Robust determination method and system for low-orbit satellite broadcast ephemeris parameters

Abstract

The invention provides a low earth orbit satellite broadcast ephemeris parameter robust determination method and system. Relates to the technical field of satellite navigation. The method comprises the following steps: performing complex collinearity analysis on a designed broadcast ephemeris model in to-be-fitted satellite precise ephemeris data to determine whether a complex collinearity relationship exists or not; when the complex collinear relation exists, determining a generalized ridge estimation step length diagonal matrix priori value according to satellite precision ephemeris data and designed broadcast ephemeris parameters; according to a generalized ridge estimation step length diagonal matrix priori value, setting a search interval and successively carrying out generalized ridge estimation to fit broadcast ephemeris parameters, calculating a fitting residual error, obtaining a generalized ridge parameter value corresponding to an optimal residual error after searching in the search interval, and according to the generalized ridge parameter value, carrying out generalized ridge estimation to fit broadcast ephemeris parameters. According to the method and the device, the problem of fitting failure caused by serious illness of the least square equation due to improper design of the broadcast ephemeris model is solved.

Description

Technical Field

[0001] This application relates to the technical field of satellite navigation, and particularly relates to a method and system for robustly determining broadcast ephemeris parameters of low-earth orbit satellites. Background Art

[0002] As an important spatio-temporal information infrastructure, the Global Navigation Satellite System (GNSS) provides all-weather navigation, positioning, and timing (PNT) services for global users. However, traditional GNSS relying on medium and high-earth orbit satellites has problems such as weak ground signals, and signals being easily spoofed and interfered, and cannot meet the high-precision and high-robust positioning requirements in scenarios such as indoors, urban canyons, and under overpasses. In view of this, the concept of enhancing GNSS through low-earth orbit navigation satellites has gradually been proposed by scholars at home and abroad in recent years. When using low-earth orbit navigation to enhance GNSS, the receiver of the user needs to obtain the precise position of the low-earth orbit enhancement satellite in real time. The broadcast ephemeris can provide the precise 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 its fitting accuracy determines the accuracy of the satellite position obtained by the user, thus affecting the accuracy of user positioning.

[0003] The fitting of the broadcast ephemeris of low-earth orbit satellites is different from that of traditional medium and high-earth orbit satellites such as GPS. Since the non-spherical gravitational perturbation and atmospheric drag perturbation of low-earth orbit satellites are more complex than those of medium and high-earth orbit satellites, its broadcast ephemeris model generally needs to be redesigned according to the perturbation force received by the low-earth orbit satellite. In recent decades, scholars at home and abroad have designed ephemeris models with 19, 21, 22, 24, 26 and other numbers of parameters that are particularly suitable for low-earth orbit satellites based on their respective studies on the GPS16 and 18 ephemeris models and the GLONASS orbit list type ephemeris model. However, during the fitting process of the broadcast ephemeris, the design matrix of the partial derivative of the satellite position with respect to the broadcast ephemeris parameters will produce strong ill-conditioning. This ill-conditioning will reduce the fitting accuracy of the broadcast ephemeris or even cause the fitting to fail. There are generally two reasons for the ill-conditioning: one is the ambiguity in the definition of the argument of perigee due to the orbital eccentricity approaching 0; the other is the ambiguity in the definition of the right ascension of the ascending node due to the orbital inclination approaching 0. Essentially, both of these reasons are that when the orbital elements take specific values, two or three of the six Keplerian elements produce approximate collinearity, thus causing the singularity of the least squares equations. When the broadcast ephemeris model is designed improperly, the reason for the ill-conditioning problem also lies in that some parameters of the designed ephemeris model are too strongly correlated with other parameters, which in turn leads to the ill-conditioning of the normal matrix.

[0004] Based on these problems, the prior art has designed different ephemeris models and fitting methods. For example, the first type of singular point-free roots and the second type of singular point-free roots are used to desingularize the broadcast ephemeris parameters, and orbital plane rotation is used to improve the singularity problem when the orbital inclination is close to 0. In addition, when solving the least squares equations, some scholars have proposed the generalized ridge estimation method. The singular point-free root method mainly obtains specific parameters that produce complex collinearity relationships (such as when the eccentricity e is close to 0, the mean anomaly M and the perigee angular distance ω produce an approximate collinear relationship) through a detailed theoretical analysis of the principle of complex collinearity, and then designs new parameters for the parameters that produce approximate linear relationships. The orbital plane rotation method mainly avoids singularities by re-defining the value of the inclination i. When the inclination i value obtained by fitting is less than the threshold, the orbital plane is rotated as a whole and then fitted, and then the fitting result is converted back to the original reference system. The generalized ridge estimation method mainly reduces the condition number of the normal equation and suppresses the morbidity of the equation system by adding a diagonal matrix to the least squares design matrix.

[0005] Both of the above-mentioned ephemeris fitting methods have certain complexity and limitations. In the final analysis, they all need to theoretically analyze the specific broadcast ephemeris model, find out the specific reasons for the generation of singularities or specific complex collinearity relationships, and then make targeted corrections to the ephemeris parameters, which undoubtedly increases the creative workload of ephemeris designers. In addition, the above two methods are limited to correcting the complex collinearity relationship generated by the six Kepler elements. However, when designing broadcast ephemeris parameters, when other non-six-element parameters produce complex collinearity due to improper design, it is difficult to theoretically analyze the existence of singularities or specific complex collinearity relationships due to the complex functional relationship between satellite positions and designed ephemeris parameters. Finally, the core of the generalized ridge estimation method lies in the selection of ridge parameters. The existing selection methods have defects to varying degrees: 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 solution is complex; the L curve method requires determining the maximum point of the curvature of the L curve, and the defects are the same as the GCV method. In the determination of generalized ridge parameters, multiple ridge parameters need to be determined simultaneously. The aforementioned solutions with high computational complexity can no longer meet the real-time requirements of ephemeris fitting. Summary of the invention

[0006] The present application provides a method and system for robustly determining the broadcast ephemeris parameters of low-earth orbit satellites to solve the problem that the least-squares equation is severely ill-conditioned due to improper design of the broadcast ephemeris model, which in turn leads to fitting failure. Specifically, the present application discovers the specific multicollinearity relationship generated in the ephemeris fitting and solves the problem of difficult determination of the ridge parameter in the generalized ridge estimation during the broadcast ephemeris fitting based on the adaptive generalized ridge estimation method, clarifies the selection criteria of the ridge parameter, improves the efficiency of ridge parameter selection, effectively alleviates the ill-conditioning of the least-squares equations caused by improper broadcast ephemeris design, and achieves the ultimate effect of increasing the fitting success rate.

[0007] In a first aspect, the present application provides a method for robustly determining the broadcast ephemeris parameters of low-earth orbit satellites, including:

[0008] Performing a 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 generalized ridge estimation step diagonal matrix according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters;

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

[0011] In a possible design, performing a 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, including:

[0012] According to the set broadcast ephemeris model, determining the function from the broadcast ephemeris parameters to the satellite position;

[0013] Making a first-order Taylor expansion on both sides of the function from the broadcast ephemeris parameters to the satellite position to obtain the least-squares equation;

[0014] Obtaining the Jacobian matrix from the least-squares equation, performing singular value decomposition on the Jacobian matrix to obtain multiple singular values, and determining the condition index through the following formula:

[0015]

[0016] In the formula, η k represents the condition index, σ1 represents the maximum value among multiple singular values, and σ k represents the k-th singular value among multiple singular values;

[0017] According to the Jacobian matrix and the conditional index, determine the variance decomposition ratio matrix through the following formula:

[0018] Orthogonally and similarly diagonalize the normal matrix of the least squares equation , that is:

[0019]

[0020] In the formula, φ k,j represents the j-th variance component of the k-th component in the least squares estimator, λ j represents the j-th diagonal element of the diagonal matrix Λ, q kj represents the element in the k-th row and j-th column of the orthogonal matrix Q, φ k represents the variance of the k-th component in 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, and the sum of the rows of the variance decomposition ratio matrix is 1.

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

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

[0023] F(p) = x

[0024] In the formula, F is the function from the broadcast ephemeris parameters to the satellite position, p is the parameter vector included 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 expressed as:

[0026]

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

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

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

[0030]

[0031] In the formula, (K0) jj represents the prior value of the generalized ridge estimation step diagonal matrix, and log 10 represents the logarithm with base 10, represents the floor function.

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

[0033] Use the least squares method to perform ephemeris fitting on the designed broadcast ephemeris model, and based on the judgment condition, judge whether the fitting is successful. The judgment condition is:

[0034]

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

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

[0037] When the fitting residuals obtained by using the least squares method to perform ephemeris fitting on the designed broadcast ephemeris model satisfy the judgment condition, directly output the fitted ephemeris parameters;

[0038] When the fitting residuals obtained by using the least squares method to perform ephemeris fitting on the designed broadcast ephemeris model do not satisfy the judgment condition, set the search interval according to the prior value of the generalized ridge estimation step diagonal matrix and successively perform generalized ridge estimation to fit the broadcast ephemeris parameters.

[0039] In a possible design, according to the prior value of the generalized ridge estimation step diagonal matrix, set the search interval and successively perform generalized ridge estimation to fit the broadcast ephemeris parameters, calculate the fitting residuals, obtain the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval, and according to the generalized ridge parameter value, perform generalized ridge estimation to fit the broadcast ephemeris parameters to obtain the fitted broadcast ephemeris parameters, including:

[0040] Determine the expression of the generalized ridge estimator, which is expressed as:

[0041]

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

[0043] Among them, the second diagonal matrix is expressed as:

[0044] K = εK0

[0045] Wherein, K0 represents the first diagonal matrix, and ε represents the scale factor from the first diagonal matrix to the second diagonal matrix;

[0046] Coarsely adjust the generalized ridge estimation parameters, iteratively perform broadcast ephemeris fitting in the interval of ε ∈ [0, 1000] with the first step size, dynamically record the ε value corresponding to the minimum residual and the number of iterations until the convergence condition is met or the threshold is reached and terminate, to obtain the neighborhood of the optimal value of the coarse search;

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

[0048] According to the generalized ridge parameter value, perform generalized ridge estimation to fit the broadcast ephemeris parameters to obtain the fitted broadcast ephemeris parameters.

[0049] In a second aspect, the present application provides a system for robust determination of low-orbit satellite broadcast ephemeris parameters. The system includes a controller, and the controller is configured to:

[0050] A multicollinearity relationship analysis module, configured to perform multicollinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted, so as to determine whether there is a multicollinearity relationship;

[0051] A prior value determination module, configured to determine the prior value of the generalized ridge estimation step diagonal matrix according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters when there is a multicollinearity relationship;

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

[0053] In a third aspect, an embodiment of the present application provides an electronic device, including: at least one processor and a memory; the memory stores computer-executable instructions; the at least one processor executes the computer-executable instructions stored in the memory, so that the at least one processor executes the method for robust determination of low-orbit satellite broadcast ephemeris parameters as described in the first aspect and various possible designs of the first aspect above.

[0054] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, in which computer-executable instructions are stored, and when the processor executes the computer-executable instructions, the method for robust determination of low-orbit satellite broadcast ephemeris parameters as described in the first aspect and various possible designs of the first aspect above is implemented.

[0055] In a fifth aspect, an embodiment of the present application provides a computer program product, including a computer program, and when the computer program is executed by a processor, the method for robust determination of low-orbit satellite broadcast ephemeris parameters as described in the first aspect and various possible designs of the first aspect above is implemented.

[0056] The method and system for robust determination of low-orbit satellite broadcast ephemeris parameters provided by the present application have at least the following beneficial effects:

[0057] 1. The present application uses the existing conditional index-variance decomposition ratio method to detect the collinearity 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 a complex ephemeris model, only the collinearity analysis of the satellite data to be fitted is required to obtain the collinearity relationship generated in the corresponding satellite data, making its design simplified from theoretical analysis to direct experimental testing.

[0058] 2. The present application adopts an adaptive generalized ridge estimation method to address the ill-conditioned problem in broadcast ephemeris fitting. Without dealing with specific collinearity relationships, it can alleviate the ill-conditioning of the least squares equation and solve the complexity problem in existing ephemeris design methods that require targeted design of corrected ephemeris based on specific collinearity relationships. In particular, an adaptive method that first determines the search step size and then synchronously searches for the ridge parameter is used to solve the problem of difficult determination of the ridge parameter when using generalized ridge estimation for ephemeris fitting. The method of searching and selecting the ridge parameter value with the smallest fitting residual ensures a definite criterion for ridge parameter selection. The synchronous search method also ensures a low algorithm complexity, achieving the ultimate effect of increasing the fitting success rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The accompanying drawings herein are incorporated into and constitute a part of this specification, showing embodiments consistent with the present application, and are used together with the specification to explain the principles of the present application.

[0060] Figure 1 It is a flowchart of a method for robust determination of low-earth orbit satellite broadcast ephemeris parameters provided by an embodiment of the present application;

[0061] Figure 2 It is a flowchart of generalized ridge parameter search provided by an embodiment of the present application;

[0062] Figure 3 It is a structural diagram of a system for robust determination of low-earth orbit satellite broadcast ephemeris parameters provided by an embodiment of the present application.

[0063] Through the above accompanying drawings, specific embodiments of the present application have been shown, and there will be more detailed descriptions hereinafter. These drawings and written descriptions are not intended to limit the scope of the concept of the present application in any way, but to illustrate the concept of the present application to those skilled in the art by referring to specific embodiments. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0064] Here, exemplary embodiments will be described in detail, and their examples are shown in the accompanying drawings. When the following description refers to the accompanying 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 the present application. Instead, they are merely examples of systems and methods consistent with some aspects of the present application as detailed in the appended claims.

[0065] In the technical solution of the present application, the collection, storage, use, processing, transmission, provision, and disclosure of information such as financial data or user data comply with the provisions of relevant laws and regulations and do not violate public order and good customs.

[0066] It should be noted that in the embodiments of the present application, some existing solutions in the industry such as certain software, components, models, etc. may be mentioned. They should be regarded as exemplary, and their purpose is only to illustrate the feasibility in the implementation of the technical solution of the present application, but it does not mean that the applicant has already or necessarily used this solution.

[0067] The following will use specific embodiments to elaborate in detail on the technical solution of the present application and how the technical solution of the present application solves the above technical problems. These several specific embodiments below can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The following will describe the embodiments of the present application in conjunction with the accompanying drawings.

[0068] The embodiments of the present application provide a method for robustly determining the broadcast ephemeris parameters of low-earth orbit satellites. The basic idea of this method is as follows: First, perform a multicollinearity analysis on the designed broadcast ephemeris model in the satellite data to be fitted. When it is detected that there is a severe ill-condition, determine the prior value of the generalized ridge estimation step-size diagonal matrix, and use the generalized ridge estimation for ephemeris fitting according to the prior value of the generalized ridge estimation step-size diagonal matrix. Perform ridge parameter search and fitting successively, and then obtain an optimal generalized ridge parameter estimation value, and calculate the corresponding ephemeris parameters with this optimal value.

[0069] As Figure 1 shown, it is a flowchart of a method for robustly determining the broadcast ephemeris parameters of low-earth orbit satellites provided by the embodiments of the present application. This method for robustly determining the broadcast ephemeris parameters of low-earth orbit satellites first performs a multicollinearity analysis on the broadcast ephemeris model. If there is no multicollinearity relationship, directly use the least squares estimation for ephemeris fitting and output the ephemeris parameters obtained by fitting. If there is a multicollinearity relationship, determine the prior value of the generalized ridge estimation step-size list, perform a generalized ridge estimation parameter search, use the optimal generalized ridge estimation parameter for ephemeris fitting, and output the ephemeris parameters obtained by fitting.

[0070] Specifically, this method for robustly determining the broadcast ephemeris parameters of low-earth orbit satellites can be implemented through the following steps S100 - S300.

[0071] S100: Perform a 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.

[0072] After the broadcast ephemeris model is designed, the functional relationship from the broadcast ephemeris parameters to the satellite position is determined, that is:

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

[0074] where F is the functional relationship from the broadcast ephemeris parameters to the satellite position, p is the parameter vector included in the designed broadcast ephemeris model, and x is the three-dimensional position vector of the satellite. Perform a first-order Taylor expansion on both sides of the expression (1) to obtain:

[0075]

[0076] Where \(p^*\) is the vector of true broadcast ephemeris parameters corresponding to the true position of the satellite, and \(x^*\) is the vector of the true position of the satellite. is the vector of estimated values of broadcast ephemeris parameters. is based on and F is the estimated position of the satellite calculated. is the Jacobian matrix of the function F. The essence of broadcast ephemeris fitting is to iteratively solve the least squares equation (2).

[0077] The main purpose of step S100 is to test this ephemeris model before officially using it. Specifically, perform a condition index - variance decomposition ratio analysis and an ephemeris fitting experiment on the Jacobian matrix generated from the measured data.

[0078] Perform a singular value decomposition on the Jacobian matrix and denote \(\sigma_1,\sigma_2,\cdots,\sigma\) n is the Jacobian matrix The singular values from largest to smallest, define the condition index \(\eta\) k as follows:

[0079]

[0080] When the condition index \(\eta\) k is greater than 1000, it is determined that the complex collinearity relationship induced by the \(k\) - th singular value \(\sigma\) k is serious; when the condition index \(\eta\) k is greater than 100 and less than 1000, it is determined that the complex collinearity relationship induced by \(\sigma\) k is relatively strong; when all condition indices are less than 100, it indicates that the complex collinearity relationship is weak.

[0081] In this embodiment, if it is determined that the complex collinearity relationship is weak, it is determined that there is no complex collinearity relationship; otherwise, it is determined that there is a complex collinearity relationship.

[0082] Orthogonally and similarly diagonalize the normal matrix of the least squares equation i.e.:

[0083]

[0084] In the formula, \(Q\) represents the orthogonal matrix obtained by orthogonally and similarly diagonalizing the said Jacobian matrix, \(T\) represents the matrix transpose, and \(\Lambda\) represents the diagonal matrix obtained by orthogonally and similarly diagonalizing.

[0085] Define the variance decomposition ratio:

[0086]

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

[0088] For the variance decomposition ratio matrix defined above, the sum of the rows is 1. If a certain column j has two or more elements greater than 0.5, and the condition index η j of the corresponding column is greater than 100, it indicates that there is a complex collinearity relationship corresponding to the j-th condition index. The elements greater than 0.5 are included in the detected complex collinearity relationship, and the greater the value of this column in the variance decomposition ratio, the stronger the correlation in the complex collinearity relationship.

[0089] Perform ephemeris fitting tests on the fitting arcs of all satellite data to be tested, and conduct complex collinearity analysis of the least squares equation according to the above condition index-variance decomposition ratio method. If there is a satellite for which a certain fitting arc fails to fit, and the condition index is greater than 1000 in the complex collinearity analysis, and there are two or more elements greater than 0.5 in the corresponding column of the corresponding variance decomposition ratio matrix, then it is determined that this model has produced ill-conditioning in the satellite data to be tested, and the detected complex collinearity relationship is as described above.

[0090] S200: When there is a complex collinearity relationship, determine the prior value of the generalized ridge estimation step size diagonal matrix according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters.

[0091] In this embodiment, taking the orbital element type ephemeris parameters as an example, use the satellite precise ephemeris to calculate the six orbital elements of the satellite at this moment and other auxiliary parameters to form the corresponding time series. Generally, the orbital element type ephemeris parameter set can be divided into the six Keplerian orbital elements, the coefficient of the linear trend term of the orbital elements, and the coefficient of the periodic trend term of the orbital elements. Calculate the corresponding parameter estimation values of this satellite in the tested satellite precise ephemeris data. The six Keplerian orbital elements can be directly deduced from the position and velocity of the satellite at this moment. The coefficient of the linear trend term can be obtained by taking out the linear term coefficient after polynomial fitting of the time series, and the coefficient of the periodic term can be determined similarly.

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

[0093]

[0094] Wherein, (K0) jj is the prior value of the diagonal matrix of the generalized ridge estimation step size, and log 10 is the logarithm to the base 10, is the floor function.

[0095] S300: According to the prior value of the diagonal matrix of the generalized ridge estimation step size, set the search interval and successively perform the generalized ridge estimation to fit the broadcast ephemeris parameters, calculate the fitting residual, and obtain the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval. According to the generalized ridge parameter value, perform the generalized ridge estimation to fit the broadcast ephemeris parameters to obtain the fitted broadcast ephemeris parameters.

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

[0097]

[0098] Wherein, 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] Wherein, K0 is a diagonal matrix, that is, the diagonal matrix determined according to step 2; ε needs to obtain an approximate optimal value through a search algorithm, and the finally obtained generalized ridge estimator is used as the solution of its parameter correction number.

[0101] Specifically, according to Figure 1 shown in the flowchart of

[0102] Before performing the ridge estimation, it is necessary to perform ephemeris fitting using the traditional least squares method and judge whether the fitting is successful through the following formula:

[0103]

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

[0105] Wherein, V k and V k+1 are the fitting residuals of the kth and (k + 1)th times respectively, and T s is a threshold related to the fitting arc length and can be set according to the fitting requirements.

[0106] If the above equation is satisfied, directly output the parameters and exit. If the number of iterations exceeds the maximum value and still does not satisfy the above equation, and the multicollinearity analysis method determines that there is a strong multicollinearity relationship, then start the adaptive generalized ridge estimation parameter search algorithm. This algorithm is divided into two steps: First, adjust the generalized ridge estimation parameter with a coarse-grained method, and perform broadcast ephemeris fitting iteratively with a step size of 1 in the interval of ε ∈ [0, 1000], dynamically record the ε value and the number of iterations corresponding to the minimum residual until the above convergence criterion is satisfied or the threshold is reached to terminate; Second, based on the neighborhood of the optimal value obtained from the coarse search, adjust the generalized ridge estimation parameter with a small step size, and set the same exit condition as the first step. After two rounds of parameter search, the generalized ridge parameter selects an optimal ridge parameter value obtained from the search, and uses this value to perform broadcast ephemeris fitting again, and finally the final parameter value corresponding to the model fitting can be obtained.

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

[0108] Exemplarily, as Figure 2 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 fitting residual satisfies Expressions 9 and 10. If so, execute S309; if not, 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 upper limit.

[0112] S304: K = εK0, use K for generalized ridge estimation. When minV k > V k , let minV k = V k , mink = k, minε = ε. Where, minV k 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 (T > maxT and V k < T s ) or ε = maxε is satisfied. If so, execute S306; if not, execute S307.

[0114] S306: Determine whether Δε = 0.01 is satisfied. If so, execute S309; if not, 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 by fitting.

[0118] The embodiment of the present application also provides a system for robust determination of low - earth - orbit satellite broadcast ephemeris parameters. As Figure 3 shown, the system for robust determination of low - earth - orbit satellite broadcast ephemeris parameters includes:

[0119] A multicollinearity relationship analysis module 301, configured to perform multicollinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted, so as to determine whether there is a multicollinearity relationship;

[0120] A prior value determination module 302, configured to determine the prior value of the generalized ridge estimation step - length diagonal matrix according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters when there is a multicollinearity relationship;

[0121] An ephemeris parameter fitting module 303, configured to set a search interval according to the prior value of the generalized ridge estimation step - length diagonal matrix, and successively perform generalized ridge estimation to fit the broadcast ephemeris parameters, calculate the fitting residuals, obtain the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval, and perform generalized ridge estimation to fit the broadcast ephemeris parameters according to the generalized ridge parameter value to obtain the fitted broadcast ephemeris parameters.

[0122] The embodiment of the present application provides an electronic device. The electronic device may include: a processor and a memory. Among them, the processor and the memory can communicate; exemplarily, the processor and the memory communicate through a communication bus.

[0123] The processor executes the computer - executable instructions stored in the memory, so that the processor executes the solutions in the above - mentioned embodiments. The processor may be a general - purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it may 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, discrete hardware components.

[0124] The communication bus can be a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The system bus can be divided into an address bus, a data bus, a control bus, etc. The transceiver is used to implement communication between the database access system and other computers (such as clients, read-write libraries, and read-only libraries). The memory may include Random Access Memory (RAM), and may also include non-volatile memory.

[0125] The electronic device provided by the embodiments of the present application can be the terminal device in the above embodiments.

[0126] The embodiments of the present application further provide a computer-readable storage medium. Computer instructions are stored in the computer-readable storage medium. When the computer instructions run on a computer, the computer is enabled to execute the technical solutions of the method for robust determination of low-earth orbit satellite broadcast ephemeris parameters in the above embodiments.

[0127] The embodiments of the present application further provide a computer program product. The computer program product includes a computer program, which is stored in a computer-readable storage medium. At least one processor can read the computer program from the computer-readable storage medium. When at least one processor executes the computer program, the technical solutions of the method for robust determination of low-earth orbit satellite broadcast ephemeris parameters in the above embodiments can be implemented.

[0128] In several embodiments provided by the present 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 example, the division of modules is only a logical function division. In actual implementation, there may be other division methods. For example, multiple modules can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces. The indirect couplings or communication connections of systems or modules can be in electrical, mechanical, or other forms.

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

[0130] In addition, in each embodiment of the present application, each functional module can be integrated in a processing unit, or each module can exist physically alone, or two or more modules can be integrated in one unit. The unit formed by the above modules can be implemented in the form of hardware, or in the form of a combination of hardware and software functional units.

[0131] The integrated module implemented in the form of a software functional module can be stored in a computer-readable storage medium. The above software functional module stored in a storage medium includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods in the various embodiments of the present application.

[0132] It should be understood that the above processor can be a Central Processing Unit (CPU for short), or other general-purpose processors, Digital Signal Processors (DSP for short), Application Specific Integrated Circuits (ASIC for short), etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in combination with the invention can be directly embodied as being executed by a hardware processor, or executed by a combination of hardware and software modules in the processor.

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

[0134] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0135] The above storage medium can be implemented by 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 memory, flash memory, magnetic disk or optical disk. The storage medium can be any available medium accessible by a general-purpose or special-purpose computer.

[0136] An exemplary storage medium is coupled to the processor, enabling the processor to read information from the storage medium and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can be located in an application specific integrated circuit (ASIC). Of course, the processor and the storage medium can also exist as discrete components in an electronic control unit or a master control device.

[0137] Those of ordinary skill in the art can understand that all or part of the steps to implement the above method embodiments can be completed by hardware related to program instructions. The foregoing program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps including the above method embodiments; and the foregoing storage medium includes various media that can store program codes, such as ROM, RAM, magnetic disk or optical disk.

[0138] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and are not intended to limit them. Although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A robust determination method for broadcast ephemeris parameters of low-earth orbit satellites, characterized in that, The method includes: Performing collinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether there is a collinearity relationship; When there is a collinearity relationship, determining the prior value of the generalized ridge estimation step diagonal matrix according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters; According to the prior value of the generalized ridge estimation step diagonal matrix, setting a search interval and successively performing generalized ridge estimation to fit the broadcast ephemeris parameters, calculating the fitting residuals, obtaining the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval, and according to the generalized ridge parameter value, performing generalized ridge estimation to fit the broadcast ephemeris parameters to obtain the fitted broadcast ephemeris parameters.

2. The robust determination method of low-earth orbit satellite broadcast ephemeris parameters according to claim 1, characterized in that Performing collinearity analysis on the designed broadcast ephemeris model in the satellite precise ephemeris data to be fitted to determine whether there is a collinearity relationship, including: Determining the function from the broadcast ephemeris parameters to the satellite position according to the set broadcast ephemeris model; Making a first-order Taylor expansion on both sides of the function from the broadcast ephemeris parameters to the satellite position to obtain the least squares equation; Obtaining the Jacobian matrix from the least squares equation, performing singular value decomposition on the Jacobian matrix to obtain multiple singular values, and determining the condition index through the following formula: where η k represents a conditional index, σ1 represents the maximum value among multiple singular values, and σ k represents the k-th singular value among multiple singular values; According to the Jacobian matrix and the condition index, determining the variance decomposition ratio matrix through the following formula: Orthogonally similar diagonalize the normal matrix of the least squares equation That is: where φ k,j represents the j-th variance component of the k-th component in the least squares estimator, λ j represents the j-th diagonal element of the diagonal matrix Λ, q kj represents the element in the k-th row and j-th column of the orthogonal matrix, φ k represents the variance of the k-th component in the least squares estimator, j represents the number of columns of the variance decomposition ratio matrix, π k,j represents the element in the k-th row and j-th column of the variance decomposition ratio matrix, and the sum of the rows of the variance decomposition ratio matrix is 1; If column j in 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 the set threshold, then it is determined that there is a multicollinearity relationship corresponding to the j-th condition index.

3. The robust determination method for low-orbit satellite broadcast ephemeris parameters according to claim 2, characterized in that, The function from the broadcast ephemeris parameters to the satellite position is expressed as: F(p) = x In the formula, F is the function from the broadcast ephemeris parameters to the satellite position, p is the parameter vector included in the designed broadcast ephemeris model, and x is the three-dimensional position vector of the satellite.

4. The robust determination method of the low-orbit satellite broadcast ephemeris parameters according to claim 3, characterized in that The least squares equation is expressed as: where \(p^*\) is the vector of true broadcast ephemeris parameters corresponding to the true position of the satellite, and \(x^*\) is the true position vector of the satellite. is the vector of estimated broadcast ephemeris parameters. is the estimated position of the satellite calculated based on and \(F\). is the Jacobian matrix.

5. The robust determination method for low-earth orbit satellite broadcast ephemeris parameters according to claim 1, wherein When there is a collinearity relationship, determining the prior value of the generalized ridge estimation step diagonal matrix according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters, including: Obtain the estimated value of the satellite corresponding to the designed broadcast ephemeris parameter m Estimated value The partial derivative corresponding to it in the Jacobi matrix is in the j-th column. Determine the first diagonal matrix K0, and use the j-th diagonal element of the first diagonal matrix K0 as the prior value of the generalized ridge estimation step diagonal matrix. The prior value of the generalized ridge estimation step diagonal matrix is expressed as: In the formula, (K0) jj represents the prior value of the generalized ridge estimation step-size diagonal matrix, log 10 represents the logarithm to the base 10, represents the floor function.

6. The robust determination method of the low-earth orbit satellite broadcast ephemeris parameters according to claim 1, wherein Before setting the search interval according to the prior value of the generalized ridge estimation step diagonal matrix and successively performing generalized ridge estimation to fit the broadcast ephemeris parameters, the method further includes: Performing ephemeris fitting on the designed broadcast ephemeris model by using the least squares method, and based on a judgment condition, judging whether the fitting is successful, where the judgment condition is: Wherein, V k and V k+1 are the fitting residuals of the k-th and (k + 1)-th times respectively, and T s is a threshold related to the fitting arc length; When the fitting residuals obtained by performing ephemeris fitting on the designed broadcast ephemeris model by using the least squares method satisfy the judgment condition, directly outputting the fitted ephemeris parameters; When the fitting residuals obtained by performing ephemeris fitting on the designed broadcast ephemeris model by using the least squares method do not satisfy the judgment condition, setting a search interval according to the prior value of the generalized ridge estimation step diagonal matrix and successively performing generalized ridge estimation to fit the broadcast ephemeris parameters.

7. The robust determination method of low-orbit satellite broadcast ephemeris parameters according to claim 6, wherein Setting a search interval according to the prior value of the generalized ridge estimation step diagonal matrix and successively performing generalized ridge estimation to fit the broadcast ephemeris parameters, calculating the fitting residuals, obtaining the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval, and according to the generalized ridge parameter value, performing generalized ridge estimation to fit the broadcast ephemeris parameters to obtain the fitted broadcast ephemeris parameters, including: Determining the expression of the generalized ridge estimator, expressed as: In the formula, represents the generalized ridge estimator, A represents the design matrix, P represents the error weight matrix, K = diag(k1, k2, …, k n ), represents the second diagonal matrix, k1, k2, k n respectively represent the 1st, 2nd, and nth diagonal elements in the second diagonal matrix, which are the generalized ridge parameter values, T represents the matrix transpose, and y represents the observed value error vector; Where the second diagonal matrix is expressed as: K = εK0 In the formula, K0 represents the first diagonal matrix, and ε represents the scale factor from the first diagonal matrix to the second diagonal matrix; The coarse-grained adjustment of the generalized ridge estimation parameters is adopted, and the broadcast ephemeris fitting is iteratively executed within the interval of ε ∈ [0, 1000] with the first step size. The ε value corresponding to the minimum residual and the number of iterations are dynamically recorded until the convergence condition is satisfied or the threshold is reached and terminated, and the neighborhood of the optimal value obtained by the coarse search is obtained; Based on the neighborhood of the optimal value obtained by the coarse search, the generalized ridge estimation parameters are adjusted with the second step size smaller than the first step size. The ε value corresponding to the minimum residual and the number of iterations are dynamically recorded until the convergence condition is satisfied or the threshold is reached and terminated, and the generalized ridge parameter value corresponding to the optimal residual is obtained; According to the generalized ridge parameter value, the generalized ridge estimation is performed to fit the broadcast ephemeris parameters, and the fitted broadcast ephemeris parameters are obtained.

8. A robust determination system for low-orbit satellite broadcast ephemeris parameters, characterized in that, The system includes: A multicollinearity relationship analysis module configured to perform 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; A prior value determination module configured to determine the prior value of the generalized ridge estimation step diagonal matrix according to the satellite precise ephemeris data and the designed broadcast ephemeris parameters when there is a multicollinearity relationship; An ephemeris parameter fitting module configured to set a search interval according to the prior value of the generalized ridge estimation step diagonal matrix and perform generalized ridge estimation to fit the broadcast ephemeris parameters successively, calculate the fitting residual, obtain the generalized ridge parameter value corresponding to the optimal residual after the search in the search interval, and perform generalized ridge estimation to fit the broadcast ephemeris parameters according to the generalized ridge parameter value to obtain the fitted broadcast ephemeris parameters.

9. An electronic device, characterized in that, Including: A processor and a memory communicatively connected to the processor; The memory stores computer execution instructions; The processor executes the computer execution instructions stored in the memory to implement the method for robust determination of low-orbit satellite broadcast ephemeris parameters according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, Computer execution instructions are stored in the computer-readable storage medium, and when the computer execution instructions are executed by the processor, they are used to implement the method for robust determination of low-orbit satellite broadcast ephemeris parameters according to any one of claims 1-7.

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