Polar shift forecasting method considering periodic time-varying characteristics

Abstract

The invention discloses a polar shift forecasting method considering periodic time-varying characteristics, which belongs to the technical field of spatial geodetic survey, is used for polar shift forecasting and comprises the following steps: preparing a data set, constructing a polar shift complex time sequence and adaptively optimizing and determining an optimal periodic parameter by using a differential evolution algorithm. Constructing a complex field harmonic model to calculate a polar shift prediction value, and extrapolating to obtain a fitting prediction value; constructing an autoregression model, and calculating a residual error sequence forecast value; and adding the fitting forecast value and the residual error sequence forecast value to obtain a final polar shift forecast result. According to the method, the time-varying period parameters in the polar shift sequence are adaptively determined by introducing the differential evolution algorithm and the global optimization algorithm, so that more accurate fitting and forecasting of key elements such as the period, the amplitude and the phase change of the Cashler swing and the annual term in the polar shift signal are realized, and a more stable residual sequence is provided for an autoregression model; and the precision and the stability of polar shift, especially medium and long-term span forecasting, are remarkably improved on the whole.

Description

TECHNICAL FIELD

[0001] The application discloses a polar motion prediction method considering period time-varying characteristics and belongs to the technical field of space geodesy. BACKGROUND

[0002] Earth orientation parameters (EOP) are key parameters for the conversion between the celestial reference system and the earth reference system. The EOP include nutation, precession, polar motion and length of day variation. Among them, polar motion refers to the change in the position of the earth rotation axis relative to the earth surface. High-precision EOP prediction is an important guarantee for the realization of spacecraft measurement and control, real-time satellite navigation, geodesy and other fields. Among them, due to complex excitation factors, high-precision polar motion prediction has always been a difficult problem in EOP prediction.

[0003] Existing researches show that polar motion mainly includes long trend items, Chandler items, annual items, seasonal items and high-frequency items. Among them, annual swing, Chandler swing and semi-annual swing are the most important components. Traditional polar motion prediction methods are generally based on the combination of least squares (LS) and auto-regressive (AR) models (LS+AR model). The basic idea of this kind of method is: first, the deterministic trend items and fixed period items in the polar motion sequence are fitted and extrapolated by using the least squares model, and then the residual sequence after least squares fitting is used to model and predict the random items by using the auto-regressive model.

[0004] However, the traditional least squares plus auto-regressive model has inherent limitations. A large number of studies have shown that the Chandler period and the annual period in the polar motion have significant time-varying characteristics, and their amplitudes and periods also have a large range of changes. The traditional model uses fixed period parameters, which cannot accurately track such time-varying characteristics, resulting in significant phase shift and error accumulation in medium and long-term prediction, thereby seriously restricting the further improvement of the prediction accuracy. SUMMARY

[0005] The purpose of the present application is to provide a polar motion prediction method considering period time-varying characteristics, so as to solve the problem of long-term prediction phase shift and error accumulation caused by the fact that the traditional least squares plus auto-regressive model cannot reflect the time-varying characteristics of Chandler swing and annual items due to the use of fixed period.

[0006] A polar motion prediction method considering period time-varying characteristics comprises: S1, prepare a data set, construct a polar motion complex time series, randomly initialize the population of the differential evolution algorithm within the preset period parameter boundary, construct a fitting sequence model with the Chandler period and annual period parameters of the population individuals, and solve the fitting values of the population individuals, determine the optimal period parameter combination by maximizing the Pearson correlation coefficient of the fitting sequence and the polar motion observed complex sequence using the differential evolution algorithm, determine the optimal individual in the polar motion complex time series through adaptive optimization, and take the period parameters of the optimal individual as the optimal period parameter combination; S2, construct a complex domain harmonic model based on the optimal period parameter combination to calculate the polar motion prediction value, obtain the optimal complex domain harmonic model by least square fitting of the polar motion complex time series, calculate the fitting prediction value according to the optimal complex domain harmonic model, and form a residual sequence based on the residual between the fitting prediction value and the polar motion observed value calculated based on the time series; S3, construct an autoregressive model for the residual sequence, determine the optimal order and optimal autoregressive coefficient through the final prediction error criterion adaptive and least square method, construct the optimal autoregressive model, and calculate the residual sequence prediction value using the optimal autoregressive model; S4, add the fitting prediction value and the residual sequence prediction value to obtain the final polar motion prediction result.

[0007] S1 includes S1.1, constructing a polar motion complex time series, taking the x direction as the real part and the y direction as the imaginary part: ; In the formula, is the polar motion observed complex sequence, is the component of the polar motion in the x direction, is the component of the polar motion in the y direction, is the imaginary unit, is the index of the time series, , is the total length of the time series; S1 includes S1.2, randomly generating an initial population containing two-dimensional vectors of real number values within the set Chandler period parameter and annual period parameter boundary, is the total number of population individuals, is the total dimension of the parameters to be optimized, and the parameters to be optimized are: ; ; ; In the formula, is the parameter to be optimized, is the index of the population individual, ​Here is the index of the dimension of the parameter to be optimized, and 0 represents the 0th iteration of the differential evolution algorithm. For the 0th generation population The first individual One parameter to be optimized. For the first The upper bound of the parameters to be optimized. For the first The lower bound of the parameters to be optimized. For in the interval A random number that is uniformly distributed within the range; S1 includes S1.3, based on the population level. The Chandler cycles and annual cycles of each individual are used to construct the first... Fitted sequence model for each individual in the population: ; In the formula, For the population number The fitted value for each individual, For trend parameters, For linear term parameters, and For the fitting parameters, For the Chandler cycle, It is an annual cycle. It is a six-month cycle. It is a natural constant. For the population number The trend term parameters of the fitted sequence model for each individual. For the population number The linear term parameters of the individual fitted sequence model, and For the population number The fitting parameters of the individual fitted sequence model For the population number Chandler cycles of individuals For the population number The annual cycle of an individual, For the population number A six-month cycle for each individual; The least squares method was used to fit the polar shift complex time series of the fitted sequence model to obtain the following results. , , and .

[0008] S1 includes S1.4, which uses the differential evolution algorithm to determine the optimal combination of periodic parameters by maximizing the Pearson correlation coefficient between the fitted sequence and the polar motion observation complex sequence. The Pearson correlation coefficient is: ; In the formula, The Pearson correlation coefficient is used. For the fitted sequence, For covariance, Standard deviation for standard deviation for standard deviation for The average value over a time series. for The average value over a time series; combinations of periodic parameters include Chandler periods and annual periods.

[0009] S1 includes, S1.5, and the first Each individual in the population undergoes a mutation operation: ; In the formula, For the mutation vector, This represents the number of iterations in the differential evolution algorithm. For the first Generation 1 The mutation vector of each individual, Scaling factor , , For interval Internal and Inequal random integers, and , , Neither pair is equal. , , For from the first Three distinct individuals randomly selected from the population; S1 includes, S1.6, and... and Perform a binary crossover operation to generate experimental vectors. : ; In the formula, For the first Generation 1 The first experimental vector Parameter values, For interval The index of the dimension variable is randomly selected within the variable. Crossover probability factor For each individual Randomly generated dimension indexes; S1 comprises S1.7, defining a fitness function , for calculating the function argument according to steps S1.3 and S1.4 , and as the function argument respectively into , selecting the better one as the parameter to be optimized of the first individual of the population: ; S1 comprises S1.8, adaptive optimization comprises repeating steps S1.3 to S1.7 until reaching a maximum number of iterations or meeting a convergence condition, obtaining an optimal individual, and taking the optimal individual as the optimal Chandler period and the optimal annual period.

[0010] S2 comprises S2.1, constructing a complex domain harmonic model based on the optimal Chandler period and the optimal annual period: ; wherein, is a polar motion prediction value, is the optimal Chandler period, the optimal annual period, is the optimal semiannual period.

[0011] S2 comprises S2.2, performing least squares fitting on the polar motion complex time series to obtain the optimal values of , , and , and setting as the optimal value of , as the optimal value of , as the optimal value of , as the optimal value of , and substituting , , and into the complex domain harmonic model to obtain an optimal complex domain harmonic model: ; wherein, is a fitting prediction value, is the optimal value of , satisfies the sum of squares of the residuals between and the polar motion observation value is the smallest; S2 comprises S2.3, calculating​ Residuals between the polar motion observations, constituting a residual series.

[0012] S3 comprises S3.1, constructing an autoregressive model based on the residual series: ; wherein, is a residual value, is a residual value at time t, is a lag term, is a model order, is an index of the model order, , is an autoregressive coefficient, is an autoregressive coefficient of the th order, is white noise, is white noise at time t.

[0013] S3 comprises S3.2, determining by the final prediction error criterion adaptive and least squares method ; ; wherein, is a final prediction error value when the autoregressive model order is is a sample size, is a residual variance of the autoregressive model with the order is an optimal , satisfying is the minimum.

[0014] S3 comprises S3.3, substituting into the autoregressive model, and calculating the corresponding autoregressive coefficients ; substituting and the corresponding into the autoregressive model, to obtain an optimal autoregressive model: ; wherein, is a residual series prediction value.

[0015] S4 comprises adding the fitting prediction value and the residual series prediction value to obtain a final polar motion prediction result: ; wherein, ​​For the final polar motion prediction result.

[0016] Compared with the prior art, the present application has the following beneficial effects: the present application introduces a differential evolution algorithm global optimization algorithm to adaptively determine the time-varying period parameters in the polar motion sequence, not only realizes more accurate fitting and prediction of the period, amplitude and phase variation of the Chandler wobble and annual term in the polar motion signal, but also provides a more stable residual sequence for the autoregressive model, thereby significantly improving the accuracy and stability of the polar motion, especially the medium and long term span prediction. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 is a technical flowchart of the present application; Figure 2 is a polar motion x-direction component average absolute error change graph; Figure 3 is a polar motion y-direction component average absolute error change graph. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical scheme and advantages of the present application clearer, the technical scheme in the present application will be described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0019] A polar motion prediction method considering period time-varying characteristics, comprising: S1, preparing a data set, constructing a polar motion complex time sequence, randomly initializing a population of a differential evolution algorithm within a preset period parameter boundary, constructing a fitting sequence model with the Chandler period and annual period parameters of the population individuals, and solving the fitting values of the population individuals, determining the optimal period parameter combination by maximizing the Pearson correlation coefficient of the fitting sequence and the polar motion observed complex sequence by using the differential evolution algorithm, determining the optimal individual in the polar motion complex time sequence by adaptive optimization, and taking the period parameters of the optimal individual as the optimal period parameter combination; S2, constructing a complex domain harmonic model to calculate the polar motion prediction value based on the optimal period parameter combination, obtaining the optimal complex domain harmonic model by least square fitting of the polar motion complex time sequence, calculating the fitting prediction value according to the optimal complex domain harmonic model, calculating the residual between the fitting prediction value and the polar motion observed value based on the time sequence, and constructing a residual sequence; S3, constructing an autoregressive model for the residual sequence, determining the optimal order and the optimal autoregressive coefficient by the final prediction error criterion adaptive and least square method, constructing the optimal autoregressive model, and calculating the residual sequence prediction value by using the optimal autoregressive model; S4. Add the fitted forecast value and the residual sequence forecast value to obtain the final polar motion forecast result.

[0020] S1 includes, S1.1, constructing a polar-shift complex time series, with the x-direction as the real part and the y-direction as the imaginary part: ; In the formula, For polar motion observation complex sequence, Let x be the polar motion component in the x-direction. Let be the polar motion component in the y-direction. The imaginary unit, For indexing time series, , This represents the total length of the time series. S1 includes, and S1.2, randomly generating parameters within the boundaries of the set Chandler period parameter and annual period parameter, including... indivual The initial population of 2D real-valued vectors. The total number of individuals in the population. The total dimension of the parameters to be optimized is: ; ; ; In the formula, For parameters to be optimized, For indexing individuals in the population, Here is the index of the dimension of the parameter to be optimized, and 0 represents the 0th iteration of the differential evolution algorithm. For the 0th generation population The first individual One parameter to be optimized. For the first The upper bound of the parameters to be optimized. For the first The lower bound of the parameters to be optimized. For in the interval A random number that is uniformly distributed within the range; S1 includes S1.3, based on the population level. The Chandler cycles and annual cycles of each individual are used to construct the first... Fitted sequence model for each individual in the population: ; In the formula, For the population number The fitted value for each individual, For trend parameters, For linear term parameters, and For the fitting parameters, For the Chandler cycle, It is an annual cycle. It is a six-month cycle. It is a natural constant. For the population number The trend term parameters of the fitted sequence model for each individual. For the population number The linear term parameters of the individual fitted sequence model, and For the population number The fitting parameters of the individual fitted sequence model For the population number Chandler cycles of individuals For the population number The annual cycle of an individual, For the population number A six-month cycle for each individual; The least squares method was used to fit the polar shift complex time series of the fitted sequence model to obtain the following results. , , and .

[0021] S1 includes S1.4, which uses the differential evolution algorithm to determine the optimal combination of periodic parameters by maximizing the Pearson correlation coefficient between the fitted sequence and the polar motion observation complex sequence. The Pearson correlation coefficient is: ; In the formula, The Pearson correlation coefficient is used. For the fitted sequence, For covariance, Standard deviation, for standard deviation for standard deviation for The average value over a time series. for The average value over a time series; combinations of periodic parameters include Chandler periods and annual periods.

[0022] S1 includes, S1.5, and the first Each individual in the population undergoes a mutation operation: ; In the formula, For the mutation vector, Let be the number of iterations in the differential evolution algorithm. For the first Generation 1 The mutation vector of each individual, Scaling factor , , For interval Internal and Inequal random integers, and , , The pairs are not equal. , , For from the first Three distinct individuals randomly selected from the population; S1 includes, S1.6, and... and Perform a binary crossover operation to generate experimental vectors. : ; In the formula, For the first Generation 1 The first experimental vector Parameter values, For interval The index of the dimension variable is randomly selected within the variable. Crossover probability factor For each individual Randomly generated dimension indexes; S1 includes S1.7, defining the fitness function. , To calculate the independent variable of the function based on steps S1.3 and S1.4 ,Will and Substitute them as the independent variables of the function. According to the greed principle, the better one is selected. Generation 1 The parameters to be optimized for each individual: ; S1 includes S1.8. Adaptive optimization includes repeating steps S1.3 to S1.7 until the maximum number of iterations is reached or the convergence condition is met, to obtain the optimal individual, and using the optimal individual as the optimal Chandler period and the optimal annual period.

[0023] S2 includes S2.1, which constructs a complex domain harmonic model based on the optimal Chandler period and the optimal annual period: ; wherein, is the polar motion prediction value, is the optimal Chandler period, is the optimal annual period, is the optimal semiannual period.

[0024] S2 includes, S2.2, obtaining the optimal values of , , and by least square fitting on the polar motion complex time series, and setting as the optimal value of , as the optimal value of , as the optimal value of , as the optimal value of , , , and into the complex domain harmonic model to obtain the optimal complex domain harmonic model: ; wherein, is the fitting prediction value, and is the optimal value of , satisfies that the sum of squares of the residuals between and the polar motion observation value is minimum; S2 includes, S2.3, calculating the residuals between and the polar motion observation value to form a residual series.

[0025] S3 includes, S3.1, constructing an autoregressive model based on the residual series: ; wherein, is the residual value, is the residual value at time , is the lag term, is the model order, is the index of the model order, , is the autoregressive coefficient, is the autoregressive coefficient of the th order, is the white noise, is the white noise at time .

[0026] S3 includes, S3.2, determining the autoregressive model by the final prediction error criterion adaptive and least square method The final pre-error criterion formula is: ; ; In the formula, is the final prediction error value when the autoregressive model order is , is the sample size, is the residual variance of the autoregressive model with order , is the optimal , which satisfies minimum. S3 includes, S3.3, substituting into the autoregressive model, and calculating the corresponding autoregressive coefficients

[0027] using the least squares method; ; Substituting and the corresponding into the autoregressive model, the optimal autoregressive model is obtained: ; In the formula, is the residual sequence prediction value.

[0028] S4 includes adding the fitting prediction value and the residual sequence prediction value to obtain the final polar motion prediction result: ; In the formula, is the final polar motion prediction result.

[0029] Further description is made below in combination with the drawings. The technical process of the present application is shown in Figure 1 , polar motion data is prepared, initial parameters are input, the number of iterations is set, population initialization is performed, a fitting sequence model is constructed, mutation operation is performed on the initial population to obtain a mutation vector, crossover operation is performed on the mutation vector to obtain an experimental vector, a fitness function is constructed, individual vectors and experimental vectors are substituted into the fitness function as independent variables, then selection operation is performed to select better individuals, conditional judgment is performed, if the stop condition is not met, the mutation operation is returned to be performed again, if the stop condition is met, the optimal period parameter combination is output, including the optimal CW (Chandler period) and the optimal AW (annual period), the optimal period parameter combination (the optimal period parameter combination meets the highest correlation between the least squares fitting data and the polar motion observation value) is used to construct an optimal complex domain harmonic model, the polar motion data is fitted, then two branches are divided, the first branch is an extrapolation prediction item based on the least squares model, the second branch is a fitting residual item, then the AR (autoregressive) model is extrapolated to obtain a residual prediction value; finally, the polar motion prediction value is obtained by combining the results of the two branches.​

[0030] To intuitively illustrate the effectiveness of the present application, the EOP 20u23 C04 polar motion sequence published by the International Earth Rotation and Reference System Service (IERS) is taken as a data set, and the parameter setting conditions include: , , , , the maximum evolutionary iteration number is 100, the Chandler period is , and the annual period is .

[0031] The final polar motion prediction results obtained by the present application are compared with the Bulletin A published by the International Earth Rotation and Reference System Service Organization (IERS) and the method of the present application. In the prediction experiment, the first prediction starting point is January 4, 2018, and then prediction is performed every 7 days, and the last prediction starting point is December 24, 2021, the same number of prediction files as Bulletin A is generated, a total of 208 periods. Among them, the basic data of each period is selected as the previous 10 years of the prediction time, and the prediction time length is 365 days. The present application selects the mean absolute error (MAE) to analyze and evaluate the prediction accuracy, and the calculation method of the MAE is: , In the formula, is the absolute error of the th period.

[0032] The prediction error results of the polar motion in the x direction are shown in Table 1: Table 1, Polar Motion X Direction Prediction Error Statistics ; The prediction error results of the polar motion in the y direction are shown in Table 2: Table 2, Polar Motion Y Direction Prediction Error Statistics ; Based on Table 1 and Table 2, in the short-term forecast of 1 to 10 days, the accuracy of the model of the application is equivalent to that of the traditional least square plus autoregressive model, and both are significantly better than Bulletin A (the maximum improvement in the x direction is 46.15%, and the maximum improvement in the y direction is 42.11%), which proves the effectiveness of the basic model framework; with the extension of the forecast span, the advantage of the application begins to stand out. Compared with Bulletin A, the prediction accuracy of the application in the x and y directions is improved by 37.27% and 25.32%, respectively, in the 365-day forecast span; compared with the traditional least square plus autoregressive model, it is also improved by 14.88% and 13.14%, respectively. This fully proves that the introduction of the differential evolution algorithm to optimize the periodic parameters effectively improves the long-term characterization ability of the model to the complex dynamics of polar motion, and alleviates the problem of rapid decay of the accuracy of the traditional model in long-term prediction. Although the error of the application is slightly higher than that of Bulletin A in individual period in the medium-term span, it is still generally better than the traditional least square plus autoregressive model.

[0033] Figure 2 and Figure 3 respectively show the average absolute error of the four polar motion prediction schemes in the x and y directions. Among them, the LS+AR model, Bulletin A and the model (DE+LS+AR) of the application are represented by blue, red and green curves respectively. The small part of the figure is a local enlarged view of the prediction result of the first 30 days. Figure 2 and 3 It can be seen from the above that, whether in the x direction or in the y direction, compared with the fixed period LS+AR model, the three schemes of the model of the application have significantly improved the prediction accuracy in the medium and long term. Relative to Bulletin A, in the x direction, the short-term (0-16 days) and long-term (135-365 days) prediction accuracy of the model of the application is obviously improved, which shows that the periodic parameters obtained by the method of the application provide a better model basis in the whole prediction period, so that the prediction trajectory is more reasonable, and thus the cumulative error is better controlled at the end of the longer prediction period. Therefore, the differential evolution algorithm combined with the least square and autoregressive model (DE+LS+AR) proposed in the application shows a significant performance improvement in polar motion prediction, especially in the medium and long-term prediction span, which reflects the advancement and reliability of the method.

[0034] In summary, the application takes into account the time-varying nature of the polar motion annual period and the Chandler period, first applies the differential evolution algorithm to the optimization of the polar motion period parameters, optimizes the polar motion period parameters according to the historical data, not only realizes more accurate fitting and prediction of the key elements such as period, amplitude and phase change of the Chandler swing and annual term in the polar motion signal, but also provides a more stable residual sequence for the autoregressive model, thereby significantly improving the accuracy and stability of the polar motion, especially in the medium and long-term prediction span.

[0035] The above embodiments are only used for illustrating the technical solutions of the present application, and are not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some or all of the technical features can be replaced by equivalent replacements, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A polar motion prediction method taking into account periodic time-varying characteristics, characterized in that, Comprise: S1, prepare data set, construct polar motion complex time series, randomly initialize the population of differential evolution algorithm within the preset period parameter boundary, construct the fitting sequence model with the Chandler period and annual period parameters of the population individuals, and solve the fitting values of the population individuals, determine the optimal period parameter combination by maximizing the Pearson correlation coefficient between the fitting sequence and the polar motion observed complex sequence by using the differential evolution algorithm, determine the optimal individual in the polar motion complex time series by adaptive optimization, and take the period parameters of the optimal individual as the optimal period parameter combination; S2, based on the optimal period parameter combination, construct a complex domain harmonic model to calculate the polar motion prediction value, obtain the optimal complex domain harmonic model by least square fitting of the polar motion complex time series, calculate the fitting prediction value according to the optimal complex domain harmonic model, and construct a residual sequence based on the residual between the time series fitting prediction value and the polar motion observed value; S3, construct an autoregressive model for the residual sequence, determine the optimal order and optimal autoregressive coefficient by the final prediction error criterion adaptive and least square method, construct the optimal autoregressive model, and calculate the residual sequence prediction value by using the optimal autoregressive model; S4, add the fitting prediction value and the residual sequence prediction value to obtain the final polar motion prediction result.

2. The polar motion prediction method of claim 1, wherein, S1 includes, S1.1, construct the polar motion complex time series, taking the x direction as the real part and the y direction as the imaginary part: ； wherein is a complex sequence of polar motion observations, is a component of polar motion in the x-direction, is a component of polar motion in the y-direction, is the imaginary unit, is an index of the time series, , is the total length of the time series; S1 comprises, S1.2, within the boundaries of the set chandler period parameter and the annual period parameter, randomly generating an initial population of individuals of two-dimensional vectors of real values, wherein N is the total number of population individuals, wherein D is the total dimensionality of the parameters to be optimized, the parameters to be optimized being: ； ； ； In the formula, For parameters to be optimized, For indexing individuals in the population, Here is the index of the dimension of the parameter to be optimized, and 0 represents the 0th iteration of the differential evolution algorithm. For the 0th generation population The first individual One parameter to be optimized. For the first The upper bound of the parameters to be optimized. For the first The lower bound of the parameters to be optimized. In the interval A random number that is uniformly distributed within the range; S1 comprises, S1.3, constructing a fitted sequence model for the population individuals based on the Chandler period and the annual period of the population individuals S1.3.1, constructing a fitted sequence model for the population individuals based on the Chandler period of the population individuals​ ； In the formula, For the population number The fitted value for each individual, For trend parameters, For linear term parameters, and For the fitting parameters, For the Chandler cycle, It is an annual cycle. It is a six-month cycle. It is a natural constant. For the population number The trend term parameters of the fitted sequence model for each individual. For the population number The linear term parameters of the individual fitted sequence model, and For the population number The fitting parameters of the individual fitted sequence model For the population number Chandler cycles of individuals For the population number The annual cycle of an individual, For the population number A six-month cycle for each individual; The least square method is used to fit the polar motion complex time series with the fitted sequence model, and the , , and are obtained.

3. The polar motion prediction method of claim 2, wherein, S1 includes, S1.4, using the differential evolution algorithm, determine the optimal period parameter combination by maximizing the Pearson correlation coefficient between the fitting sequence and the polar motion observed complex sequence, and the Pearson correlation coefficient is: ； wherein is the Pearson correlation coefficient, is the fitted sequence, is the covariance, is the standard deviation, is the standard deviation of is the standard deviation of is the average over the time series, is the average over the time series; the combination of periodic parameters comprises the Chandler period and the annual period.

4. The polar motion prediction method of claim 3, wherein, S1 includes, S1.5, and the first Each individual in the population undergoes a mutation operation: ； In the formula, For the mutation vector, Let be the number of iterations in the differential evolution algorithm. For the first Generation 1 The mutation vector of each individual, Scaling factor , , For interval Internal and Inequal random integers, and , , The pairs are not equal. , , For from the first Three distinct individuals randomly selected from the population; S1 comprises, S1.6, performing a binary cross operation on and the experimental vectors : ； In the formula, For the first Generation 1 The first experimental vector Parameter values, For interval The index of the dimension variable is randomly selected within the variable. Crossover probability factor For each individual Randomly generated dimension indexes; S1 includes S1.7, defining the fitness function. , To calculate the independent variable of the function based on steps S1.3 and S1.4 ,Will and Substitute them as the independent variables of the function. According to the greed principle, the better one is selected. Generation 1 The parameters to be optimized for each individual: ； S1 includes, S1.8, adaptive optimization includes, repeat steps S1.3 to S1.7 until the maximum iteration number is reached or the convergence condition is met, obtain the optimal individual, and take the optimal individual as the optimal Chandler period and the optimal annual period.

5. The polar motion prediction method of claim 4, wherein, S2 includes, S2.1, based on the optimal Chandler period and the optimal annual period, construct a complex domain harmonic model: ； wherein is the polar motion prediction value, is the optimal Chandler period, is the optimal annual period, is the optimal semiannual period.

6. The polar motion prediction method of claim 5, wherein, S2 comprises, S2.2, performing least square fitting on the polar motion complex time series to obtain , , and optimal values, set as the optimal value of , as the optimal value of , as the optimal value of , as the optimal value of , , , and into the complex domain harmonic model to obtain the optimal complex domain harmonic model: ； wherein is the optimal value of is the optimal value of satisfies the sum of squares of the residuals between the polar motion observations and the predicted values is minimized. S2 comprises, S2.3, based on calculating the residuals between the polar motion observations and the calculated polar motion values, constituting a residual series.

7. The polar motion prediction method of claim 6, wherein, S3 includes, S3.1, based on the residual sequence, construct an autoregressive model: ； In the formula, The residual value, for The residual value at time step, It is a lagged term. The model order is... For the index of the model order, , These are the autoregressive coefficients. For the first The autoregressive coefficient of order, It is white noise. for White noise at any given moment.

8. The polar motion prediction method of claim 7, wherein, S3 comprises, S3.2, determining by a final pre-error criterion adaptation and least square method The final pre-error criterion formula is: ； ； wherein is the final prediction error value when the autoregressive model order is , is the sample size, is the residual variance of the autoregressive model of order , is the optimal satisfying is minimal.

9. The polar motion prediction method of claim 8, wherein, S3 comprises, S3.3, determining Substitute into the autoregressive model, using the least squares method to calculate the corresponding autoregressive coefficients ; The and the corresponding substituted into the autoregressive model, the optimal autoregressive model is obtained: ； In the formula, is the prediction value for the residual sequence.

10. The polar motion prediction method of claim 9, wherein, S4 includes, add the fitting prediction value and the residual sequence prediction value to obtain the final polar motion prediction result: ； In the formula, is the final polar motion prediction result.

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