A combined LS+MAR method for predicting Earth rotation parameters

Abstract

A combined LS+MAR method for predicting Earth's rotation parameters includes the following steps: S1, acquiring polar motion observation data via files or the network; S2, fitting the trend and periodic terms of the predicted polar motion using the LS method, and calculating the random term of the polar motion; S3, predicting the random term of the polar motion using the MAR method based on Kalman filtering; S4, combining the trend, periodic, and random terms of the predicted polar motion to obtain the predicted polar motion. This LS+MAR combined method for predicting Earth's rotation parameters utilizes the real-time processing capabilities of Kalman filtering to construct an observation model and state equation model suitable for MAR model estimation, thereby significantly improving the accuracy of polar motion prediction.

Description

Technical Field

[0001] This invention relates to the fields of geodesy and satellite navigation technology, and in particular to a method for predicting Earth rotation parameters using a combination of LS+MAR, which is mainly applicable to improving the accuracy of polar motion prediction. Background Technology

[0002] Polar motion (PM, comprising two parameters PMx and PMy) can be accurately observed and estimated using modern space geodesy techniques such as LLR, SLR, GNSS, DORIS, and VLBI. However, the complexity of data processing and measurement models makes estimating accurate PMx and PMy extremely time-consuming. Therefore, accurate PMx and PMy are typically only available hours to days after observation, which is insufficient for real-time navigation requirements of satellites and spacecraft. Thus, accurate prediction of PMx and PMy is crucial.

[0003] Improving the accuracy of short-term polar motion prediction has always been a hot topic of concern and research in the fields of geodesy and satellite navigation. Currently, the LS+AR method is mainly recommended both domestically and internationally for short-term polar motion prediction. Furthermore, research has shown that the LS+MAR method is beneficial for predicting Earth's rotation parameters. However, the current accuracy of polar motion predictions does not fully meet user expectations, and no one has yet constructed a Kalman-based LS+MAR combined model, thus limiting the current accuracy of polar motion predictions. Summary of the Invention

[0004] The purpose of this invention is to overcome the defects and problems of low polar motion prediction accuracy in the existing technology, and to provide a high-accuracy LS+MAR combined Earth rotation parameter prediction method.

[0005] To achieve the above objectives, the technical solution of this invention is: a method for predicting Earth rotation parameters using a combination of LS+MAR, which includes the following steps:

[0006] S1. Obtain polar motion observation data via file or network;

[0007] S2. Fit the trend and periodic terms of the predicted polar shift using the LS method, and calculate the random term of the polar shift;

[0008] S3. The MAR method based on Kalman filtering predicts the random term of polar shift;

[0009] S4. The predicted polar motion is obtained by combining the trend, periodic and stochastic terms of the predicted polar motion.

[0010] In step S3, the observation model for the random term of the polar shift is:

[0011]

[0012] In the formula, The polar shift random term at time t, For the coefficients of the MAR model at time t, Let ε be the unknown parameter to be estimated in the MAR model at time t. t To observe noise.

[0013] In step S3, during the estimation of the MAR model... At that time, the state equation model is constructed as follows:

[0014]

[0015] φ t，t-1 =I

[0016]

[0017] In the formula, φ t，t-1 Let be the state transition matrix of the parameter to be estimated. Let D be the unknown parameter to be estimated in the MAR model at time t-1. t for The covariance matrix, where I is the identity matrix, J t Let D be the gain matrix. t，t-1 This is the covariance matrix used to predict from time t-1 to time t.

[0018] In step S3, D t，t-1 and J t The calculation formula is as follows:

[0019]

[0020]

[0021] In the formula, D t-1 for The covariance matrix, φ is the state transition matrix of the parameter to be estimated. t，t-1 The transpose of R ε This is the observation noise matrix.

[0022] In step S3, the observation noise matrix R ε for:

[0023]

[0024] In the formula, R1 and R2 represent the magnitude of the observation noise in the two polar motion directions, respectively.

[0025] In step S3, before each set of Earth rotation parameters is predicted, historical experience data is used to perform simulation prediction error statistics using R2 = (0.01~100)R1 and R1 = 0.1 respectively to obtain the coefficient β with the smallest prediction error. Then, R2 is calculated using R2 = βR1 and R1 = 0.1.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] In this invention, a combined LS+MAR method for predicting Earth rotation parameters utilizes the real-time processing capabilities of Kalman filtering to construct an observation model and a state equation model suitable for MAR model estimation, thereby significantly improving the accuracy of polar motion prediction. Therefore, this invention improves the accuracy of polar motion prediction. Attached Figure Description

[0028] Figure 1 This is a flowchart of the LS+MAR combined Earth rotation parameter prediction method of the present invention.

[0029] Figure 2 This is a schematic diagram showing the mean absolute error of the polar shift X-direction prediction results of the present invention and the conventional method.

[0030] Figure 3 This is a schematic diagram showing the mean absolute error of the polar shift Y-direction prediction results of the present invention and the traditional method. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] See Figure 1 A method for predicting Earth rotation parameters using a combination of LS and MAR methods, comprising the following steps:

[0033] S1. Obtain polar motion observation data via file or network;

[0034] S2. Fit the trend and periodic terms of the predicted polar shift using the LS method, and calculate the random term of the polar shift;

[0035] S3. The MAR method based on Kalman filtering predicts the random term of polar shift;

[0036] S4. The predicted polar motion is obtained by combining the trend, periodic and stochastic terms of the predicted polar motion.

[0037] In step S3, the observation model for the random term of the polar shift is:

[0038]

[0039] In the formula, The polar shift random term at time t, For the coefficients of the MAR model at time t, Let ε be the unknown parameter to be estimated in the MAR model at time t. t To observe noise.

[0040] In step S3, during the estimation of the MAR model... At that time, the state equation model is constructed as follows:

[0041]

[0042] φ t，t-1 =I

[0043]

[0044] In the formula, φ t，t-1 Let be the state transition matrix of the parameter to be estimated. Let D be the unknown parameter to be estimated in the MAR model at time t-1. t for The covariance matrix, where I is the identity matrix, J t Let D be the gain matrix. t，t-1 This is the covariance matrix used to predict from time t-1 to time t.

[0045] In step S3, D t，t-1 and J t The calculation formula is as follows:

[0046]

[0047]

[0048] In the formula, D t-1 for The covariance matrix, φ is the state transition matrix of the parameter to be estimated. t，t-1 The transpose of R ε This is the observation noise matrix.

[0049] In step S3, the observation noise matrix R ε for:

[0050]

[0051] In the formula, R1 and R2 represent the magnitude of the observation noise in the two polar motion directions, respectively.

[0052] In step S3, before each set of Earth rotation parameters is predicted, historical experience data is used to perform simulation prediction error statistics using R2 = (0.01~100)R1 and A1 = 0.1 respectively to obtain the coefficient β with the smallest prediction error. Then, R2 is calculated using R2 = βR1 and R1 = 0.1.

[0053] The principle of this invention is explained as follows:

[0054] This invention proposes a novel method for predicting Earth rotation parameters based on the Kalman LS+MAR combined model. On one hand, it leverages the inherent suitability of Kalman filtering for real-time processing; on the other hand, it fully utilizes the advantages of the MAR model in handling multiple parameters. Therefore, fully exploring and utilizing this information will help improve the existing accuracy of polar motion prediction. Compared with traditional LS+AR and traditional LS+MAR techniques, this design, based on the Kalman real-time estimation principle, significantly improves the accuracy of polar motion prediction by constructing an observation model and a state equation model suitable for MAR model estimation.

[0055] Example:

[0056] See Figure 1 A method for predicting Earth rotation parameters using a combination of LS and MAR methods, comprising the following steps:

[0057] S1. Obtain polar motion observation data via file or network;

[0058] S2. Fit the trend and periodic terms of the predicted polar shift using the LS method, and calculate the random term of the polar shift;

[0059] S3. The MAR method based on Kalman filtering predicts the random term of polar shift;

[0060] The observation model for the random term of polar shift is:

[0061]

[0062] In the formula, The polar shift random term at time t, For the coefficients of the MAR model at time t, Let ε be the unknown parameter to be estimated in the MAR model at time t. t To observe noise;

[0063] In estimating the MAR model At that time, the state equation model is constructed as follows:

[0064]

[0065] φ t，t-1 =I

[0066]

[0067] In the formula, φ t，t-1 Let be the state transition matrix of the parameter to be estimated. Let D be the unknown parameter to be estimated in the MAR model at time t-1. t for The covariance matrix, where I is the identity matrix, J t Let D be the gain matrix. t，t-1 The covariance matrix used to predict from time t-1 to time t;

[0068] D t，t-1 and J t The calculation formula is as follows:

[0069]

[0070]

[0071] In the formula, D t-1 for The covariance matrix, φ is the state transition matrix of the parameter to be estimated. t，t-1 The transpose of R ε The observation noise matrix;

[0072] Observation noise matrix R ε for:

[0073]

[0074] In the formula, R1 and R2 represent the magnitude of the observation noise in the two directions of polar motion, respectively;

[0075] Before each set of Earth rotation parameters is predicted, historical experience data is used to perform simulation prediction error statistics using R2 = (0.01~100)R1 and R1 = 0.1 respectively, to obtain the coefficient β with the smallest prediction error. Then, R2 is calculated using R2 = βR1 and R1 = 0.1. Thus, the mathematical model of the MAR method based on Kalman filtering in this prediction can be obtained.

[0076] Therefore, based on the model constructed above, the random term of polar shift can be predicted using the MAR method with Kalman filtering;

[0077] S4. The predicted polar motion is obtained by combining the trend, periodic and stochastic terms of the predicted polar motion.

[0078] See Figure 2 , Figure 3This embodiment presents statistical results from 210 forecasts, each forecasting 1 to 10 days in advance. Here, MAE represents the mean absolute error of the predicted polar motion, PMx represents the polar motion in the X direction, and PMY represents the polar motion in the Y direction. LS+AR and LS+MAR represent the forecast error results of the conventional methods, while LS+MAR+Kalman represents the forecast error results of this invention. Therefore, the results show that the polar motion prediction results obtained by the novel Kalman-based LS+MAR combined Earth rotation parameter prediction method of this invention significantly improve the prediction accuracy in the Y direction of polar motion compared to the traditional LS+AR and LS+MAR methods, demonstrating a clear advantage.

Claims

1. A method for predicting Earth rotation parameters using a combined LS+MAR method, characterized in that, The method includes the following steps: S1. Obtain polar motion observation data via file or network; S2. Fit the trend and periodic terms of the predicted polar shift using the LS method, and calculate the random term of the polar shift; S3. The MAR method based on Kalman filtering predicts the random term of polar shift; The observation model for the random term of polar shift is: In the formula, The polar shift random term at time t, For the coefficients of the MAR model at time t, Let ε be the unknown parameter to be estimated in the MAR model at time t. t To observe noise; In estimating the MAR model At that time, the state equation model is constructed as follows: f t，t-1 =I; In the formula, φ t,t-1 Let be the state transition matrix of the parameter to be estimated. Let D be the unknown parameter to be estimated in the MAR model at time t-1. t for The covariance matrix, where I is the identity matrix, J t Let D be the gain matrix. t,t-1 The covariance matrix used to predict from time t-1 to time t; D t，t-1 and J t The calculation formula is as follows: In the formula, D t-1 for The covariance matrix, φ is the state transition matrix of the parameter to be estimated. t，t-1 The transpose of R ε The observation noise matrix; Observation noise matrix R ε for: In the formula, R1 and R2 represent the magnitude of the observation noise in the two directions of polar motion, respectively; Before each set of Earth rotation parameters is predicted, historical experience data is used to perform simulation prediction error statistics using R2 = (0.01~100)R1 and R1 = 0.1 respectively to obtain the coefficient β with the smallest prediction error. Then, R2 is calculated using R2 = βR1 and R1 = 0.

1. S4. The predicted polar motion is obtained by combining the trend, periodic and stochastic terms of the predicted polar motion.

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