Intelligent segmental arc association method based on minimum optical allowable domain

Abstract

The invention discloses an intelligent segmental arc correlation method based on a minimum optical admissible domain, belongs to the field of intelligent calculation optimization of space target monitoring, solves the problem of large calculation amount of segmental arc correlation, and comprises the following steps: constructing the minimum optical admissible domain by a first observation segmental arc; uniformly sampling in the minimum optical tolerance domain, performing orbit propagation on each sampling point under a J2 perturbation model to obtain theoretical optical observation data of a second observation arc section, and calculating an angle root-mean-square error of the second observation arc section to obtain an angle loss function; using a DBSCAN clustering algorithm to identify wave troughs; selecting an initial value of a simplex method in each wave trough to obtain an angle optimal solution; a probability loss function is obtained through Bayesian theorem calculation; substituting the angle optimal solution into a probability loss function, and obtaining a probability optimal solution by using an LM algorithm; a threshold value is set according to the probability loss function obeying chi-square distribution, and when the probability optimal solution is smaller than the threshold value, the two arc segments are associated successfully; according to the invention, the calculation cost is saved, and the space target observation accuracy is improved.

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 spacecraft 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 angular measurement values of space targets, such as right ascension and declination in the inertial coordinate system or azimuth and elevation angles 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 is first necessary to match it 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 used to accurately estimate the state of a new space target and then carry out 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 an 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, device, 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-time orbital extrapolations result in a huge computational amount for arc segment correlation, making it impossible to observe space targets in real time, thus reducing the accuracy of observing space targets. Summary of the Invention

[0007] To solve the problem of how to reduce the computational amount of arc segment correlation and improve the accuracy of observing space targets, the present invention provides an intelligent arc segment correlation method based on the minimum optical allowable domain. This method can quickly determine whether two optical observation arc segments belong to the same space target. In addition, intelligent optimization and correlation of arc segments based on the minimum optical allowable domain can greatly save computational costs, improve the accuracy of observing space targets, contribute to orbit determination, tracking, cataloging, etc. of space targets, and the arc segment correlation 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 correlation method based on the minimum optical allowable domain, and this method includes:

[0010] Step 1: According to the observation time, select the first observation arc segment and the second observation arc segment to be correlated; based on the 3σ criterion of normal distribution, construct the 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 each sampling point propagates the orbit under the J 2 perturbation model to obtain the second theoretical optical observation data corresponding to the time period in the second observation arc segment for each sampled orbit;

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

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

[0014] Step 5: Select the sampling point with the minimum mean square error of the angle 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;

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

[0016] Step 7: Substitute the optimal angle solution as the initial value into the probability loss function, and use the LM algorithm to find the minimum value, obtaining 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 fails, and it is considered that the two arc segments come from different space targets.

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

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

[0020] Eliminate the sampling points that meet the loss function value and only include the sampling points that meet into the minimum optical allowable domain as the boundary of the minimum optical allowable domain, and construct the minimum optical allowable 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 J 2 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, J 2 is the J 2 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, m 2 is the number of groups of optical observation data, and i is the serial number.

[0034] In step four, the method of using the DBSCAN clustering algorithm to automatically identify the number and position of the valleys of the angle loss function 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, and form a cluster; select another core object from the unvisited samples 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;

[0036] S2. Repeat step S1 until all core objects are visited, then the clustering process is completed, and the number and position of the valleys of the angle loss function are obtained.

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

[0038] Take three initial value points that are not collinear 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] Reflect the centroid of the highest point x (3) through the lowest point x (1) and the middle point x (2) to obtain the reflection 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.

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

[0041]

[0042] where 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 that the probability loss function follows is:

[0044]

[0045] where J optim is the probability optimal solution, A 2 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 that the probability loss function follows.

[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] where 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 computational amount associated with arc segments, improves the accuracy of space target observation, has a simple and reliable arc segment association algorithm, and is applicable to any dynamic model.

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

[0052] 3. By introducing the minimum optical admissible domain, the basic domain of optical arc segment association is greatly reduced, and the computational cost is saved to a large extent.

[0053] 4. Using the J 2 perturbation model simplifies the dynamic model used in arc segment association. Only considering the non-spherical perturbation of the earth does not affect the association result and reduces the computational amount.

[0054] 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.

[0055] 6. By analyzing the chi-square distribution followed by the probability loss function, the threshold for determining whether the first observation arc segment and the second observation arc segment are associated is set, rather than obtained empirically, making the association result more mathematically based and more in line with real 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 trough.

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

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

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

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

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

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

[0064] Figure 8It is a schematic diagram of the LEO arc segment with a span of 24.2 hours in the arc segment association example 6.

[0065] Figure 9 It is a schematic diagram of the HEO arc segment with a span of 2.6 hours in the arc segment 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. Detailed implementation manner

[0068] An embodiment of the present invention provides an intelligent arc segment association method based on the minimum optical tolerance domain. The method includes:

[0069] Step 1: According to the observation time, select the first observation arc segment and the second observation arc segment to be associated; based on the 3σ criterion of the normal distribution, construct the minimum optical tolerance 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 tolerance domain, and each sampling point performs orbit propagation under the J 2 term 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: According to Bayes' theorem, calculate the probability loss function of the theoretical prediction value and covariance of the second observation arc segment;

[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: According to the chi-square distribution obeyed by the probability loss function, a threshold is set to determine 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 fail to be associated, and it is considered that the two arc segments come from different space targets.

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

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

[0079] Eliminate the loss function value The sampling points that meet The sampling points of are included in the minimum optically allowable domain as the boundary of the minimum optically allowable domain, and the minimum optically allowable domain is constructed; wherein the loss function is:

[0080]

[0081] Wherein, m is the total number of the first optical observation data; i is the sequence number;

[0082] It is the first actual optical observation right ascension; The right ascension for the first theoretical optical observation; 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 the matrix transpose;

[0083] It was the first practical optical observation of 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 most space targets, J in the non-spherical perturbation of the Earth 2 The term is the most important perturbation term. 2 If the long-term effect of the perturbation on the orbit is considered, then the orbital elements have an analytical solution. Using an analytical form of the dynamic model can greatly improve the calculation speed. 2The influence of the long-term perturbation on the right ascension of the ascending node, the argument of perigee, and the mean anomaly is obtained as the J in Step 2 2 -th order perturbation model:

[0085]

[0086] where is the right ascension of the ascending node, is the argument of perigee, is the mean anomaly, J 2 is the -th order perturbation term in the Earth's non-spherical perturbation, μ 2 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. E In Step 3, the angular loss function is:

[0087] where

[0088] is the m

[0089] -th group of the second theoretical optical observation data included in the second observation arc; 2 is the m

[0090] -th group of the second actual optical observation data included in the second observation arc; 2 J

[0091] is the root mean square error of the angle, representing the fitting degree of the orbit to the second observation arc (without considering weighting); m angle is the number of groups of optical observation data, and i is the serial number. 2 In Step 4, the method of using the DBSCAN clustering algorithm to automatically identify the number and positions of the valleys of the angular loss function includes:

[0092] S1. Starting from any core object in the angular 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 unvisited samples to form another cluster; where ε in the neighborhood parameters is the sampling step of the samples, and MinPts is the threshold of the number of samples in the neighborhood;

[0093] S2. Repeat Step S1 until all core objects have been visited, then the clustering process is completed, and the number and positions of the valleys of the angular loss function are obtained.

[0094] S2. Repeat step S1 until all core objects are visited, and the clustering process is completed, obtaining the number and positions of the valleys of the angular loss function.

[0095] The DBSCAN clustering algorithm determines the clustering result based on the density of the sample distribution and does not require setting the number of clusters in advance, making it very suitable for trough recognition. The DBSCAN clustering algorithm characterizes the tightness of the sample distribution based on a set of neighborhood parameters (ε, MinPts). The DBSCAN clustering algorithm defines the concept of a cluster as the largest density-connected sample set derived from the density-reachable relationship.

[0096] In the embodiment of the present invention, let MinPts = 2, where δ ρ 、 are the sampling step sizes of ρ and respectively. Figure 1 shows the clustering result of the DBSCAN clustering algorithm. It can be seen that different troughs can be well recognized. In each 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 obtaining the local optimal solution of the angular loss function using the simplex method includes:

[0098] Take three non-collinear initial 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, and n is the dimension of the optimization space. In the embodiment of the present invention, the optimization space is two-dimensional, so n = 2, and the formed initial simplex is as shown in Figure 2 .

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

[0103] In step seven, the optimal angle solution obtained in step five is used as the initial value and substituted into the probability loss function, and the LM (Levenberg-Marquardt) algorithm is used to find the minimum value. 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 , an orbit 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 come from the same space target, analyzing the probability loss function in step six 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 seven is less than the association threshold, the two arc segments are successfully associated, and it is considered that the two arc segments come from the same space target; then, in step eight, the chi-square distribution followed by the probability loss function is:

[0105]

[0106] In the formula, J optim is the probability optimal solution, A 2 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.

[0107] 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:

[0108]

[0109] In the formula, 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 come from the same observation target, then J optim is less than The probability is 99.5%. Since the kinetic model used by the association algorithm cannot be exactly the same as the real kinetic model, the embodiments of the present invention amplify the threshold and set it as 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 come from different space targets.

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

[0112] This example takes different types of space targets as the research object 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 arc segments of GEO targets, with time spans of 1 day, 1.9 days, and 3.1 days respectively; Examples 4 - 6 are the observation arc segments of LEO targets, with time spans of 1.6 hours, 19.0 hours, and 24.2 hours respectively; Examples 7 - 9 are the observation arc segments 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 arc segments 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 position, true value, and global optimal solution 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 92.3, and the association is successful.

[0118] Table 2 gives the comparison between the orbital state corresponding to the optimal solution of the GEO arc segment association result and the true value. It can be seen that once the two arc segments are successfully associated, the combined orbit determination result of the two arc segments will have high accuracy. Among them, the semi - major axis error is about 1 kilometer.

[0119] Table 2

[0120]

[0121]

[0122] Example 2, Numerical Examples 4 - 6: LEO Arc Segment

[0123] The arc segments to be associated in Numerical Examples 4 - 6 all come from LEO targets, and the results are as shown in Figure 6 、 Figure 7 and Figure 8 、Table 3. Table 3 shows the association results of the LEO arc segment. The time spans of the three numerical examples are 1.6 hours, 19.0 hours, and 24.2 hours respectively, and the number of 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 troughs in 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 association is successful. After the association 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, Numerical Examples 7 - 9: HEO Arc Segment

[0128] The arc segments to be associated in Numerical Examples 7 - 9 all come from HEO targets, and the results are as shown in Figure 9 、 Figure 10 and Figure 11 、Table 4. Table 4 shows the association results of the HEO arc segment. The time spans of the three numerical examples are 2.6 hours, 21.6 hours, and 29.1 hours respectively, and the number of 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 association is successful.

[0129] Table 4

[0130]

[0131]

[0132] Nine simulation numerical examples show that the arc segment association 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 as follows:

[0134] 1. The technical solution disclosed by the present invention reduces the computational amount associated with arc segments, improves the observation accuracy of space targets, has a simple and reliable arc segment association algorithm, and is applicable to any dynamic model.

[0135] 2. Using optical observation data, intelligent arc segment association between short arc segments can be achieved.

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

[0137] 4. Using the J 2 -order perturbation model simplifies 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 angle optimal 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. By analyzing the chi-square distribution followed by the probability loss function, the threshold for determining whether the first observation arc segment and the second observation arc segment are associated is set, rather than obtained 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 within 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 arc segment intelligent association method based on the minimum optical allowable domain, characterized in that: The method includes: Step 1: According to the observation time, the first observation arc segment and the second observation arc segment to be associated are selected; based on the 3σ criterion of normal distribution, the minimum optical allowable domain is constructed through the loss function according to the first optical observation data in the first observation arc segment; Step 2: uniformly sample in the minimum optical permissible domain, and perform orbital propagation at each sampling point under the J2 perturbation model to obtain the second theoretical optical observation data of each sampling orbit in the corresponding time period in the second observation arc segment; Step 3: Calculate the angle root mean square error 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 location of troughs in the angle loss function; Step 5: Select the sampling point with the smallest angle mean square error in each trough 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: Using 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, use the LM algorithm to find the minimum value, and obtain the probability optimal solution; Step 8: According to the chi-square distribution obeyed by the probability loss function, a threshold is set to determine 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 fail to be associated, and it is considered that the two arc segments come from different space targets.

2. The method according to claim 1, characterized in that In step 1, based on the 3σ criterion of normal distribution, the method of constructing the minimum optical allowable domain through the loss function according to the first optical observation data in the first observation arc segment includes: Based on the 3σ criterion of normal distribution, the threshold is set to 3, and the loss function is used to calculate the loss of each sampling point in the first optical observation data in the first observation arc segment. The loss function value Eliminate the loss function value The sampling points that meet The sampling points are included in the minimum optically allowable domain as the boundary of the minimum optically allowable domain, and the minimum optically allowable domain is constructed.

3. The method according to claim 1 or 2, characterized in that In step 1, the loss function for: Wherein, m is the total number of the first optical observation data; i is the sequence number; It is the first actual optical observation right ascension; The right ascension for the first theoretical optical observation; 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 the matrix transpose; It was the first practical optical observation of 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, characterized in that 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 angle, J2 is the J2 perturbation term in the non-spherical perturbation of the Earth, μ E is 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.

5. The method according to claim 1, characterized in that In step 3, the angle loss function is: in, is the second theoretical optical observation data, is the second actual optical observation data; J angle is the angle root mean square error, m2 is the number of groups of optical observation data, and i is the serial number.

6. The method according to claim 1, characterized in that 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: 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; 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.

7. The method according to claim 1, characterized in that In step 5, the method of using the simplex method to obtain the local optimal solution of the angle loss function includes: Take three non-collinear initial points on the plane Construct the 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; Set the highest point x (3) Passing the lowest point x (1) and the midpoint x (2) Centroid Reflect and get the reflection point x (4) As a local optimal solution; In the formula, For x (1) and x (2) The centroid of: b is the reflection coefficient.

8. The method according to claim 1, characterized in that In step 6, the probability loss function is calculated as: 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, and T is the sign of the matrix transpose.

9. The method according to claim 8, characterized in that In step 8, the chi-square distribution of the probability loss function is: In the formula, J optim is the probabilistic optimal solution, A2 is the actual observation value of the second observation arc segment, is the theoretical prediction value of the second observed arc segment, T is the sign of the matrix transpose, is the covariance of the second observed arc segment, Σ A2 is the covariance after propagation, The probability loss function follows a chi-square distribution with 4 degrees of freedom.

10. The method according to claim 9, characterized in that 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 as follows: In the formula, P is the probability, J is optim is the probability optimal solution, is the α quantile, and α is the significance level.

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