A fast convergence method for low-orbit satellite broadcast ephemeris fitting

Abstract

The present application relates to a method for fast convergence of low-orbit satellite broadcast ephemeris fitting. The method comprises: estimating the change of the ephemeris parameter vector of the current iteration according to the least squares principle for the estimated ephemeris parameter vector; obtaining the change of the semi-major axis parameter of the round from the change, judging whether the change of the semi-major axis parameter is less than a given threshold, if the change of the semi-major axis parameter is less than the given threshold, it is considered that the semi-major axis parameter has converged; calculating the final estimate of the semi-major axis parameter, treating it as a known value in subsequent iterations, performing the next iteration, calculating the change of the remaining ephemeris parameter vector, estimating the remaining ephemeris parameter vector according to the change of the remaining ephemeris parameter vector; judging whether the remaining ephemeris parameters estimated in the next iteration converge, if converged, calculating the final estimate of the parameter, and exiting the iteration. The use of this method can improve the computational efficiency and availability of the ephemeris fitting algorithm.

Description

Technical Field

[0001] The present application relates to the field of satellite fitting technology, and in particular to a fast convergence method for low-orbit satellite broadcast ephemeris fitting. Background Art

[0002] At present, the mainstream satellite navigation system constellations in the world are mainly composed of medium and high orbit satellites. The altitude of their satellite orbits is usually around 20,000 to 36,000 km, and the orbital period is about 12 hours. The satellite position information is calculated from the broadcast ephemeris parameters in the navigation message. The broadcast ephemeris parameters are obtained through the broadcast ephemeris fitting algorithm. The commonly used GNSS broadcast ephemeris parameter models are 16-parameter model and 18-parameter model. The parameters mainly include 1 reference epoch parameter, 6 Kepler orbit parameters, 3 to 5 orbit parameter variation parameters and 6 1 / 2 period harmonic parameters. Compared with GNSS satellites, the orbital altitude of low-orbit satellites is usually around 300 to 2000 km, and their orbital operation period is usually 90 to 120 minutes. During their on-orbit operation, they are greatly affected by atmospheric drag and have a more complex force environment. Therefore, in order to improve the accuracy of low-orbit satellite broadcast ephemeris fitting, it is necessary to add several additional harmonic term parameters on the basis of the 18-parameter model to compensate for the impact of short-term orbital changes. The commonly used low-orbit broadcast ephemeris model is the 22-parameter model. Compared with the 18-parameter model, it adds two orbit radial 1 / 3 period harmonic term coefficients and two orbit inclination 1 / 3 period harmonic term coefficients.

[0003] In practical applications, although the 22-parameter ephemeris model can improve the accuracy of low-orbit satellite broadcast ephemeris fitting, when judging the iterative convergence of the estimated parameters, the existing methods use the modulus of the parameter change less than a given empirical threshold as the iteration exit condition. Due to the increase in the number of parameters, the numerical stability of the parameter change in the iteration often deteriorates and fails to converge, which greatly reduces the computational efficiency and the availability of ephemeris parameters. Summary of the invention

[0004] Based on this, it is necessary to provide a fast convergence method for low-orbit satellite broadcast ephemeris fitting that can improve the computational efficiency and usability of the ephemeris fitting algorithm in response to the above technical problems.

[0005] A fast convergence method for low-orbit satellite broadcast ephemeris fitting, the method comprising:

[0006] Step 1: Obtain the ephemeris parameter vector to be estimated of the low-orbit satellite broadcast ephemeris; estimate the change of the ephemeris parameter vector of the current iteration according to the least squares principle;

[0007] Step 2: Obtain the change amount of the semi-major axis parameter of this round from the change amount, and determine whether the change amount of the semi-major axis parameter is less than a given threshold. If the change amount of the semi-major axis parameter is less than the given threshold, it is considered that the semi-major axis parameter has converged; calculate the final estimate of the semi-major axis parameter, and regard it as a known value in subsequent iterations, perform the next round of iterations, calculate the change amount of the remaining ephemeris parameter vector, and estimate the remaining ephemeris parameter vector according to the change amount of the remaining ephemeris parameter vector; if the change amount of the semi-major axis parameter is not less than the given threshold, repeat steps 1 to 2;

[0008] Step 3: Determine whether the remaining ephemeris parameters estimated in the next round of iteration have converged, that is, calculate the standard deviation of the post-verification residuals and determine whether it is less than the convergence threshold. If it is less than the convergence threshold, it is considered that the remaining ephemeris parameters have converged, calculate the final estimate of the parameters, and exit the iteration; if the standard deviation of the post-verification residuals is not less than the convergence threshold, repeat step 3; if the convergence condition is still not met after reaching the maximum number of iterations set in advance, it is considered that the ephemeris parameter vector to be estimated does not converge, the ephemeris parameters cannot be obtained, and the iteration is exited.

[0009] In one embodiment, obtaining the estimated ephemeris parameter vector of the low-orbit satellite broadcast ephemeris includes:

[0010] If the low-orbit satellite broadcast ephemeris is a low-orbit broadcast ephemeris 22-parameter model, for a given ephemeris reference time parameter , 21 ephemeris parameters need to be estimated, assuming that the ephemeris parameter vector to be estimated is:

[0011] ;

[0012] in, is the ephemeris parameter vector to be estimated, is the square root of the semi-major axis at the reference time, is the orbital inclination at the reference time, is the mean anomaly at the reference time, is the longitude of the ascending node at the zero hour of the weekly calendar era, is the eccentricity, is the perigee angle, is the rate of change of the semi-major axis, is the orbital inclination change rate, is the rate of change of the longitude of the ascending node, are the difference between the satellite average angular velocity at the reference time and the calculated value, and their rate of change, is the amplitude of the cosine and sine harmonic correction term of 1 / 2 period of orbit radius, is the amplitude of the cosine and sine harmonic correction term of the 1 / 2 period of the orbital inclination, is the amplitude of the cosine and sine harmonic correction term of the 1 / 2 period of orbital argument, is the amplitude of the cosine and sine harmonic correction term of 1 / 3 period of orbit radius, It is the amplitude of the cosine and sine harmonic correction terms of 1 / 3 period of orbital inclination.

[0013] In one embodiment, estimating the change of the ephemeris parameter vector of the current iteration according to the least squares principle for the ephemeris parameter vector to be estimated includes:

[0014] Assume that the satellite position calculation algorithm of the low-orbit satellite broadcast ephemeris 22 parameter model is:

[0015] ;

[0016] in, is the satellite three-dimensional coordinate vector, is the satellite position calculation function, is the ephemeris reference time parameter;

[0017] Linearize the equation of the satellite's three-dimensional coordinate vector. Round iteration, there are:

[0018] ;

[0019] in, For the The parameter vector estimated by round iterations, For the The change in the parameter vector estimated by the round iteration is such that , Calculate the partial derivatives of the function with respect to the parameter vector for the satellite position;

[0020] According to the least squares principle, The change of the ephemeris parameter vector estimated by round iteration is

[0021] ;

[0022] Where:

[0023] ;

[0024] in, is the design matrix for the least squares equation, is the observation vector of the normal equation.

[0025] In one embodiment, calculating a final estimate of the semi-major axis parameter includes:

[0026] The final estimate of the semi-major axis parameter is calculated as

[0027] ;

[0028] in, represents the change in the semi-major axis parameter, No. The semi-major axis parameters are estimated by rounds of iterations.

[0029] In one embodiment, calculating the change in the remaining ephemeris parameter vector includes:

[0030] Calculate the change in the remaining ephemeris parameter vector as

[0031] ;

[0032] in:

[0033] ;

[0034] in, and are the design matrix and observation vector of the least squares equation for estimating the remaining parameters, is the final estimate of the semi-major axis parameter, is the ephemeris reference time parameter, For the The remaining parameter vector to be estimated after the round of iterative estimation.

[0035] In one embodiment, calculating the standard deviation of the posterior residual includes:

[0036] The standard deviation of the post-test residuals is calculated as

[0037] ;

[0038] Among them, the subscript Indicates Sample points, For the The three-dimensional coordinates of the sample points after the test are residuals, It means to find the modulus of the vector. is the standard deviation of the posterior residuals of the three-dimensional coordinates, is the convergence threshold of the posterior residual standard deviation, is the change of the remaining ephemeris parameter vector, and are the design matrix and observation vector of the least squares equation for estimating the remaining parameters, respectively.

[0039] In one embodiment, the process of determining the convergence threshold includes:

[0040] Calculate the theoretical variance of the posterior residual; determine the convergence threshold according to the theoretical variance of the posterior residual and the threshold adjustment coefficient:

[0041] ;

[0042] in, Represents the threshold adjustment coefficient, which is an empirical value in the interval [0.75,1.25] and is usually 1. represents the theoretical variance of the post-test residual.

[0043] In one embodiment, the theoretical variance of the posterior residual is calculated as

[0044] ;

[0045] in, is the variance of the sample point position error; is the variance of the fitting error of the current ephemeris fitting algorithm.

[0046] In one embodiment, if it is less than the convergence threshold, it is considered that the remaining ephemeris parameters have converged, and the final estimate of the parameters is calculated, and the iteration is exited, including:

[0047] If the standard deviation of the posterior residual is less than the convergence threshold, the remaining parameters are considered to have converged. Calculate the final estimates of the remaining parameters. At this point, all parameters have been estimated and the iteration is exited. For the The remaining parameter vector to be estimated after rounds of iterative estimation, is the change of the remaining ephemeris parameter vector.

[0048] The above-mentioned method for fast convergence of broadcast ephemeris fitting for low-orbit satellites adopts a "two-step method" to estimate ephemeris parameters. The semi-major axis parameters are first iteratively estimated, and after convergence, they are used as known values, and the standard deviation of the post-test residual is less than the convergence threshold as the convergence judgment condition, and the remaining parameters are estimated. Starting from the most important semi-major axis parameters, the key parameters are converged first, and other parameters are gradually fixed. The step-by-step optimization method makes the entire calculation process more efficient, especially when there are a large number of parameters. By quickly judging which parameters have converged in each round of iteration, unnecessary calculations are avoided, thereby improving the calculation efficiency. The availability and stability of the calculation results are guaranteed by reasonable convergence judgment conditions and maximum number of iterations. In particular, the accuracy of broadcast ephemeris fitting for low-orbit satellites is increased. After the number of harmonic terms and parameters is increased, it is common for the parameters to not converge or converge slowly during the iteration process. In order to reasonably determine the convergence threshold, the accuracy of the sample points is considered in the calculation of the threshold, so that the number of iterations of parameter estimation can be significantly reduced without losing the accuracy of ephemeris fitting, thereby improving the calculation efficiency and availability of the ephemeris fitting algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1A schematic diagram of a flow chart of a fast convergence method for low-orbit satellite broadcast ephemeris fitting in one embodiment;

[0050] Figure 2 Schematic diagram of comparison of the number of iterations of the present application and the existing method in an embodiment; wherein (a) is a schematic diagram of the number of iterations of the present application, (b) is a schematic diagram of the number of iterations corresponding to a convergence threshold of 1e-4 in the existing method, (c) is a schematic diagram of the number of iterations corresponding to a convergence threshold of 1e-7 in the existing method, and (d) is a schematic diagram of the number of iterations corresponding to a convergence threshold of 1e-10 in the existing method;

[0051] Figure 3 It is a schematic diagram comparing the fitting accuracy of the present invention and the existing method in an embodiment. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0053] In one embodiment, Figure 1 As shown, a fast convergence method for low-orbit satellite broadcast ephemeris fitting is provided, comprising the following steps:

[0054] Step 1: Obtain the ephemeris parameter vector to be estimated of the low-orbit satellite broadcast ephemeris; estimate the change of the ephemeris parameter vector of the current iteration based on the least squares principle.

[0055] The ephemeris parameters to be estimated are estimated according to the least squares principle, and then the change in the current round is calculated. The least squares method is a technique commonly used to estimate model parameters. It can minimize the fitting error, so that the estimated value has good accuracy and reliability. By obtaining the change to compare the difference between the current parameters and the previous round, unnecessary full parameter estimation is avoided. As long as the change meets certain conditions, it can be judged whether it has converged, saving unnecessary computational overhead.

[0056] Step 2: Obtain the change amount of the semi-major axis parameter of this round from the change amount, and determine whether the change amount of the semi-major axis parameter is less than a given threshold. If the change amount of the semi-major axis parameter is less than the given threshold, it is considered that the semi-major axis parameter has converged; calculate the final estimate of the semi-major axis parameter, and regard it as a known value in subsequent iterations, perform the next round of iterations, calculate the change amount of the remaining ephemeris parameter vector, and estimate the remaining ephemeris parameter vector according to the change amount of the remaining ephemeris parameter vector; if the change amount of the semi-major axis parameter is not less than the given threshold, repeat steps 1 to 2.

[0057] Convergence is determined by judging whether the change in the semi-major axis parameter is less than a given threshold. If converged, the parameter is considered known and the next round of iteration is used to calculate other parameters. The semi-major axis is a key parameter that describes the satellite orbit. If it has converged, it can be fixed and no further adjustments are made, thereby reducing the number of parameters calculated in subsequent iterations. This method avoids unnecessary calculations and optimizes the solution process. By converging the semi-major axis parameters early, unnecessary adjustments in the calculation process can be reduced, improving the calculation accuracy and efficiency of subsequent iterations.

[0058] Step 3: Determine whether the remaining ephemeris parameters estimated in the next round of iteration have converged, that is, calculate the standard deviation of the post-verification residuals and determine whether it is less than the convergence threshold. If it is less than the convergence threshold, it is considered that the remaining ephemeris parameters have converged, calculate the final estimate of the parameters, and exit the iteration; if the standard deviation of the post-verification residuals is not less than the convergence threshold, repeat step 3; if the convergence condition is still not met after reaching the maximum number of iterations set in advance, it is considered that the ephemeris parameter vector to be estimated does not converge, the ephemeris parameters cannot be obtained, and the iteration is exited.

[0059] The standard deviation of the posterior-validation residuals is calculated to determine whether the remaining ephemeris parameters have converged. If the posterior-validation residual is less than the convergence threshold, the remaining parameters are considered to have converged and the iteration is exited; if the condition is not met, the iteration continues. The maximum number of iterations is set as the exit condition to prevent infinite loops. This design ensures that the algorithm will not iterate indefinitely even in extreme cases (such as slow parameter convergence). Setting the maximum number of iterations and the posterior-validation residual threshold is an important guarantee in real-world applications, preventing the calculation process from getting stuck and improving the stability and reliability of the algorithm. The standard deviation of the posterior-validation residual is an important indicator for measuring the fitting accuracy. If it is less than the convergence threshold, it means that the parameters are very close to the true value and no further adjustment is required. With this standard, the algorithm can determine when to stop more quickly, reducing the number of unnecessary iterations.

[0060] The above-mentioned method for fast convergence of broadcast ephemeris fitting for low-orbit satellites adopts a "two-step method" to estimate ephemeris parameters. The semi-major axis parameters are first iteratively estimated, and after convergence, they are used as known values, and the standard deviation of the post-test residual is less than the convergence threshold as the convergence judgment condition, and the remaining parameters are estimated. Starting from the most important semi-major axis parameters, the key parameters are converged first, and other parameters are gradually fixed. The step-by-step optimization method makes the entire calculation process more efficient, especially when there are a large number of parameters. By quickly judging which parameters have converged in each round of iteration, unnecessary calculations are avoided, thereby improving the calculation efficiency. The availability and stability of the calculation results are guaranteed by reasonable convergence judgment conditions and maximum number of iterations. In particular, the accuracy of broadcast ephemeris fitting for low-orbit satellites is increased. After the number of harmonic terms and parameters is increased, it is common for the parameters to not converge or converge slowly during the iteration process. In order to reasonably determine the convergence threshold, the accuracy of the sample points is considered in the calculation of the threshold, so that the number of iterations of parameter estimation can be significantly reduced without losing the accuracy of ephemeris fitting, thereby improving the calculation efficiency and availability of the ephemeris fitting algorithm.

[0061] In one embodiment, obtaining the estimated ephemeris parameter vector of the low-orbit satellite broadcast ephemeris includes:

[0062] If the low-orbit satellite broadcast ephemeris is a low-orbit broadcast ephemeris 22-parameter model, for a given ephemeris reference time parameter , 21 ephemeris parameters need to be estimated, assuming that the ephemeris parameter vector to be estimated is:

[0063] ;

[0064] in, is the ephemeris parameter vector to be estimated, is the square root of the semi-major axis at the reference time, is the orbital inclination at the reference time, is the mean anomaly at the reference time, is the longitude of the ascending node at the zero hour of the weekly calendar era, is the eccentricity, is the perigee angle, is the rate of change of the semi-major axis, is the orbital inclination change rate, is the rate of change of the longitude of the ascending node, are the difference between the satellite average angular velocity at the reference time and the calculated value, and their rate of change, is the amplitude of the cosine and sine harmonic correction term of 1 / 2 period of orbit radius, is the amplitude of the cosine and sine harmonic correction term of the 1 / 2 period of the orbital inclination, is the amplitude of the cosine and sine harmonic correction term of the 1 / 2 period of orbital argument, is the amplitude of the cosine and sine harmonic correction term of 1 / 3 period of orbit radius, It is the amplitude of the cosine and sine harmonic correction terms of 1 / 3 period of orbital inclination.

[0065] In one embodiment, estimating the change of the ephemeris parameter vector of the current iteration according to the least squares principle for the ephemeris parameter vector to be estimated includes:

[0066] Assume that the satellite position calculation algorithm of the low-orbit satellite broadcast ephemeris 22 parameter model is:

[0067] ;

[0068] in, is the satellite three-dimensional coordinate vector, is the satellite position calculation function, is the ephemeris reference time parameter;

[0069] Linearize the equation of the satellite's three-dimensional coordinate vector. Round iteration, there are:

[0070] ;

[0071] in, For the The parameter vector estimated by round iterations, For the The change in the parameter vector estimated by the round iteration is such that , Calculate the partial derivatives of the function with respect to the parameter vector for the satellite position;

[0072] According to the least squares principle, The change of the ephemeris parameter vector estimated by round iteration is

[0073] ;

[0074] Where:

[0075] ;

[0076] in, is the design matrix for the least squares equation, is the observation vector of the normal equation.

[0077] In one embodiment, calculating a final estimate of the semi-major axis parameter includes:

[0078] The final estimate of the semi-major axis parameter is calculated as

[0079] ;

[0080] in, represents the change in the semi-major axis parameter, No. The semi-major axis parameters are estimated by rounds of iterations.

[0081] In a specific embodiment, for step 1, The estimated parameter change in the round iteration , take the change of the semi-major axis parameter, that is Since the semi-major axis The physical meaning of is clear and is in meters. If the uncertainty of the satellite position calculation result is to be less than millimeters, the parameter The convergence accuracy reaches 0.01 Therefore, in step 2, the semi-major axis parameter The convergence threshold Set to 0.01, that is, for the Round iteration, if the following conditions are met:

[0082] ;

[0083] The semi-major axis parameter is considered Convergence. It should be noted that The value of can be flexibly adjusted according to the actual application requirements. If the calculation accuracy requirement is low, Take a slightly larger threshold appropriately.

[0084] Semi-major axis parameter After convergence, As the final estimate of the parameter, in the subsequent iteration (i.e. rounds of iterations) as known values, the remaining parameter vector to be estimated is:

[0085] .

[0086] In one embodiment, calculating the change in the remaining ephemeris parameter vector includes:

[0087] Calculate the change in the remaining ephemeris parameter vector as

[0088] ;

[0089] in:

[0090] ;

[0091] in, and are the design matrix and observation vector of the least squares equation for estimating the remaining parameters, is the final estimate of the semi-major axis parameter, is the ephemeris reference time parameter, For the The remaining parameter vector to be estimated after the round of iterative estimation.

[0092] In one embodiment, calculating the standard deviation of the posterior residual includes:

[0093] The standard deviation of the post-test residuals is calculated as

[0094] ;

[0095] Among them, the subscript Indicates Sample points, For the The three-dimensional coordinates of the sample points after the test are residuals, It means to find the modulus of the vector. is the standard deviation of the posterior residuals of the three-dimensional coordinates, is the convergence threshold of the posterior residual standard deviation, is the change of the remaining ephemeris parameter vector, and are the design matrix and observation vector of the least squares equation for estimating the remaining parameters, respectively.

[0096] In one embodiment, the process of determining the convergence threshold includes:

[0097] Calculate the theoretical variance of the posterior residual; determine the convergence threshold according to the theoretical variance of the posterior residual and the threshold adjustment coefficient:

[0098] ;

[0099] in, Represents the threshold adjustment coefficient, which is an empirical value in the interval [0.75,1.25] and is usually 1. represents the theoretical variance of the post-test residual.

[0100] In one embodiment, the theoretical variance of the posterior residual is calculated as

[0101] ;

[0102] in, is the variance of the position error of the sample point, which is a known value and can be obtained in advance through the positioning accuracy evaluation of the sample point. The specific process is not within the scope of the present invention and will not be described in detail. is the variance of the fitting error of the current ephemeris fitting algorithm. A set of high-precision orbits or simulated orbits can be fitted with ephemeris in advance, and the variance of the fitting residual can be taken as The value of .

[0103] In a specific embodiment, the posterior residual can be expressed as the sum of the sample point error and the fitting residual, that is:

[0104] ;

[0105] in, represents the position error of the sample point, represents the fitting error (the error introduced only by the fitting algorithm. When the sample points have no error, ). In general, the sample point error and the fitting error are considered to be independent random vectors. Therefore, according to the error propagation rate, we can get:

[0106] ;

[0107] in, is the theoretical variance of the post-test residual; is the variance of the sample point position error. The specific value can be obtained by comparing the coordinates of the sample points with the true value of the coordinates. is the variance of the fitting error of the current ephemeris fitting algorithm, which can be obtained by fitting a set of sample points with true coordinate values. Through the above analysis, the theoretical variance of the posterior residual can be obtained: The specific value of is related to the position accuracy of the sample points used in the ephemeris fitting and the current ephemeris fitting algorithm. Therefore, the convergence threshold of the standard deviation of the posterior residual can be determined by the following formula:

[0108] ;

[0109] in, Represents the threshold adjustment coefficient, which is an empirical value in the interval [0.75,1.25], usually 1, and can be adjusted according to actual conditions.

[0110] In one embodiment, if it is less than the convergence threshold, it is considered that the remaining ephemeris parameters have converged, and the final estimate of the parameters is calculated, and the iteration is exited, including:

[0111] If the standard deviation of the posterior residual is less than the convergence threshold, the remaining parameters are considered to have converged. Calculate the final estimates of the remaining parameters. At this point, all parameters have been estimated and the iteration is exited. For the The remaining parameter vector to be estimated after rounds of iterative estimation, is the change of the remaining ephemeris parameter vector.

[0112] In a specific embodiment, if , then the remaining parameters are considered to have converged, through Calculate the final estimates of the remaining parameters. At this point, all parameters have been estimated and the algorithm exits successfully.

[0113] like , the remaining parameters are considered to be non-convergent, and step 3 is repeated. If the convergence condition is still not met after reaching the maximum number of iterations set in advance, the set of ephemeris parameters is considered to be non-convergent, and the ephemeris parameters cannot be calculated. The program gives a warning and exits the iteration.

[0114] In the simulation experiment, the convergence threshold of the semi-major axis parameter obtained by this application is 0.01 Then, by simulating the trajectory of the low-orbit satellite, setting the coordinate point error to 3 cm, the fitting error to 4 cm, and the threshold adjustment coefficient to 1.0, the convergence value can be obtained. =0.0025 , by simulating the motion trajectory of the low-orbit satellite, and setting the coordinate point error to 3cm. The motion trajectory of the satellite is fitted with ephemeris by the method of the present invention and the existing method, respectively. It is assumed that the trajectory arc length of each set of broadcast ephemeris parameters is 30 minutes, and a total of 39 sets of ephemeris parameters are fitted. Then, the performance of the ephemeris fitting algorithm is compared by comparing the number of iterations and fitting accuracy required for estimating each set of ephemeris parameters by each method, thereby verifying the effect of the present invention. Among them, the judgment condition for judging the convergence of parameters by the existing method is: for the current iteration, the modulus of the change in 21 ephemeris parameters is less than a given threshold. In this experiment, the convergence thresholds of the existing methods are 1e-4, 1e-7, and 1e-10 (dimensionless), respectively.

[0115] Figure 2 The number of iterations required for estimating a set of ephemeris parameters by the present application and the existing ephemeris fitting method is shown in Figure 1. The maximum number of iterations is set to 1000. When this number of iterations is reached, it indicates that the algorithm cannot obtain a set of converged ephemeris parameters. Figure 2 (a) is a schematic diagram of the number of iterations of this application, Figure 2 (b) is a schematic diagram of the number of iterations corresponding to the convergence threshold of 1e-4 in the existing method. Figure 2 (c) is a schematic diagram of the number of iterations corresponding to the convergence threshold of 1e-7 in the existing method. Figure 2 (d) is a schematic diagram of the number of iterations corresponding to the convergence threshold of 1e-10 in the existing method. It can be seen from the figure that the method of the present invention requires the least number of iterations and has the highest computational efficiency. In contrast, the traditional method needs to continuously try the appropriate convergence threshold due to the unclear meaning of the parameter convergence judgment quantity, and the number of iterations required for different convergence thresholds is significantly different. If the threshold is set unreasonably, the problem of non-convergence of ephemeris parameters often occurs, which reduces the universality of the traditional method.

[0116] The satellite coordinates at the time of the sample point can be recalculated using the ephemeris parameters obtained through ephemeris fitting. By comparing the coordinates with the sample point coordinates, the fitting accuracy of the ephemeris fitting algorithm can be obtained. Figure 3 A comparison chart of the fitting accuracy of the present invention and the existing method is given. From the chart, it can be seen that the fitting accuracy of the present method and the existing ephemeris fitting algorithm is basically the same.

[0117] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0118] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0119] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A fast convergence method for low-orbit satellite broadcast ephemeris fitting, characterized in that: The method comprises: Step 1: Obtain the ephemeris parameter vector to be estimated of the low-orbit satellite broadcast ephemeris; estimate the change of the ephemeris parameter vector of the current iteration according to the least squares principle; Step 2: Obtain the change amount of the semi-major axis parameter of this round from the change amount, and determine whether the change amount of the semi-major axis parameter is less than a given threshold. If the change amount of the semi-major axis parameter is less than the given threshold, it is considered that the semi-major axis parameter has converged; calculate the final estimate of the semi-major axis parameter, and regard it as a known value in subsequent iterations, perform the next round of iterations, calculate the change amount of the remaining ephemeris parameter vector, and estimate the remaining ephemeris parameter vector according to the change amount of the remaining ephemeris parameter vector; if the change amount of the semi-major axis parameter is not less than the given threshold, repeat steps 1 to 2; Step 3: Determine whether the remaining ephemeris parameters estimated in the next round of iteration have converged, that is, calculate the standard deviation of the post-verification residuals and determine whether it is less than the convergence threshold. If it is less than the convergence threshold, it is considered that the remaining ephemeris parameters have converged, calculate the final estimate of the parameters, and exit the iteration; if the standard deviation of the post-verification residuals is not less than the convergence threshold, repeat step 3; if the convergence condition is still not met after reaching the maximum number of iterations set in advance, it is considered that the ephemeris parameter vector to be estimated does not converge, the ephemeris parameters cannot be obtained, and the iteration is exited.

2. The method according to claim 1, characterized in that Get the estimated ephemeris parameter vector of the low-orbit satellite broadcast ephemeris, including: If the low-orbit satellite broadcast ephemeris is a low-orbit broadcast ephemeris 22-parameter model, for a given ephemeris reference time parameter , 21 ephemeris parameters need to be estimated, assuming that the ephemeris parameter vector to be estimated is: in, is the ephemeris parameter vector to be estimated, is the square root of the semi-major axis at the reference time, is the orbital inclination at the reference time, is the mean anomaly at the reference time, is the longitude of the ascending node at the zero hour of the weekly calendar era, is the eccentricity, is the perigee angle, is the rate of change of the semi-major axis, is the orbital inclination change rate, is the rate of change of the longitude of the ascending node, are the difference between the satellite average angular velocity at the reference time and the calculated value, and their rate of change, is the amplitude of the cosine and sine harmonic correction term of 1 / 2 period of orbit radius, is the amplitude of the cosine and sine harmonic correction term of the 1 / 2 period of the orbital inclination, is the amplitude of the cosine and sine harmonic correction term of the 1 / 2 period of orbital argument, is the amplitude of the cosine and sine harmonic correction term of 1 / 3 period of orbit radius, It is the amplitude of the cosine and sine harmonic correction terms of 1 / 3 period of orbital inclination.

3. The method according to claim 2, characterized in that The change of the ephemeris parameter vector of the current iteration is estimated based on the least squares principle, including: Assume that the satellite position calculation algorithm of the low-orbit satellite broadcast ephemeris 22 parameter model is: in, is the satellite three-dimensional coordinate vector, is the satellite position calculation function, is the ephemeris reference time parameter; Linearize the equation of the satellite's three-dimensional coordinate vector. Round iteration, there are: in, For the The parameter vector estimated by round iterations, For the The change in the parameter vector estimated by the round iteration is such that , Calculate the partial derivatives of the function with respect to the parameter vector for the satellite position; According to the least squares principle, The change of the ephemeris parameter vector estimated by round iteration is Where: in, is the design matrix for the least squares equation, is the observation vector of the normal equation.

4. The method according to any one of claims 1 to 3, characterized in that: Calculate the final estimate of the semimajor axis parameters, including: The final estimate of the semi-major axis parameter is calculated as in, represents the change in the semi-major axis parameter, No. The semi-major axis parameters are estimated by rounds of iterations.

5. The method according to claim 3, characterized in that: Calculate the changes in the remaining ephemeris parameter vector, including: Calculate the change of the remaining ephemeris parameter vector as in: in, and are the design matrix and observation vector of the least squares equation for estimating the remaining parameters, is the final estimate of the semi-major axis parameter, is the ephemeris reference time parameter, For the The remaining parameter vector to be estimated after the round of iterative estimation.

6. The method according to claim 1, characterized in that Calculate the standard deviation of the post-test residuals, including: The standard deviation of the post-test residuals is calculated as Among them, the subscript Indicates Sample points, For the The three-dimensional coordinates of the sample points after the test are residuals, It means to find the modulus of the vector. is the standard deviation of the posterior residuals of the three-dimensional coordinates, is the convergence threshold of the posterior residual standard deviation, is the change of the remaining ephemeris parameter vector, and are the design matrix and observation vector of the least squares equation for estimating the remaining parameters, respectively, and n represents the residual standard deviation after calculation. The total number of sample points involved in the calculation.

7. The method according to claim 6, characterized in that The process of determining the convergence threshold includes: Calculate the theoretical variance of the posterior residual; determine the convergence threshold according to the theoretical variance of the posterior residual and the threshold adjustment coefficient: in, Represents the threshold adjustment coefficient, which is an empirical value in the interval [0.75,1.25]. represents the theoretical variance of the post-test residual.

8. The method according to claim 7, characterized in that The theoretical variance of the calculated posterior residual is in, is the variance of the sample point position error; is the variance of the fitting error of the current ephemeris fitting algorithm.

9. The method according to claim 1, characterized in that: If it is less than the convergence threshold, the remaining ephemeris parameters are considered to have converged, the final estimate of the parameters is calculated, and the iteration is exited, including: If the standard deviation of the posterior residual is less than the convergence threshold, the remaining parameters are considered to have converged. Calculate the final estimates of the remaining parameters. At this point, all parameters have been estimated and the iteration is exited. For the The remaining parameter vector to be estimated after rounds of iterative estimation, is the change of the remaining ephemeris parameter vector.

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