An intelligent arc segment correlation method based on the minimum optical tolerance domain

Abstract

The present invention discloses an intelligent arc segment correlation method based on the minimum optical tolerance domain, belonging to the field of intelligent computing optimization for space target surveillance, which solves the problem of large computational volume of arc segment correlation, and includes: constructing a minimum optical tolerance domain from the first observation arc segment; uniformly sampling in the minimum optical tolerance domain, and propagating the orbit of each sampling point under the J2 perturbation model to obtain the theoretical optical observation data of the second observation arc segment and calculating the root mean square error of the angle of the second observation arc segment to obtain an angle loss function; using the DBSCAN clustering algorithm to identify the wave valleys; selecting the initial value of the simplex method in each wave valley to obtain the optimal angle solution; calculating the probability loss function by the Bayesian theorem; substituting the optimal angle solution into the probability loss function and using the LM algorithm to obtain the optimal probability solution; setting a threshold according to the chi-square distribution of the probability loss function, and when the optimal probability solution is less than the threshold, the two arc segments are successfully correlated; the present invention saves computational costs and improves the accuracy of space target observation.

Description

Technical Field

[0001] The present invention belongs to the technical field of emerging software and new information technology services in the new generation of information technology, and relates to the technical field of intelligent computing optimization for space target surveillance, and particularly relates to an intelligent arc segment association method based on the minimum optical admissible domain. Background Art

[0002] Space targets refer to spacecrafts and space debris operating in space, which move regularly along their respective orbits. The space target surveillance system can detect, track, catalog, and manage important space targets through calculations. Optical telescopes are important detection devices in the space target surveillance system and can be used for the surveillance of space targets of all orbit types. By receiving the sunlight reflected by space targets and based on technologies such as astronomical positioning and axis system positioning, the telescope can obtain the angular measurement values of space targets, such as right ascension and declination in the inertial coordinate system or azimuth and elevation angle in the station horizon coordinate system.

[0003] Arc segment association is an important research content in the field of space target surveillance. After the optical sensor obtains the observation data, it first needs to be matched with the cataloged orbit library, such as the TLE database, to confirm which space target the observed arc segment belongs to. For the arc segments that fail to match (unmatched arc segments), due to the limited length of the arc segments, accurate orbit determination cannot be performed. Therefore, arc segment association needs to be carried out between unmatched arc segments to determine which arc segments belong to the same space target. Usually, at least three to four arc segments are required to accurately estimate the state of a new space target and then perform subsequent tracking. Therefore, arc segment association is crucial for the cataloging of new targets.

[0004] The admissible domain method is a common means for processing short arc optical measurement data. This method uses arc segment attributes to describe the information contained in an observation: by selecting a certain epoch moment, the right ascension, declination, and their rates of change (which can be obtained by polynomial fitting) at this moment constitute the arc segment attributes. If the slant range at this moment, that is, the distance from the station to the target and the rate of change of the slant range are known, the target state can be completely determined by these six parameters. In other words, a slant range - slant range rate of change combination determines an orbit. The admissible domain is a region in the slant range - slant range rate of change plane, and all orbits within the admissible domain satisfy the energy constraint of the elliptical orbit, that is, the energy is negative.

[0005] For example: the application number is 202410606917.X, the publication number is CN118520674A, and the patent name is "Probability Density Distribution Analysis Method, System, Equipment, and Medium for Initial Orbit Determination of Optical Short Arcs Based on the Minimum Admissible Domain". Through calculations, the problem of overly large uncertainty analysis range for initial orbit determination of optical short arcs is solved, and this breakthrough lays a foundation for the optimized design of intelligent association of optical arc segments.

[0006] When the observed arc segment is short or the time interval between arc segments is long, there are often multiple extreme value regions in the allowable domain, making it difficult to find the global optimal solution. Multiple long-term orbit extrapolations result in a huge computational cost for arc segment association, making it impossible to observe space targets in real time, thus reducing the accuracy of space target observation. Summary of the Invention

[0007] To solve the problem of how to reduce the computational cost of arc segment association and improve the accuracy of space target observation, the present invention provides an intelligent arc segment association method based on the minimum optical allowable domain, which can quickly determine whether two optical observation arc segments belong to the same space target. In addition, intelligent optimization association of arc segments based on the minimum optical allowable domain can greatly save computational costs, improve the accuracy of space target observation, contribute to orbit determination, tracking, cataloging, etc. of space targets, and the arc segment association algorithm is simple and reliable and applicable to any dynamic model.

[0008] The object of the present invention is specifically realized through the following technical solutions:

[0009] The present invention discloses an intelligent arc segment association method based on the minimum optical allowable domain, which includes:

[0010] Step 1: Select a first observation arc segment and a second observation arc segment to be associated according to the observation time; based on the 3σ criterion of normal distribution, construct a minimum optical allowable domain through a loss function according to the first optical observation data in the first observation arc segment;

[0011] Step 2: Uniformly sample in the minimum optical allowable domain, and perform orbit propagation for each sampling point under the J2 perturbation model to obtain the second theoretical optical observation data corresponding to the time period in the second observation arc segment for each sampling orbit;

[0012] Step 3: Calculate the root mean square error of the angles between the second theoretical optical observation data and the second actual optical observation data in the second observation arc segment to obtain an angular loss function;

[0013] Step 4: Use the DBSCAN clustering algorithm to automatically identify the number and positions of the troughs of the angular loss function;

[0014] Step 5: Select the sampling point with the minimum mean square error of angles in each trough as the initial value of the simplex method; use the simplex method to obtain the local optimal solution of the angular loss function; the local optimal solution with the smallest value among all local optimal solutions is the angular optimal solution;

[0015] Step 6: Calculate the probability loss function of the theoretical prediction value and covariance of the second observation arc segment by Bayes' theorem;

[0016] Step 7: Substitute the optimal angle solution as the initial value into the probability loss function, and use the LM algorithm to optimize for the minimum value to obtain the optimal probability solution;

[0017] Step 8: According to the chi-square distribution that the probability loss function follows, set a threshold for determining whether the first observation arc segment and the second observation arc segment are associated. When the optimal probability solution is less than the threshold, the first observation arc segment and the second observation arc segment are successfully associated, and it is considered that the two arc segments come from the same space target; otherwise, the first observation arc segment and the second observation arc segment are associated unsuccessfully, and it is considered that the two arc segments come from different space targets.

[0018] In Step 1, the method for constructing the minimum optical tolerance domain based on the first optical observation data in the first observation arc segment through the loss function according to the 3σ criterion of the normal distribution includes:

[0019] Based on the 3σ criterion of the normal distribution, set the threshold to 3, and calculate the loss function value of each sampling point in the first optical observation data in the first observation arc segment through the loss function of the loss function

[0020] Eliminate the sampling points that meet the loss function value and only include the sampling points that meet into the minimum optical tolerance domain as the boundary of the minimum optical tolerance domain to construct the minimum optical tolerance domain.

[0021] In Step 1, the loss function is:

[0022]

[0023] In the formula, m is the total number of the first optical observation data; i is the serial number;

[0024] is the first actual optical observation right ascension; is the first theoretical optical observation right ascension; is the right ascension observation error; is the Jacobian matrix of the right ascension propagation corresponding to the least squares solution orbit; Σ A is the uncertainty matrix; T is the symbol of matrix transpose;

[0025] is the first actual optical observation declination; is the first theoretical optical observation declination; σ 2 is the declination observation error; is the Jacobian matrix of the declination propagation corresponding to the least squares solution orbit.

[0026] In Step 2, the J2 perturbation model is:

[0027]

[0028] In the formula, is the right ascension of the ascending node, is the argument of perigee, is the mean anomaly, J2 is the J2 term perturbation term in the Earth's non-spherical perturbation, μ E is the Earth's gravitational constant, a is the semi-major axis, R E is the Earth's radius, I is the orbital inclination, and e is the eccentricity.

[0029] In step three, the angle loss function is:

[0030] where

[0031] is the second theoretical optical observation data,

[0032] is the second actual optical observation data;

[0033] J angle is the root mean square error of the angle, m2 is the number of groups of optical observation data, and i is the serial number.

[0034] In step four, the method for automatically identifying the number and position of the troughs of the angle loss function using the DBSCAN clustering algorithm includes:

[0035] S1. Starting from any core object in the angle loss function, use the neighborhood parameters (ε, MinPts) in the DBSCAN clustering algorithm to access all samples that are density-reachable, forming a cluster; select another core object from the unvisited samples to form another cluster; where ε in the neighborhood parameters is the sampling step size of the samples, and MinPts is the sample number threshold in the neighborhood.

[0036] S2. Repeat step S1 until all core objects have been visited, and the clustering process is completed to obtain the number and position of the troughs of the angle loss function.

[0037] In step five, the method for obtaining the local optimal solution of the angle loss function using the simplex method includes:

[0038] Take three non-collinear initial points on the plane to form an initial simplex; in the formula, x (1) is the lowest point, x (2) is the middle point, x (3) is the highest point, is a real number, and n is the dimension of the optimization space;

[0039] Move the highest point x (3) through the lowest point x (1)and the centroid x of the middle point (2) of the centroid is reflected to obtain the reflection point x (4) as the local optimal solution; where In the formula is x (1) and x (2) of the centroid: b is the reflection coefficient.

[0040] In step six, the calculation method of the probability loss function is:

[0041]

[0042] In the formula is the covariance of the second observation arc segment is the theoretical predicted value of the second observation arc segment is the Jacobian matrix of the theoretical predicted value of the second observation arc segment, Σ A1 is the initial covariance, and T is the symbol of matrix transpose.

[0043] In step eight, the chi-square distribution followed by the probability loss function is:

[0044]

[0045] In the formula, J optim is the probability optimal solution, A2 is the actual observed value of the second observation arc segment is the theoretical predicted value of the second observation arc segment, T is the symbol of matrix transpose is the covariance of the second observation arc segment, Σ A2 is the propagated covariance is the chi-square distribution with 4 degrees of freedom followed by the probability loss function.

[0046] In step eight, the method for setting the threshold for determining whether the first observation arc segment and the second observation arc segment are associated is:

[0047]

[0048] In the formula, P is the probability, J optim is the probability optimal solution is the α quantile, and α is the significance level.

[0049] The beneficial effects of the present invention are:

[0050] 1. The technical solution disclosed by the present invention reduces the calculation amount of arc segment association, improves the observation accuracy of space targets, the arc segment association algorithm is simple and reliable, and is applicable to any dynamic model.

[0051] 2. Using optical observation data, intelligent association between short arcs can be achieved.

[0052] 3. By introducing the minimum optical admissible domain, the basic domain for optical arc association is greatly reduced, saving a large amount of computational cost.

[0053] 4. Using the J2 perturbation model simplifies the dynamic model used in arc association. Only considering the non-spherical perturbation of the earth will not affect the association result and reduces the amount of calculation.

[0054] 5. First, obtain the optimal angle solution using the angle loss function, then substitute it as the initial value into the probability loss function, and use the LM algorithm to find the minimum value. The obtained result is more accurate and can obtain the global optimal solution.

[0055] 6. Analyze the chi-square distribution that the probability loss function follows, and set the threshold for determining whether the first observation arc and the second observation arc are associated, rather than obtaining it empirically. This makes the association result more mathematically based and more in line with real-world logic. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The present invention will be further described in detail below with reference to the drawings and embodiments.

[0057] Figure 1 It is a schematic diagram of the automatic recognition result of the wave valley.

[0058] Figure 2 It is a schematic diagram of the simplex method.

[0059] Figure 3 It is a schematic diagram of the GEO arc with a span of 1 day in Arc Association Example 1.

[0060] Figure 4 It is a schematic diagram of the GEO arc with a span of 2 days in Arc Association Example 2.

[0061] Figure 5 It is a schematic diagram of the GEO arc with a span of 3 days in Arc Association Example 3.

[0062] Figure 6 It is a schematic diagram of the LEO arc with a span of 1.6 hours in Arc Association Example 4.

[0063] Figure 7 It is a schematic diagram of the LEO arc with a span of 19.0 hours in Arc Association Example 5.

[0064] Figure 8 It is a schematic diagram of the LEO arc with a span of 24.2 hours in Arc Association Example 6.

[0065] Figure 9 It is a schematic diagram of the HEO arc with a span of 2.6 hours in Arc Association Example 7.

[0066] Figure 10 It is a schematic diagram of the HEO arc segment with a span of 21.6 hours in the arc segment association example 8.

[0067] Figure 11 It is a schematic diagram of the HEO arc segment with a span of 29.1 hours in the arc segment association example 9. Specific implementation manner

[0068] The embodiment of the present invention provides an intelligent arc segment association method based on the minimum optical allowable domain, and the method includes:

[0069] Step 1: Select a first observation arc segment and a second observation arc segment to be associated according to the observation time; based on the 3σ criterion of the normal distribution, construct a minimum optical allowable domain through a loss function according to the first optical observation data in the first observation arc segment;

[0070] Step 2: Uniformly sample in the minimum optical allowable domain, and perform orbit propagation on each sampling point under the J2 perturbation model to obtain the second theoretical optical observation data corresponding to the time period in the second observation arc segment for each sampling orbit;

[0071] Step 3: Calculate the root mean square error of the angles between the second theoretical optical observation data and the second actual optical observation data in the second observation arc segment to obtain an angle loss function;

[0072] Step 4: Use the DBSCAN clustering algorithm to automatically identify the number and positions of the wave valleys of the angle loss function;

[0073] Step 5: Select the sampling point with the minimum mean square error of the angles in each wave valley as the initial value of the simplex method; use the simplex method to obtain the local optimal solution of the angle loss function; the local optimal solution with the smallest value among all local optimal solutions is the angle optimal solution;

[0074] Step 6: Calculate the probability loss function of the theoretical prediction value and covariance of the second observation arc segment by the Bayes' theorem;

[0075] Step 7: Substitute the angle optimal solution as the initial value into the probability loss function, and use the LM algorithm to perform minimum value optimization to obtain the probability optimal solution;

[0076] Step 8: Set a threshold for determining whether the first observation arc segment and the second observation arc segment are associated according to the chi-square distribution followed by the probability loss function. When the probability optimal solution is less than the threshold, the first observation arc segment and the second observation arc segment are successfully associated, and it is considered that the two arc segments come from the same space target; otherwise, the first observation arc segment and the second observation arc segment are associated failed, and it is considered that the two arc segments come from different space targets.

[0077] In Step 1, based on the 3σ criterion of the normal distribution, the method for constructing the minimum optical tolerance domain according to the first optical observation data in the first observation arc through the loss function includes:

[0078] Based on the 3σ criterion of the normal distribution, set the threshold to 3, and calculate the loss function value of each sampling point in the first optical observation data in the first observation arc through the loss function The loss function value represents the average angular deviation of the orbit;

[0079] Eliminate the sampling points that meet the loss function value and only include the sampling points that meet into the minimum optical tolerance domain as the boundary of the minimum optical tolerance domain to construct the minimum optical tolerance domain; where the loss function is:

[0080]

[0081] In the formula, m is the total number of the first optical observation data; i is the serial number;

[0082] is the first actual optical observation right ascension; is the first theoretical optical observation right ascension; is the right ascension observation error; is the Jacobian matrix of the right ascension propagation corresponding to the least squares solution orbit; Σ A is the uncertainty matrix; T is the symbol of matrix transpose;

[0083] is the first actual optical observation declination; is the first theoretical optical observation declination; σ 2 is the declination observation error; is the Jacobian matrix of the declination propagation corresponding to the least squares solution orbit.

[0084] For the vast majority of space targets, the J2 term in the Earth's non-spherical perturbation is the most important perturbation term. Only considering the long-term influence of the J2 term perturbation on the orbit, there is an analytical solution for the orbital elements. Using the analytical form of the dynamic model can greatly improve the calculation speed. The influence of the J2 term long-term perturbation on the right ascension of the ascending node, the argument of perigee, and the mean anomaly is obtained as the J2 term perturbation model in Step 2:

[0085]

[0086] In the formula, is the right ascension of the ascending node, is the argument of perigee, is the mean anomaly, J2 is the J2 term perturbation item in the Earth's non-spherical perturbation, μ Eis the Earth's gravitational constant, a is the semi-major axis, R E is the radius of the Earth, I is the orbital inclination, and e is the eccentricity.

[0087] In step 3, the angle loss function is:

[0088] in,

[0089] The m2 group of second theoretical optical observation data included in the second observation arc;

[0090] The m2 group of second actual optical observation data included in the second observation arc segment;

[0091] J angle is the angle root mean square error, which characterizes the fit between the orbit and the second observation arc (without considering weighting); m2 is the number of groups of optical observation data, and i is the serial number.

[0092] In step 4, the method of automatically identifying the number and location of troughs of the angle loss function using the DBSCAN clustering algorithm includes:

[0093] S1. Starting from any core object in the angle loss function, use the neighborhood parameters (ε, MinPts) in the DBSCAN clustering algorithm to visit all density-reachable samples to form a cluster; select a core object again from the samples that have not been visited to form another cluster; where ε in the neighborhood parameters is the sampling step of the sample, and MinPts is the threshold of the number of samples in the neighborhood;

[0094] S2. Repeat step S1 until all core objects are visited, and the clustering process is completed, and the number and position of the troughs of the angle loss function are obtained.

[0095] The DBSCAN clustering algorithm determines the clustering result by the density of sample distribution, and does not need to set the number of clusters in advance, which is very suitable for trough identification; the DBSCAN clustering algorithm is based on a set of neighborhood parameters (ε, MinPts) to characterize the compactness of sample distribution. The DBSCAN clustering algorithm defines the concept of cluster as: the largest set of density-connected samples derived from a density-reachable relationship.

[0096] In the embodiment of the present invention, MinPts = 2, where δ ρ , are ρ and The sampling step length of . Figure 1The clustering results of the DBSCAN clustering algorithm are shown. It can be seen that different wave troughs can be well identified. In each wave trough, the sampling point with the minimum mean square error of the angle is found, which can be used as the initial value of the optimization algorithm to find the local minimum of the loss function.

[0097] In step five, the method of using the simplex method to obtain the local optimal solution of the angle loss function includes:

[0098] Take three non-collinear initial value points on the plane to form an initial simplex; where x (1) is the lowest point, x (2) is the middle point, x (3) is the highest point, is a real number, n is the dimension of the optimization space. In the embodiment of the present invention, the optimization space is 2-dimensional, so n = 2. The formed initial simplex is as Figure 2 shown.

[0099] Since the points x (1) , x (2) on the left side of the line connecting them have larger function values, points with smaller function values may be found on the right side of the line. Reflect the highest point x (3) through the centroid of the lowest point x (1) and the middle point x (2) to obtain the reflection point x (4) as the local optimal solution; where, In the formula, where is the centroid of x (1) and x (2) : b is the reflection coefficient, preferably 1.

[0100] In step six, the calculation method of the probability loss function is:

[0101]

[0102] In the formula, is the covariance of the second observation arc segment, is the theoretical prediction value of the second observation arc segment, is the Jacobian matrix of the theoretical prediction value of the second observation arc segment, Σ A1 is the initial covariance, is the transpose of the Jacobian matrix.

[0103] In step seven, substitute the angle optimal solution obtained in step five into the probability loss function, and use the LM (Levenberg-Marquardt) algorithm to perform minimum value optimization. The optimal solution obtained at this time is denoted as the probability optimal solution J optim .

[0104] After obtaining the probability optimal solution J optim a trajectory that best fits the two arc segments is found. Finally, a threshold needs to be designed to determine whether the two arc segments are associated. Without considering factors such as dynamic model errors, if the two arc segments are from the same space target, analyzing the probability loss function in Step 6 reveals that it follows a chi-square χ 2 distribution with 4 degrees of freedom. According to the characteristics of the chi-square distribution, the threshold for determining association is set to 92.33. When the probability optimal solution in Step 7 is less than the association threshold, the two arc segments are successfully associated, and it is considered that the two arc segments are from the same space target; then, in Step 8, the chi-square distribution followed by the probability loss function is:

[0105]

[0106] where J optim is the probability optimal solution, A2 is the actual observation value of the second observation arc segment, is the theoretical predicted value of the second observation arc segment, T is the symbol for matrix transpose, is the covariance of the second observation arc segment, Σ A2 is the propagated covariance, is the chi-square distribution with 4 degrees of freedom followed by the probability loss function.

[0107] In Step 8, the method for setting the threshold for determining whether the first observation arc segment and the second observation arc segment are associated is:

[0108]

[0109] where P is the probability, J optim is the probability optimal solution, is the α quantile, and α is the significance level.

[0110] When α = 0.005, the meaning of the above formula is: If the two arc segments are from the same observation target, then the probability that J optim is less than is 99.5%. Since the dynamic model used in the association algorithm cannot be exactly the same as the true dynamic model, in the embodiment of the present invention, the threshold is amplified and set to If J optim < 92.33, it is considered that the two arc segments are successfully associated; otherwise, it is considered that the two arc segments are from different space targets.

[0111] To more clearly explain the technical solution of the present invention, specific examples are now provided to elaborate on the technical solution of the present invention:

[0112] This example takes different types of space targets as the research objects to verify the effectiveness of the association algorithm. As shown in Table 1, Table 1 is the verification of the arc segment association algorithm - example design, and a total of 9 simulation experiments are designed. Among them, Examples 1 - 3 are the observation arcs of GEO targets, with time spans of 1 day, 1.9 days, and 3.1 days respectively; Examples 4 - 6 are the observation arcs of LEO targets, with time spans of 1.6 hours, 19.0 hours, and 24.2 hours respectively; Examples 7 - 9 are the observation arcs of HEO targets, with time spans of 2.6 hours, 21.6 hours, and 29.1 hours respectively.

[0113] Table 1

[0114]

[0115]

[0116] Example 1, Examples 1 - 3: GEO arcs

[0117] The arcs to be associated in Examples 1 - 3 all come from GEO targets, and the time spans increase in sequence. Figure 3 、 Figure 4 and Figure 5 respectively show the original admissible domain, trough positions, true values, and global optimal solutions of the three examples. The time span of Example 1 is about 1 day, with 4 trough regions, and the loss function corresponding to the global optimal solution is 17.366; the time span of Example 2 is about 2 days, with 5 troughs, and the loss function of the global optimal solution is 15.463; the time span of Example 3 is about 3 days, and the number of troughs increases to 9, and the loss function of the optimal solution is 19.201. The loss functions of the three examples are all less than the threshold of 92.3, and the association is successful.

[0118] Table 2 gives the comparison between the orbital states corresponding to the optimal solutions of the GEO arc association results and the true values. It can be seen that once two arcs are successfully associated, the combined orbit determination results of the two arcs will have high precision. Among them, the semi - major axis error is about 1 km.

[0119] Table 2

[0120]

[0121]

[0122] Example 2, Examples 4 - 6: LEO arcs

[0123] The arcs to be associated in Examples 4 - 6 all come from LEO targets, and the results are as shown in Figure 6 、 Figure 7 and Figure 8, as shown in Table 3, where Table 3 shows the LEO arc segment correlation results. The time spans of the three examples are 1.6 hours, 19.0 hours, and 24.2 hours respectively, and the number of wave troughs are 1, 7, and 18 respectively. It can be seen that as the time span between the two arc segments increases, the number of wave troughs of the LEO arc segment increases rapidly, which means there are more local optimal solutions - this is due to the short orbital period of the LEO target.

[0124] The loss functions corresponding to the global optimal solutions are 0.114, 0.015, and 5.072 respectively, all of which are less than the threshold, and the correlation is successful. After the correlation is successful, the estimation of the orbital state has high accuracy. Among them, the semi-major axis error is only a few meters or dozens of meters.

[0125] Table 3

[0126]

[0127] Example 3, Examples 7 - 9: HEO arc segment

[0128] The arc segments to be correlated in Examples 7 - 9 all come from HEO targets, and the results are as Figure 9 , Figure 10 and Figure 11 shown in Table 4, where Table 4 shows the HEO arc segment correlation results. The time spans of the three examples are 2.6 hours, 21.6 hours, and 29.1 hours respectively, and the number of wave troughs are 1, 3, and 6 respectively. The loss functions corresponding to the global optimal solutions are 41.657, 13.867, and 3.634 respectively, all of which are less than the threshold, and the correlation is successful.

[0129] Table 4

[0130]

[0131]

[0132] Nine simulation examples show that the arc segment correlation algorithm proposed in this paper is universal for observation arc segments of different orbital types and different time spans.

[0133] The beneficial effects of the embodiments of the present invention are:

[0134] 1. The technical solution disclosed in the present invention reduces the computational amount of arc segment correlation, improves the observation accuracy of space targets, the arc segment correlation algorithm is simple and reliable, and is applicable to any dynamic model.

[0135] 2. Using optical observation data, intelligent correlation of arc segments between short arc segments can be realized.

[0136] 3. By introducing the minimum optical allowable domain, the basic domain of optical arc segment correlation is greatly reduced, and the computational cost is saved to a great extent.

[0137] 4. The J2 perturbation model is used to simplify the dynamic model used in arc segment association. Only the non-spherical perturbation of the earth is considered, which will not affect the association result and reduces the computational amount.

[0138] 5. First, the optimal angle solution is obtained using the angle loss function, and then it is used as the initial value and substituted into the probability loss function. The LM algorithm is used to find the minimum value, and the obtained result is more accurate and can obtain the global optimal solution.

[0139] 6. Analyze the chi-square distribution followed by the probability loss function to set the threshold for determining whether the first observation arc segment and the second observation arc segment are associated, rather than obtaining it empirically. This makes the association result more mathematically based and more in line with real-world logic.

[0140] As described above, the above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. An intelligent arc segment association method based on the minimum optical allowable domain, characterized in that The method includes: Step 1: Select a first observation arc segment and a second observation arc segment to be associated according to the observation time; based on the 3σ criterion of the normal distribution, construct a minimum optical tolerance domain through a loss function according to the first optical observation data in the first observation arc segment; Step 2: Uniformly sample in the minimum optical tolerance domain, and perform orbit propagation on each sampling point under the J2 perturbation model to obtain the second theoretical optical observation data corresponding to the corresponding time period in the second observation arc segment for each sampling orbit; Step 3: Calculate the root mean square error of the angles between the second theoretical optical observation data and the second actual optical observation data in the second observation arc segment to obtain an angle loss function; Step 4: Use the DBSCAN clustering algorithm to automatically identify the number and positions of the valleys of the angle loss function; Step 5: Select the sampling point with the minimum mean square error of the angles in each valley as the initial value of the simplex method; use the simplex method to obtain the local optimal solution of the angle loss function; the local optimal solution with the smallest value among all local optimal solutions is the angle optimal solution; Step 6: According to Bayes' theorem, calculate the probability loss function of the theoretical prediction value and covariance of the second observation arc segment; Step 7: Substitute the angle optimal solution as the initial value into the probability loss function, and use the LM algorithm to perform minimum value optimization to obtain the probability optimal solution; Step 8: According to the chi-square distribution followed by the probability loss function, set a threshold for determining whether the first observation arc segment and the second observation arc segment are associated. When the probability optimal solution is less than the threshold, the first observation arc segment and the second observation arc segment are successfully associated, and it is considered that the two arc segments come from the same space target; otherwise, the first observation arc segment and the second observation arc segment are associated unsuccessfully, and it is considered that the two arc segments come from different space targets; In Step 2, the J2 perturbation model is: In the formula, is the right ascension of the ascending node, is the argument of perigee, is the mean anomaly, J2 is the J2 term perturbation in the Earth's non-spherical perturbation, μ E is the Earth's gravitational constant, a is the semi-major axis, R E is the Earth's radius, I is the orbital inclination, e is the eccentricity; In Step 5, the method of using the simplex method to obtain the local optimal solution of the angle loss function includes: Take three initial points on a plane that are not collinear to form an initial simplex; where i = 1, 2, 3, x (1) is the lowest point, x (2) is the middle point, x (3) is the highest point, is a real number, and n is the dimension of the optimization space; Reflect the centroid of the highest point x (3) through the lowest point x (1) and the middle point x (2) to obtain the reflected point x as the local optimal solution; where (4) in the formula where is the centroid of x (1) and x (2) : b is the reflection coefficient.

2. The method according to claim 1, wherein In Step 1, the method of constructing a minimum optical tolerance domain through a loss function according to the first optical observation data in the first observation arc segment based on the 3σ criterion of the normal distribution includes: Based on the 3σ criterion of the normal distribution, set the threshold to 3, and calculate the loss function value of each sampling point in the first optical observation data in the first observation arc segment through the loss function of the loss function Eliminate the sampling points that meet the loss function value , and only include the sampling points that meet in the minimum optical tolerance domain as the boundary of the minimum optical tolerance domain, and construct the minimum optical tolerance domain.

3. The method according to claim 1 or 2, characterized in that, In step one, the loss function is as follows: where m is the total number of the first optical observation data; i is the serial number; is the first actual optical observation right ascension; is the first theoretical optical observation right ascension; is the right ascension observation error; is the Jacobian matrix of the right ascension propagation corresponding to the least squares solution orbit; Σ A is the uncertainty matrix; T is the symbol of matrix transpose; is the first actual optical observation declination; is the first theoretical optical observation declination; σ 2 is the declination observation error; is the Jacobian matrix of the declination propagation corresponding to the least squares solution orbit.

4. The method according to claim 1, wherein In Step 3, the angle loss function is: Among them, is the second theoretical optical observation data, is the second actual optical observation data; J angle where is the root mean square error of the angle, m2 is the number of groups of optical observation data, and i is the serial number.

5. The method according to claim 1, characterized in that, In Step 4, the method of using the DBSCAN clustering algorithm to automatically identify the number and positions of the valleys of the angle loss function includes: S1. Starting from any core object in the angle loss function, use the neighborhood parameters (ε, MinPts) in the DBSCAN clustering algorithm to access all samples that are density-reachable, and form a cluster; select another core object from the samples that have not been accessed to form another cluster; where ε in the neighborhood parameters is the sampling step size of the sample, and MinPts is the sample number threshold in the neighborhood; S2. Repeat Step S1 until all core objects have been accessed, then the clustering process is completed, and the number and positions of the valleys of the angle loss function are obtained.

6. The method according to claim 1, wherein In Step 6, the calculation method of the probability loss function is: Wherein, is the covariance of the second observation arc segment, is the theoretical predicted value of the second observation arc segment, is the Jacobian matrix of the theoretical predicted value of the second observation arc segment, Σ A1 is the initial covariance, and T is the symbol of matrix transpose.

7. The method according to claim 6, characterized in that, In Step 8, the chi-square distribution followed by the probability loss function is: where J optim is the probability optimal solution, A2 is the actual observation value of the second observation arc segment, is the theoretical predicted value of the second observation arc segment, T is the symbol of matrix transpose, is the covariance of the second observation arc segment, Σ A2 is the propagated covariance, is the chi-square distribution with 4 degrees of freedom that the probability loss function follows.

8. The method according to claim 7, wherein In Step 8, the method of setting the threshold for determining whether the first observation arc segment and the second observation arc segment are associated is: Where P is the probability and J optim is the optimal solution of probability, is the α quantile, and α is the significance level.

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