A method and system for detecting relative orbital maneuvers of spacecraft based on cluster analysis

Abstract

A method for detecting relative orbital maneuvers of spacecraft based on cluster analysis includes: reading the TLE historical data of the master star of the spacecraft formation and calculating the instantaneous orbital elements, using the SGP4 model for recursion to obtain the orbital state at the moment when the latitude angle is 0; reading the TLE historical data of the slave star of the spacecraft formation and calculating the instantaneous orbital elements, using the SGP4 model to recursively calculate the orbital state at the same time as the master star data, and realizing the time synchronization of the dual-star data; calculating the relative distance of the spacecraft formation, and performing data denoising and normalization to obtain a data set; using the silhouette coefficient to determine the number of clusters, that is, the number of orbital maneuver types; using the fuzzy C-means algorithm for cluster analysis, obtaining a clustering result based on the relative distance of the spacecraft orbit, and realizing orbital maneuver detection. The method of the present invention can effectively avoid the influence of human subjective cognition and experience on the judgment of orbital maneuvers, meet the timeliness requirements of orbital maneuver detection, and significantly improve the accuracy of orbital control maneuver detection.

Description

Technical Field

[0001] The present invention relates to the technical field of spacecraft orbital maneuver detection, and in particular to a method and system for detecting relative orbital maneuvers of a spacecraft. Background Art

[0002] As the world's space activities become more frequent, the number of spacecraft in orbit increases, generating a massive amount of orbital information. How to use this data more effectively has become a major issue in the aerospace field: on the one hand, orbital information can be used to analyze and predict orbital behavior and determine the history and real-time status of spacecraft, such as orbit entry, orbit holding, and deorbiting operations; on the other hand, fast and accurate orbital maneuver detection will become an important factor in ensuring the safe operation of spacecraft in orbit.

[0003] Affected by the perturbations of the complex space environment and the requirements of space missions, spacecraft often need to perform orbital maneuvers to adjust their current operating status. At present, the orbit detection of spacecraft mainly relies on two-line elements (TLE) as the source of on-orbit data, and uses the simplified general perturbations model (SGP4) to predict the orbit within a certain period of time. According to the change law of orbital elements, the orbital maneuver behavior of the spacecraft is judged. For a single spacecraft, the time interval between TLE data points is about half a day to one day, which means that the target will generate at least 730 discrete data points per year on average. Taking the "YAOGAN-9" formation as an example, since its launch in 2010, it has accumulated more than 6200×3 TLE data points. How to efficiently and quickly process such a huge amount of data and extract key information of orbital maneuvers is a difficult problem currently faced by spacecraft orbit detection.

[0004] With the development of data mining technology, extracting unknown and valuable rules or behaviors from a large amount of orbital data will effectively improve the efficiency of spacecraft orbital maneuver detection. However, existing methods often use supervised classification methods, that is, the training data contains prior class labels, and the algorithm is used to obtain a rule that can fit the relationship between data and class labels. When applied, the data without prior class labels are divided into different class labels. This type of method is affected by human subjective cognition and experience and cannot reveal potential information that has not been discovered. The unsupervised classification method (also known as the cluster analysis method) is a process in which the data is divided into different classes or clusters according to certain rules without prior class labels. The data in the same cluster has a high similarity, and the similarity between different clusters is low. Cluster analysis can effectively save the workload of early data classification, help to reveal the undiscovered rules hidden in the data, and meet the timeliness requirements of orbital maneuver detection. Summary of the invention

[0005] The problem to be solved by the present invention is: the present invention solves the technical problem that the existing methods are highly dependent on human subjective cognition and experience judgment and are difficult to accurately analyze a large amount of orbital data. It provides an orbital maneuver detection method and system that uses a data mining method to process TLE historical data, uses a cluster analysis method to discover the unconventional evolution behavior of the orbital state, and realizes the acquisition of spacecraft relative orbital maneuver information under a large amount of orbital data.

[0006] The technical solution adopted by the present invention is: a method for detecting relative orbital maneuvers of spacecraft based on cluster analysis, comprising the following steps:

[0007] Step 1: Read the TLE historical data of the main satellite of the spacecraft formation and calculate the instantaneous orbital elements. Use the SGP4 model for recursion to obtain the orbital state when the latitude argument is 0, including:

[0008] To ensure the number of samples in the data set, the number of TLE data samples read in the specified time period should be more than 1000 groups, as follows:

[0009] S011: Read the specified time period C Compile the TLE history data of the host star and convert the TLE data in character form into the instantaneous orbit elements of the spacecraft;

[0010] S012: Use the SGP4 model to recursively push forward and backward each group of primary star orbital states by one orbital period, find the moment when the primary star latitude argument is 0, and record the primary star Julian day time set when the primary star latitude argument is 0 With the main star orbit state set in, represents the Julian day time of the primary star of the i-th group, Indicates the orbital state of the primary star of the i-th group, i=1,2,3,...,n C , n C is the number of samples in the main star dataset.

[0011] Step 2: Read the TLE historical data of the spacecraft formation slave satellite and calculate the instantaneous orbital elements. Use the SGP4 model to recursively infer the orbital state at the same time as the master satellite data to achieve dual satellite data time synchronization, including:

[0012] Since the TLE data time of different spacecraft is different, it is necessary to first use the SGP4 model to recursively extrapolate the orbital state of the formation binary to the same specified time. The specific steps are as follows.

[0013] S021: Read the n times in the same time period as the main star D Compile the satellite TLE historical data, convert the character TLE data into the spacecraft instantaneous orbit elements, and record the satellite Julian day time set With track status set in, Indicates the Julian day time of the pth group from the star, represents the orbital state of the pth group of slave stars, p=1,2,3,...,n D , n D is the number of samples from the star data set;

[0014] S022: Julian Day Time Collection from Stars Julian day time set with the main star Match and compare, using the main star Julian day time set As a reference, calculate the Julian day time set from the star The elements in the Julian day time of the i-th group of main stars The shortest time difference Record the shortest time difference ΔT of group i i The corresponding orbital state of the slave star is recorded as Get the new slave state set

[0015] S023: Based on the shortest time difference ΔT i , using the SGP4 model, each new set of slave star orbital states Recursively calculate ΔT forward and backward i +2 hours, find the state set of the slave star when the latitude argument of the master star is 0, recorded as in, It indicates the orbital state of the slave satellite of the i-th group when the latitude argument of the master satellite is 0, realizing the time synchronization of the dual-satellite data.

[0016] Step 3: Calculate the relative distance of the spacecraft formation, perform data denoising and normalization, and obtain a data set, including:

[0017] Set the status of the main star of the spacecraft formation at the same time With the status set from the star The position vector in is subtracted and the absolute value is taken to obtain the relative distance set of the spacecraft Where ΔX (i) Represents the relative distance of the i-th group; uses wavelet filtering to reduce data noise and obtain relatively smooth and continuous data; performs differential analysis on two adjacent data after noise reduction to obtain a differential value set Among them, δX (i) Represents the difference value of the i-th group; the normalized relative distance data set is obtained by using the maximum and minimum standardization Among them, δx (i) is the normalized relative distance of the i-th group, and the calculation formula is:

[0018]

[0019] Step 4: Use the silhouette coefficient to determine the number of clusters, that is, the number of orbital maneuver types, including:

[0020] First select the data set For the 1 / 3 data, set the number of clusters c t =2,...,10, use K-means method to perform cluster analysis on data with different cluster numbers and calculate the corresponding silhouette coefficient. Calculate sample δx (i) The average distance to other samples in the same cluster is a (i) ; Calculate sample δx (i) The minimum value b of the average distance to samples in other different clusters (i) . The silhouette coefficient of the data sample is defined as:

[0021]

[0022] The number of clusters is c t The silhouette coefficient is the mean of all sample silhouette coefficients,

[0023]

[0024] Select the silhouette coefficient The number of clusters corresponding to the maximum value is taken as the optimal number of clusters c opt , the optimal number of clusters c opt As the number of spacecraft orbital maneuver types.

[0025] Step 5: Use the fuzzy C-means algorithm to perform cluster analysis and obtain clustering results based on the relative distance of the spacecraft orbit to achieve orbital maneuver detection, including:

[0026] For the problem of spacecraft relative orbit maneuver detection, the objective function of fuzzy C-means clustering optimization is:

[0027]

[0028] in, is the membership matrix, u ki Represents the i-th group of data δx (i) For the membership of the kth cluster, c opt ; is the set of cluster centers, v k represents the kth cluster center; d ki =||δx (i) -v k || represents the i-th group of data δx (i) To the kth cluster center v kThe Euclidean distance of ; m is the power index, which is used to control the flexibility of the algorithm. In order to obtain the best clustering of the data set, it is necessary to iteratively solve the solution under the min(J(U,V)) constraint.

[0029] The specific steps of clustering the relative distances of spacecraft orbits using the fuzzy C-means algorithm are as follows:

[0030] S051: Enter the optimal number of clusters c opt , power index m>1, initial membership matrix Membership termination tolerance ε u >0;

[0031] S052: Calculate the cluster center V of the lth iteration (l) The elements in:

[0032] The cluster center V of the lth iteration (l) The kth cluster center in for

[0033]

[0034] in is the i-th group of data δx in the l-1th iteration (i) For the membership of the kth cluster;

[0035] S053: Modify the membership matrix U of the lth iteration (l) The elements in:

[0036] The membership matrix U of the lth iteration (l) The i-th group of data δx (i) For the membership of the kth cluster for

[0037]

[0038] in is the i-th group of data δx in the l-th iteration (i) To the kth cluster center The Euclidean distance of is the i-th group of data δx in the l-th iteration (i) To the jth cluster center Euclidean distance, j = 1, 2, 3, ..., c opt ; and calculate the objective function J of the lth iteration (l) ,

[0039]

[0040] S054: When When l=l+1, stop the iteration and obtain the final membership matrix and cluster center to minimize the objective function. Determine the classification of the sample data according to the values ​​of the elements in the final membership matrix and obtain the maneuver type to which the orbital maneuver belongs; otherwise l=l+1, go to step S052.

[0041] At this point, the relative orbital maneuver detection of spacecraft has been achieved with a large amount of orbital data.

[0042] The detection system according to the above-mentioned spacecraft relative orbit maneuver detection method based on cluster analysis includes:

[0043] The first module is used to read the TLE historical data of the main satellite of the spacecraft formation and calculate the instantaneous orbital elements, and use the SGP4 model for recursion to obtain the orbital state when the latitude argument is 0;

[0044] The second module is used to read the TLE historical data of the spacecraft formation slave satellite and calculate the instantaneous orbital elements, and use the SGP4 model to recursively deduce the orbital state at the same time as the master satellite data to achieve time synchronization of the dual satellite data;

[0045] The third module is used to calculate the relative distance of the spacecraft formation and perform data noise reduction and normalization to obtain a data set;

[0046] The fourth module is used to determine the number of clusters using the silhouette coefficient as the number of orbital maneuver types;

[0047] The fifth module is used to perform cluster analysis using the fuzzy C-means algorithm to obtain clustering results based on the relative distance of the spacecraft orbits and realize orbital maneuver detection.

[0048] The advantages of the present invention compared with the prior art are:

[0049] (1) The method of the present invention is different from the traditional method of determining the characteristic variable threshold based on experience. It can effectively avoid the influence of human subjective cognition and experience and reveal the maneuvering rules hidden in a large amount of orbit data.

[0050] (2) The method of the present invention performs automatic clustering based on the cluster analysis intelligent algorithm, which effectively saves the workload of early data classification and meets the timeliness requirements of orbital maneuver detection;

[0051] (3) The method of the present invention makes an overall comprehensive judgment on the operating status of the spacecraft formation, which can significantly improve the accuracy of orbital control maneuver detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flow chart of the orbital maneuver detection method of the present invention;

[0053] Figure 2 is the silhouette coefficient under different numbers of clusters;

[0054] Figure 3 It is the clustering result based on relative distance data. DETAILED DESCRIPTION

[0055] The present invention will be further described in detail below with reference to the accompanying drawings.

[0056] The present invention utilizes the TLE historical data accumulated by spacecraft and the SGP4 prediction model, and through data mining technology, combines the knowledge of traditional aerospace dynamics and control, proposes a spacecraft orbital maneuver detection method based on fuzzy C-means clustering, studies and analyzes the knowledge hidden in the TLE historical data, and inverts the spacecraft orbital control action, which will help to reversely design orbital maneuvers and maintenance plans, and assist the design of traditional orbital control strategies.

[0057] The present invention aims at a spacecraft binary formation, obtains inter-satellite relative distance information based on TLE historical data, uses a cluster analysis method to explore the unconventional evolution behavior of the orbital state, and realizes an orbital maneuver detection method for obtaining spacecraft relative orbital maneuver information under a large amount of orbital data.

[0058] The present invention is a method for detecting relative orbital maneuvers of spacecraft based on cluster analysis, the flow chart of which is as follows: Figure 1 As shown, the following steps are included:

[0059] Step 1: Read the TLE historical data of the main satellite of the spacecraft formation and calculate the instantaneous orbital elements. Use the SGP4 model for recursion to obtain the orbital state when the latitude argument is 0, including:

[0060] Due to the high temporal discretization of TLE data, the spacecraft acquires data at different times every day, and the adjacent time intervals are different, so the orbital data time must be unified. Therefore, the SGP4 model is used to recursively obtain the orbital state of the spacecraft when the latitude argument is 0, in preparation for calculating the relative distance of the formation. In order to ensure the number of samples in the data set, the number of TLE data samples read in the specified time period should be more than 1000 groups. The specific steps are as follows.

[0061] S011: Read the specified time period C Compile the TLE history data of the host star and convert the TLE data in character form into the instantaneous orbit elements of the spacecraft;

[0062] S012: Use the SGP4 model to recursively push forward and backward each group of primary star orbital states by one orbital period, find the moment when the primary star latitude argument is 0, and record the primary star Julian day time set when the primary star latitude argument is 0 With the main star orbit state set in, represents the Julian day time of the primary star of the i-th group, Indicates the orbital state of the primary star of the i-th group, i=1,2,3,...,n C , n C is the number of samples in the main star dataset.

[0063] Step 2: Read the TLE historical data of the spacecraft formation slave satellite and calculate the instantaneous orbital elements. Use the SGP4 model to recursively infer the orbital state at the same time as the master satellite data to achieve dual satellite data time synchronization, including:

[0064] The relative distance of the spacecraft formation cannot be obtained directly, and needs to be obtained by subtracting the absolute orbital states of the two satellites at the same time. Since the TLE data time of different spacecraft is generally different, it is impossible to directly obtain the synchronization information of the two satellites in the spacecraft formation. Therefore, it is necessary to first use the SGP4 model to recursively infer the orbital states of the two satellites in the formation to the same specified time. The specific steps are as follows.

[0065] S021: Read the n times in the same time period as the main star D Compile the satellite TLE historical data, convert the character TLE data into the spacecraft instantaneous orbit elements, and record the satellite Julian day time set With track status set in, Indicates the Julian day time of the pth group from the star, represents the orbital state of the pth group of slave stars, p=1,2,3,...,n D , n D is the number of samples from the star data set;

[0066] S022: Julian Day Time Collection from the Stars Julian day time set with the main star Match and compare, using the main star Julian day time set As a reference, calculate the Julian day time set from the star The elements in the Julian day time of the i-th group of main stars The shortest time difference Record the shortest time difference ΔT of group i i The corresponding orbital state of the slave star is recorded as Get the new slave state set

[0067] S023: According to ΔT i , using the SGP4 model, each new set of slave star orbital states Recursively calculate ΔT forward and backward i +2 hours, find the state set of the slave star when the latitude argument of the master star is 0, recorded as in, It indicates the orbital state of the slave satellite of the i-th group when the latitude argument of the master satellite is 0, realizing the time synchronization of the dual-satellite data.

[0068] Step 3: Calculate the relative distance of the spacecraft formation, perform data denoising and normalization, and obtain a data set, including:

[0069] Set the status of the main star of the spacecraft formation at the same time With the status set from the star The position vector in is subtracted and the absolute value is taken to obtain the relative distance set of the spacecraft Where ΔX (i) Represents the relative distance of the i-th group. Disturbances such as environmental perturbations and measurement errors will cause more noise in the data, so wavelet filtering is first used to reduce data noise to obtain relatively smooth and continuous data.

[0070] Next, the two adjacent data after noise reduction are differentiated to obtain the differential value Among them, δX (i) Indicates the difference value of the ith group. During the natural evolution of the orbit, some difference results may be quite close to 0. This type of data is not conducive to cluster analysis and exceeds the floating point precision of the computer. Therefore, normalization is performed to avoid this problem. The normalized relative distance data set is obtained by using the maximum and minimum normalization. Among them, δx (i) is the normalized relative distance of the i-th group, and the calculation formula is:

[0071]

[0072] The normalization method linearly transforms the original data into the range of [0,1].

[0073] Step 4: Use the silhouette coefficient to determine the number of clusters as the number of orbital maneuver types, including:

[0074] The silhouette coefficient is a way to evaluate the clustering effect. First, select the data set For the 1 / 3 data, set the number of clusters c t =2,...,10, use K-means method to perform cluster analysis on data with different cluster numbers and calculate the corresponding silhouette coefficient. Calculate sample δx (i) The average distance to other samples in the same cluster is a (i) ; Calculate sample δx (i) The minimum value b of the average distance to samples in other different clusters (i) . The silhouette coefficient of the data sample is defined as:

[0075]

[0076] The number of clusters is c tThe silhouette coefficient is the mean of all sample silhouette coefficients,

[0077]

[0078] Select the silhouette coefficient The number of clusters corresponding to the maximum value is the optimal number of clusters c opt , the optimal number of clusters c opt As the number of spacecraft orbital maneuver types.

[0079] Step 5: Use the fuzzy C-means algorithm to perform cluster analysis and obtain clustering results based on the relative distance of the spacecraft orbit to achieve orbital maneuver detection, including:

[0080] The fuzzy C-means algorithm is an optimization classification process that uses membership as the evaluation criterion. Using this algorithm, the relative motion law of spacecraft can be revealed to achieve the detection of orbital maneuvers. For the problem of detecting relative orbital maneuvers of spacecraft, the objective function of clustering optimization is:

[0081]

[0082] in, is the membership matrix, u ki Represents the i-th group of data δx (i) For the membership of the kth cluster, c opt ; is the set of cluster centers, v k represents the kth cluster center; d ki =||δx (i) -v k || represents the i-th group of data δx (i) To the kth cluster center v k Euclidean distance; m is the power index, which is used to control the flexibility of the algorithm. In order to obtain the best clustering of the data set, it is necessary to iteratively solve the solution under the constraint of min(J(U,V)). The fuzzy C-means method has small computational complexity and high efficiency. It can form a fuzzy similarity matrix based on relevant data and directly process the similarity matrix, avoiding repeated calls and scans of the database. The parameter m can be dynamically adjusted as needed, and has good scalability.

[0083] The specific steps of clustering the relative distances of spacecraft orbits using the fuzzy C-means algorithm are as follows:

[0084] S051: Enter the optimal number of clusters c opt , power index m>1, initial membership matrix Membership termination tolerance ε u >0;

[0085] S052: Calculate the cluster center V of the lth iteration (l) Each element in, the kth cluster center for

[0086]

[0087] in is the i-th group of data δx in the l-1th iteration (i) For the membership of the kth cluster;

[0088] S053: Modify the membership matrix U of the lth iteration (l) Each element in the i-th group of data δx (i) For the membership of the kth cluster for

[0089]

[0090] in is the i-th group of data δx in the l-th iteration (i) To the kth cluster center The Euclidean distance of is the i-th group of data δx in the l-th iteration (i) To the jth cluster center Euclidean distance, j = 1, 2, 3, ..., c opt ; and calculate the objective function J of the lth iteration (l) ,

[0091]

[0092] S054: When When l=l+1, stop the iteration and obtain the final membership matrix and cluster center to minimize the objective function. Determine the classification of the sample data according to the values ​​of the elements in the final membership matrix and obtain the maneuver type to which the orbital maneuver belongs; otherwise l=l+1, go to step S052.

[0093] At this point, the relative orbital maneuver detection of spacecraft has been achieved with a large amount of orbital data.

[0094] The detection system according to the above-mentioned spacecraft relative orbit maneuver detection method based on cluster analysis includes:

[0095] The first module is used to read the TLE historical data of the main satellite of the spacecraft formation and calculate the instantaneous orbital elements, and use the SGP4 model for recursion to obtain the orbital state when the latitude argument is 0;

[0096] The second module is used to read the TLE historical data of the spacecraft formation slave satellite and calculate the instantaneous orbital elements, and use the SGP4 model to recursively deduce the orbital state at the same time as the master satellite data to achieve time synchronization of the dual satellite data;

[0097] The third module is used to calculate the relative distance of the spacecraft formation and perform data noise reduction and normalization to obtain a data set;

[0098] The fourth module is used to determine the number of clusters using the silhouette coefficient as the number of orbital maneuver types;

[0099] The fifth module is used to perform cluster analysis using the fuzzy C-means algorithm to obtain clustering results based on the relative distance of the spacecraft orbits and realize orbital maneuver detection.

[0100] Embodiment 1:

[0101] 1000 sets of TLE data from the long-term control of the A and B satellites of the YAOGAN-9 formation were selected. With A as the master satellite and B as the slave satellite, the relative distances were calculated and cluster analysis was performed to obtain their orbit keeping strategy.

[0102] The method of the present invention is used to read the historical TLE data of the A and B satellites of the "YAOGAN-9" formation, and the SGP4 model is used to recursively synchronize the data time, calculate the relative distance and perform data processing to obtain a data set. Then, the silhouette coefficient under different cluster numbers is calculated, such as Figure 2 As shown, the optimal number of clusters c is obtained opt =2. Then, the fuzzy C-means algorithm is used for cluster analysis, and the optimal number of clusters c is input. opt , power index m = 2, membership termination tolerance ε u =10 -6 , iteratively calculate until the objective function is minimized, and obtain the clustering result based on the relative distance of the spacecraft orbit, such as Figure 3 As shown, orbital maneuver detection is achieved.

[0103] Parts of the present invention that are not described in detail belong to the well-known technology for those skilled in the art.

Claims

1. A method for detecting relative orbital maneuvers of spacecraft based on cluster analysis, characterized in that: include: Read the TLE historical data of the main satellite of the spacecraft formation and calculate the instantaneous orbital elements, and use the SGP4 model for recursion to obtain the orbital state when the latitude argument is 0; Read the TLE historical data of the spacecraft formation slave satellite and calculate the instantaneous orbital elements, use the SGP4 model to recursively infer the orbital state at the same time as the master satellite data, and achieve time synchronization of dual satellite data; Calculate the relative distance of the spacecraft formation, perform data denoising and normalization, and obtain a data set; The silhouette coefficient is used to determine the optimal number of clusters as the number of orbital maneuver types; The method of determining the optimal number of clusters by using the silhouette coefficient as the number of orbital maneuver types includes: Selecting Datasets For the 1 / 3 data, set the number of clusters c t =2,...,10, use K-means method to perform cluster analysis on data with different cluster numbers and calculate the corresponding silhouette coefficient; calculate sample δx (i) The average distance to other samples in the same cluster is a (i) ; Calculate sample δx (i) The minimum value b of the average distance to samples in other different clusters (i) ; The silhouette coefficient of the data sample is defined as: The number of clusters c t The silhouette coefficient is the mean of the silhouette coefficients of all samples, Select the silhouette coefficient The number of clusters corresponding to the maximum value is taken as the optimal number of clusters c opt , the optimal number of clusters c opt as the number of spacecraft orbital maneuver types; Cluster analysis is performed using the fuzzy C-means algorithm to obtain clustering results based on the relative distance of the spacecraft orbits, thereby achieving orbital maneuver detection.

2. The method for detecting relative orbital maneuvers of a spacecraft based on cluster analysis according to claim 1, characterized in that: The process of reading the TLE historical data of the main satellite of the spacecraft formation and calculating the instantaneous orbital elements, and recursively using the SGP4 model to obtain the orbital state at the moment when the latitude argument is 0 includes: Read the specified time period n C Compile the TLE history data of the host star and convert the TLE data in character form into the instantaneous orbit elements of the spacecraft; The SGP4 model is used to recurse the orbital state of each group of primary stars forward and backward by one orbital period, find the moment when the primary star latitude argument is 0, and record the primary star Julian day time set when the primary star latitude argument is 0. With the main star orbit state set in, represents the Julian day time of the primary star of the i-th group, Indicates the orbital state of the primary star in the i-th group; i=1,2,3,...,n C ;n C is the number of samples in the main star dataset.

3. The method for detecting relative orbital maneuvers of spacecraft based on cluster analysis according to claim 1, characterized in that: The method of reading the TLE historical data of the slave satellite of the spacecraft formation and calculating the instantaneous orbital elements, and recursively calculating the orbital state at the same time as the master satellite data using the SGP4 model to achieve dual-satellite data time synchronization includes: Read the same time period as the main star n D The satellite TLE historical data is converted into the instantaneous orbital elements of the spacecraft, and the Julian day time set of the satellite is recorded. With track status set in, Indicates the Julian day time of the pth group from the star, Indicates the orbital state of the pth group of slave stars; p = 1, 2, 3, ..., n D ;n D is the number of samples from the star data set; Set the Julian date from the star Julian day time set with the main star Match and compare, using the main star Julian day time set As a reference, calculate the Julian day time set from the star The elements in the Julian day time of the i-th group of main stars The shortest time difference Record the shortest time difference ΔT of group i i The corresponding orbital state of the slave star Get the new slave state set According to the shortest time difference ΔT i , using the SGP4 model, each new set of slave star orbital states Recursively calculate ΔT forward and backward i +2 hours, find the slave star status set when the master star's latitude argument is 0 in, It indicates the orbital state of the slave satellite of the i-th group when the latitude argument of the master satellite is 0, realizing the time synchronization of the dual-satellite data.

4. The method for detecting relative orbital maneuvers of a spacecraft based on cluster analysis according to claim 1, characterized in that: The relative distance of the spacecraft formation is calculated, and data noise reduction and normalization are performed to obtain a data set, including: Set the status of the main star of the spacecraft formation at the same time With the status set from the star The position vector in is subtracted and the absolute value is taken to obtain the relative distance set of the spacecraft Where ΔX (i) represents the relative distance of the i-th group; Wavelet filtering is used to reduce data noise and obtain relatively smooth and continuous data; the difference between two adjacent data after noise reduction is obtained to obtain the difference value set. Among them, δX (i) represents the difference value of the i-th group; The normalized relative distance data set is obtained by using the maximum and minimum normalization Among them, δx (i) is the normalized relative distance of the i-th group.

5. The method for detecting relative orbital maneuvers of spacecraft based on cluster analysis according to claim 4, characterized in that: δx (i) The calculation formula is:

6. The method for detecting relative orbital maneuvers of spacecraft based on cluster analysis according to claim 1, characterized in that: In the fuzzy C-means algorithm, the objective function of fuzzy C-means clustering optimization is: in, is the membership matrix, u ki Represents the i-th group of data δx (i) For the membership of the kth cluster, is the set of cluster centers, v k represents the kth cluster center; d ki =||δx (i) -v k || represents the i-th group of data δx (i) To the kth cluster center v k Euclidean distance; m is the power exponent, which is used to control the flexibility of the algorithm.

7. The method for detecting relative orbital maneuvers of spacecraft based on cluster analysis according to claim 6, characterized in that: The clustering analysis using the fuzzy C-means algorithm to obtain the clustering results based on the relative distance of the spacecraft orbits includes: Iteratively solve the solution under the min(J(U,V)) constraint to obtain the best clustering of the data set as the clustering result based on the relative distance of the spacecraft orbits, as follows: S051: Enter the optimal number of clusters c opt , power index m>1, initial membership matrix Membership termination tolerance ε u >0; S052: Calculate the cluster center V of the lth iteration (l) The elements in: in, is the cluster center V of the lth iteration (l) The kth cluster center in ; is the i-th group of data δx in the l-1th iteration (i) For the membership of the kth cluster; S053: Modify the membership matrix U of the lth iteration (l) The elements in: in, is the membership matrix U of the lth iteration (l) The i-th group of data δx (i) For the membership of the kth cluster, is the i-th group of data δx in the l-th iteration (i) To the kth cluster center The Euclidean distance of is the i-th group of data δx in the l-th iteration (i) To the jth cluster center Euclidean distance, j = 1, 2, 3, ..., c opt ; And calculate the objective function J of the lth iteration (l) , S054: When When l=l+1, stop the iteration and obtain the final membership matrix and cluster center to minimize the objective function. Determine the classification of the sample data according to the values ​​of the elements in the final membership matrix and obtain the maneuver type to which the orbital maneuver belongs; otherwise l=l+1, go to step S052.

8. The method for detecting relative orbital maneuvers of spacecraft based on cluster analysis according to claim 7, characterized in that: In S051, uniformly distributed random numbers on [0,1] are used as the initial membership matrix U (0) , let the initial number of iterations l = 1.

9. The detection system of the spacecraft relative orbit maneuver detection method based on cluster analysis according to any one of claims 1 to 8, characterized in that: include: The first module is used to read the TLE historical data of the main satellite of the spacecraft formation and calculate the instantaneous orbital elements, and use the SGP4 model for recursion to obtain the orbital state when the latitude argument is 0; The second module is used to read the TLE historical data of the spacecraft formation slave satellite and calculate the instantaneous orbital elements, and use the SGP4 model to recursively deduce the orbital state at the same time as the master satellite data to achieve time synchronization of the dual satellite data; The third module is used to calculate the relative distance of the spacecraft formation and perform data noise reduction and normalization to obtain a data set; The fourth module is used to determine the number of clusters using the silhouette coefficient as the number of orbital maneuver types; The fifth module is used to perform cluster analysis using the fuzzy C-means algorithm to obtain clustering results based on the relative distance of the spacecraft orbits and realize orbital maneuver detection.

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