Radar and optical observation segmental arc correlation method and system for space debris

Abstract

The invention provides a radar and optical observation segmental arc correlation method and system for space debris. A joint probability density function is obtained through a kernel density estimation algorithm. A radar observation arc section and an optical observation arc section are input. And converting the observation data into a geocentric celestial coordinate system. And acquiring system parameters of the observation equipment. Radar observation data and optical observation data are unified to the same dimension, and a distance measurement value weight and an angle measurement value weight are set. And calculating an initial orbit by the radar observation arc section. And calculating a joint objective function corresponding to the current orbit position speed. And if the convergence condition is met, outputting the minimum value of the joint objective function and the orbit position speed corresponding to the minimum value. Otherwise, updating the track position speed, and repeating until the convergence condition is met. And according to the minimum value of the joint objective function and the joint probability density function, judging whether association is carried out, and outputting confidence during association. The method is easy to implement and can be effectively applied to association of the space debris radar and the optical observation arc section.

Description

Technical Field

[0001] The present invention relates to the technical field of space situation awareness, and specifically, to a method and system for associating radar and optical observation arcs of space debris. Background Art

[0002] Currently, space debris monitoring devices mainly rely on ground-based monitoring devices, including radars and optical telescopes. The radar detects by an active method, which can be not restricted by atmospheric conditions, sunlight, etc., and can obtain ranging and angle measurement data simultaneously. The optical telescope detects by a passive method. Although it can only obtain angle measurement data, the angle measurement accuracy is very high. When the data of both the radar and the optical telescope are available, the data of the two types of devices can play a complementary role, greatly improving the frequency of space debris monitoring and the accuracy of orbit determination.

[0003] The radar and the optical telescope independently obtain observation data respectively. In applications, it is necessary to associate the radar observation arc with the optical observation arc. Especially when discovering new space debris, without historical prior information, it is necessary to make an association judgment on the radar observation arc and the optical observation arc. Only on the premise of correctly associating multiple observation arcs can further precise orbit determination and other links be effectively implemented, so as to monitor and forecast space debris.

[0004] Regarding the association problem of optical-only angle measurement arcs, Literature 1 (Initial Orbit Association of Very Short Arcs of Low-Earth Orbit Space Targets, Journal of Wuhan University (Information Science Edition), 2020, 45(10)), Literature 2 (Research on Initial Orbit Association of Space Debris with Only Angle Very Short Arcs, Doctoral Thesis of Wuhan University, 2019), and Literature 3 (Research on Initial Orbit Association of Space Debris with Only Angle Very Short Arcs, Acta Geodaetica et Cartographica Sinica, 2021, 50(2)) proposed a geometric method for associating only angle measurement observation data. After determining the initial orbits of two arcs, the initial orbits are propagated to the intermediate time by the analytical method, the differences between the two initial orbits are calculated, and the initial orbits are adjusted. After multiple iterations, it is judged whether they are associated according to the differences between the two initial orbits. Literature 4 (Short Arc Association Analysis Method Based on Only Optical Observation, Chinese Space Science and Technology, 2021, 41(3)) is based on the method of the tolerance domain, and determines the minimum error between the angle prediction value and the true angle measurement value by finding the optimal orbit that fits multiple groups of observation data. And an error limit is given, and the association between arcs is determined by the chi-square test. Literature 5 (Research on the Association Problem of Optical Observation Arcs of Space Debris Based on the Mean Shift Clustering Method, 2021 Annual Meeting of the Chinese Astronomical Society) constructed an arc association method based on the mean shift clustering framework, taking the observation data as "points", the orbital elements as "centers", and the residuals as "distance" metrics. The methods in the existing literature are all based on the calculation of the initial orbits of both arcs.

[0005] Patent Document 1 (A Method for Autonomous Arc Segment Association and Orbit Determination of GEO Targets for Space - based Optical Monitoring, CN111578950A) discloses a method for autonomous arc segment association and orbit determination of GEO targets for space - based optical monitoring. It uses two initial orbits to solve the Lambert equation, assigns distances to the angle - measuring data using the near - circular hypothesis, further improves the initial orbit under perturbation conditions, and uses the slope of the observation residual as the judgment threshold. Patent Document 2 (A Method for Initial Orbit Determination and Association of Space - based Optical Angle - measuring Arc Segments for GEO Targets, CN113204917A) discloses an association method for GEO targets. After obtaining the initial orbit, it calculates the sub - satellite point trajectory and uses the difference in the average longitude of the sub - satellite points of two arc segments as the judgment threshold. Both Patent 1 and Patent 2 are for GEO targets and are not applicable to space debris of other types of orbits.

[0006] Regarding the problem of associating radar and optical observation arc segments of space debris, the present invention proposes a new association method that does not require calculating the initial orbit of the optical angle - only measurement arc segment, quickly solves the optimization problem based on the AdaFactor algorithm, and gives the association confidence level through the joint probability density function. Summary of the Invention

[0007] Aiming at the defects in the prior art, the purpose of the present invention is to provide a method and system for associating radar and optical observation arc segments of space debris.

[0008] According to a method for associating radar and optical observation arc segments of space debris provided by the present invention, it includes:

[0009] Step S1, statistically analyze the orbital elements of existing space debris, and obtain the joint probability density function by the kernel density estimation algorithm;

[0010] Step S2, input a radar observation arc segment and an optical observation arc segment. The data of the radar observation arc segment includes: time t at multiple sampling moments i , the distance l between the space debris and the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , with subscript i = 1, 2, …… M, where M is the total number of sampling points of the radar observation data; the data of the optical observation arc segment includes: time τ at multiple sampling moments j , the right ascension α of the space debris relative to the observation station in the geocentric celestial coordinate system j , declination δ j , with subscript j = 1, 2, …… N, where N is the total number of sampling points of the optical observation data;

[0011] Step S3: Convert the angle measurement values and the observation station position values of the radar observation arc segment and the optical observation arc segment to the geocentric celestial coordinate system, and obtain the line-of-sight unit vector of the radar observation in the geocentric celestial coordinate system The line-of-sight unit vector of the optical observation The position of the radar observation station The position of the optical observation station

[0012] Step S4: Obtain the system parameters of the observation equipment, including the ranging error σ range , the angle measurement error σ angle , and the angle measurement error σ of the optical telescope optic ;

[0013] Step S5: Unify the data of the radar observation arc segment and the optical observation arc segment to the same dimension, and obtain the observation time series t k , the angle measurement value series The observation station position series The ranging series l k , with the subscript k = 1, 2,..., M + N, and set the ranging value weight k of the observation data corresponding to the observation time series t and the angle measurement value weight θ k ;

[0014] Step S6: Calculate the initial orbit from the radar observation arc segment, and obtain the initial values of the orbit position and the initial value of the velocity

[0015] Step S7: Calculate the joint objective function corresponding to the current orbit position and velocity

[0016] Step S8: If the convergence condition is reached, output the minimum value of the joint objective function and the orbit position and velocity corresponding to the minimum value; otherwise, update the orbit position and velocity, and repeat to trigger Steps S7 to S8 until the convergence condition is reached;

[0017] Step S9: Compare the minimum value of the joint objective function with the associated threshold. If it is greater than the threshold, the judgment result is non-associated; if it is less than the threshold, calculate the association confidence level according to the joint probability density function. If the calculation result of the association confidence level is 0, the judgment result is non-associated; otherwise, the judgment result is associated, and output the corresponding association confidence level.

[0018] Further, Step S1 includes:

[0019] Step S1.1: Convert the orbital elements of the existing space debris from Keplerian elements to Poincaré elements:

[0020]

[0021] Among them, a is the semi-major axis, e is the eccentricity, and i nc is the orbital inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, and M a is the mean anomaly, and P1, P2, P3, P4, P 5、 P6 are the six parameters of the Poincaré elements;

[0022] Step S1.2: A 5D data sample is formed by the 2nd to 6th parameters of the Poincaré elements of existing space debris, and the joint probability density function of the discrete data of existing space debris is obtained based on Gauss kernel density estimation.

[0023] Furthermore, in step S5, the observation time series, the angle measurement value series, and the station position series are directly spliced from the data obtained in steps S2 and S3, and the optical ranging value is obtained by padding with zeros:

[0024]

[0025] Furthermore, in step S5, the ranging weight corresponding to the radar observation arc segment is calculated by the ranging error σ of the radar range , the ranging weight of the optical observation arc segment is set to 0, and the angle measurement weight is calculated by the angle measurement error σ of the radar angle , the angle measurement error σ of the optical telescope optic , that is:

[0026]

[0027] Furthermore, step S7 includes:

[0028] Step S7.1: With the orbital position and velocity at t0 being , perform perturbed orbit propagation to obtain the position estimates corresponding to each moment in t k respectively

[0029] Step S7.2: Calculate the distance estimate l k of the space debris relative to the observation station and the estimated value of the line-of-sight unit vector k,guess corresponding to each moment in t

[0030] Step S7.3: Calculate the difference between the distance estimate and the measured value l k,Δ , and the difference between the estimated value of the line-of-sight vector and the measured value u k,Δ :

[0031]

[0032] Among them, < > represents the inner product calculation of two vectors;

[0033] Step S7.4, calculate the objective function

[0034]

[0035] Furthermore, in step S8, the convergence condition includes any one of the following:

[0036] The number of iterations reaches a given maximum number of iterations;

[0037] The number of iterations is greater than a preset threshold, and the minimum value of the objective function is greater than a preset threshold;

[0038] The objective function is less than a preset threshold;

[0039] The number of consecutive non-decreasing steps of the objective function reaches a preset threshold.

[0040] Furthermore, in step S8, the AdaFactor optimization algorithm is selected as the orbital position and velocity update method, and the initial step size γ is set as follows:

[0041]

[0042] where f (0) is the combined objective function value calculated from the initial orbital position and the initial velocity

[0043] Furthermore, in step S9, the correlation confidence c onf is calculated as follows:

[0044]

[0045] where σ n correspond to the standard deviations of the 5D data samples formed by the 2nd to 6th parameters of the Poincaré elements of the existing space debris respectively. The subscript n takes 2, 3, 4, 5 or 6, and p df is the joint probability density function.

[0046] Furthermore, in step S1.2, the 1st parameter of the Poincaré elements of the existing space debris is ignored.

[0047] According to a radar and optical observation arc association system for space debris provided by the present invention, it includes:

[0048] Module M1, which statistically analyzes the orbital elements of the existing space debris and obtains the joint probability density function by the kernel density estimation algorithm;

[0049] ​Module M2 inputs a radar observation arc segment and an optical observation arc segment. The data of the radar observation arc segment includes: time t at multiple sampling moments i , distance l of the space debris relative to the observation station i , azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , altitude angle h i , subscript i = 1, 2, …… M, where M is the total number of sampling points of the radar observation data; the data of the optical observation arc segment includes: time τ at multiple sampling moments j , right ascension α of the space debris relative to the observation station in the geocentric celestial coordinate system j , declination δ j , subscript j = 1, 2, …… N, where N is the total number of sampling points of the optical observation data;

[0050] Module M3 converts the angular measurement values and observation station position values of the radar observation arc segment and the optical observation arc segment to the geocentric celestial coordinate system, and obtains the line-of-sight unit vector of the radar observation in the geocentric celestial coordinate system The line-of-sight unit vector of the optical observation The position of the radar observation station The position of the optical observation station

[0051] Module M4 obtains the system parameters of the observation equipment, including the ranging error σ of the radar range , the angular measurement error σ angle , the angular measurement error σ of the optical telescope optic ;

[0052] Module M5 unifies the data of the radar observation arc segment and the optical observation arc segment to the same dimension, and obtains the observation time series t k , the angular measurement value series The observation station position series The ranging series l k , subscript k = 1, 2, …… M + N, and sets the ranging value weight k of the observation data corresponding to the observation time series t and the angular measurement value weight θ k ;

[0053] Module M6 calculates the initial orbit from the radar observation arc segment, and obtains the initial values of the orbit position and the initial value of the velocity at the corresponding t0 moment

[0054] Module M7 calculates the joint objective function corresponding to the current orbit position and velocity

[0055] Module M8, if the convergence condition is met, outputs the minimum value of the joint objective function and the orbital position and velocity corresponding to the minimum value; otherwise, updates the orbital position and velocity, and repeatedly triggers modules M7 and M8 until the convergence condition is met;

[0056] Module M9 compares the minimum value of the joint objective function with the association threshold. If it is greater than the threshold, the judgment result is no association. If it is less than the threshold, the association confidence is calculated according to the joint probability density function. If the calculated result of the association confidence is 0, the judgment result is no association. Otherwise, the judgment result is association, and the corresponding association confidence is output.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] This paper proposes a method for unifying the dimensions of radar and optical observation data. It also provides different weighting methods based on observation equipment system parameters. Arc segment associations are solved based on the optimization of a joint objective function, using the AdaFactor algorithm to optimize the step size and calculate the confidence level of the radar and optical segment associations. This method is rational, computationally simple, and easy to implement. It can be effectively applied to determine the association between radar and optical observation segments without prior knowledge. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0060] Figure 1 Flowchart of the present invention.

[0061] Figure 2 This is the association confidence obtained by testing 100 groups of positive samples in the present invention. DETAILED DESCRIPTION

[0062] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0063] To determine whether a radar observation arc is associated with an optical observation arc, we need to find a reasonable trajectory that keeps the estimated value and the measured value sufficiently small. This presents two challenges: first, how to find a trajectory that keeps the estimated value and the measured value sufficiently small, and second, once a trajectory is found, how to determine its plausibility.

[0064] For the problem of judging the rationality of an orbit, the present invention performs statistical analysis on the existing space debris that has been mastered to obtain the probability distribution of its relative orbital elements. If the solved orbit is similar to these orbits, the confidence level is high; if the solved orbit is very different from the existing orbits, the possibility of existence is also low, so the confidence level is low or it is judged as non-existent.

[0065] As Figure 1 shown, the present invention provides a method for correlating radar and optical observation arcs of space debris, including:

[0066] Step S1, statistically analyze the orbital elements of the existing space debris, and obtain the joint probability density function by the kernel density estimation algorithm.

[0067] Step S2, input a radar observation arc and an optical observation arc. The data of the radar observation arc includes: the time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , with the subscript i = 1, 2,..., M, where M is the total number of sampling points of the radar observation data; the data of the optical observation arc includes: the time τ at multiple sampling moments j , the right ascension α of the space debris relative to the observation station in the geocentric celestial coordinate system j , the declination δ j , with the subscript j = 1, 2,..., N, where N is the total number of sampling points of the optical observation data.

[0068] Step S3, convert the angular measurement values and observation station position values of the radar observation arc and the optical observation arc to the geocentric celestial coordinate system, and obtain the line-of-sight unit vector of the radar observation in the geocentric celestial coordinate system the line-of-sight unit vector of the optical observation the position of the radar observation station the position of the optical observation station

[0069] Step S4, obtain the system parameters of the observation equipment, including the ranging error σ of the radar range , the angular measurement error σ angle , the angular measurement error σ of the optical telescope optic .

[0070] Step S5, unify the data of the radar observation arc and the data of the optical observation arc to the same dimension, and obtain the observation time series t k , the angular measurement value series the observation station position series the ranging series l k, the subscript k = 1, 2, …… M+N, and set the corresponding observation time series t k Observation data ranging value weight and the angular measurement value weight θ k .

[0071] Step S6, calculate the initial orbit from the radar observation arc segment to obtain the initial value of the orbit position at the corresponding t0 moment Initial velocity value

[0072] Step S7, calculate the joint objective function corresponding to the current orbit position and velocity

[0073] Step S8, if the convergence condition is reached, output the minimum value of the joint objective function and the orbit position and velocity corresponding to the minimum value; otherwise, update the orbit position and velocity, and repeat to trigger Steps S7 to S8 until the convergence condition is reached.

[0074] Step S9, compare the minimum value of the joint objective function with the associated threshold. If it is greater than the threshold, the judgment result is non-associated; if it is less than the threshold, calculate the association confidence level according to the joint probability density function. If the calculation result of the association confidence level is 0, the judgment result is non-associated; otherwise, the judgment result is associated, and output the corresponding association confidence level.

[0075] First, count the orbital elements of existing space debris, and obtain the joint probability density function by the kernel density estimation algorithm. To avoid the singularity problem of the commonly used Kepler elements (semi-major axis a, eccentricity e, orbital inclination i nc , right ascension of the ascending node Ω, argument of perigee ω, mean anomaly M a ) when the eccentricity and orbital inclination are close to 0, convert the orbital elements of existing space debris into Poincaré elements. The calculation method of converting from Kepler elements to Poincaré elements (six parameters, namely P1, P2, P3, P4, P 5、 P6) is as follows:

[0076]

[0077] The first parameter of the Poincaré element is a quantity that changes rapidly with time and does not determine the orbit shape, so it is ignored in the statistics. A 5D data sample is composed of the 2nd to 6th parameters, and the joint probability density function of the discrete data of existing space debris is obtained based on the Gauss kernel density estimation. The more the number of samples, the more accurate the joint probability density function is theoretically.

[0078] For processing in the same space, it is necessary to convert the angular measurement values and the observation station position values of the radar observation arc segment and the optical observation arc segment data to the geocentric celestial coordinate system. Obtain the line-of-sight unit vector of the radar observation in the geocentric celestial coordinate system The line-of-sight unit vector of the optical observation The position of the radar observation station The position of the optical observation station The biggest difference between the radar and optical observation arcs is that the optical observation arc can only generate angular measurement data and no ranging data. In order to facilitate processing during processing, the radar observation data and the optical observation data are unified to the same dimension to obtain the observation time series t k , the angular measurement value sequence The station position sequence The ranging sequence l k . The subscript k ranges from 1, 2,..., M + N. And set the ranging value weight k of the observation data corresponding to the observation time series t and the angular measurement value weight θ k .

[0079] The observation time series, the angular measurement value sequence, and the station position sequence can be directly obtained by directly splicing the data obtained in Step 2 and Step 3, while the optical ranging value is obtained by padding with zeros, that is:

[0080]

[0081]

[0082] The ranging weight corresponding to the radar observation data is calculated by the ranging error σ range of the radar, the ranging weight of the optical observation data is set to 0, and the angular measurement weight is calculated by the radar angular measurement error σ angle , the angular measurement error σ optic of the optical telescope, that is:

[0083]

[0084] In order to find an orbit that makes the estimated value and the measured value small enough, it is first necessary to determine a quantitative judgment basis for the closeness of the estimated value and the measured value, which is called the objective function. Since both the radar and optical observation arcs need to be comprehensively considered in the present invention, the objective function is also called the joint objective function

[0085]

[0086] Among them, l k,Δ is the difference between the distance estimated value l k,guess and the measured value l k , u k,Δis the estimated value of the line-of-sight vector and the measured value difference

[0087]

[0088] Among them, <> represents the inner product calculation of two vectors. Through data unified setting, in the calculation of the objective function, the position data of all radar and optical observation times can be obtained recursively at one time, and all ranging and angle measurement calculations can be completed at one time without separate processing. It can be seen from the objective function that by setting the ranging weight of the optical observation data to 0, no matter what value the optical ranging is assigned, it will ultimately have no contribution to the objective function, that is, all contributions of the optical observation arc segment come from angle measurement.

[0089] After the objective function is determined, an optimization algorithm is needed to find the orbit that minimizes the objective function. The present invention uses the AdaFactor optimization algorithm to update and iterate the position and velocity of the orbit. The initial value of the iteration is given by the radar observation data that is relatively easy to calculate for the initial orbit. The AdaFactor optimization algorithm needs to set the initial iteration step size γ. Since in the association problem, the initial value calculated from the radar observation data may correspond to an uncertain value of the joint objective function, a piecewise function can be used to set it:

[0090]

[0091] where f (0) is the value of the joint objective function calculated from the initial value of the orbit position and the initial value of the velocity

[0092] If the radar observation arc segment and the optical observation arc segment do indeed come from the same space debris, there should be an orbit that makes the value of the joint objective function reach a smaller value. In this case, it can be judged whether it has converged according to whether the objective function is less than a given threshold. For the case where the radar observation arc segment and the optical observation arc segment actually come from different space debris, it is possible that the global minimum value of the objective function cannot reach the given threshold. To avoid excessive meaningless iterative consumption of processing time, the present invention uses the number of consecutive non-decreasing steps of the objective function and whether the minimum value of the objective function is greater than a given threshold after the number of iterations is greater than a certain threshold to judge whether to end the iteration.

[0093] The final convergence conditions are set as follows: (1) The number of iterations reaches the given maximum number of iterations (500); (2) The number of iterations is greater than a certain threshold (100), and the minimum value of the objective function is greater than the given threshold (1e4); (3) The objective function is less than the given threshold (8); (4) The number of consecutive non-decreasing steps of the objective function reaches the given threshold (100). Any one of the conditions is satisfied. ​

[0094] After the iterative solution is completed, the minimum value of the joint objective function obtained in the iteration is compared with the association threshold. If it is greater than the threshold, the result is judged as no association. If it is less than the threshold, the association confidence is calculated according to the joint probability density function. Since the joint probability density function reflects the probability density, and the association expects to output a confidence of 0 to 100%, the association confidence needs to be normalized by multiplying a factor on the basis of the joint probability density. The association confidence c onf The calculation method is:

[0095]

[0096] Among them, σ n The second to sixth parameters of the Poincaré roots of the existing space debris (subscript n is 2, 3, 4, 5, 6) respectively constitute the standard deviation of the 5-dimensional data sample. df is the joint probability density function.

[0097] If the calculated result of the association confidence is 0, the track is considered unreasonable; otherwise, the result is considered to be associated, and the corresponding association confidence is output.

[0098] In general, a radar arc segment data for observing space debris includes: the time t of multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth A of the instantaneous true horizontal coordinate system of the observation station i , altitude angle h i , the subscript i ranges from 1, 2, ..., M. M is the total number of sampling points of the observation data. The coordinates of the observation station in the earth-fixed coordinate system, the system parameters of the radar observation equipment, including the ranging error σ range , angle measurement error σ angle It is known information.

[0099] The effectiveness of the method of the present invention is verified by combining data. In order to ensure that there are absolute true values for comparison during the test process, the test is based on simulated data. 100 groups of positive samples were constructed, that is, a radar and an optical arc segment from the same space debris. At the same time, 100 groups of negative samples were constructed, that is, a radar and an optical arc segment from different space debris. The method of the present invention was used to test 200 groups of sample data. The outputs of the 100 groups of negative samples were all uncorrelated, and 98 groups of the 100 groups of positive sample test results were judged to be correlated. The confidence results of the 100 groups of positive sample outputs are shown in the attached figure. Figure 2 As shown (confidence level 0 means no correlation).

[0100] The present invention also provides a system for associating radar and optical observation arcs of space debris. The system for associating radar and optical observation arcs of space debris can be implemented by executing the process steps of the method for associating radar and optical observation arcs of space debris. That is, those skilled in the art can understand the method for associating radar and optical observation arcs of space debris as a preferred implementation manner of the system for associating radar and optical observation arcs of space debris. The system includes:

[0101] Module M1, which calculates the orbital elements of existing space debris and obtains the joint probability density function by the kernel density estimation algorithm;

[0102] Module M2, which inputs a radar observation arc and an optical observation arc. The data of the radar observation arc includes: the time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , with the subscript i = 1, 2,..., M, where M is the total number of sampling points of the radar observation data; the data of the optical observation arc includes: the time τ at multiple sampling moments j , the right ascension α of the space debris relative to the observation station in the geocentric celestial coordinate system j , the declination δ j , with the subscript j = 1, 2,..., N, where N is the total number of sampling points of the optical observation data;

[0103] Module M3, which converts the angular measurement values and the observation station position values of the radar observation arc and the optical observation arc to the geocentric celestial coordinate system, and obtains the line-of-sight unit vector of the radar observation in the geocentric celestial coordinate system the line-of-sight unit vector of the optical observation the position of the radar observation station the position of the optical observation station

[0104] Module M4, which obtains the system parameters of the observation equipment, including the ranging error σ of the radar range , the angular measurement error σ angle , the angular measurement error σ of the optical telescope optic ;

[0105] Module M5, which unifies the data of the radar observation arc and the data of the optical observation arc to the same dimension, and obtains the observation time series t k , the angular measurement value series the observation station position series the ranging series l k , with the subscript k = 1, 2,..., M + N, and sets the ranging value weight of the observation data corresponding to the observation time series t k of and the weight θ of the angle measurement value k ;

[0106] Module M6 calculates the initial orbit from the radar observation arc segment to obtain the initial value of the orbit position at the corresponding t0 moment Initial velocity value

[0107] Module M7 calculates the joint objective function corresponding to the current orbit position and velocity

[0108] Module M8, if the convergence condition is reached, outputs the minimum value of the joint objective function and the orbit position and velocity corresponding to the minimum value; otherwise, updates the orbit position and velocity, and repeatedly triggers the work of Module M7 and Module M8 until the convergence condition is reached;

[0109] Module M9 compares the minimum value of the joint objective function with the associated threshold. If it is greater than the threshold, the judgment result is non-associated. If it is less than the threshold, the association confidence is calculated according to the joint probability density function. If the calculation result of the association confidence is 0, the judgment result is non-associated; otherwise, the judgment result is associated, and the corresponding association confidence is output.

[0110] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers to achieve the same function. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or structures within the hardware component.

[0111] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for associating radar and optical observation arcs of space debris, characterized in that, Including: Step S1, statistically calculate the orbital elements of existing space debris, and obtain the joint probability density function by the kernel density estimation algorithm; Step S2: Input a radar observation arc segment and an optical observation arc segment. The data of the radar observation arc segment includes: time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , with subscript i = 1, 2, …… M, where M is the total number of sampling points of the radar observation data; the data of the optical observation arc segment includes: time τ at multiple sampling moments j , the right ascension α of the space debris relative to the observation station in the geocentric celestial coordinate system j , declination δ j , with subscript j = 1, 2, …… N, where N is the total number of sampling points of the optical observation data; Step S3: Convert the angle measurement values and the observation station position values of the radar observation arc segment and the optical observation arc segment to the geocentric celestial coordinate system, and obtain the line-of-sight unit vector of the radar observation in the geocentric celestial coordinate system The line-of-sight unit vector of the optical observation The position of the radar observation station The position of the optical observation station Step S4, obtain the system parameters of the observation device, including the ranging error σ of the radar range , the angle measurement error σ angle , and the angle measurement error σ of the optical telescope optic ; Step S5: Unify the data of the radar observation arc segment and the data of the optical observation arc segment to the same dimension to obtain the observation time series t k , angle measurement sequence Station position sequence Ranging sequence l k , subscript k = 1, 2, ... M + N, and set the corresponding observation time series t k The weight of the observation data ranging value and the angle measurement weight θ k ; Step S6: Calculate the initial orbit from the radar observation arc to obtain the initial values of the orbital position corresponding to the time t0 Initial velocity value Step S7, calculate the combined objective function corresponding to the current orbital position velocity Step S8, if the convergence condition is reached, output the minimum value of the joint objective function and the corresponding orbital position and velocity at the minimum value; otherwise, update the orbital position and velocity, and repeatedly trigger Steps S7 to S8 until the convergence condition is reached; Step S9, compare the minimum value of the joint objective function with the correlation threshold. If it is greater than the threshold, the judgment result is uncorrelated; if it is less than the threshold, calculate the correlation confidence level according to the joint probability density function. If the calculation result of the correlation confidence level is 0, the judgment result is uncorrelated; otherwise, the judgment result is correlated, and output the corresponding correlation confidence level.

2. The method for associating radar and optical observation arcs of space debris according to claim 1, wherein Step S1 includes: Step S1.1, convert the orbital elements of existing space debris from Kepler elements to Poincaré elements: where a is the semi-major axis, e is the eccentricity, i nc is the orbital inclination, Ω is the right ascension of the ascending node, ω is the argument of perigee, M a is the mean anomaly, and P1, P2, P3, P4, P5, P6 are the six parameters of the Poincaré elements; Step S1.2, form a 5D data sample from the 2nd to the 6th parameters of the Poincaré elements of existing space debris, and obtain the joint probability density function of the discrete data of existing space debris based on Gauss kernel density estimation.

3. The method for associating radar and optical observation arcs of space debris according to claim 1, wherein, In Step S5, the observation time series, the angular measurement value series, and the station position series are directly spliced from the data obtained in Steps S2 and S3, and the optical ranging value is obtained by zero padding:

4. The method for associating radar and optical observation arcs of space debris according to claim 1, wherein In step S5, the ranging weight corresponding to the radar observation arc segment is calculated from the ranging error σ of the radar range The ranging weight of the optical observation arc segment is set to 0, and the angle measurement weight is calculated from the radar angle measurement error σ angle , the angle measurement error σ of the optical telescope optic That is:

5. The method for correlating radar and optical observation arcs of space debris according to claim 1, wherein Step S7 includes: Step S7.1, with the orbital position and velocity at time t0 being perform perturbed orbit recurrence to obtain the position estimates corresponding to each time t k in Step S7.2, calculate the distance estimate value l of the space debris relative to the observation station corresponding to the time t k respectively k,guess and the estimated value of the line-of-sight unit vector Step S7.3, calculate the difference l between the distance estimated value and the measured value k,Δ , and the difference u between the estimated value and the measured value of the line-of-sight vector k,Δ :[[-END]] where, <> represents the inner product calculation of two vectors; Step S7.4, calculate the objective function 6. The method for associating radar and optical observation arcs of space debris according to claim 1, wherein In Step S8, the convergence condition includes any one of the following: The number of iterations reaches the given maximum number of iterations; The number of iterations is greater than the preset threshold, and the minimum value of the objective function is greater than the preset threshold; The objective function is less than the preset threshold; The number of steps in which the objective function has not decreased continuously reaches the preset threshold.

7. The radar and optical observation arc segments of space debris according to claim 1 are associated, characterized in that, In Step S8, the orbital position and velocity update method selects the AdaFactor optimization algorithm, and the initial step size γ is set as follows: Among them, f (0) is the initial value of the orbital position and the initial value of the velocity from which the combined objective function value is calculated.

8. The method for associating radar and optical observation arcs of space debris according to claim 1, wherein In step S9, the association confidence c onf The calculation method is as follows: Among them, σ n respectively corresponds to the standard deviation of the 5-dimensional data sample composed of the 2nd to 6th parameters of the Poincaré root numbers of the existing space debris. The subscript n takes 2, 3, 4, 5, or 6, and p df is the joint probability density function.

9. The method for associating radar and optical observation arcs of space debris according to claim 2, wherein In Step S1.2, the 1st parameter of the Poincaré elements of existing space debris is ignored.

10. A radar and optical observation arc segment correlation system for space debris, characterized in that, Including: Module M1, statistically calculate the orbital elements of existing space debris, and obtain the joint probability density function by the kernel density estimation algorithm; Module M2 inputs a radar observation arc segment and an optical observation arc segment. The data of the radar observation arc segment includes: time t at multiple sampling moments i , the distance l of the space debris relative to the observation station i , the azimuth angle A in the instantaneous true horizon coordinate system of the observation station i , the altitude angle h i , with subscript i = 1, 2, …… M, where M is the total number of sampling points of the radar observation data; the data of the optical observation arc segment includes: time τ at multiple sampling moments j , the right ascension α of the space debris relative to the observation station in the geocentric celestial coordinate system j , declination δ j , with subscript j = 1, 2, …… N, where N is the total number of sampling points of the optical observation data; Module M3, which converts the angle measurement values and the observation station position values of the radar observation arc segment and the optical observation arc segment to the geocentric celestial coordinate system, and obtains the line-of-sight unit vector of the radar observation in the geocentric celestial coordinate system The line-of-sight unit vector of the optical observation The position of the radar observation station The position of the optical observation station Module M4, which obtains the system parameters of the observation device, including the ranging error σ of the radar range , the angle measurement error σ angle , and the angle measurement error σ of the optical telescope optic ; Module M5 unifies the data of the radar observation arc and the optical observation arc into the same dimension to obtain the observation time series t k , angle measurement sequence Station position sequence Ranging sequence l k , subscript k = 1, 2, ... M + N, and set the corresponding observation time series t k The weight of the observation data ranging value and the angle measurement weight θ k ; Module M6 calculates the initial orbit from the radar observation arc segment to obtain the initial value of the orbit position at the corresponding time t0 Initial velocity value Module M7, calculating the combined objective function corresponding to the current orbital position velocity Module M8, if the convergence condition is reached, output the minimum value of the joint objective function and the corresponding orbital position and velocity at the minimum value; otherwise, update the orbital position and velocity, and repeatedly trigger the work of Module M7 and Module M8 until the convergence condition is reached; Module M9, compare the minimum value of the joint objective function with the correlation threshold. If it is greater than the threshold, the judgment result is uncorrelated; if it is less than the threshold, calculate the correlation confidence level according to the joint probability density function. If the calculation result of the correlation confidence level is 0, the judgment result is uncorrelated; otherwise, the judgment result is correlated, and output the corresponding correlation confidence level.

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