CN114971003B - Earth rotation motion prediction method and system based on rotation parameter prediction model - Google Patents

Abstract

The invention provides an earth rotation motion prediction method and system based on a rotation parameter prediction model, comprising the steps of carrying out data preprocessing operation on an original sequence, and selecting a periodic item with the largest amplitude by utilizing Fourier spectrum analysis; judging whether the maximum amplitude in the spectrum analysis result is smaller than a set threshold value, if so, ending iteration, if not, subtracting the part of the periodic item with the maximum amplitude in the original sequence by the original sequence to form a new sequence, and returning to iteration to carry out Fourier spectrum analysis on the new sequence; after the iteration is finished, constructing a weight matrix by using the observation precision of the earth rotation parameter sequence; combining the Fourier fitting model and the polynomial curve fitting model to establish a combined mathematical model; fitting is carried out by utilizing all the cycle items and the order items extracted before, and the earth rotation motion prediction result is output through cycle extraction and time sequence fitting.

Description

Earth rotation motion prediction method and system based on rotation parameter prediction model

Technical Field

The invention belongs to the field of space geodesy, and relates to a new method for predicting the earth's rotation motion by fitting the earth's rotation parameters with a weighted Fourier joint polynomial curve based on period extraction using a step-by-step method.

Background Art

The existing methods for predicting the Earth's rotation motion have the following main defects:

1. A common method in the statistical analysis of the Earth's rotation parameters is spectrum analysis based on Fourier transform, while the traditional method usually adopts a one-step method for period extraction of spectrum analysis results, that is, directly setting a threshold for screening, which will lead to noise in the extraction results and some periods that contribute less to the Earth's rotation parameter sequence.

Second, when fitting and predicting the Earth's rotation parameter sequence, there are currently mainly linear models and nonlinear models. Among the linear models, the one with better accuracy is the Fourier fitting + autoregression (LS+AR) model based on least squares, in which the LS fitting part mainly uses constant terms, linear terms, and periodic terms for fitting; while the polynomial curve fitting (PCF) in the linear model uses constant terms and different order terms for fitting, and the calculation method mostly uses indirect adjustment based on least squares for calculation. Using these two technologies alone has their own shortcomings:

(1) The least squares-based Fourier fitting can achieve good fitting results in some time periods. However, due to the influence of periodic term extraction, overfitting or underfitting may occur in some time periods.

(2) Polynomial curve fitting can only reflect the changes of the entire time series because there is no periodic term added. Its fitting result cannot accurately match the original series.

3. In addition, when fitting and predicting the Earth's rotation parameter sequence, traditional methods ignore the impact of different observation accuracies of the observation sequence in different time periods.

Summary of the invention

In view of the above-mentioned first defect of the prior art, the present invention, based on the previous research of scholars, proposes to use a step-by-step method to extract the period of the spectrum analysis results, so as to more accurately obtain the inherent period of the earth's rotation parameters.

In response to the above-mentioned second defect of the prior art, the present invention, based on the previous research of scholars, proposes a combination of Fourier fitting and polynomial curve fitting, which can utilize the overall stability of the polynomial curve and the advantage of high fitting accuracy of Fourier fitting in some time periods, thereby achieving a better fitting effect than the two.

In view of the third defect of the prior art, the present invention proposes, based on previous studies, to use observation accuracy to construct a weight matrix to replace the unit weight matrix for fitting and forecasting.

In order to achieve the above object, the present invention proposes a method for predicting the earth's rotation motion based on a rotation parameter prediction model, comprising the following steps:

a) Firstly, the original sequence is preprocessed, and then Fourier spectrum analysis is used to select the periodic item with the largest amplitude;

b) determining whether the maximum amplitude in the spectrum analysis result is less than a set threshold value, if so, proceeding to step d), if not, proceeding to step c);

c) subtracting the portion of the periodic term with the largest amplitude in the original sequence from the original sequence to form a new sequence, and returning to step a) to perform Fourier spectrum analysis on the new sequence;

d) Constructing the weight matrix using the observation accuracy of the Earth's rotation parameter sequence;

e) combining the Fourier fitting model and the polynomial curve fitting model to establish an earth rotation parameter fitting model;

f) Based on the Earth rotation parameter fitting model, all the periodic terms and order terms extracted previously are used for fitting, and the prediction results of the Earth rotation motion are output through period extraction and time series fitting.

Furthermore, in step a), data preprocessing operations are performed on the original sequence, including deducting the solid earth tide term in the day length variation LOD.

Furthermore, in step c), when the period T _nc extracted for the ncth time is substituted into the following formula, a new sequence is calculated;

Where nc represents the number of extracted cycles, nc = 1, 2, ..., tc, tc is the total number of extracted cycle items; The t-th value of the Earth's rotation parameter before the nc-th extraction; is the t-th Earth rotation parameter value after subtracting the nc-th extracted periodic term, A _nc is the amplitude of the signal at period T _nc , is the phase of the signal in period T _nc , c _nc and d _nc are intermediate parameters.

Moreover, in step d), the weight matrix P is constructed using the observation accuracy of the earth's rotation parameters as follows:

in is the observation accuracy of each element in the Earth rotation parameter sequence, is the unit weighted observation accuracy, and n is the number of Earth rotation parameters in the Earth rotation parameter sequence.

Furthermore, in step e), the earth rotation parameter fitting model is established as follows:

Where _Xt is the tth value of the Earth rotation parameter; a is a constant term; g is the order of the order term, g = 1, 2, ..., p, p is the number of order terms, _bg is the coefficient of each order term; r is the number of periodic terms, r = 1, 2, ..., q, q is the total number of periodic terms, A _r is the amplitude of the Earth rotation parameter sequence at period T _r , is the phase of the signal in period _Tr , _cr and _dr are intermediate parameters; ε _LS+PCF (t) is the observed noise.

Moreover, in step f), the LOD sequence of day length variation is fitted using the earth rotation parameter fitting model, and the result is used to establish an ERP prediction model to provide an ERP prediction value; the ERP is the earth rotation parameter.

Moreover, it is used by the GNSS Analysis Center for ultra-rapid orbit prediction.

Moreover, for satellite navigation, when the satellite enters the autonomous orbit determination mode, the uplink communication link from the ground to the satellite is interrupted, and the long-term predicted EOP is used to achieve the conversion between the Earth's center of mass celestial reference system and the international earth reference system.

On the other hand, the present invention provides an earth rotation motion prediction system based on a rotation parameter prediction model, which is used to implement the earth rotation motion prediction method based on a rotation parameter prediction model as described above.

Furthermore, it includes a processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute the above-mentioned method for predicting the earth's rotation motion based on the rotation parameter prediction model.

Compared with the prior art, the present invention has the advantages of high fitting accuracy and fast fitting speed in the fitting of earth rotation parameters;

Compared with the prior art, the present invention can provide longer-term and more accurate prediction values of the earth's rotation for autonomous navigation satellites; and under the condition of the same prediction accuracy, the present invention requires less measured data in the solution, and has the advantage of higher data utilization;

Compared with the prior art, the present invention has the advantages of wide application and strong practicality. It can be applied not only to the fields of astronomical geodesy, satellite autonomous orbit determination and satellite navigation positioning, but also to provide important technical support for the research in the fields of geophysics, global atmospheric motion, global ocean motion, etc.

The solution of the present invention is simple and convenient to implement, has strong practicality, solves the problems of low practicality and inconvenience in actual application existing in related technologies, can improve user experience, and has important market value.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method according to an embodiment of the present invention.

DETAILED DESCRIPTION

The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

The present invention proposes that, first, Fourier spectrum analysis is performed on the original sequence, and then the periodic term with the largest amplitude is selected, and then the portion of the periodic term in the original sequence is subtracted from the original sequence to form a new sequence; spectrum analysis is then performed on the new sequence, and then the periodic term with the largest amplitude is selected, and the portion of the periodic term is subtracted to form a new sequence, and this cycle is repeated until the maximum amplitude in the spectrum analysis result is less than a set threshold.

Then the Fourier fitting model and the polynomial curve fitting model are combined to establish the Earth rotation parameter fitting model. The weight matrix is constructed using the observation accuracy, and the results of the step-by-step method period extraction and the appropriate order are used for fitting. Then, mathematical indicators such as RMSE and determination coefficient ^R2 are calculated to judge the model accuracy.

Referring to FIG. 1 , an embodiment of the present invention proposes a method for fitting and predicting the rotation of the earth based on an improved prediction model of rotation parameters, comprising the following steps:

a) First, the original sequence is preprocessed (only for the LOD of day length change), and then the periodic item with the largest amplitude is selected by Fourier spectrum analysis;

b) determining whether the maximum amplitude in the spectrum analysis result is less than a set threshold value, if so, proceeding to step d), if not, proceeding to step c);

c) subtracting the portion of the periodic term with the largest amplitude in the original sequence from the original sequence to form a new sequence; and returning to step a) to perform Fourier spectrum analysis on the new sequence;

d) Constructing the weight matrix using the observation accuracy of the Earth's rotation parameter sequence;

e) combining the Fourier fitting model and the polynomial curve fitting model to establish an earth rotation parameter fitting model;

f) Use the results of the step-by-step period extraction (i.e., all period terms extracted by the previous iterative execution of steps a)-c) and the order terms for fitting. In specific implementation, the control can be adjusted by changing the number of order terms to obtain the best fitting effect. After fitting, mathematical indicators such as RMSE can be calculated to judge the accuracy of the model. Through period extraction and time series fitting, the final prediction result of the earth's rotation motion is output.

For ease of implementation and reference, the above steps a, b, and c are explained in detail as follows:

1) Perform data preprocessing on the original sequence (only for the day length change LOD), that is, deduct the solid earth tidal term in the LOD. The tidal term δΔLOD is calculated as follows:

where _αj is the abbreviation of _αj (l,l′,F,D,Ω), _αj (l,l′,F,D,Ω) is the basic parameter of the solar and lunar nutation, _aij represents the integer multiplication factor of _αj (l,l′,F,D,Ω), the number of harmonic tidal terms is 62, so the value of variable i ranges from 1 to 62; there are 5 basic parameters of the solar and lunar nutation, namely l, l′, F, D, Ω, so the value of variable j ranges from 1 to 5; _ξi is the parameter of the sine and cosine of the harmonic tidal terms in the day length variation sequence; _B′i is the multiplication factor of the cosine part of the harmonic tidal term in the day length variation sequence; _C′i is the multiplication factor of the sine part of the harmonic tidal term in the day length variation sequence; the values of _aij , _B′i and _C′i can be found in IERS Conventions (2010) published on the IERS official website.

l, l′, F, D, and Ω are the basic parameters of the solar and lunar nutation, and their calculation formulas are as follows: where t is the Julian century number, and MJD comes from the EOP 14C04 product released on the IERS official website.

l＝134.96340251°+1717915923.2178″t+31.8792″t ² +0.051635″t ³ -0.00024470″t ⁴

l′＝357.52910918°+129596581.0481″t-0.5532″t ² +0.000136″t ³ -0.00001149″t ⁴

F＝93.27209062°+1739527262.8478″t-12.7512″t ² -0.001037″t ³ +0.00000417″t ⁴

F＝93.27209062°+1739527262.8478″t-12.7512″t ² -0.001037″t ³ +0.00000417″t ⁴

Ω＝125.04455501°-6962890.5431″t+7.4722″t ² +0.007702″t ³ -0.00005939″t ⁴

t＝(MJD-51544.5)/36525

2) Then use Fourier transform to calculate the amplitude spectrum, the formula is as follows;

Where n is the number of earth rotation parameters in the earth rotation parameter sequence; parameter label t = 1, 2, ..., n; _xt represents the earth rotation parameter sequence; i is the number of harmonic components calculated by Fourier transform, i = 1, 2, ..., int(n/2), int represents rounding down; si _is the spectrum amplitude of the i-th harmonic component in the signal.

3) Then perform period extraction, substitute the period T _nc extracted for the ncth time into the following formula to calculate the new sequence;

Where nc represents the number of extracted cycles, nc = 1, 2, ..., tc, tc is the total number of extracted cycle items, and the value of tc depends on the set threshold value; The t-th value of the Earth's rotation parameter before the nc-th extraction; is the t-th Earth rotation parameter value after subtracting the nc-th extracted periodic term, A _nc is the amplitude of the signal at period T _nc , is the phase of the signal in period T _nc , c _nc and d _nc are intermediate parameters.

For ease of implementation and reference, the above step d is explained in detail as follows:

The weight matrix P is constructed using the observation accuracy of the Earth's rotation parameters; is the observation accuracy of each element in the Earth rotation parameter sequence, is the unit weight observation accuracy.

For ease of implementation and reference, the above steps e and f are explained in detail as follows:

The Fourier fitting model and the polynomial curve fitting model are combined to establish the Earth rotation parameter fitting model, that is, the Fourier combined polynomial curve fitting model, which can be recorded as the LS+PCF model. The specific form of the model is as follows:

Where _Xt is the tth value of the Earth rotation parameter; a is a constant term; g is the order of the order term, g = 1, 2, ..., p, p is the number of order terms, _bg is the coefficient of each order term ^tg ; r is the number of periodic terms, r = 1, 2, ..., q, q is the total number of periodic terms, A _r is the amplitude of the Earth rotation parameter sequence at period T _r , is the phase of the signal in period _Tr , _cr and _dr are intermediate parameters; ε _LS+PCF (t) is the observed noise.

If n>2q+p+1, the parameters of the LS+PCF model can be calculated by the following formula:

α＝( ^{ATPA ) -1ATPL}

α＝[ab ₁ ... b _p c ₁ d ₁ ... c _q d _q ] ^T

L＝[x ₁ x ₂ ... x _n ] ^T

Where α is the parameter to be determined, A is the coefficient matrix, L is the observation vector, and P is the observation vector weight matrix and is usually the unit matrix. (1 ¹ ,...,1 ^p ) are the different order terms in the fitting function corresponding to the first value in the Earth rotation parameter sequence, (2 ¹ ,...,2 ^p ) are the different order terms in the fitting function corresponding to the second value in the Earth rotation parameter sequence, ... Similarly, (n ¹ ,...,n ^p ) are the different order terms in the fitting function corresponding to the nth or last value in the Earth rotation parameter sequence; (T ₁ ,...,T _q ) are the values of different periodic terms in the Earth rotation parameter sequence.

In specific implementation, if n>2q+p+1 is not satisfied, the amount of data n can be increased, or the number of periodic terms q and the number of order terms p can be reduced.

The above-mentioned Earth rotation parameter fitting model was used to fit the LOD series of day length variation. The results showed that the model inherited the advantages of high fitting accuracy of Fourier fitting in some time periods and high overall stability of polynomial curve fitting. The fitting results showed that the RMSE was reduced to 0.0001 seconds, while the RMSE of a single Fourier fitting was close to 0.0003 seconds. The coefficient of determination ^R2 was increased to about 0.97, which was significantly improved compared to 0.8 of a single Fourier fitting.

This method can provide a new period extraction method and time series fitting method for the establishment of the existing Earth rotation parameter (ERP) prediction model in the prior art (i.e., the rotation parameter prediction model referred to in the present invention, which will not be described in detail), thereby establishing a more accurate ERP prediction model, and providing important ERP prediction values for the fields of astronomical geodesy, satellite autonomous orbit determination, and satellite navigation and positioning. For example, when the GNSS analysis center is performing ultra-rapid orbit prediction, it is usually only possible to use the ERP prediction value for ultra-rapid orbit prediction because it is unable to obtain accurate ERP in real time; or in satellite navigation technology, in order to reduce the dependence of navigation satellites on the ground control segment and improve their survivability under navigation warfare conditions, an autonomous navigation mode will be adopted. However, when the satellite enters the autonomous orbit determination mode, the uplink communication link from the ground to the satellite is interrupted, and only the long-term predicted EOP can be used to achieve the conversion between the Earth's center of mass celestial reference system and the international earth reference system.

The embodiment uses the above principle to establish a software platform to perform fitting and solving on the traditional method and the new method respectively, and verifies them with actual data and simulation data.

In specific implementation, the method proposed in the technical solution of the present invention can be implemented by technical personnel in this field using computer software technology to realize automatic operation process. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of the present invention and computer equipment running the corresponding computer program, should also be within the protection scope of the present invention.

In some possible embodiments, a system for predicting the earth's rotation motion based on a rotation parameter prediction model is provided, comprising a processor and a memory, wherein the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a method for predicting the earth's rotation motion based on a rotation parameter prediction model as described above.

In some possible embodiments, a system for predicting the earth's rotation motion based on a rotation parameter prediction model is provided, comprising a readable storage medium having a computer program stored thereon. When the computer program is executed, a method for predicting the earth's rotation motion based on a rotation parameter prediction model as described above is implemented.

The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims (7)

1. The earth rotation motion prediction method based on the rotation parameter prediction model is characterized by comprising the following steps of: comprises the steps of,

A) Firstly, carrying out data preprocessing operation on an original sequence, and then utilizing Fourier spectrum analysis to select a periodic item with the maximum amplitude;

b) Judging whether the maximum amplitude in the spectrum analysis result is smaller than a set threshold value, if so, entering the step d), otherwise, entering the step c);

c) Subtracting the part of the periodic item with the largest amplitude in the original sequence from the original sequence to form a new sequence, and returning to the step a) to perform Fourier spectrum analysis on the new sequence;

d) Constructing a weight matrix by utilizing the observation precision of the earth rotation parameter sequence;

e) Combining the Fourier fitting model and the polynomial curve fitting model to establish an earth rotation parameter fitting model;

f) Based on the earth rotation parameter fitting model, fitting by utilizing all the period items and the order items extracted before, and outputting an earth rotation motion prediction result through period extraction and time sequence fitting;

In step c), when the period T _nc extracted for the nc-th time is brought into the following formula, a new sequence is calculated;

Where nc represents the number of extraction cycles, nc=1, 2,..tc, tc is the total number of extracted cycle terms; The value of the t-th earth rotation parameter before the nc-th extraction; To subtract the value of the tth earth rotation parameter after the period term of the nc-th extraction, a _nc is the amplitude of the signal at period T _nc, Is the phase of the signal at period T _nc, c _nc、d_nc is an intermediate parameter;

In step d), the weight matrix P is constructed using the observation accuracy of the earth rotation parameter as follows,

Wherein the method comprises the steps ofIs the observation precision of each element in the earth rotation parameter sequence,The unit weight observation precision is that n is the number of the earth rotation parameters in the earth rotation parameter sequence;

In step e), an earth rotation parameter fitting model is established as follows,

Wherein X _t is the t-th earth rotation parameter value; a is a constant term; g is the order of the order terms, g=1, 2,..p, p is the number of order terms, b _g is the coefficient of each order term; r is the number of terms of the period term, r=1, 2,..q, q is the total number of period terms, a _r is the amplitude of the earth rotation parameter sequence at period T _r,Is the phase of the signal at period T _r, c _r、d_r is an intermediate parameter; epsilon _LS+PCF (t) is the observed noise.

2. The earth rotation motion prediction method based on the rotation parameter prediction model according to claim 1, wherein: in step a), the original sequence is subjected to a data preprocessing operation, including subtraction of solid earth tide terms in the log variation LOD.

3. The earth rotation motion prediction method based on the rotation parameter prediction model according to claim 1 or 2, characterized in that: in the step f), fitting the solar length variation LOD sequence by using an earth rotation parameter fitting model, wherein the result is used for establishing an ERP forecasting model and providing an ERP forecasting value; the ERP is an earth rotation parameter.

4. The earth rotation motion prediction method based on rotation parameter prediction model according to claim 3, wherein: the method is used for the GNSS analysis center to conduct ultra-fast orbit forecasting.

5. The earth rotation motion prediction method based on rotation parameter prediction model according to claim 3, wherein: when the satellite enters the autonomous orbit determination mode, the uplink communication chain from the ground to the satellite is interrupted, and the long-term forecast EOP is used for realizing the conversion between the earth centroid celestial sphere reference system and the international earth reference system.

6. An earth rotation motion prediction system based on a rotation parameter prediction model is characterized in that: an earth rotation motion prediction method based on rotation parameter prediction model according to any one of claims 1-5.

7. The earth rotation motion prediction system based on rotation parameter prediction model according to claim 6, wherein: the method comprises a processor and a memory, wherein the memory is used for storing program instructions, and the processor is used for calling the stored instructions in the memory to execute the earth rotation motion prediction method based on the rotation parameter prediction model according to any one of claims 1-5.