Method and device for improving pole-approaching real-time forecasting precision by fusing time-varying characteristics

Abstract

The invention provides a method and equipment for improving the precision of pole-shifting proximity real-time prediction by fusing time-varying characteristics, and the method comprises the steps: carrying out the data preprocessing of a pole-shifting PM, and extracting a trend term, a period term and a residual term; constructing a Prony method-based PM time-varying characteristic fused least square model, and performing dynamic parameter estimation and extrapolation prediction on the period term and the trend term; constructing a polar shift residual prediction model based on ARIMA (autoregressive integrated moving average), and predicting the residual item; and reconstructing the prediction results of the period term, the trend term and the residual term to generate a polar shift prediction result. According to the method, the amplitude, damping, period and phase change in the PM signal can be independently and effectively analyzed, and then the corresponding prediction model is constructed, so that the precision of near-real-time PM prediction is improved.

Description

Technical Field

[0001] The present invention belongs to the field of space geodesy and relates to a technical solution for improving the accuracy of near-real-time prediction of polar motion by integrating time-varying characteristics. Background Art

[0002] With the growing demand for real-time calculation and prediction of polar motion (PM) parameters in fields such as precise satellite orbit determination and deep space exploration, the massive amount of data acquired by existing space geodetic techniques must undergo complex analysis and processing to provide high-precision PM results, resulting in a certain degree of time lag. For example, PM observations obtained using high-precision observation data such as very long baseline interferometry and satellite laser ranging typically experience a delay of 2 to 5 days. While PM observations obtained using the global navigation satellite system (GNSS) are faster, they still require a lag of 2 to 3 hours. Furthermore, PM observations derived from GNSS are susceptible to systematic errors and have poor long-term stability. Therefore, short-term PM prediction is crucial for multiple near-real-time applications, including GNSS meteorology, precision guidance in military environments, and real-time satellite orbit determination.

[0003] Traditional PM prediction models, such as least squares (LS) models, rely primarily on extrapolating empirical periodic signals with fixed amplitude and phase. However, the temporal variations in the amplitude, damping, period, and phase of these signals can be caused by ongoing geophysical processes within and outside the Earth, including mantle flow, atmospheric and ocean dynamics, and tidal forces. These signals exhibit irregular, rather than constant, variations, making them challenging for traditional methods to handle, particularly when performing short-term PM predictions. Summary of the Invention

[0004] In response to the above problems, the present invention breaks through traditional conventional technologies and proposes a solution based on the Prony method to improve the near-real-time prediction accuracy of PM by integrating time-varying characteristics.

[0005] The technical solution of the present invention provides a method for improving the accuracy of near-real-time prediction of polar motion by integrating time-varying characteristics, including the following steps:

[0006] Data preprocessing is performed on the polar motion PM to extract trend terms, period terms and residual terms;

[0007] Constructing a least squares model of PM time-varying characteristics based on the Prony method, and performing dynamic parameter estimation and extrapolation prediction on the periodic term and trend term;

[0008] Constructing an ARIMA-based polar motion residual prediction model to predict the residual term;

[0009] The prediction results of the periodic term, trend term and residual term are reconstructed to generate a polar motion prediction result.

[0010] Moreover, the polar motion data are preprocessed based on complex singular spectrum analysis to extract trend terms, periodic terms and residual terms.

[0011] Moreover, the polar motion data is preprocessed based on complex singular spectrum analysis, including constructing a PM signal in complex form, wherein the polar motion X-direction component and the polar motion Y-direction component at each time point are combined into a complex number, and then extracting the time series of the trend term, the period term and the residual term.

[0012] Moreover, in the least squares model integrating PM time-varying characteristics, signal representation is performed based on the Prony method, and the instantaneous amplitude, phase, period and damping coefficient of the PM periodic term are dynamically adjusted through the decomposition results of complex singular spectrum analysis, and parameter extrapolation is performed based on the least squares method.

[0013] Moreover, the parameters of the ARIMA-based polar motion residual prediction model are determined by determining the autoregressive order p and the moving average order q according to the autocorrelation function and the partial autocorrelation function of the residual sequence;

[0014] Combined with statistical information criteria, the combination of p and q values is optimized.

[0015] Moreover, the periodic term includes components of Chandler wobble CW and annual wobble AW, and the corresponding instantaneous parameters are accurately estimated by the extended Prony method.

[0016] Moreover, the accuracy of the polar motion prediction results is evaluated by the mean absolute error and compared and verified.

[0017] On the other hand, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the method of integrating time-varying characteristics to improve the accuracy of near-real-time prediction of polar motion as described above is implemented.

[0018] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method of integrating time-varying characteristics to improve the accuracy of near-real-time prediction of polar motion as described above.

[0019] On the other hand, the present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the method of integrating time-varying characteristics to improve the accuracy of near-real-time prediction of polar motion as described above.

[0020] The technical solution of the present invention can autonomously and effectively analyze the amplitude, damping, period, and phase changes in PM signals, and then construct a corresponding prediction model, thereby improving the accuracy of PM near-real-time forecasts. Compared with traditional prediction methods, the present invention can not only accurately capture the non-steady-state characteristics of PM signals, but also has adaptability in the parameter estimation process, and can dynamically adjust model parameters to adapt to the changing trends of actual observed signals. In addition, the method of the present invention effectively solves the problem that traditional methods are difficult to autonomously decompose and accurately describe the dynamic changes of periodic signal parameters by combining the complex singular spectrum analysis algorithm (Complex Singular Spectrum Analysis, CSSA) with the extended Prony method, thereby significantly improving the ability to capture key periodic components such as Chandler wobble (CW) and annual wobble (AW). At the same time, the model of the present invention has a simple structure, high computational efficiency, and is easy to deploy and apply in practice. It can meet the timeliness requirements of near-real-time predictions and has strong practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Flowchart of an embodiment of the present invention.

[0022] Figure 2 This is a time series diagram of extracting trend terms, period terms, and residual terms based on the CSSA method in an embodiment of the present invention.

[0023] Figure 3 2 is a schematic diagram showing a comparison of the mean absolute error (MAE) of PMX and PMY predictions for the next 30 days according to an embodiment of the present invention. DETAILED DESCRIPTION

[0024] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0025] See also Figure 1 The embodiment of the present invention provides a method for improving the accuracy of near-real-time prediction of polar motion by integrating time-varying characteristics, including the following steps:

[0026] Step 1: Preprocess the PM data based on complex singular spectrum analysis and extract the time series of periodic terms.

[0027] The present invention proposes that complex singular spectrum analysis is preferably used to implement PM data preprocessing. Complex singular spectrum analysis (CSSA) is a signal decomposition method for complex time series. It combines traditional singular spectrum analysis (SSA) with complex signal processing technology, and can effectively extract trend terms, periodic terms and residual terms in the signal while retaining the time-varying characteristics of the signal (such as dynamic changes in amplitude, phase and frequency). By adopting CSSA, an efficient decomposition tool for complex time series, the matrix decomposition capability of singular spectrum analysis SSA and the phase analysis characteristics of complex signals can be integrated, significantly improving the extraction accuracy of time-varying components in multidimensional signals such as polar motion, providing key technical support for dynamic modeling and forecasting.

[0028] The preferred implementation process of the embodiment includes constructing a complex PM signal, wherein the polar motion X-direction component and the polar motion Y-direction component at each time point are combined into a complex number; embedding the complex signal into a Hankel matrix and performing singular value decomposition to obtain complex subcomponents; and performing anti-diagonal averaging and group reconstruction on the subcomponents to obtain a time series of trend terms, period terms, and residual terms. The specific implementation steps are as follows:

[0029] a) Complex signal construction

[0030] Let x[n] represent the polar motion X-direction (PMX) component at the nth time point, and y[n] represent the polar motion Y-direction (PMY) component, where n = 0, 1, ..., N-1, and N is the length of the time series. Then the PM complex signal at the nth time point is constructed as:

[0031] z[n]=x[n]-iy[n](1)

[0032] Where z[n]∈￡ represents the PM signal in complex form at the nth time point, ￡ represents the complex set; i is the imaginary unit, satisfying i 2 =-1.

[0033] b) Hankel matrix embedding

[0034] Select the window length L and define the extension length K = N-L+1. Embed the complex sequence {z[n]} into a complex Hankel matrix H∈￡ L×K , ￡ L×K Represents a complex matrix with L rows and K columns, then it is expressed as:

[0035]

[0036] c) Singular Value Decomposition

[0037] Perform singular value decomposition (SVD) on the matrix H and obtain:

[0038]

[0039] Where r is the selected effective rank; σ j is the jth singular value; are the corresponding left and right singular vectors, represent the complex vector spaces of length L and K respectively; Indicates v j The conjugate transpose of represents the rank-1 reconstruction matrix.

[0040] d) Anti-diagonal average

[0041] For each H j ∈￡ L×K Perform the anti-diagonal averaging operation to restore it to a one-dimensional time series component s j [n]∈￡,s j [n] represents the value of the jth basic component at the nth time point.

[0042] e) Component Grouping and Reconstruction

[0043] For the obtained r complex subcomponents {s j [n]} performs correlation analysis and divides it into several subsets according to the frequency characteristics or signal energy distribution, which are used to reconstruct the trend term (Trend), periodic term (including Chandler wobble (CW) and annual wobble (AW)) and residual term (Residual). Figure 2 This is a time series diagram of the trend term, period term, and residual term extracted based on the CSSA method in the embodiment, wherein each term includes the results of the polar shift in the X direction and the polar shift in the Y direction respectively.

[0044] Step 2: Construct a least squares model of the time-varying characteristics of the fused PM based on the Prony method

[0045] In the least squares model of PM time-varying characteristics based on the Prony method, the instantaneous amplitude, phase, period and damping coefficient of the PM periodic term are dynamically adjusted according to the CSSA decomposition results, and the parameters are extrapolated based on the least squares method.

[0046] The construction implementation process of the embodiment specifically includes the following sub-steps:

[0047] a) Signal representation based on Prony method

[0048] First, based on the existing Prony method, the signal representation is performed. Let the PM signal to be processed be z(t), which is a complex signal containing PMX and PMY components. The signal can be represented as:

[0049]

[0050] Where q is the number of sinusoidal terms in the signal; A k is the instantaneous amplitude of the kth sinusoidal term; α k is the instantaneous damping of the kth sinusoidal term; t is the time variable, indicating the sampling time; T k is the instantaneous period of the kth sinusoidal term; θ k is the instantaneous damping of the kth sine term, and exp() represents the exponential form.

[0051] b) Constructing a least squares extrapolation model for the time-varying characteristics of PM

[0052] Based on the Prony method, the present invention proposes constructing a least squares (LS) extrapolation model based on the Prony method, based on the time-varying characteristics of the trend and periodic terms of PM extracted by the CSSA algorithm in step 1. This method effectively improves PM prediction accuracy by modeling the periodic and residual components of the PM signal and adaptively adjusting parameters such as frequency, amplitude, and damping. Its expression is as follows:

[0053]

[0054] Where z(t) periodic+trend represents the extrapolated value of the PM period component and trend component; a and b are the trend item parameters of the PM series; t is the time variable, indicating the sampling time; A CW 、A AW Indicates the instantaneous amplitude of CW and AW; α CW is the instantaneous damping of CW; T CW 、T AW Indicates the instantaneous period of CW and AW; θ CW ,θ AW Indicates the instantaneous phase of CW and AW. Different from the traditional method of setting it as a constant, the present invention obtains the parameter A through formula (5) CW 、A AW , α CW 、T CW 、T AW ,θ CW ,θ AW , to achieve dynamic adjustment.

[0055] The principle of this model is to propose an effective extrapolation prediction model based on the traditional Prony method, combined with the CSSA algorithm and the LS method, targeting the non-stationary characteristics of the PM sequence. Specifically, the CSSA method is first used to effectively decompose the trend term, period term and residual term of the complex PM signal to fully capture the long-term trend change and periodic oscillation characteristics of the PM sequence. Subsequently, based on the extended Prony method (i.e., based on the improvement of formula (4) without involving exp(α k In part t), the model accurately estimates the parameters of the extracted periodic signals (particularly the CW and AW components), including amplitude, phase, period, and damping coefficient, to reflect the dynamic characteristics of each periodic component of the PM sequence. Finally, the LS method is used to extrapolate these parameters to achieve an optimal fit between the model parameters and the observed data. This comprehensive analysis approach demonstrates significant advantages in prediction accuracy, flexibility, and the ability to adaptively capture the non-stationary characteristics of the PM sequence, thereby improving the accuracy of short- and medium-term polar motion forecasts.

[0056] c) Constructing PM residual prediction model based on autoregressive integrated moving average model ARIMA

[0057] Based on the time-varying characteristics of the residual term of PM extracted by the CSSA algorithm in step 1, an ARIMA forecast model is constructed, which can be expressed as:

[0058]

[0059] Where z(t) residual is the predicted value of the PM residual term at time point t; c is the constant term; is the parameter of the autoregressive (AR) term; z t-1 ,z t-2 ,…,z t-s are the s autoregressive lag terms before time point t; θ1,θ2,…,θ s is the parameter of the Moving Average (MA) term; ε t-1 ,ε t-2 ,…,ε t-s represents the error term of the first s time steps; ε tis the error term at the current moment. In practical applications, the values of p and s are typically determined through statistical analysis of the PM residual sequence. Specifically, a preliminary judgment can be made by plotting the sequence's autocorrelation function (ACF) and partial autocorrelation function (PACF). The ACF plot is typically used to determine the moving average order s, while the PACF plot is used to determine the autoregressive order p. Generally speaking, when the PACF is significantly truncated after a certain order (truncation means that the value after this order significantly approaches zero), the autoregressive order p is selected as that truncation order; whereas, when the ACF is significantly truncated at a certain order, the moving average order s is typically selected as that truncation order. Furthermore, to further optimize the determined parameters, multiple different combinations of p and s can be tried. Model optimization can be performed using statistical information criteria (such as AIC and BIC). The model that minimizes the information criterion value is selected to determine the optimal autoregressive order p and moving average order s.

[0060] d) Prediction results of the periodic component, trend component, and residual component of the reconstructed PM signal

[0061] Following these steps, we obtain the prediction results for the PM signal's periodic component, trend component, and residual component. These three components are reconstructed into a formula: forecast value = extrapolated value of the periodic component + extrapolated value of the trend component + predicted value of the residual component. Ultimately, the PM signal forecast result is obtained and output.

[0062] In order to evaluate the forecast accuracy, the mean absolute error (MAE) was used as the measurement standard, and the forecast results were compared with the official Bulletin A. The results are shown in Table 1 and Figure 3 shown. Figure 3 The mean absolute error (MAE) of the PMX and PMY forecasts for the next 30 days is compared in the table. The official bulletin A is in red and the model of the present invention is in blue.

[0063] Table 1 Comparison of PM prediction mean absolute error (MAE, unit: milliarcsecond) of different models

[0064]

[0065]

[0066] During implementation, those skilled in the art may use software technology to automate the above process. Accordingly, providing a solution for integrating time-varying characteristics to improve the accuracy of near-real-time predictions of polar motion, including a computer or server, and executing the above process on the computer or server to integrate time-varying characteristics to improve the accuracy of near-real-time predictions of polar motion, would also fall within the scope of protection of the present invention.

[0067] In another embodiment, it also relates to an electronic device, including at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the above-mentioned method of integrating time-varying characteristics to improve the accuracy of near-real-time prediction of polar motion.

[0068] In another embodiment, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to enable the computer to execute the above-mentioned method of integrating time-varying characteristics to improve the accuracy of near-real-time prediction of polar motion.

[0069] In another embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the method for improving the accuracy of near-real-time prediction of polar motion by integrating time-varying characteristics is implemented.

[0070] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0071] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the existing technology can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0072] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or replacements within the technical scope disclosed by the present invention, which should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for improving the accuracy of near-real-time polar motion prediction by integrating time-varying characteristics, characterized in that: The following steps are involved: Data preprocessing is performed on the polar motion PM to extract trend terms, period terms and residual terms; Constructing a least squares model of PM time-varying characteristics based on the Prony method, and performing dynamic parameter estimation and extrapolation prediction on the periodic term and trend term; Constructing an ARIMA-based polar motion residual prediction model to predict the residual term; The prediction results of the periodic term, trend term and residual term are reconstructed to generate a polar motion prediction result.

2. The method for improving the accuracy of near-real-time polar motion prediction by integrating time-varying characteristics according to claim 1 is characterized by: The polar motion data are preprocessed based on complex singular spectrum analysis to extract trend terms, periodic terms and residual terms.

3. The method for improving the accuracy of near-real-time polar motion prediction by integrating time-varying characteristics according to claim 1 is characterized by: The polar motion data are preprocessed based on complex singular spectrum analysis, including constructing a PM signal in complex form, wherein the polar motion X-direction component and the polar motion Y-direction component at each time point are combined into a complex number, and then the time series of the trend term, the period term and the residual term are extracted.

4. The method for improving the accuracy of near-real-time polar motion prediction by integrating time-varying characteristics according to claim 2 is characterized by: In the least squares model integrating PM time-varying characteristics, signal representation is performed based on the Prony method, the instantaneous amplitude, phase, period and damping coefficient of the PM periodic term are dynamically adjusted through the decomposition results of complex singular spectrum analysis, and parameter extrapolation is performed based on the least squares method.

5. The method for improving the accuracy of near-real-time polar motion prediction by integrating time-varying characteristics according to claim 1 is characterized by: The parameters of the ARIMA-based polar motion residual prediction model are determined in the following way: Determine the autoregressive order p and the moving average order q based on the autocorrelation function and partial autocorrelation function of the residual sequence; Combined with statistical information criteria, the combination of p and q values is optimized.

6. The method for improving the accuracy of near-real-time polar motion prediction by integrating time-varying characteristics according to claim 1 is characterized by: The periodic term includes components of Chandler wobble CW and annual wobble AW, and the corresponding instantaneous parameters are accurately estimated by the extended Prony method.

7. The method for improving the accuracy of near-real-time polar motion prediction by integrating time-varying characteristics according to claim 1 is characterized by: The accuracy of the polar motion prediction results is evaluated by the mean absolute error and compared and verified.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for improving the accuracy of near-real-time prediction of polar motion by integrating time-varying characteristics as described in any one of claims 1 to 7 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for improving the accuracy of near-real-time prediction of polar motion by integrating time-varying characteristics as described in any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program, characterized in that: When the computer program is executed by a processor, the method for improving the accuracy of near-real-time prediction of polar motion by integrating time-varying characteristics as described in any one of claims 1 to 7 is implemented.

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