GPS satellite clock error combined forecasting method based on entropy weight method

Abstract

The invention discloses a GPS satellite clock error combined forecasting method based on an entropy weight method, which relates to the field of GPS satellite clock error forecasting, and comprises the following steps: constructing a quadratic polynomial model and a grey model, and respectively substituting original satellite clock error data into the quadratic polynomial model and the grey model to carry out first clock error forecasting and second clock error forecasting; generating an error matrix of a quadratic polynomial model and a gray model according to the first clock error forecast and the second clock error forecast; standardizing the error matrix to obtain a standard error matrix, and calculating information entropy of data in the standard error matrix; entropy weights of the quadratic polynomial model and the gray model are calculated; and multiplying the forecast value of the first clock correction forecast by the entropy weight of the quadratic polynomial model, multiplying the forecast value of the second clock correction forecast by the entropy weight of the gray model to obtain a combined forecast model, forecasting the GPS satellite clock correction through the combined forecast model, and obtaining a forecast result with higher precision by using a weighted combination method.

Description

Technical Field

[0001] The invention relates to the field of GPS satellite clock error prediction, in particular to a GPS satellite clock error combined prediction method based on an entropy weight method. Background Art

[0002] The Global Navigation Satellite System (GNSS) is a time-based system. The accuracy of its navigation, positioning and timing (PNT) depends largely on the accuracy of time measurement. In the Precise Point Positioning (PPP) technology, in order to obtain centimeter-level positioning accuracy, it is necessary to use the predicted satellite clock difference as a known quantity to substitute into the equation for positioning solution. Therefore, predicting high-precision satellite clock difference is an important prerequisite for realizing centimeter-level PPP technology, and its accuracy will directly affect the positioning performance of PPP technology.

[0003] Many scholars at home and abroad have conducted extensive and in-depth research and achieved a series of research results. For example, the quadratic polynomial model (QPM), the grey model (GM(1,1)), the auto-regressive moving average model (ARMA) and the spectrum analysis model (SA). These methods are applicable to the prediction of navigation satellite atomic clock clock errors under different conditions, but each method has its scope of application and limitations. For example, the quadratic polynomial model uses time as an independent variable to fit historical clock error data. It is easy to calculate and has high short-term prediction accuracy, but its long-term prediction accuracy will decrease significantly with time. The grey model is suitable for small samples and uncertain data and has strong anti-interference ability, but its adaptability on different satellite clocks is different and it is highly dependent on the amount of data, which may lead to large errors. The auto-regressive moving average model can effectively capture the linear dependence structure of time series data and is suitable for the prediction of stationary series clock errors, but it has poor adaptability to non-stationary series and the choice of model order is difficult to determine. The spectral analysis model can process clock error series with periodic characteristics, but it may not perform well on non-periodic data and its parameter estimation is more complicated.

[0004] In order to solve these problems, it is urgent to develop a GPS satellite clock error combined prediction method based on the entropy weight method to achieve optimal fusion of the model and use the weighted combination method to obtain more accurate prediction results. Summary of the invention

[0005] In order to solve the above problems and improve the accuracy and stability of satellite clock error prediction, this application proposes a GPS satellite clock error combined prediction method based on the entropy weight method, the specific contents are as follows:

[0006] The GPS satellite clock error combined prediction method based on the entropy weight method includes the following steps:

[0007] S1. Construct a quadratic polynomial model and a grey model, obtain original satellite clock difference data, and bring the original satellite clock difference data into the quadratic polynomial model and the grey model for the first clock difference prediction and the second clock difference prediction;

[0008] S2, generating error matrices Z′ of a quadratic polynomial model and a grey model according to the first clock error forecast and the second clock error forecast;

[0009] S3. Standardize the error matrix Z′ to obtain the standard error matrix Z, and calculate the information entropy e of the data in the standard error matrix Z. j ;

[0010] S4. According to the information entropy of the data j Calculate the entropy weight w of the quadratic polynomial model and the grey model, where the entropy weight of the quadratic polynomial model is denoted as w1 and the entropy weight of the grey model is denoted as w2;

[0011] S5. Multiply the predicted value of the first clock error prediction by the entropy weight w1 of the quadratic polynomial model, and multiply the predicted value of the second clock error prediction by the entropy weight w2 of the grey model to obtain a combined prediction model, and predict the GPS satellite clock error through the combined prediction model.

[0012] Preferably, the quadratic polynomial model in S1 is constructed in the following manner:

[0013] A set of satellite clock error time series is preset as y1, y2, ..., y n , the corresponding time is t1, t2, ..., t n , the following quadratic polynomial model is established for this set of satellite clock error time series:

[0014]

[0015] Among them, t i (i=1,2,…,n) is the time, ε i (i=1,2,…,n) is the residual, quadratic polynomial coefficients a0, a1 and a2.

[0016] Preferably, the quadratic polynomial coefficients a0, a1 and a2 are determined by the least squares method, that is, the sum of squares S of the residuals is minimized;

[0017] The expression of the residual sum of squares S is:

[0018]

[0019] Among them, y i (i=1,2,…,n) is t i Satellite clock error at time (i=1,2,…,n).

[0020] By taking the partial derivatives of S with respect to a0, a1 and a2 and setting them equal to zero, we can get a set of linear equations, which are expressed as follows:

[0021]

[0022] The linear equation is arranged to obtain the standard linear equation, and the standard linear equation expression is:

[0023]

[0024] The standard linear equation is expressed as a matrix equation to obtain the linear matrix equation, and the expression of the linear matrix equation is:

[0025]

[0026] The linear matrix equation is processed and calculated using the least squares method to obtain the quadratic polynomial coefficients a0, a1 and a2.

[0027] Preferably, the expression of the grey model in S1 is:

[0028]

[0029] in, The predicted satellite clock error parameter c is the development coefficient, and parameter d is the gray action. is the original sequence of satellite clock errors in the grey model, is the cumulative sequence of the original sequence, e is a natural constant, and k is the kth number.

[0030] Preferably, in S2, it is assumed that there are α satellite clock error prediction models and β error indicators, then there is an error matrix Z′, and the expression of the error matrix Z′ is:

[0031]

[0032] Preferably, in S3, each data in the error matrix Z′ is standardized using a deviation standardization method to obtain a standard error matrix Z;

[0033] The deviation standardization formula is as follows:

[0034]

[0035] Among them, max z′ij and min z′ ij are z′ ij The maximum and minimum values ​​of .

[0036] Preferably, the information entropy e of the data in the standard error matrix Z is calculated in S3 j , where the information entropy e of the jth data is j for

[0037]

[0038] Here, F is a coefficient and satisfies F·ln(β)=1.

[0039] Preferably, in S4, according to the information entropy e of the data j Calculate the entropy weight w of the quadratic polynomial model and the grey model, where the weight coefficient of the j-th attribute component is calculated as:

[0040]

[0041] Among them, k j is the weight of a single model, h j is the difference coefficient of the j-th attribute component and satisfies h j =1-e j , other parameters.

[0042] The weight of the i-th forecast model is the weight coefficient k of the model j Add

[0043] The entropy weight of the i-th prediction model is m is the number of forecast models.

[0044] Preferably, the combined forecast model expression in S5 is:

[0045]

[0046] Among them, C(q) is the forecast value of the combined model at time q, q is the forecast time, k1 is the entropy weight of the first model, k2 is the entropy weight of the second model, is the predicted value of the first model at time q, is the predicted value of the second model at time q.

[0047] To sum up, compared with traditional technology, the method of combined prediction of GPS satellite clock error based on entropy weight method of the present invention first adopts quadratic polynomial model and grey model to make single prediction of satellite clock error, and generates two sets of prediction results; then, by calculating the error information entropy of the two sets of prediction results, the weight of each model is determined to realize the optimization fusion of the model; finally, the entropy weight combination method is used to obtain more accurate prediction results and verify the superiority and effectiveness of this method.

[0048] The technical method of the present invention is further described in detail below through the drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a step diagram of the GPS satellite clock error combined prediction method based on the entropy weight method of the present invention;

[0050] Figure 2 : are clock error variation diagrams of satellites of the present invention, wherein a in the figure is a clock error variation diagram of satellite PRN02, b in the figure is a clock error variation diagram of satellite PRN05, c in the figure is a clock error variation diagram of satellite PRN06, d in the figure is a clock error variation diagram of satellite PRN15, e in the figure is a clock error variation diagram of satellite PRN20, and f in the figure is a clock error variation diagram of satellite PRN23;

[0051] Figure 3 6h satellite clock difference prediction error change diagram, Figure a is the 6h satellite clock difference prediction error change diagram of PRN02, Figure b is the 6h satellite clock difference prediction error change diagram of PRN05, Figure c is the 6h satellite clock difference prediction error change diagram of PRN06, Figure d is the 6h satellite clock difference prediction error change diagram of PRN15, Figure e is the 6h satellite clock difference prediction error change diagram of PRN20 and Figure f is the 6h satellite clock difference prediction error change diagram of PRN23;

[0052] Figure 4 Figure 2 is a graph showing the changes in the 6-hour average forecast accuracy, stability and improvement rate. Figure a is a graph showing the changes in the 6-hour average forecast accuracy, stability and improvement rate of QPM, GM (1, 1) and the combined model. Figure b is a graph showing the changes in the 6-hour average forecast accuracy, stability and improvement rate of the combined model ~ QPM and the combined model ~ GM (1, 1). DETAILED DESCRIPTION

[0053] The technical method of the present invention is further described below by means of the accompanying drawings and embodiments. It should be noted that unless otherwise specifically stated, the relative arrangement of the components and steps, numerical expressions and numerical values ​​described in these embodiments do not limit the scope of the present application.

[0054] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the present application, its application, or uses.

[0055] Technologies, systems, and devices known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, systems, and devices should be considered part of the specification.

[0056] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0057] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0058] The present invention provides a combined prediction method for GPS satellite clock error based on the entropy weight method. In order to improve the accuracy of satellite clock error prediction and make full use of the respective advantages of the models, this paper proposes a combined prediction method for satellite clock error based on the entropy weight method. The method first uses a quadratic polynomial model and a gray model to make a single prediction of the satellite clock error to generate two sets of prediction results; then, by calculating the error information entropy of the two sets of prediction results, the weights of each model are determined to achieve the optimization fusion of the model; finally, a weighted combination method is used to obtain a more accurate prediction result. The precise satellite clock error product released by the GNSS Analysis Center of Wuhan University was used, and six different types of GPS satellites were randomly selected for prediction experiments. The results show that this method can make high-precision medium- and short-term predictions of GPS satellite clock errors, and its 6h average prediction accuracy and stability are 0.31ns and 0.69ns respectively, which are 47.5% and 62.7% higher than the average prediction accuracy of the quadratic polynomial model and the gray model, and the stability is increased by 42.5% and 54.0% respectively.

[0059] The GPS satellite clock error combined prediction method based on the entropy weight method includes the following steps:

[0060] S1. Construct a quadratic polynomial model and a grey model, obtain original satellite clock difference data, and bring the original satellite clock difference data into the quadratic polynomial model and the grey model for the first clock difference prediction and the second clock difference prediction;

[0061] Preferably, the quadratic polynomial model in S1 is constructed in the following manner:

[0062] A set of satellite clock error time series is preset as y1, y2, ..., y n , the corresponding time is t1, t2, ..., t n , the following quadratic polynomial model is established for this set of satellite clock error time series:

[0063]

[0064] Among them, t i (i=1,2,…,n) is the time, ε i (i=1,2,…,n) is the residual, quadratic polynomial coefficients a0, a1 and a2.

[0065] Preferably, the quadratic polynomial coefficients a0, a1 and a2 are determined by the least squares method, that is, the sum of squares S of the residuals is minimized;

[0066] The expression of the residual sum of squares S is:

[0067]

[0068] Among them, y i (i=1,2,…,n) is t i Satellite clock error at time (i=1,2,…,n).

[0069] By taking the partial derivatives of S with respect to a0, a1 and a2 and setting them equal to zero, we can get a set of linear equations, which are expressed as follows:

[0070]

[0071] The linear equation is arranged to obtain the standard linear equation, and the standard linear equation expression is:

[0072]

[0073] The standard linear equation is expressed as a matrix equation to obtain the linear matrix equation, and the expression of the linear matrix equation is:

[0074]

[0075] The linear matrix equation is processed and calculated using the least squares method to obtain the quadratic polynomial coefficients a0, a1 and a2.

[0076] Preferably, the expression of the grey model in S1 is:

[0077]

[0078] in, The predicted satellite clock error parameter c is the development coefficient, and parameter d is the gray action. is the original sequence of satellite clock errors in the grey model, is the cumulative sequence of the original sequence, e is a natural constant, and k is the kth number.

[0079] The Grey Forecast Model (GreyModel, GM(1,1)) uses cumulative generation and whitening technology to transform the original nonlinear time series into a nearly linear series, which is suitable for forecasting small sample data. The algorithm principle is as follows:

[0080] Suppose a set of satellite clock error time series is: (0) ={x (0) (1),x (0) (2),...,x (0) (n)}, the cumulative sequence constructed for this time series is: x (1) ={x (1) (1),x (1) (2),...,x (1) (n)}, where

[0081] The first-order differential equation for the cumulative sequence is:

[0082] Among them, parameter c is the development coefficient and parameter d is the gray action.

[0083] To facilitate solving, the differential equation is converted into the form of a difference equation:

[0084] x (0) (k)+cz (1) (k) = d

[0085] Among them, z (1) (k) is x (1) The nearest mean of generates a sequence, and

[0086]

[0087] The least squares method can be used to estimate the estimated values ​​of parameters c and d and

[0088] Define the matrix as: Denoted as BP = Y;

[0089] By the least square method P = (B T B) -1 B T Y, you can find the estimated values ​​of parameters c and d and

[0090] Based on the estimated parameters and The forecast results of the cumulative generated sequence are:

[0091]

[0092] Since the sequence x (1) is the original sequence x (0) The cumulative sequence of , so the prediction model of the original satellite clock difference sequence is:

[0093] This model can be used to predict the satellite clock error at any time in the future.

[0094] The entropy weight method measures the uncertainty of indicators by calculating the entropy value of each evaluation indicator. Indicators with high entropy values ​​mean less information and higher uncertainty, while indicators with low entropy values ​​mean rich information and lower uncertainty. Based on the entropy value, the weight of each indicator can be further calculated to highlight those indicators that have a greater impact on the decision-making results. The steps to solve the weights of each model are as follows:

[0095] S2, generating error matrices Z′ of a quadratic polynomial model and a grey model according to the first clock error forecast and the second clock error forecast;

[0096] Preferably, in S2, it is assumed that there are α satellite clock error prediction models and β error indicators, then there is an error matrix Z′, and the expression of the error matrix Z′ is:

[0097]

[0098] S3. Standardize the error matrix Z′ to obtain the standard error matrix Z, and calculate the information entropy e of the data in the standard error matrix Z. j ;

[0099] Preferably, in S3, each data in the error matrix Z′ is standardized using a deviation standardization method to obtain a standard error matrix Z;

[0100] The deviation standardization formula is as follows:

[0101]

[0102] Among them, max z′ ij and min z′ ij are z′ ij The maximum and minimum values ​​of .

[0103] Preferably, the information entropy e of the data in the standard error matrix Z is calculated in S3 j , where the information entropy e of the jth data is j for

[0104]

[0105] Here, F is a coefficient and satisfies F·ln(β)=1.

[0106] S4. According to the information entropy of the dataj Calculate the entropy weight w of the quadratic polynomial model and the grey model, where the entropy weight of the quadratic polynomial model is denoted as w1 and the entropy weight of the grey model is denoted as w2;

[0107] Preferably, in S4, according to the information entropy e of the data j Calculate the entropy weight w of the quadratic polynomial model and the grey model, where the weight coefficient of the j-th attribute component is calculated as:

[0108]

[0109] Among them, k j is the weight of a single model, h j is the difference coefficient of the j-th attribute component and satisfies h j =1-e j , other parameters.

[0110] The weight of the i-th forecast model is the weight coefficient k of the model j Add

[0111] The entropy weight of the i-th prediction model is m is the number of forecast models.

[0112] S5. Multiply the predicted value of the first clock error prediction by the entropy weight w1 of the quadratic polynomial model, and multiply the predicted value of the second clock error prediction by the entropy weight w2 of the grey model to obtain a combined prediction model, and predict the GPS satellite clock error through the combined prediction model.

[0113] Preferably, the combined forecast model expression in S5 is:

[0114]

[0115] Among them, C(q) is the forecast value of the combined model at time q, q is the forecast time, k1 is the entropy weight of the first model, k2 is the entropy weight of the second model, is the predicted value of the first model at time q, is the predicted value of the second model at time q.

[0116] In order to verify the effectiveness and feasibility of the combined model, the GPS post-precision satellite clock error products released by the GNSS Analysis Center of Wuhan University on August 11, 2024 were used as test data, with a sampling time interval of 5 minutes. There are more than 30 GPS satellites in orbit during this period, and their onboard clocks are of the following five types: BLOCK IIR-Rb clock, BLOCK IIF-Rb clock, BLOCK IIF-Cs clock, BLOCK IIR-M-Rb clock and BLOCK III-A-Rb clock. The onboard atomic clocks carried by my country's Beidou satellite navigation system are roughly similar to the atomic clocks carried by the GPS global positioning system, especially in the Beidou-2 system, where all satellites are equipped with rubidium atomic clocks. In order to make the research results provide some reference for the clock error prediction of my country's Beidou satellite navigation system, the clock error data of six satellites, GPS II-R-Rb PRN02, GPS IIR-M-Rb PRN05, GPS II-F-Rb PRN06, GPSIIR-M-Rb PRN15, GPS II-R-Rb PRN20 and GPS III-A-Rb PRN23, were randomly selected for prediction experiments. The relevant information is shown in Table 1.

[0117] Table 1 Related information of the selected satellites

[0118]

[0119] The changes in the precise satellite clock error time series of these six satellites 6 hours before August 11, 2024 are as follows: Figure 2 As shown in the figure, the clock difference time series of PRN02 and PRN20 satellites show a monotonically decreasing trend, the clock difference time series of PRN05, PRN06, PRN15 and PRN23 satellites show a monotonically increasing trend, and the clock difference time series of PRN05 and PRN20 satellites show obvious nonlinear change characteristics, which is fully representative.

[0120] In order to fully analyze the prediction performance of the proposed method, the satellite clock difference data of GPS 6 hours before August 11, 2024 are used to establish a quadratic polynomial prediction model (QPM), a gray prediction model (GM (1,1)) and a combined prediction model based on the entropy weight method (abbreviated as: combined model) to predict the satellite clock difference in the next 6 hours. The prediction error of each model can be obtained by subtracting the final precise satellite clock difference of the next 6 hours released by the GNSS Analysis Center of Wuhan University from the corresponding satellite clock difference predicted by each model. Since this paper uses the precise satellite clock difference product released by the GNSS Analysis Center of Wuhan University, the error of the clock difference itself is less than 0.1ns, so it can be used as the "true value", and the root mean square error (RMS) and range (Range), that is, the maximum error value minus the minimum error value, are used to evaluate and compare the prediction accuracy and stability of each model. The calculation formula of the root mean square error and range is:

[0121]

[0122] The forecast error changes and error statistics of each model are shown in Figure 2. Figure 3 As shown in Table 2:

[0123] Table 2 Statistics of satellite clock error prediction errors (unit: ns)

[0124]

[0125]

[0126] Table 3 Average forecast accuracy and improvement rate of each model for 6 hours

[0127]

[0128] Combination Figure 3-Figure 4 From Table 2-Table 3, we can see that:

[0129] In the 6-hour short-term forecast, the average forecast accuracy and stability of the quadratic polynomial model are 0.59ns and 1.20ns respectively; the average forecast accuracy and stability of the grey model are 0.83ns and 1.50ns respectively; and the average forecast accuracy and stability of the combined model based on the entropy weight method are 0.31ns and 0.69ns respectively, which are 47.50% and 42.50% higher than those of the quadratic polynomial model, and 62.70% and 54.00% higher than those of the grey model. The clock error prediction effect of the combined model for recently launched satellites is significantly better than that for early launched satellites and mid-term launched satellites. In addition, the prediction accuracy of the combined model for satellites with monotonically decreasing clock errors is generally higher than that for satellites with monotonically increasing clock errors, with an accuracy improvement of about 50%, indicating that the combined model is more effective in predicting the clock error of satellites with monotonically decreasing clock errors.

[0130] In summary, in order to further improve the accuracy and stability of satellite clock error prediction, this application proposes a satellite clock error combined prediction method based on the entropy weight method. This method first uses a quadratic polynomial model and a gray model to make a single prediction of the satellite clock error to generate two sets of prediction results; then, by calculating the error information entropy of the two sets of prediction results, the weights of each model are determined to achieve the optimization fusion of the model; finally, a weighted combination method is used to obtain a more accurate prediction result. This combined model can organically combine the prediction advantages of the two models, further improve the prediction performance of the model, and thus improve the accuracy of satellite clock error prediction. After theoretical and prediction test analysis, the results also show the effectiveness and feasibility of the combined model, which provides a new method and idea for the high-precision prediction of satellite clock errors. In addition, the prediction accuracy of the combined model for satellites with monotonically decreasing clock errors is generally higher than that for satellites with monotonically increasing clock errors.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical method of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical method of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical method to deviate from the spirit and scope of the technical method of the present invention.

Claims

1. A GPS satellite clock error combined prediction method based on entropy weight method, characterized in that: The following steps are involved: S1. Construct a quadratic polynomial model and a grey model, obtain original satellite clock difference data, and bring the original satellite clock difference data into the quadratic polynomial model and the grey model for the first clock difference prediction and the second clock difference prediction; S2, generating the error matrix Z′ of the quadratic polynomial model and the grey model according to the first clock forecast and the second clock forecast; S3. Standardize the error matrix Z′ to obtain the standard error matrix Z, and calculate the information entropy e of the data in the standard error matrix Z. j ; S4. According to the information entropy of the data j Calculate the entropy weight w of the quadratic polynomial model and the grey model, where the entropy weight of the quadratic polynomial model is denoted as w1 and the entropy weight of the grey model is denoted as w2; S5, multiplying the predicted value of the first clock error prediction by the entropy weight w1 of the quadratic polynomial model, and multiplying the predicted value of the second clock error prediction by the entropy weight w2 of the grey model to obtain a combined prediction model, and predicting the GPS satellite clock error through the combined prediction model; The combined forecast model expression in S5 is: Among them, C(q) is the forecast value of the combined model at time q, q is the forecast time, k1 is the entropy weight of the first model, k2 is the entropy weight of the second model, is the predicted value of the first model at time q, is the predicted value of the second model at time q.

2. The GPS satellite clock error combined prediction method based on the entropy weight method according to claim 1 is characterized in that: The construction method of the quadratic polynomial model in S1 includes: A set of satellite clock error time series is preset as y1, y2, ..., y n , the corresponding time is t1, t2, ..., t n , the following quadratic polynomial model is established for this set of satellite clock error time series: Among them, t i (i=1,2,…,n) is the time, ε i (i=1,2,…,n) is the residual, quadratic polynomial coefficients a0, a1 and a2.

3. The GPS satellite clock error combined prediction method based on the entropy weight method according to claim 2 is characterized in that: The quadratic polynomial coefficients a0, a1 and a2 are determined by the least square method, that is, the sum of squares S of the residuals is minimized; The expression of the residual sum of squares S is: Among them, y i (i=1,2,…,n) is t i Satellite clock error at time (i=1,2,…,n); By taking the partial derivatives of S with respect to a0, a1 and a2 and setting them equal to zero, we can get a set of linear equations, which are expressed as follows: The linear equation is arranged to obtain the standard linear equation, and the standard linear equation expression is: The standard linear equation is expressed as a matrix equation to obtain the linear matrix equation, and the expression of the linear matrix equation is: The linear matrix equation is processed and calculated using the least squares method to obtain the quadratic polynomial coefficients a0, a1 and a2.

4. The GPS satellite clock error combined prediction method based on the entropy weight method according to claim 1, characterized in that: The expression of the grey model in S1 is: in, is the predicted satellite clock error, parameter c is the development coefficient, parameter d is the gray action, is the original sequence of satellite clock errors in the grey model, is the cumulative sequence of the original sequence, e is a natural constant, and k is the kth number.

5. The GPS satellite clock error combined prediction method based on the entropy weight method according to claim 4 is characterized in that: In S2, it is assumed that there are α satellite clock error prediction models and β error indicators, then there is an error matrix Z′, and the expression of the error matrix Z′ is:

6. The GPS satellite clock error combined prediction method based on the entropy weight method according to claim 5 is characterized in that: In S3, each data in the error matrix Z′ is standardized by using the deviation standardization method to obtain the standard error matrix Z; The deviation standardization formula is as follows: Among them, maxz i ' j and Minz i ' j They are z i ' j The maximum and minimum values ​​of .

7. The GPS satellite clock error combined prediction method based on the entropy weight method according to claim 6 is characterized in that: Calculate the information entropy e of the data in the standard error matrix Z in S3 j , where the information entropy e of the jth data is j for Here, F is a coefficient and satisfies F·ln(β)=1.

8. The GPS satellite clock error combined prediction method based on entropy weight method according to claim 1, characterized in that: In S4, the information entropy e of the data is j Calculate the entropy weight w of the quadratic polynomial model and the grey model, where the weight coefficient of the j-th attribute component is calculated as: Among them, L j is the weight of a single model, h j is the difference coefficient of the j-th attribute component and satisfies h j =1-e j ; The weight of the i-th forecast model is the weight coefficient k of the model j Add The entropy weight of the i-th prediction model is m is the number of forecast models.

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