Low-orbit satellite broadcast ephemeris parameter robust determination method and system

Abstract

The application provides a low-orbit satellite broadcast ephemeris parameter robust determination method and system. It relates to the field of satellite navigation technology. The method comprises: performing multiple collinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether there is a multiple collinearity relationship; when the multiple collinearity relationship exists, determining the generalized ridge estimation step diagonal matrix prior value according to the satellite precise ephemeris data and the designed broadcast ephemeris parameter; setting a search interval and fitting the broadcast ephemeris parameter by generalized ridge estimation step by step according to the generalized ridge estimation step diagonal matrix prior value, calculating the fitting residual, obtaining the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval is completed, and fitting the broadcast ephemeris parameter according to the generalized ridge parameter value. The application solves the problem that the least square equation is seriously ill due to improper design of the broadcast ephemeris model, which further leads to fitting failure.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of satellite navigation technology, and in particular to a low-orbit satellite broadcast ephemeris parameter robust determination method and system. BACKGROUND

[0002] Global Navigation Satellite System (GNSS) as an important space-time information infrastructure, provides all-weather navigation, positioning and timing (PNT) services for global users. However, the traditional GNSS relying on medium-high orbit satellites has the problems of weak landing signal, signal vulnerable to fraud and interference, etc., and cannot meet the high-precision and high-robust positioning requirements in indoor, urban canyons, underpasses, etc. In view of this, the idea of enhancing GNSS by low-orbit navigation satellites has been gradually proposed by domestic and foreign scholars in recent years. In order to enhance GNSS by low-orbit navigation satellites, the user's receiver needs to obtain the accurate position of the low-orbit enhancement satellite in real time, and the broadcast ephemeris can provide the accurate position of the satellite at any time for the user in real time. Usually, the predicted precise orbit data in the ground station is fitted into the form of broadcast ephemeris parameters, and the fitting accuracy determines the accuracy of the satellite position obtained by the user, thereby affecting the accuracy of the user's positioning.

[0003] The broadcast ephemeris fitting of low-orbit satellites is different from the broadcast ephemeris fitting of traditional GPS and other medium-high orbit satellites. Because the low-orbit satellites are subjected to more complex non-spherical gravity perturbations and atmospheric drag perturbations of the earth than the medium-high orbit satellites, the broadcast ephemeris model of the low-orbit satellites generally needs to be redesigned according to the perturbation forces received by the low-orbit satellites. In recent decades, domestic and foreign scholars have designed ephemeris models with 19, 21, 22, 24, 26, etc. parameter numbers specially adapted to low-orbit satellites on the basis of GPS16, 18 ephemeris models and GLONASS orbit list type ephemeris models. However, in the broadcast ephemeris fitting process, the partial derivative design matrix of the satellite position with respect to the broadcast ephemeris parameters will produce strong ill-conditioned. This ill-conditioned will reduce the accuracy of the broadcast ephemeris fitting or even cause the fitting to fail. The reasons for the ill-conditioned are generally two: one is the definition ambiguity of the perigee distance caused by the orbit eccentricity close to 0; the other is the definition ambiguity of the ascending node right ascension caused by the orbit inclination close to 0. The two reasons are essentially that when the orbit elements take certain values, two or three of the six Kepler elements become approximately collinear, thereby causing the singularity of the least squares equation system. When the broadcast ephemeris model is designed improperly, the reason for the ill-conditioned also exists that some parameters of the ephemeris model are too strongly related to other parameters, thereby causing the ill-conditioned of the design matrix.

[0004] The prior art designs different ephemeris models and fitting methods based on these problems. For example, the first and second types of non-singular roots are used to broadcast ephemeris parameters to eliminate singular points, and the orbit plane is rotated to improve the singular point problem when the orbit inclination is close to 0. In addition, when solving the least squares equation set, some scholars have proposed a generalized ridge estimation method. The non-singular root method mainly analyzes the principle of producing complex collinearity in detail, obtains the specific parameters that produce approximate collinearity (such as the mean anomaly M and the argument of perigee ω when the eccentricity e is close to 0), and then designs new parameters for the parameters that produce approximate linear relationship. The orbit plane rotation method mainly avoids singular points by redefining the value of the inclination i. When the fitted inclination i value is less than the threshold, the orbit plane is rotated and then fitted, and then the fitting result is converted back to the original reference system. The generalized ridge estimation method mainly increases a diagonal matrix in the least squares design matrix to reduce the condition number of the equation and suppress the ill-conditioned equation set.

[0005] Both of the above ephemeris fitting methods have certain complexity and limitations. Ultimately, they all need to analyze the specific reasons for the existence of singular points or the specific complex collinearity relationship in the specific broadcast ephemeris model, and then modify the ephemeris parameters accordingly, which undoubtedly increases the creative workload of ephemeris designers. In addition, the above two methods are only limited to modifying the complex collinearity relationship caused by the six roots of Kepler. However, when other non-six root parameters are designed in the broadcast ephemeris, and the complex collinearity relationship is caused by improper design, it is difficult to analyze the existence of singular points or the specific complex collinearity relationship theoretically due to the complex functional relationship between satellite position and designed ephemeris parameters. Finally, the core of the generalized ridge estimation method is the selection of the ridge parameter, and the existing selection methods all have different defects: the ridge trace method lacks strict judgment criteria and is difficult to program; the GCV method requires solving the minimum point of the GCV function, and the computer has high complexity; the L curve method needs to determine the maximum curvature point of the L curve, and has the same defects as the GCV method. In the determination of the generalized ridge parameter, multiple ridge parameters need to be determined at the same time, and the aforementioned high-complexity solutions cannot meet the real-time requirements of ephemeris fitting. SUMMARY

[0006] The application provides a low-orbit satellite broadcast ephemeris parameter robust determination method and system to solve the problem of serious ill-condition of least square equation caused by improper broadcast ephemeris model design, and further fitting failure. Specifically, the application finds the specific multicollinearity relationship generated in ephemeris fitting, solves the difficulty in determining the ridge parameter when performing generalized ridge estimation in broadcast ephemeris fitting based on an adaptive generalized ridge estimation method, clearly defines the selection criteria of the ridge parameter, improves the efficiency of ridge parameter selection, effectively alleviates the ill-condition of the least square equation caused by improper broadcast ephemeris design, and achieves the final effect of increasing the fitting success rate.

[0007] In a first aspect, the application provides a low-orbit satellite broadcast ephemeris parameter robust determination method, comprising:

[0008] Performing multicollinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether there is a multicollinearity relationship;

[0009] When there is a multicollinearity relationship, determining the prior value of the step diagonal matrix of the generalized ridge estimation according to the satellite precise ephemeris data and the designed broadcast ephemeris parameter;

[0010] According to the prior value of the step diagonal matrix of the generalized ridge estimation, setting a search interval and performing generalized ridge estimation fitting of the broadcast ephemeris parameter, calculating the fitting residual, obtaining the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval is completed, performing generalized ridge estimation fitting of the broadcast ephemeris parameter according to the generalized ridge parameter value, and obtaining the fitted broadcast ephemeris parameter.

[0011] In a possible design, multicollinearity analysis is performed on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether there is a multicollinearity relationship, comprising:

[0012] Determining a function of the broadcast ephemeris parameter to the satellite position according to the set broadcast ephemeris model;

[0013] Performing first-order Taylor expansion on both sides of the function of the broadcast ephemeris parameter to the satellite position to obtain a least square equation;

[0014] Obtaining a Jacobian matrix from the least square equation, performing singular value decomposition on the Jacobian matrix to obtain a plurality of singular values, and determining a condition index through the following formula:

[0015]

[0016] In the formula, η k represents the condition index, σ1 represents the maximum value in the plurality of singular values, σ k represents the kth singular value in the plurality of singular values;

[0017] According to the Jacobian matrix and the condition index, a variance decomposition ratio matrix is determined by the following formula:

[0018] The normal matrix of the least squares equation is Orthogonal similarity diagonalization, that is,

[0019]

[0020] In the formula, φ k,j represents the jth variance component of the kth component of the least squares estimator, λ j represents the jth diagonal element of the diagonal matrix Λ, q kj represents the element of the kth row and jth column of the orthogonal matrix Q, φ k represents the variance of the kth component of the least squares estimator, j represents the number of columns of the variance decomposition ratio matrix, π k,j represents the variance decomposition ratio matrix, the sum of the rows of the variance decomposition ratio matrix is 1,

[0021] If the column j of the variance decomposition ratio matrix has two or more elements greater than 0.5, and the condition index η j of column j is greater than a set threshold value, then it is determined that there is a multicollinearity relationship corresponding to the jth condition index.

[0022] In a possible design, the function of the broadcast ephemeris parameters to the satellite position is represented as:

[0023] F(p)=x

[0024] In the formula, F is the function of the broadcast ephemeris parameters to the satellite position, p is the parameter vector contained in the designed broadcast ephemeris model, and x is the three-dimensional position vector of the satellite.

[0025] In a possible design, the least squares equation is represented as:

[0026]

[0027] In the formula, p* is the real broadcast ephemeris parameter vector corresponding to the real position of the satellite, x* is the real position vector of the satellite, is the estimated value vector of the broadcast ephemeris parameters, is the estimated position of the satellite calculated according to and F, is the Jacobian matrix.

[0028] In a possible design, when there is a multicollinearity relationship, the prior value of the generalized ridge estimation step diagonal matrix is determined according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters, and includes:

[0029] The estimated value of the satellite corresponding to the designed broadcast ephemeris parameter m is obtained estimated value The partial derivative corresponding to the Jacobian matrix is ​​in the j-th column. The first diagonal matrix K0 is determined, and the j-th diagonal element of the first diagonal matrix K0 is used as the prior value of the generalized ridge estimation step size diagonal matrix. The prior value of the generalized ridge estimation step size diagonal matrix is ​​expressed as:

[0030]

[0031] In the formula, (K0) jj Let log represent the prior value of the step-size diagonal matrix of the generalized ridge estimation. 10 Represents the logarithm to base 10. This represents the floor function.

[0032] In one possible design, before setting the search interval based on the prior value of the generalized ridge estimation step-size diagonal matrix and successively performing generalized ridge estimation to fit the broadcast ephemeris parameters, the method further includes:

[0033] The designed broadcast ephemeris model is fitted using the least squares method, and the success of the fit is determined based on the following criteria:

[0034]

[0035] ||V k || <T s

[0036] In the formula, V k and V k+1 These are the fitting residuals for the k-th and (k+1)-th iterations, respectively, T s It is a threshold related to the fitted arc length;

[0037] When the fitting residual obtained by fitting the designed broadcast ephemeris model using the least squares method satisfies the judgment condition, the fitted ephemeris parameters are directly output.

[0038] When the fitting residual obtained by fitting the designed broadcast ephemeris model using the least squares method does not meet the judgment condition, a search interval is set according to the prior value of the step size diagonal matrix of the generalized ridge estimation, and the broadcast ephemeris parameters are fitted by generalized ridge estimation one by one.

[0039] In one possible design, based on the prior value of the generalized ridge estimation step-size diagonal matrix, a search interval is set, and the generalized ridge estimation is performed successively to fit the broadcast ephemeris parameters. The fitting residual is calculated, and after the search within the search interval is completed, the generalized ridge parameter value corresponding to the optimal residual is obtained. Based on the generalized ridge parameter value, the generalized ridge estimation is performed to fit the broadcast ephemeris parameters, resulting in the fitted broadcast ephemeris parameters, including:

[0040] The expression for determining the generalized ridge estimator is expressed as:

[0041]

[0042] In the formula, Let A denote the generalized ridge estimator, P denote the design matrix, and K = diag(k1, k2, ..., k n ), representing the second diagonal matrix, k1,k2,k n Let represent the 1st, 2nd, and nth diagonal elements in the second diagonal matrix, respectively, which are the generalized ridge parameter values. Let T denote the matrix transpose, and y denote the observation error vector.

[0043] The second diagonal matrix is ​​represented as:

[0044] K=εK0

[0045] In the formula, K0 represents the first diagonal matrix, and ε represents the scaling factor from the first diagonal matrix to the second diagonal matrix;

[0046] The generalized ridge estimation parameters are adjusted with coarse-grained adjustment. Broadcast ephemeris fitting is performed iteratively in the interval ε∈[0,1000] with a first step length. The ε value and the number of iterations corresponding to the minimum residual are dynamically recorded until the convergence condition is met or the threshold is reached to terminate the coarse search for the optimal value neighborhood.

[0047] Based on the coarse search of the optimal value neighborhood, the generalized ridge estimation parameters are adjusted with a second step size smaller than the first step size. The ε value and the number of iterations corresponding to the minimum residual are dynamically recorded until the convergence condition is met or the threshold is reached to terminate the process and obtain the generalized ridge parameter value corresponding to the optimal residual.

[0048] Based on the generalized ridge parameter values, generalized ridge estimation is performed to fit the broadcast ephemeris parameters, thus obtaining the fitted broadcast ephemeris parameters.

[0049] Secondly, this application provides a robust system for determining ephemeris parameters for low-Earth orbit satellite broadcasts, the system including a controller configured to:

[0050] The multicollinearity analysis module is configured to perform multicollinearity analysis on the designed broadcast ephemeris model in the satellite's precise ephemeris data to be fitted, in order to determine whether multicollinearity exists.

[0051] The prior value determination module is configured to determine the prior value of the generalized ridge estimation step size diagonal matrix based on the satellite's precise ephemeris data and the designed broadcast ephemeris parameters when a complex collinearity relationship exists.

[0052] The ephemeris parameter fitting module is configured to set a search interval based on the prior value of the diagonal matrix of the generalized ridge estimation step size, and successively perform generalized ridge estimation to fit the broadcast ephemeris parameters, calculate the fitting residual, obtain the generalized ridge parameter value corresponding to the optimal residual after the search is completed within the search interval, and perform generalized ridge estimation to fit the broadcast ephemeris parameters based on the generalized ridge parameter value to obtain the fitted broadcast ephemeris parameters.

[0053] Thirdly, embodiments of this application provide an electronic device, including: at least one processor and a memory; the memory stores computer execution instructions; the at least one processor executes the computer execution instructions stored in the memory, causing the at least one processor to perform the robust determination method for low-Earth orbit satellite broadcast ephemeris parameters as described in the first aspect and various possible designs of the first aspect.

[0054] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions. When a processor executes the computer-executable instructions, it implements the robust determination method for low-orbit satellite broadcast ephemeris parameters as described in the first aspect and various possible designs of the first aspect.

[0055] Fifthly, embodiments of this application provide a computer program product, including a computer program that, when executed by a processor, implements the robust determination method for low-Earth orbit satellite broadcast ephemeris parameters as described in the first aspect and various possible designs of the first aspect.

[0056] The robust method and system for determining low-Earth orbit satellite broadcast ephemeris parameters provided in this application have at least the following beneficial effects:

[0057] 1. This application uses the existing condition index-variance decomposition ratio method to detect the multicollinearity relationship in the broadcast ephemeris fitting. Compared with the need to perform theoretical analysis on the function of satellite position on broadcast ephemeris parameters in complex ephemeris models, it is only necessary to perform multicollinearity analysis on the satellite data to be fitted to obtain the multicollinearity relationship generated in the corresponding satellite data, which simplifies the design from theoretical analysis to direct experimental testing.

[0058] 2. This application employs an adaptive generalized ridge estimation method to address the ill-conditioned problem in broadcast ephemeris fitting. It alleviates the ill-conditioned nature of the least squares equations without needing to handle specific multicollinearity relationships, thus solving the complexity of existing ephemeris design methods that require tailored design based on specific multicollinearity relationships. In particular, the adaptive method, which uses prior determination of the search step size and then synchronous search for ridge parameters, solves the difficulty in determining ridge parameters when using generalized ridge estimation for ephemeris fitting. The method of searching for and selecting the ridge parameter value with the minimum fitting residual ensures a definite ridge parameter selection criterion, and the synchronous search method guarantees low algorithm complexity, ultimately increasing the fitting success rate. Attached Figure Description

[0059] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0060] Figure 1 A flowchart illustrating a robust method for determining ephemeris parameters for low-Earth orbit satellite broadcasting, provided in this application embodiment;

[0061] Figure 2 A flowchart of the generalized ridge parameter search provided for embodiments of this application;

[0062] Figure 3 This is a structural diagram of a robust system for low-Earth orbit satellite broadcast ephemeris parameters provided in an embodiment of this application.

[0063] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0064] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of systems and methods consistent with some aspects of this application as detailed in the appended claims.

[0065] The collection, storage, use, processing, transmission, provision, and disclosure of financial data or user data involved in the technical solution of this application all comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0066] It should be noted that in the embodiments of this application, certain software, components, models and other existing solutions in the industry may be mentioned. These should be regarded as exemplary and are only intended to illustrate the feasibility of implementing the technical solution of this application. However, it does not mean that the applicant has used or necessarily used the solution.

[0067] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0068] This application provides a robust method for determining broadcast ephemeris parameters for low-Earth orbit satellites. The basic idea of ​​this method is as follows: First, perform multicollinearity analysis on the designed broadcast ephemeris model in the satellite data to be fitted. When severe ill-conditioned conditions are detected, determine the prior value of the diagonal matrix of the generalized ridge estimation step size. Based on the prior value of the diagonal matrix of the generalized ridge estimation step size, use the generalized ridge estimation to perform ephemeris fitting. Perform ridge parameter search and fitting successively to obtain an optimal generalized ridge parameter estimate. Use this optimal value to calculate the corresponding ephemeris parameters.

[0069] like Figure 1 The diagram shows a flowchart of a robust method for determining broadcast ephemeris parameters for low-Earth orbit (LEO) satellites according to an embodiment of this application. This method first performs multicollinearity analysis on the broadcast ephemeris model. If no multicollinearity exists, least squares estimation is used directly for ephemeris fitting, and the fitted ephemeris parameters are output. If multicollinearity exists, a priori values ​​for the generalized ridge estimation step size list are determined, a generalized ridge estimation parameter search is performed, and the optimal generalized ridge estimation parameters are used for ephemeris fitting, outputting the fitted ephemeris parameters.

[0070] Specifically, the robust determination method for low-orbit satellite broadcast ephemeris parameters can be implemented through the following steps S100-S300.

[0071] S100: Perform multicollinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted, in order to determine whether multicollinearity exists.

[0072] After the broadcast ephemeris model is designed, the functional relationship between the broadcast ephemeris parameters and the satellite positions is determined, namely:

[0073] F(p)=x (1)

[0074] Where F is the functional relationship between the broadcast ephemeris parameters and the satellite position, p is the parameter vector contained in the designed broadcast ephemeris model, and x is the three-dimensional position vector of the satellite. A first-order Taylor expansion on both sides of expression (1) yields:

[0075]

[0076] Where p* is the true broadcast ephemeris parameter vector corresponding to the satellite's true position, and x* is the satellite's true position vector. It is a vector of broadcast ephemeris parameter estimates. It is based on The estimated satellite position calculated by F, It is the Jacobian matrix of the function F. Broadcast ephemeris fitting is essentially an iterative solution of the least squares equation (2).

[0077] The main purpose of step S100 is to test the ephemeris model before it is officially used. Specifically, this involves testing the Jacobian matrix generated from the measured data. Condition index-variance decomposition ratio analysis and ephemeris fitting experiment were conducted.

[0078] Jacobian matrix Perform singular value decomposition, denoted as σ1, σ2, ..., σ n It is a Jacobian matrix Singular values ​​from largest to smallest, defining the conditional index η. k as follows:

[0079]

[0080] When the condition index η k When the value is greater than 1000, determine the k-th singular value σ. k The guided multicollinearity is severe; when the condition index η k When σ is greater than 100 but less than 1000, determine σ. k The guided multicollinearity is relatively strong; when all conditional indicators are less than 100, it indicates that the multicollinearity is relatively weak.

[0081] In this embodiment, if the multicollinearity relationship is determined to be weak, then it is determined that there is no multicollinearity relationship; otherwise, it is determined that there is a multicollinearity relationship.

[0082] The normal matrix of the least squares equation Orthogonal similarity diagonalization, i.e.:

[0083]

[0084] In the formula, Q represents the orthogonal matrix obtained by orthogonally similar diagonalizing the Jacobian matrix, T represents the matrix transpose, and Λ represents the diagonal matrix obtained by orthogonally similar diagonalizing;

[0085] Define the variance decomposition ratio:

[0086]

[0087] In the formula, φ k,j Let λ represent the j-th variance component of the k-th component in the least squares estimator. j Let q represent the j-th diagonal element of matrix Λ. kj φ represents the element in the k-th row and j-th column of an orthogonal matrix. k The matrix π represents the variance of the k-th component in the least squares estimator. k,j =Π is the variance decomposition ratio matrix.

[0088] If the row sum of the variance decomposition ratio matrix defined above is 1, and if a column j has two or more elements greater than 0.5, and the corresponding column's condition index η j When the value is greater than 100, it indicates that there is a multicollinearity relationship corresponding to the j-th condition index. Elements greater than 0.5 are included in the detected multicollinearity relationship. The larger the value of this column in the variance decomposition ratio, the stronger the correlation in the multicollinearity relationship.

[0089] Ephemeris fitting tests are performed on the fitted arc segments of all satellite data to be tested, and least squares equation multicollinearity analysis is performed according to the condition index-variance decomposition ratio method mentioned above. If a satellite fails to fit a certain fitted arc segment, and the condition index is greater than 1000 in the multicollinearity analysis, and the corresponding column in the variance decomposition ratio matrix has two or more elements greater than 0.5, then it is determined that the model has produced ill-conditioned behavior in the satellite data to be tested. The detected multicollinearity relationship is as described above.

[0090] S200: When a complex collinearity relationship exists, determine the prior value of the generalized ridge estimation step size diagonal matrix based on the satellite's precise ephemeris data and the designed broadcast ephemeris parameters.

[0091] In this embodiment, taking orbital element-type ephemeris parameters as an example, the satellite's orbital six elements and other auxiliary parameters at this moment are calculated using precise satellite ephemeris data to form a corresponding time series. A typical orbital element-type ephemeris parameter set can be divided into Keplerian orbital six elements, linear trend term coefficients, and periodic trend term coefficients. The corresponding parameter estimates for this satellite are calculated from the tested precise satellite ephemeris data. The Keplerian orbital six elements can be directly derived from the satellite's position and velocity at this moment. The linear trend term coefficients can be obtained by performing polynomial fitting on the time series, and the periodic term coefficients can be determined similarly.

[0092] Suppose the estimated value of the satellite corresponding to the designed broadcast ephemeris parameter m is... Its in matrix If the corresponding partial derivative is in the j-th column, then a diagonal matrix K0 can be determined, and its j-th diagonal element is:

[0093]

[0094] In the formula, (K0) jj To estimate the prior values ​​of the step-size diagonal matrix for the generalized ridge, log 10 It is a logarithm with base 10. It is a floor function.

[0095] S300: Based on the prior value of the step size diagonal matrix of the generalized ridge estimation, a search interval is set and the broadcast ephemeris parameters are fitted by generalized ridge estimation one by one. The fitting residual is calculated. After the search is completed within the search interval, the generalized ridge parameter value corresponding to the optimal residual is obtained. Based on the generalized ridge parameter value, the broadcast ephemeris parameters are fitted by generalized ridge estimation to obtain the fitted broadcast ephemeris parameters.

[0096] Specifically, the expression for the generalized ridge estimator is:

[0097]

[0098] In the formula, matrix A is the design matrix, matrix P is the error weight matrix, and matrix K = diag(k1,k2,…,k n () is a diagonal matrix, and the n diagonal elements in the diagonal matrix are called generalized ridge parameters, which can be expressed by the following formula:

[0099] K=εK0 (8)

[0100] In the formula, K0 is a diagonal matrix, that is, the diagonal matrix determined according to step 2; ε needs to be obtained through a search algorithm to obtain an approximate optimal value, and the final generalized ridge estimator is used as the solution of its parameter correction.

[0101] Specifically, according to Figure 1 The flowchart is shown below:

[0102] Before performing ridge estimation, ephemeris fitting should be performed using the traditional least squares method, and the following formula should be used to determine whether the fitting is successful:

[0103]

[0104] ||V k || <T s (10)

[0105] In the formula, V k and V k+1 These are the fitting residuals for the k-th and (k+1)-th iterations, respectively, T s It is a threshold related to the fitted arc length, which can be set according to the fitting needs.

[0106] If the above formula is satisfied, the parameters are directly output and the process exits. If the number of iterations exceeds the maximum value and the above formula is still not satisfied, and the multicollinearity analysis method determines that there is a strong multicollinearity relationship, then the adaptive generalized ridge estimation parameter search algorithm is started. This algorithm consists of two steps: First, the generalized ridge estimation parameters are adjusted with coarse granularity, and broadcast ephemeris fitting is iteratively performed in the interval ε∈[0,1000] with a step size of 1, dynamically recording the ε value corresponding to the minimum residual and the number of iterations, until the above convergence criterion is met or the threshold is reached and the process terminates; Second, the generalized ridge estimation parameters are adjusted with a small step size based on the neighborhood of the optimal value search, and the exit condition is set in the same way as in the first step. After two rounds of parameter search, the generalized ridge parameters select an optimal ridge parameter value obtained from the search, and broadcast ephemeris fitting is performed again using this value, and finally the final parameter value corresponding to the model fitting can be obtained.

[0107] When there are multiple fitted arc segments, step S300 is performed for each fitted arc segment until all arc segments are fitted.

[0108] For example, such as Figure 2 As shown, the generalized ridge parameter search is performed through the following steps:

[0109] S301: Perform broadcast ephemeris fitting using the least squares iterative method.

[0110] S302: Determine whether the fitted residuals satisfy expressions 9 and 10. If yes, execute S309; ​​otherwise, execute S303.

[0111] S303: Initialize variables: K0 = diag(k1, k2, ... k n ); ε = 1, Δε = 1; maxε = 1000, maxT = 60s; where maxT represents the maximum search time, Δε represents the current search step size, and maxε represents the current maximum search limit.

[0112] S304: K = εK0, using K for generalized ridge estimation, when minV k >V k Let minV k =V k , mink=k, minε=ε. Among them, minV k mink represents the current minimum residual value, mink represents the number of iterations corresponding to the current minimum residual value, and minε represents the ε value corresponding to the current minimum residual value.

[0113] S305: Determine whether the condition (T > maxT and V) is satisfied. k <T s ) or ε = maxε. If yes, execute S306; otherwise, execute S307.

[0114] S306: Determine if Δε = 0.01 is satisfied. If yes, execute S309; ​​otherwise, execute S308.

[0115] S307: ε=ε+Δε, and return to S304.

[0116] S308: maxε=minε+1, ε=minε-1, Δε=0.01, return to S304.

[0117] S309: Output the ephemeris parameters obtained from the fitting.

[0118] This application also provides a robust system for determining the ephemeris parameters of low-Earth orbit satellites, such as... Figure 3 As shown, the robust determination system for low-Earth orbit satellite broadcast ephemeris parameters includes:

[0119] The multicollinearity analysis module 301 is configured to perform multicollinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted, in order to determine whether multicollinearity exists;

[0120] The prior value determination module 302 is configured to determine the prior value of the generalized ridge estimation step size diagonal matrix based on the satellite precise ephemeris data and the designed broadcast ephemeris parameters when a complex collinearity relationship exists.

[0121] The ephemeris parameter fitting module 303 is configured to set a search interval based on the prior value of the diagonal matrix of the generalized ridge estimation step size, and successively perform generalized ridge estimation to fit the broadcast ephemeris parameters, calculate the fitting residual, obtain the generalized ridge parameter value corresponding to the optimal residual after the search is completed within the search interval, and perform generalized ridge estimation to fit the broadcast ephemeris parameters based on the generalized ridge parameter value to obtain the fitted broadcast ephemeris parameters.

[0122] This application provides an electronic device. The electronic device may include a processor and a memory, wherein the processor and the memory can communicate; exemplarily, the processor and the memory communicate via a communication bus.

[0123] The processor executes computer execution instructions stored in memory, causing the processor to perform the scheme in the above embodiments. The processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0124] The communication bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The system bus can be divided into address bus, data bus, control bus, etc. Transceivers are used to enable communication between the database access system and other computers (e.g., clients, read-write libraries, and read-only libraries). Memory may include random access memory (RAM) and may also include non-volatile memory.

[0125] The electronic device provided in this application embodiment can be the terminal device described in the above embodiments.

[0126] This application also provides a computer-readable storage medium storing computer instructions. When the computer instructions are executed on a computer, the computer performs the technical solution of the robust determination method for low-orbit satellite broadcast ephemeris parameters described in the above embodiments.

[0127] This application also provides a computer program product, which includes a computer program stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When the at least one processor executes the computer program, it can implement the technical solution of the robust determination method for low-orbit satellite broadcast ephemeris parameters described in the above embodiments.

[0128] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between systems or modules may be electrical, mechanical, or other forms.

[0129] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to implement the solution of this embodiment according to actual needs.

[0130] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The unit composed of the above modules can be implemented in hardware or in the form of hardware plus software functional units.

[0131] The integrated modules described above, implemented as software functional modules, can be stored in a computer-readable storage medium. These software functional modules, stored in a storage medium, include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) or processor to execute some steps of the methods of the various embodiments of this application.

[0132] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. A general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly manifested as being executed by a hardware processor, or executed by a combination of hardware and software modules within the processor.

[0133] The memory may include high-speed RAM, and may also include non-volatile storage (NVM), such as at least one disk storage device, and may also be a USB flash drive, external hard drive, read-only memory, disk or optical disc, etc.

[0134] Buses can be Industry Standard Architecture (ISA) buses, Peripheral Component Interconnect (PCI) buses, or Extended Industry Standard Architecture (EISA) buses, etc. Buses can be categorized into address buses, data buses, control buses, etc.

[0135] The aforementioned storage medium can be implemented from any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The storage medium can be any available medium accessible to general-purpose or special-purpose computers.

[0136] An exemplary storage medium is coupled to a processor, enabling the processor to read information from and write information to the storage medium. Alternatively, the storage medium can be an integral part of the processor. The processor and storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and storage medium can exist as discrete components in an electronic control unit or main control device.

[0137] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A robust determination method of low earth orbit satellite broadcast ephemeris parameters, characterized in that, The method comprises: Performing multicollinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether a multicollinearity relationship exists; When the multicollinearity relationship exists, determining a generalized ridge estimation step diagonal matrix prior value according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters; According to the generalized ridge estimation step diagonal matrix prior value, setting a search interval and performing generalized ridge estimation fitting of the broadcast ephemeris parameters successively to calculate fitting residuals, and obtaining a generalized ridge parameter value corresponding to optimal residuals after search in the search interval is completed, fitting of the broadcast ephemeris parameters is performed according to the generalized ridge parameter value to obtain fitted broadcast ephemeris parameters. 2.The robust determination of low earth orbit satellite broadcast ephemeris parameters method according to claim 1, characterized in that, Performing multicollinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether a multicollinearity relationship exists, comprising: Determining a function of the broadcast ephemeris parameters to satellite position according to the set broadcast ephemeris model; Performing first-order Taylor expansion on both sides of the function of the broadcast ephemeris parameters to satellite position to obtain a least square equation; Obtaining a Jacobian matrix from the least square equation, performing singular value decomposition on the Jacobian matrix to obtain a plurality of singular values, and determining a condition index through the following formula: In the formula, represents a condition index, represents a maximum value in the plurality of singular values, represents the kth singular value in the plurality of singular values; Determining a variance decomposition ratio matrix through the following formula according to the Jacobian matrix and the condition index: The normal matrix of the least squares equation Orthogonal similarity diagonalization, i.e.: wherein denotes the jth variance component of the kth component of the least squares estimator, denotes the jth diagonal element of the diagonal matrix denotes the jth diagonal element of the diagonal matrix denotes the element in the kth row and jth column of the orthogonal matrix denotes the variance of the kth component of the least squares estimator, j denotes the column number of the variance decomposition ratio matrix, denotes the element in the kth row and jth column of the variance decomposition ratio matrix, the rows of the variance decomposition ratio matrix sum to 1 ; F is a function broadcasting the ephemeris parameters to the satellite position, p is a parameter vector contained in the designed broadcast ephemeris model; If the variance decomposition has two or more elements greater than 0.5 for column j in the matrix and the conditional index for column j is greater than a set threshold, then it is determined that there is a complex collinearity relationship corresponding to the jth conditional index. th conditional index.​ 3.The robust determination of LEO satellite broadcast ephemeris parameters method according to claim 2, characterized in that, The function of the broadcast ephemeris parameters to satellite position is expressed as: In the formula, x is a three-dimensional position vector of the satellite.

4. The method of claim 3, wherein, The least square equation is expressed as: where p* is the true broadcast ephemeris parameter vector corresponding to the true satellite position, x* is the true satellite position vector, is the broadcast ephemeris parameter estimate vector, is calculated according to and F, is the satellite estimated position calculated from is the Jacobian matrix. 5.The robust determination of low earth orbit satellite broadcast ephemeris parameters method according to claim 1, characterized in that, When the multicollinearity relationship exists, determining a generalized ridge estimation step diagonal matrix prior value according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters, comprising: obtaining an estimate of a satellite parameter m corresponding to a designed broadcast ephemeris parameter m , the estimate corresponding partial derivative in the Jacobian matrix is in the jth column, determining a first diagonal matrix , the jth diagonal element of the first diagonal matrix as a generalized ridge estimate step size diagonal matrix prior value, the generalized ridge estimate step size diagonal matrix prior value being expressed as: wherein denotes the generalized ridge step size diagonal matrix prior, denotes the base-10 logarithm, denotes the floor function.

6. The method of claim 1, wherein, Before setting a search interval and performing generalized ridge estimation fitting of the broadcast ephemeris parameters successively according to the generalized ridge estimation step diagonal matrix prior value, the method further comprises: Performing ephemeris fitting of the designed broadcast ephemeris model by using a least square method, and judging whether the fitting is successful based on a judgment condition, the judgment condition being: wherein, and are the kth and (k+1)th fitting residuals, respectively, is a threshold value related to the fitting arc length; When the fitting residuals obtained by performing ephemeris fitting of the designed broadcast ephemeris model by using a least square method satisfy the judgment condition, directly outputting the ephemeris parameters obtained by fitting; When the fitting residuals obtained by performing ephemeris fitting of the designed broadcast ephemeris model by using a least square method do not satisfy the judgment condition, setting a search interval and performing generalized ridge estimation fitting of the broadcast ephemeris parameters successively according to the generalized ridge estimation step diagonal matrix prior value.

7. The method of claim 6, wherein, According to the generalized ridge estimation step diagonal matrix prior value, setting a search interval and performing generalized ridge estimation fitting of the broadcast ephemeris parameters successively to calculate fitting residuals, and obtaining a generalized ridge parameter value corresponding to optimal residuals after search in the search interval is completed, fitting of the broadcast ephemeris parameters is performed according to the generalized ridge parameter value to obtain fitted broadcast ephemeris parameters, comprising: Determining an expression of the generalized ridge estimator, expressed as: wherein denotes a generalized ridge estimator, A denotes a design matrix, P denotes an error weight matrix, denotes a second diagonal matrix, denote the first, second, and n-th diagonal elements of the second diagonal matrix, respectively, is a generalized ridge parameter value, T denotes a matrix transpose, and y denotes an observation error vector; In the formula, the second diagonal matrix is expressed as: wherein denotes a first diagonal matrix, denotes a scale factor from the first diagonal matrix to the second diagonal matrix; The coarse-grained adjustment generalized ridge estimation parameter is used to perform broadcast ephemeris fitting in the first step size in the interval of epsilon epsilon [0, 1000] iteration, and the minimum residual corresponding epsilon value and iteration number are dynamically recorded until the convergence condition is met or the threshold is terminated, and the coarse search optimal value neighborhood is obtained; Based on the coarse search optimal value neighborhood, the generalized ridge estimation parameter is adjusted with a second step size smaller than the first step size, and the minimum residual corresponding epsilon value and iteration number are dynamically recorded until the convergence condition is met or the threshold is terminated, and the optimal residual corresponding generalized ridge parameter value is obtained; According to the generalized ridge parameter value, the generalized ridge estimation fitting broadcast ephemeris parameter is performed to obtain the fitted broadcast ephemeris parameter. 8.A low earth orbit satellite broadcast ephemeris parameter robust determination system, characterized in that, The system comprises: The multiple collinearity relationship analysis module is configured to perform multiple collinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether there is a multiple collinearity relationship; The prior value determination module is configured to determine the generalized ridge estimation step size diagonal matrix prior value according to the satellite precise ephemeris data and the designed broadcast ephemeris parameter when there is a multiple collinearity relationship; The ephemeris parameter fitting module is configured to set a search interval and perform generalized ridge estimation fitting broadcast ephemeris parameter in sequence according to the generalized ridge estimation step size diagonal matrix prior value, calculate the fitting residual, and obtain the optimal residual corresponding generalized ridge parameter value after the search in the search interval is completed, perform generalized ridge estimation fitting broadcast ephemeris parameter according to the generalized ridge parameter value, and obtain the fitted broadcast ephemeris parameter.

9. An electronic device, comprising: It comprises: A processor and a memory connected in communication with the processor; The memory stores computer execution instructions; The processor executes the computer execution instructions stored in the memory to realize the low-orbit satellite broadcast ephemeris parameter robust determination method in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores computer execution instructions, and the computer execution instructions are executed by the processor to realize the low-orbit satellite broadcast ephemeris parameter robust determination method in any one of claims 1-7.

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