 1e-6. The decomposition formula after initialization is:

[0034]

[0035] In formulas (4)-(6), represents the Wiener filtering in the modal components, is the corresponding Fourier transform of the signal f(t), represents the Fourier transform of the modal components, represents the Fourier transform of the initial modal component during the iteration process, is the corresponding Fourier transform of the Lagrange multiplier, represents the center frequency of the corresponding modal component, ω represents the frequency value, represents the Lagrange multiplier obtained in the previous iteration, then represents the Lagrange multiplier updated in this iteration, and τ represents the update parameter of the Lagrange multiplier.

[0036] The decomposed modal components can more carefully reflect the changing characteristics of the clock error data at different frequency components, which helps the LSTM model capture the changing patterns of the clock error data at different scales during fitting and improve the forecast accuracy.

[0037] Step S4) standardizes the various modal component data of the decomposed satellite real-time clock difference data.

[0038] The modal component data obtained in step S3 are standardized and scaled to a smaller range to help reduce the convergence time of the forecast model, improve the fitting effect of the forecast model, and achieve better forecast accuracy.

[0039] The standardization processing method includes: using a zero-mean normalization method to process each modal component data, and the normalization formula is:

[0040]

[0041] In formula (7), μ is the mean of the modal component data x, δ is the standard deviation of the modal component data x, which is obtained based on the standard deviation calculation formula, and x' is the normalized data.

[0042] After normalizing the modal component data, the data can satisfy the standard normal distribution. The mean μ and standard deviation δ used to normalize the modal component data are saved separately for later restoration of the modal component data.

[0043] Step S5) The normalized modal component data are divided into a training set and a validation set using a sliding window method, and a VMD-LSTM prediction model is established and trained.

[0044] The network structure of the VMD-LSTM prediction model is the same as that of the existing LSTM model, and will not be repeated here. The VMD-LSTM prediction model described here specifically refers to the LSTM model whose input data is the various modal components obtained by decomposing the various modal components using the VMD method in step S3 and then undergoing the normalization process in step S4.

[0045] For a set of modal component data {x1, x2, ...x N}, N is the number of modal component data. The sliding window method is used to divide the modal component data. The first L modal component data are used as the input data for fitting the LSMT model, and the L+1th modal component data are regarded as the output data of the LSMT model. The output data here is used to simulate the output data of the LSTM model and is regarded as the true value for comparison with the actual output data of the LSTM model. In this paper, the window size L value can be set to 24.

[0046] Since the fitting of the LSTM model requires specifying a specific output value for each input data, the sliding window method is used to split the continuous modal component data into multiple fixed-size windows. Each window contains a section of continuous modal component data, which makes it easier for the LSTM model to capture the short-term dependencies of the modal component data more accurately.

[0047] A set of input data and corresponding output data constitutes a sample. The multiple samples formed after the division are randomly divided into training sets and validation sets for training the LSTM model.

[0048] Existing technologies can be used to train LSTM models. The following is a brief introduction: When inputting the training and validation sets into the LSTM model for training, the mean squared error (MSE) loss function is used. Based on the downward trend of the loss function, the model learning rate and number of iterations are selected to be appropriate for the modal component data, avoiding overfitting. Ultimately, the desired VMD-LSTM model suitable for modal component data is obtained. After multiple experiments, the number of iterations was set to 10, meaning that training of the LSTM model was terminated after 10 iterations. This approach achieves a relatively ideal LSTM model while avoiding overfitting.

[0049] Step S6) The received satellite real-time clock difference data is processed in steps S1-4 to obtain standardized various modal component data, which is input into the VMD-LSTM prediction model. The output data is denormalized to restore the various modal component data, and then the various modal component data are inversely differentiated to obtain the final clock difference prediction result.

[0050] In order to convert the output data of the VMD-LSTM prediction model into satellite clock errors, it is necessary to perform denormalization and inverse difference processing in sequence. Denormalization and inverse difference processing are: using the standardized mean and standard deviation of each modal component data saved in step S4 to restore the output data of the VMD-LSTM prediction model into various modal component data, merging the various modal component data and performing first-order difference data recovery processing (i.e., inverse difference processing) to obtain the final clock error prediction result. For those skilled in the art, the methods of denormalization and inverse difference processing are common knowledge and therefore will not be described in detail.

[0051] The above content is a further detailed description of the present invention in conjunction with specific implementation methods. It cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, they can make several simple deductions or substitutions without departing from the concept of the present invention, which should be regarded as falling within the scope of protection determined by the claims submitted for the present invention.

Claims

1. A satellite real-time clock difference prediction method based on the VMD-LSTM model, comprising: Step S1) Receive satellite real-time clock difference data and perform first-order difference processing on it, use the gross error detection method of the MAD method to obtain the jump data and the epoch where it is located, and compensate all the original clock error data before the next jump data; Step S2) determining gross error data from the satellite real-time clock difference data after jump compensation and obtaining its location, and compensating the gross error data in the satellite real-time clock difference data using a cubic spline interpolation method; Step S3) using the VMD method to decompose the satellite real-time clock difference data obtained in step S2 to obtain various modal component data; Step S4) standardizing the various modal component data of the decomposed satellite real-time clock difference data; Step S5) using a sliding window method to divide the normalized modal component data into a training set and a validation set, and establishing and training a VMD-LSTM prediction model; Step S6) The received satellite real-time clock difference data is processed in steps S1-4 to obtain standardized various modal component data, which is input into the VMD-LSTM prediction model. The output data is denormalized to restore the various modal component data, and then the various modal component data are inversely differentiated to obtain the final clock difference prediction result.

2. A satellite real-time clock difference prediction method based on the VMD-LSTM model according to claim 1, wherein the step S1) further comprises: Calculate the median of the first-order difference data, set 10 times the median as the detection threshold, consider the first-order difference data greater than the detection threshold as jump data, mark the position of the jump data in the first-order difference data, add 1 to the epoch where the marked position is, and it is the epoch where the jump data is located in the original clock error sequence data. Use a linear polynomial to fit the clock error data of the 10 epochs before the jump, predict the clock error data of the epoch where the jump data is located, use the difference between the actually received clock error data and the predicted value as the compensation value, subtract the compensation value from the original clock error data to perform compensation on all the original clock error data before the next jump.

3. A satellite real-time clock difference prediction method based on the VMD-LSTM model according to claim 1, wherein the step S2) further comprises: The gross error detection method of the MAD method is used to judge the gross error data, and a gross error detection threshold is set. The data exceeding the gross error detection threshold in the satellite real-time clock difference data after jump compensation is considered to be gross error data.

4. A method for predicting satellite real-time clock differences based on a VMD-LSTM model according to claim 3, wherein the method for compensating for gross error data in satellite real-time clock difference data using a cubic spline interpolation method comprises: For a set of clock error data {y1,y2,…,y n }, n is the number of data, construct a set of data points {(x1,y1),(x2,y2),...,(x i ,y i ),...,(x n ,y n )}, where {x1,x2,...,x n } is divided into {1, 2, 3, ..., n} according to the number of clock error data, and the cubic spline interpolation formula is: S i (x)=a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 Among them, S i (x) is the interpolation result, a i is a constant term, b i is the coefficient of the first term, c i is the coefficient of the quadratic term, d i is the coefficient of the cubic term; When the basic difference condition is met: S i (x i )=y i and S i (x i+1 )=y i+1 , and the smoothness condition is: the first-order derivative S i '(x i+1 )=S' i+1 (x i+1 ) and the second-order derivative S" i (x i+1 )=S” i+1 (x i+1 ) is used to derive the cubic spline interpolation formula and calculate the constant term a i and the other three coefficients b i ,c i ,d i The value of a i ,b i ,c i ,d i The value of is brought into the cubic spline interpolation formula to calculate the interpolation result at the location of the gross error data.

5. A satellite real-time clock difference prediction method based on the VMD-LSTM model according to claim 1, wherein in step S4), the normalization process comprises: The zero-mean normalization method is used to process the data of each modal component. The normalization formula is: Where μ is the mean of the modal component data x, δ is the standard deviation of the modal component data x, and x' is the normalized data.

6. A satellite real-time clock difference prediction method based on the VMD-LSTM model according to claim 5, wherein the mean μ and standard deviation δ used to standardize each modal component data are saved.

7. A satellite real-time clock difference prediction method based on the VMD-LSTM model according to claim 1, wherein the step of using a sliding window method to divide the modal component data obtained by the standardized processing into a training set and a validation set comprises: The sliding window method is used to divide the group of modal component data. The first L modal component data are used as the input data of the LSMT model, the L+1th modal component data are regarded as the output data of the LSMT model, and the L+1th modal component data are regarded as the true value for comparison with the actual output data of the LSTM model. A group of input data and the corresponding output data constitute a sample, and the multiple samples formed after the division are randomly divided into training set and validation set.

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