GPS satellite clock error combination prediction method based on entropy weight method

Abstract

The application discloses a GPS satellite clock error combination prediction method based on an entropy weight method, relates to the field of GPS satellite clock error prediction, and comprises the following steps: constructing a quadratic polynomial model and a grey model, and bringing original satellite clock error data into the quadratic polynomial model and the grey model respectively to perform first clock error prediction and second clock error prediction; generating an error matrix of the quadratic polynomial model and the grey model according to the first clock error prediction and the second clock error prediction; standardizing the error matrix to obtain a standard error matrix, and calculating information entropy of data in the standard error matrix; calculating entropy weight values of the quadratic polynomial model and the grey model; multiplying the prediction value of the first clock error prediction by the entropy weight value of the quadratic polynomial model, multiplying the prediction value of the second clock error prediction by the entropy weight value of the grey model to obtain a combination prediction model, and predicting the GPS satellite clock error through the combination prediction model, so that a higher-precision prediction result is obtained by using a weighted combination method.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of GPS satellite clock error prediction, in particular to a GPS satellite clock error combination prediction method based on an entropy weight method. BACKGROUND

[0002] A Global Navigation Satellite System (GNSS) is a time-based system, and the accuracy of its navigation, positioning and timing (PNT) depends largely on the accuracy of time measurement. In Precise Point Positioning (PPP) technology, in order to obtain centimeter-level positioning accuracy, a predicted satellite clock error needs to be used as a known quantity to be substituted into the equation for positioning calculation. Therefore, predicting a high-precision satellite clock error is an important prerequisite for implementing centimeter-level PPP technology, and its accuracy will directly affect the positioning performance of PPP technology.

[0003] Many domestic and foreign scholars have conducted extensive and in-depth research and have achieved a series of research results. For example, Quadratic Polynomial Model (QPM), Grey Model (GM (1, 1)), Auto-Regressive Moving Average (ARMA) and Spectrum Analysis (SA) and the like. These methods are suitable for navigation satellite atomic clock error prediction under different conditions, but each method has its applicable scope and limitations. For example, the Quadratic Polynomial Model uses time as the independent variable to fit historical clock error data, is simple to calculate, and has high short-term prediction accuracy, but its long-term prediction accuracy decreases significantly with time. The Grey Model is suitable for small samples and uncertain data, has strong anti-interference ability, but has different adaptability on different satellite clocks and strong dependence on data quantity, which may result in large errors. The Auto-Regressive Moving Average Model can effectively capture the linear dependence structure of time series data, is suitable for predicting stationary sequence clock errors, but has poor adaptability to non-stationary sequences, and the selection of model order is difficult to determine. The Spectrum Analysis Model can process clock error sequences with periodic characteristics, but its performance on non-periodic data may not be good, and parameter estimation is relatively complex.

[0004] In order to solve these problems, it is urgent to develop a GPS satellite clock error combination prediction method based on an entropy weight method to realize the optimized fusion of the model and obtain higher-precision prediction results by using a weighted combination method. SUMMARY

[0005] To solve the above problems, improve the accuracy and stability of satellite clock error prediction, the application proposes a GPS satellite clock error combination prediction method based on entropy weight method, the specific content is as follows:

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

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

[0008] S2, generate the error matrix Z' of the quadratic polynomial model and the grey model according to the first clock error prediction and the second clock error prediction;

[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, calculate the entropy weight value w of the quadratic polynomial model and the grey model according to the information entropy e j , wherein the entropy weight value of the quadratic polynomial model is represented as w1 and the entropy weight value of the grey model is represented as w2;

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

[0012] Preferably, the construction method of the quadratic polynomial model in S1 comprises:

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

[0014]

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

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

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

[0018]

[0019] wherein, y i (i = 1, 2, …, n) is the satellite clock error at time t i (i = 1, 2, …, n) is the satellite clock error at time t

[0020] By taking partial derivative of S with respect to a0, a1 and a2 and setting it equal to zero, a set of linear equations can be obtained, and the linear equation expression is:

[0021]

[0022] The standard linear equation expression is obtained by arranging the linear equation, and the standard linear equation expression is:

[0023]

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

[0025]

[0026] The quadratic polynomial coefficients a0, a1 and a2 are calculated by using the least square method to process the linear matrix equation.

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

[0028]

[0029] wherein, is the predicted satellite clock error parameter c is the development coefficient, and parameter d is the grey action, is the original sequence of satellite clock error 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 kinds of satellite clock error prediction models, and β error indicators, and there is an error matrix Z', and the error matrix Z' expression is:

[0031]

[0032] Preferably, in S3, the standard deviation normalization method is used to standardize each data in the error matrix Z' to obtain a standard error matrix Z.

[0033] The standard deviation normalization formula is as follows:

[0034]

[0035] wherein, max z'ij and min z′ ij are the maximum and minimum values of z′ ij respectively.

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

[0037]

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

[0039] Preferably, in S4, the entropy weight w of the quadratic polynomial model and the grey model is calculated according to the information entropy e j of the data, where the weight coefficient k

[0040]

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

[0042] The weight of the ith prediction model is the sum of all the weight coefficients k j of the model, i.e.

[0043] The entropy weight of the ith prediction model is where m is the number of prediction models.

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

[0045]

[0046] where C(q) is the prediction value of the combined model at time q, q is the prediction time, k1 is the entropy weight of the first model, k2 is the entropy weight of the second model, is the prediction value of the first model at time q, is the prediction value of the second model at time q.

[0047] In summary, compared with the traditional technology, the GPS satellite clock error combination prediction method based on the entropy weight method firstly adopts a quadratic polynomial model and a grey model for single prediction of the satellite clock error, generates two sets of prediction results; then, the weight of each model is determined by calculating the error information entropy of the two sets of prediction results, and the optimization fusion of the model is realized; finally, a higher precision prediction result is obtained by using the entropy weight combination method, and the superiority and effectiveness of the method are verified.

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

[0049] Figure 1 The figure is a step diagram of the GPS satellite clock error combination prediction method based on the entropy weight method of the present application.

[0050] Figure 2 The figure is a satellite clock error change graph, wherein a is a clock error change graph of PRN02 satellite, b is a clock error change graph of PRN05 satellite, c is a clock error change graph of PRN06 satellite, d is a clock error change graph of PRN15 satellite, e is a clock error change graph of PRN20 satellite, and f is a clock error change graph of PRN23 satellite.

[0051] Figure 3 The figure is a 6h satellite clock error prediction error change graph, wherein a is a 6h satellite clock error prediction error change graph of PRN02, b is a 6h satellite clock error prediction error change graph of PRN05, c is a 6h satellite clock error prediction error change graph of PRN06, d is a 6h satellite clock error prediction error change graph of PRN15, e is a 6h satellite clock error prediction error change graph of PRN20, and f is a 6h satellite clock error prediction error change graph of PRN23.

[0052] Figure 4 The figure is a 6h average prediction accuracy, stability and improvement rate change graph, wherein a is a 6h average prediction accuracy, stability and improvement rate change graph of QPM, GM(1,1) and combination model, and b is a 6h average prediction accuracy, stability and improvement rate change graph of combination model~QPM and combination model~GM(1,1). DETAILED DESCRIPTION

[0053] The technical method of the present application is further described below through the drawings and examples. It should be noted that: unless otherwise specifically stated, the relative arrangement, numerical expression and numerical value of the components and steps set forth in these examples do not limit the scope of the present application.

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

[0055] Techniques, systems, and devices known to those of ordinary skill in the relevant art can not be discussed in detail, but should be considered as part of the specification, where appropriate.

[0056] In all of the compositions shown and discussed herein, any particular value should be construed as merely exemplary, and not as a limitation. Thus, other examples of the exemplary embodiments can have different values.

[0057] Unless otherwise defined, technical terms or scientific terms used in the present application shall have the ordinary meaning as understood by a person of ordinary skill in the art to which the present application pertains.

[0058] The present application provides a GPS satellite clock error combination prediction method based on entropy weight method. In order to improve the accuracy of satellite clock error prediction, the advantages of each model are fully utilized. A satellite clock error combination prediction method based on entropy weight method is proposed. The method first uses quadratic polynomial model and grey model for 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 and fusion of the model. Finally, the weighted combination method is used to obtain the prediction result with higher accuracy. The precise satellite clock error product released by Wuhan University GNSS Analysis Center is used for prediction test of six GPS satellites of different types selected at random. The results show that the method can realize high-precision medium and short-term prediction of GPS satellite clock error, and the average prediction accuracy and stability of 6h are 0.31ns and 0.69ns respectively, which is 47.5% and 62.7% higher than the average prediction accuracy of quadratic polynomial model and grey model, and the stability is increased by 42.5% and 54.0% respectively.

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

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

[0061] Preferably, the construction method of the quadratic polynomial model in S1 comprises:

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

[0063]

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

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

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

[0067]

[0068] wherein, y i (i = 1, 2, …, n) is t i (i = 1, 2, …, n) moment satellite clock error.

[0069] By taking partial derivative of S with respect to a0, a1 and a2 and setting it equal to zero, a set of linear equations can be obtained, and the expression of the linear equations is:

[0070]

[0071] The standard linear equations are obtained by arranging the linear equations, and the expression of the standard linear equations is:

[0072]

[0073] The standard linear equations are expressed as a matrix equation, and the linear matrix equation is obtained, and the expression of the linear matrix equation is:

[0074]

[0075] The quadratic polynomial coefficients a0, a1 and a2 are obtained by processing and calculating the linear matrix equation by least square method.

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

[0077]

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

[0079] Grey Model (GM (1, 1)) is a model that transforms original nonlinear time series into linear time series by using the cumulative generation and whitening technique, which is suitable for small sample data prediction. The algorithm principle is as follows:

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

[0081] A first-order differential equation is established for the cumulative sequence as:

[0082] Wherein, the parameter c is the development coefficient, and the parameter d is the grey action amount.

[0083] In order to facilitate the solution, the differential equation is converted into the form of difference equation as:

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

[0085] Wherein, z (1) (k) is the adjacent mean value generated sequence of x (1) , and

[0086]

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

[0088] The matrix is defined as: Denoted as BP=Y;

[0089] The estimated values of parameters c and d can be obtained by the least square method P=(B T B) -1 B T Y, that is, And

[0090] Based on the estimated parameters And The prediction result of the cumulative generated sequence is:

[0091]

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

[0093] Using the model, the satellite clock error at any future time can be predicted.

[0094] The entropy weight method measures the uncertainty of the index by calculating the entropy value of each evaluation index. The index with high entropy value means less information and higher uncertainty, while the index with low entropy value means more information and lower uncertainty. Based on the entropy value, the weight of each index can be further calculated to highlight the indexes that have greater impact on the decision result. The steps for solving the weight of each model are as follows:

[0095] S2, generating error matrix Z' of the quadratic polynomial model and the grey model according to the first clock error prediction and the second clock error prediction;

[0096] Preferably, in S2, there are α kinds of satellite clock error prediction models and β error indexes, and there is error matrix Z', and the expression of error matrix Z' is:

[0097]

[0098] S3, standardizing error matrix Z' to obtain standard error matrix Z, and calculating the information entropy e j of the data in standard error matrix Z;

[0099] Preferably, in S3, each data in error matrix Z' is standardized by using the dispersion standardization method to obtain standard error matrix Z;

[0100] The dispersion standardization formula is as follows:

[0101]

[0102] Wherein, max z′ ij and min z′ ij are the maximum and minimum values of z′ ij .

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

[0104]

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

[0106] S4, calculating the entropy weight w of the quadratic polynomial model and the grey model, wherein the entropy weight of the quadratic polynomial model is denoted as w1 and the entropy weight of the grey model is denoted as w2; j calculating the entropy weight w of the quadratic polynomial model and the grey model, wherein 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, the information entropy e of the data is calculated according to the following formula: j calculating the entropy weight w of the quadratic polynomial model and the grey model, wherein the entropy weight of the quadratic polynomial model is denoted as w1 and the entropy weight of the grey model is denoted as w2;

[0108]

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

[0110] The weight of the ith prediction model is the sum of all weight coefficients k j of the model, that is,

[0111] The entropy weight of the ith prediction model is m is the number of prediction models.

[0112] S5, multiplying the prediction value of the first clock difference prediction by the entropy weight w1 of the quadratic polynomial model and multiplying the prediction value of the second clock difference prediction by the entropy weight w2 of the grey model to obtain a combined prediction model, and predicting the GPS satellite clock difference through the combined prediction model.

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

[0114]

[0115] wherein C(q) is the prediction value of the combined model at q, q is the prediction time, k1 is the entropy weight of the first model, k2 is the entropy weight of the second model, is the prediction value of the first model at q, is the prediction value of the second model at q.

[0116] To verify the effectiveness and feasibility of the combined model, the post-hoc precise satellite clock bias product of GPS released by the GNSS Analysis Center of Wuhan University on August 11, 2024, was used as experimental data, with a sampling interval of 5 minutes. During this period, there were more than 30 GPS satellites in orbit, and their onboard clocks were 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 of my country's BeiDou Navigation Satellite System are roughly similar to those of the GPS Global Positioning System, especially in the BeiDou-2 system, where all satellites are equipped with rubidium atomic clocks. To provide a reference for clock bias prediction of my country's BeiDou Navigation Satellite System, clock bias data from six satellites—GPS II-R-Rb PRN02, GPS IIR-M-Rb PRN05, GPS II-F-Rb PRN06, GPS IIR-M-Rb PRN15, GPS II-R-Rb PRN20, and GPS III-A-Rb PRN23—were randomly selected for prediction experiments. Relevant information is shown in Table 1.

[0117] Table 1 shows the relevant information of the selected satellites.

[0118]

[0119] The changes in the precise satellite clock bias time series of these six satellites in the six hours prior to August 11, 2024 are as follows: Figure 2 As shown, the clock bias time series of PRN02 and PRN20 satellites exhibit a monotonically decreasing trend, while the clock bias time series of PRN05, PRN06, PRN15, and PRN23 satellites exhibit a monotonically increasing trend. Furthermore, the clock bias time series of PRN05 and PRN20 satellites show obvious non-linear variation characteristics, making them highly representative.

[0120] In order to fully analyze the prediction performance of the method in this paper, the satellite clock error data of GPS on August 11, 2024 for the previous 6 hours were used to establish a quadratic polynomial prediction model (QPM), a grey prediction model (GM (1, 1)), and a combination prediction model based on the entropy weight method (abbreviated as: combination model), respectively, to predict the satellite clock error for the next 6 hours. The post-event final precise satellite clock error published by the GNSS Analysis Center of Wuhan University for the next 6 hours was subtracted from the satellite clock error predicted by each model, which obtained the prediction error of each model. Since the precise satellite clock error product published by the GNSS Analysis Center of Wuhan University was used in this paper, the error of the clock error itself is less than 0.1 ns, so it can be used as the "true value", and the root mean square error (RMS) and the range, i.e. the maximum error value minus the minimum error value, were used to evaluate and compare the prediction accuracy and stability of each model. The calculation formulas of the root mean square error and the range are:

[0121]

[0122] The prediction error change and error statistical results of each model are shown in Figure 3 and Table 2:

[0123] Table 2: Satellite clock error prediction error statistical results (unit: ns)

[0124]

[0125]

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

[0127]

[0128] Combining Figures 3-4 and Table 2-Table 3:

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

[0130] In summary, in order to further improve the accuracy and stability of the satellite clock error prediction, the present application proposes a satellite clock error combined prediction method based on the entropy weight method. The method first uses the quadratic polynomial model and the grey model to make single prediction on the satellite clock error, generating two groups of prediction results; then, by calculating the error information entropy of the two groups of prediction results, the weight of each model is determined to realize the optimization and fusion of the model; finally, a higher accuracy prediction result is obtained by using the weighted combination method. 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 the satellite clock error prediction. Theoretical and prediction test analysis results also show the effectiveness and feasibility of the combined model, which provides a new method and idea for high-precision prediction of the satellite clock error. In addition, the prediction accuracy of the combined model on the satellite with monotonically decreasing clock error is generally higher than that on the satellite with monotonically increasing clock error.

[0131] Finally, it should be noted that: the above examples are only used to illustrate the technical method of the present application and not to limit it, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical method of the present application can still be modified or equivalently replaced, and these modifications or equivalent replacements cannot make the modified technical method deviate from the spirit and scope of the technical method of the present application.

Claims

1. A GPS satellite clock error combination prediction method based on an entropy weight method, characterized in that, The method comprises the following steps: S1, constructing a quadratic polynomial model and a grey model, obtaining original satellite clock error data, and bringing the original satellite clock error data into the quadratic polynomial model and the grey model respectively for first clock error prediction and second clock error prediction; S2, generating error matrices for the quadratic polynomial model and the grey model from the first clock difference prediction and the second clock difference prediction ; S3, error matrix S3, error matrix S3, error matrix S3, error matrix ; S4, entropy of information according to data Calculating entropy weight values of the quadratic polynomial model and the grey model wherein the entropy weight value of the quadratic polynomial model is expressed as and the entropy weight value of the grey model is expressed as ; S5, multiplying the predicted value of the first clock error prediction by the entropy weight value of the quadratic polynomial model multiplying the predicted value of the second clock error prediction by the entropy weight value of the grey model obtaining a combined prediction model, and predicting the GPS satellite clock error through the combined prediction model The expression of the combined prediction model in S5 is: ； wherein, is the forecast value of the first model at time t, is the forecast value of the second model at time t, is the forecast time, is the entropy weight value of the first model, is the entropy weight value of the second model, is the forecast value of the first model at time t, is the forecast value of the second model at time t. is the forecast value of the first model at time t, is the forecast value of the second model at time t. 2.The GPS satellite clock error combination forecasting method based on entropy weight method according to claim 1, characterized in that, The construction method of the quadratic polynomial model in S1 comprises: A set of satellite clock error time series is preset as The corresponding time is A quadratic polynomial model is established for the set of satellite clock error time series as follows: ； wherein, is time, is residual, quadratic polynomial coefficient and . 3.The GPS satellite clock error combination forecasting method based on entropy weight method according to claim 2, characterized in that, The quadratic polynomial coefficients And By least squares, i.e. the sum of the squares of the residuals Minimum; Sum of squares of residuals The expression for the sum of squares of residuals is ； wherein, is the satellite clock error at the time instant; By taking the partial derivative of the function with respect to the variable x and setting it equal to zero, a set of linear equations can be obtained. With respect to And Taking the partial derivative and setting it equal to zero, a set of linear equations can be obtained, which can be expressed as: ； The standard linear equation is obtained by arranging the linear equation, and the expression of the standard linear equation is: ； The standard linear equation is expressed as a matrix equation to obtain a linear matrix equation, and the expression of the linear matrix equation is: ； The quadratic polynomial coefficients are calculated by using least square method to process the linear matrix equation and . 4.The GPS satellite clock error combination forecasting method based on entropy weight method according to claim 1, characterized in that, The expression of the grey model in S1 is: ； wherein, is the predicted satellite clock error, parameter is the development coefficient, parameter is the grey action amount, is the original sequence of satellite clock error in the grey model, is the cumulative sequence of the original sequence, is the natural constant, is the first number.

5. The GPS satellite clock error combination forecasting method based on entropy weight method according to claim 4, characterized in that, In S2, it is assumed that A satellite clock error prediction model, An error index, then the error matrix The expression of the error matrix is 。 6. The GPS satellite clock error combination forecasting method based on entropy weight method according to claim 5, characterized in that, In S3, each data in error matrix is normalized by using deviation standardization method to obtain standard error matrix . ; The standardization formula of the deviation is as follows: ； wherein and are respectively the maximum and minimum values.

7. The GPS satellite clock error combination forecasting method based on the entropy weight method according to claim 6, characterized in that, S3 calculates standard error matrix Information entropy of data where the information entropy of the th data is ； wherein are coefficients and satisfy . 8.The GPS satellite clock error combination forecasting method based on entropy weight method according to claim 1, characterized in that, S4 in the information entropy of data Computing entropy weight values of quadratic polynomial model and grey model , wherein the weight coefficient of the first The weight coefficient of the first attribute component is ； wherein, is a weight for the single model, is the difference coefficient for the attribute component and satisfies ; The weight of the ith prediction model is all the weight coefficients of the model The addition is ; The entropy weight value of the ith prediction model is , and m is the number of prediction models.

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