Star cluster cooperative space target searching and orbit determination method
By employing a cluster-based collaborative space target search and orbit determination method, and utilizing the collaborative work of satellite nodes with large and narrow fields of view, combined with prior guidance data and cross-line-of-sight networks, the problem of single satellite acquisition and orbit determination under large space uncertainty targets was solved, achieving efficient target acquisition and accurate space orbit determination.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI TAIYI MICRO-SPACE TECHNOLOGY CO LTD
- Filing Date
- 2026-04-28
- Publication Date
- 2026-05-29
AI Technical Summary
When facing targets with significant spatial uncertainty, a single optical satellite struggles to balance wide-area search with high-precision target locking. Furthermore, the lack of depth-oriented observation data results in a low probability of target acquisition. In existing multi-satellite collaborative schemes, data transmission delays between satellite nodes lead to guidance deviations.
Using a cluster-based collaborative approach, the ground computing center generates prior guidance data. The cluster schedules large-field-of-view satellite nodes for gridded scanning and dimensionality reduction. Narrow-field-of-view satellite nodes combine prior distance error variance and geocentric inertial coordinate system for benchmark alignment and state extrapolation, generating an extrapolated three-dimensional error ellipsoid. State convergence is achieved through a cross-line-of-view network, ultimately realizing the physical locking and orbit determination of the target.
It has achieved effective acquisition and high-precision orbit determination of space targets, overcome the problems of narrow field of view and deep blind zone of single optical satellites, and ensured the accuracy of cluster cooperative search and orbit determination.
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Figure CN122108169A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of space target detection technology, specifically a method for space target search and orbit determination using a cluster-based approach. Background Technology
[0002] The search and orbit determination of space targets is a crucial task in the aerospace field, and space-based optical satellites are commonly used for observation. However, when dealing with targets with significant spatial uncertainties, the limitations of a single optical satellite are imposed by its physical performance. Wide-field-of-view optical payloads offer broad coverage in a single operation but have lower measurement accuracy; narrow-field-of-view optical payloads offer high measurement accuracy but have a narrow physical field of view, making it difficult to achieve effective coverage within a large range of target positional errors. Furthermore, the limited search range of a single payload makes it difficult to simultaneously meet the requirements of wide-area searching and high-precision target acquisition, resulting in a low probability of target acquisition.
[0003] Meanwhile, the optical sensors on a single satellite can only acquire two-dimensional line-of-sight angle measurement data of the target, and cannot directly measure the target's distance and depth information in the line-of-sight direction. Due to the lack of depth direction observation data, the target is unobservable in this direction. Relying solely on the two-dimensional angle measurement data of a single satellite is insufficient to achieve convergence of the three-dimensional state in space, making it difficult for existing schemes to independently complete space orbit determination.
[0004] Existing technologies enhance detection capabilities through multi-satellite collaborative observation. However, during multi-satellite collaborative guidance, cross-link data transmission and status resolution between satellite nodes consume time. Since space targets are in high-speed motion, directly using received historical observation data to guide narrow-field-of-view payloads for maneuvering and tracking can lead to uncompensated communication and processing time delays, causing spatial positional deviations and resulting in missed targets. This compromises the accuracy of inter-satellite collaborative search and orbit determination. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention provides a cluster-based method for space target search and orbit determination, which solves the problem that a single optical satellite, when facing targets with high spatial uncertainty, is limited by its narrow physical field of view and lack of observation depth information, making it difficult to achieve target acquisition and space orbit determination.
[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for space target search and orbit determination using a cluster-based approach, comprising the following steps:
[0007] The ground computing center generates prior guidance data for the space target and uploads it to the star cluster;
[0008] The cluster scheduling large field-of-view satellite nodes perform sky search based on prior guidance data, and extract the two-dimensional observation error covariance of space targets through dimensionality reduction and shift overlay processing;
[0009] The wide field-of-view satellite node will send inter-satellite data frames containing two-dimensional observation error covariance and instantaneous pose to the narrow field-of-view satellite node;
[0010] Narrow field-of-view satellite nodes receive inter-satellite data frames, combine prior distance error variance with geocentric inertial coordinate system to perform reference alignment and state extrapolation, and generate extrapolated three-dimensional error ellipsoids;
[0011] Narrow field-of-view satellite nodes generate line-of-sight maneuver trajectories based on extrapolated three-dimensional error ellipsoids to obtain physical locks on space targets, and the star clusters perform state convergence based on cross-line-of-sight networks to complete the final cooperative orbit determination.
[0012] Preferably, the specific processing steps for the ground computing center to generate prior guidance data for space targets and inject it uplink into the star cluster include:
[0013] Historical observation data of space targets are acquired. After time-stamp synchronization and matching of historical observation data including radar ranging sequences and optical angle measurement sequences, orbit recursion is performed based on the orbit dynamics model to calculate and generate the nominal spatial state parameters and three-dimensional state error covariance matrix of the target at the predicted observation time.
[0014] The nominal spatial state parameters and the three-dimensional state error covariance matrix are combined to form prior guidance data, which is then injected into the star cluster.
[0015] Preferably, before the cluster scheduling of large field-of-view satellite nodes performs a sky search based on prior guidance data, the method further includes a step of extracting the prior distance error variance, specifically including:
[0016] The prior guidance data is analyzed, and the extracted three-dimensional state error covariance matrix is decomposed into eigenvalues and transformed into an initial error ellipsoid physical model.
[0017] Compare the expansion geometric scale of the initial error ellipsoid physical model on the lateral observation plane or radial depth plane with the single-star field-of-view coverage limit parameter. When it is determined that the expansion geometric scale is greater than the single-star field-of-view coverage limit parameter, the cluster cooperative search mission planning is triggered.
[0018] In response to the constellation collaborative search mission planning, a local line-of-sight coordinate system is established, and the three-dimensional state error covariance matrix is projected into this coordinate system. The error component corresponding to the target line-of-sight depth after projection is extracted, defined as the prior distance error variance, and written into the shared state library. This step achieves spatial dimension decoupling, converting the three-dimensional position error into a single distance error, compensating for the depth deficiency of pure angle-measuring optical sensors.
[0019] Preferably, the specific steps for cluster scheduling of large field-of-view satellite nodes to perform sky search based on prior guidance data include:
[0020] Extract the position error probability density distribution function from the prior guidance data, and perform spatial discretization grid segmentation on the uncertain sky region that exceeds the single-star field of view coverage limit parameter. After grid segmentation, allocate independent staring and step-scan task sequences to drive large field of view satellite nodes to perform gridded parallel search.
[0021] During the gridded parallel search process, optical image sequences are continuously acquired. Based on the principle of optical collinearity equation, a nonlinear observation equation is constructed from the local three-dimensional space to the two-dimensional optical focal plane. The Jacobian matrix is obtained by solving the partial derivatives of the nonlinear observation equation.
[0022] By using the Jacobian matrix, the velocity error envelope in 3D space is reduced in dimension and mapped to a 2D physical focal plane, generating an analytical search boundary for pixel-level angular velocity errors. This process transforms the search blind zone in 3D space into a pixel traversal boundary on the focal plane, avoiding the increased computational load caused by exhaustive 3D velocity enumeration.
[0023] Preferably, the specific steps for extracting the two-dimensional observation error covariance of space targets through dimensionality reduction and shift stacking processing include:
[0024] Within the analytical search boundary, a hierarchical multi-hypothesis shift and superposition algorithm is used to generate a hypothetical velocity vector. Pixel-level shift and gray-level superposition operations are performed on the continuously acquired image sequence. The signal-to-noise ratio value is obtained by calculating the ratio of the mean gray level of the target signal pixel to the standard deviation of the gray level of the local background region.
[0025] When the signal-to-noise ratio value is determined to be greater than the low detection threshold, the corresponding candidate pixel position vector set is extracted, and the weighted scattering center is calculated and generated using the weighted scattering center formula.
[0026] Using the focal plane weighted scattering center as the calculation benchmark, the two-dimensional observation covariance reconstruction formula is used to calculate, generate and extract the two-dimensional observation error covariance;
[0027] The low detection threshold is set to a feature value that is 3 to 5 times higher than the variance of the image background thermal noise distribution. This process characterizes the energy dispersion of the optical sensor through the signal-to-noise ratio distribution, and completes the quantitative reconstruction of local observation errors.
[0028] Preferably, the specific steps for a large field-of-view satellite node to send inter-satellite data frames containing two-dimensional observation error covariance and instantaneous pose to a narrow field-of-view satellite node include:
[0029] The reference timestamp of the target imaging exposure moment is obtained by the satellite platform time, and the spatial orbit state parameters and three-dimensional attitude parameters of the large field of view satellite node at the moment of imaging exposure are simultaneously latched. The spatial orbit state parameters and three-dimensional attitude parameters are uniformly reduced to the J2000 geocentric inertial coordinate system to generate instantaneous pose.
[0030] The previously generated focal plane weighted scattering center, the extracted two-dimensional observation error covariance, the reference timestamp, and the instantaneous pose are structurally combined and encapsulated to generate inter-satellite data frames.
[0031] An inter-satellite communication link is established to directionally transmit inter-satellite data frames to narrow field-of-view satellite nodes. A combination of various parameter structures provides a reference benchmark for the receiver to perform space geometry inversion.
[0032] Preferably, in the process of narrow field-of-view satellite nodes receiving inter-satellite data frames and performing datum alignment and state extrapolation by combining prior distance error variance with the geocentric inertial coordinate system to generate an extrapolated three-dimensional error ellipsoid, the specific steps for performing datum alignment include:
[0033] Analyze inter-satellite data frames to extract the pixel centroid coordinates of the target on the two-dimensional focal plane, the two-dimensional observation error covariance, and the reference timestamp;
[0034] Access the shared state library and retrieve the saved prior distance error variance;
[0035] In the local polar coordinate system, the three-dimensional covariance of the local polar coordinate system is constructed using the formula. The extracted two-dimensional observation error covariance and the retrieved prior distance error variance are reconstructed in dimension, and the three-dimensional covariance matrix of the local polar coordinate system is calculated and generated.
[0036] A nonlinear spatial mapping function from the local polar coordinate system to the J2000 geocentric inertial coordinate system is constructed, and the first-order partial derivative is obtained to obtain the coordinate system transformation Jacobian matrix. The spatial reference alignment mapping formula is used to calculate the three-dimensional covariance matrix of the local polar coordinate system, and the initial three-dimensional covariance matrix of the geocentric inertial coordinate system is obtained and output. This step utilizes the polar coordinate system to achieve orthogonal fusion of angle measurement and ranging errors, isolates cross-coupling components, and overcomes the depth blind zone of optical loads.
[0037] Preferably, in the process of receiving inter-satellite data frames by a narrow field-of-view satellite node, combining the prior distance error variance with the geocentric inertial coordinate system to perform reference alignment and state extrapolation, and generating the extrapolated three-dimensional error ellipsoid, the specific steps for performing state extrapolation and generating the extrapolated three-dimensional error ellipsoid include:
[0038] The current target timestamp is obtained using the onboard clock, and the time delay span is extracted by differential operation with the extracted reference timestamp. The dynamic equation containing the perturbation terms of Earth's non-spherical gravity and atmospheric drag is constructed and linearized to obtain the state transition matrix.
[0039] Using the error ellipsoid dynamic extrapolation formula and based on the state transition matrix, the initial three-dimensional covariance matrix of the geocentric inertial coordinate system is dynamically extrapolated and calculated to generate the extrapolated three-dimensional error covariance matrix at the current execution time.
[0040] The eigenvectors and eigenvalues of the extrapolated 3D error covariance matrix are mapped to 3D confidence intervals in geometric space, thereby generating and outputting the extrapolated 3D error ellipsoid. The dynamic state extrapolation process compensates for the time delay span of communication resolution between nodes, preventing narrow field-of-view load maneuvering guidance from missing the target.
[0041] Preferably, the specific steps for a narrow field-of-view satellite node to generate a line-of-sight maneuver trajectory based on an extrapolated three-dimensional error ellipsoid to obtain a physical lock on a space target include:
[0042] The extrapolated three-dimensional error ellipsoid is orthogonally projected onto the two-dimensional physical focal plane along the current observation line direction using the view plane covariance projection formula to calculate the two-dimensional error covariance matrix of the view plane. The major and minor semi-axis dimensions and principal axis rotation angle are extracted by eigenvalue decomposition to reconstruct the two-dimensional search error envelope.
[0043] The scanning traversal trajectory that adaptively generates and covers the two-dimensional search error envelope by combining the instantaneous effective field of view size is used as the line-of-sight maneuver trajectory to drive the entire satellite to perform nonlinear line-of-sight maneuvers;
[0044] During the scanning traversal trajectory maneuver, the signal-to-noise ratio and centroid pixel jitter variance are combined for judgment. When the signal-to-noise ratio is higher than the signal-to-noise ratio set threshold and the centroid jitter variance of multiple consecutive frames is lower than the pixel-level convergence threshold, it is determined that physical lock-on is obtained for the spatial target.
[0045] The signal-to-noise ratio threshold is set to a value of 5 to 6 based on the statistical characteristics of background star noise, and the pixel-level convergence threshold is set to a variance boundary value of 0.1 to 0.5 pixels.
[0046] Preferably, the specific steps for star clusters to achieve final cooperative orbit determination through state convergence based on a cross-line-of-sight network include:
[0047] Multiple nodes distributed in different orbital planes in the scheduling cluster synchronously track and aim at space targets that are physically locked. The spatiotemporal reference is unified by a polynomial interpolation algorithm, and a heterogeneous network topology with multiple points of intersection is formed in the space physical configuration as an intersecting line-of-sight network.
[0048] Collect multi-source observation elements within the cross-line-of-sight network, calculate the line-of-sight direction residual vector using the cross-line-of-sight observation residual formula, and suspend residual calculation to trigger an avoidance mechanism when the relative spatial distance norm is less than the preset safety collision avoidance threshold, thereby obtaining multi-source residual feedback.
[0049] Based on multi-source residual feedback, the extended Kalman filter algorithm is used to perform closed-loop iterative correction of the target's three-dimensional position and velocity state, thereby achieving state convergence and completing the final collaborative orbit determination.
[0050] The safety collision avoidance threshold is set at a distance limit of 100 to 150 meters. This step utilizes multi-node physical convergence to eliminate the unobservability of a single star in the depth direction, thereby enabling the determination of the target's orbit.
[0051] This invention provides a method for space target search and orbit determination using a cluster-based cooperative system. It offers the following advantages:
[0052] 1. This invention utilizes cluster-based collaborative scheduling. First, large-field-of-view satellite nodes perform gridded scanning and dimensionality-reduced shifting and overlay processing based on prior guidance data to extract the two-dimensional observation error covariance of the target. Then, narrow-field-of-view satellite nodes are guided to generate line-of-sight maneuver trajectories based on this covariance to achieve physical lock-on. This scheme combines the physical characteristics of optical payloads with different fields of view, overcoming the limitation of a single optical satellite's narrow physical field of view when facing targets with high spatial uncertainty. It solves the problem of limited search range for a single payload and achieves effective target acquisition.
[0053] 2. This invention extracts the prior distance error variance, reconstructs its dimension in a local polar coordinate system by combining it with the two-dimensional observation error covariance, and schedules multiple satellite nodes distributed in different orbital planes to form a cross-line-of-sight network for synchronous target tracking and state convergence. This process utilizes the spatial geometric intersection of multiple nodes and orthogonal error fusion to compensate for the lack of observation depth information in pure optical sensors, eliminates the unobservability of the target in the depth direction, and solves the problem of the difficulty of achieving space orbit determination with a single optical satellite.
[0054] 3. After receiving inter-satellite data frames containing timestamps and instantaneous poses, this invention uses the onboard clock to obtain the time delay and performs state extrapolation calculations based on the dynamic equations containing perturbation terms to generate an extrapolated three-dimensional error ellipsoid for the current execution time. This state extrapolation process compensates for the inherent time delay in communication transmission and data parsing between satellite nodes, preventing narrow-field-of-view satellites from missing their targets due to time differences during line-of-sight maneuvers, thus ensuring the accuracy of cluster cooperative search and orbit determination guidance. Attached Figure Description
[0055] Figure 1 This is a diagram illustrating the information flow and functional logic of the star cluster collaborative system of the present invention.
[0056] Figure 2 This is a flowchart illustrating the overall workflow of the star cluster cooperative space target search and orbit determination method of the present invention;
[0057] Figure 3 This is a convergence curve of three-dimensional position and orbit determination error according to an embodiment of the present invention;
[0058] Figure 4 This is a comparison chart of target capture success rates according to an embodiment of the present invention. Detailed Implementation
[0059] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0060] See attached document Figure 1 This invention provides a cluster-based method for space target search and orbit determination, which relies on a cluster-based cooperative system. The cluster-based cooperative system includes a ground-based computing center and clusters of stars operating in space orbit.
[0061] The constellation comprises satellite nodes with varying detection capabilities, specifically divided into wide-field-of-view (HFOP) and narrow-field-of-view (NFR) satellite nodes. HFOP satellite nodes carry wide-field-of-view optical payloads, inter-satellite communication terminals, attitude actuators, and onboard processing units, including an image processing module. NFR satellite nodes carry narrow-field-of-view optical payloads, inter-satellite communication terminals, attitude actuators, and onboard processing units, including a dynamics calculation module. The field of view of the wide-field-of-view optical payload is larger than that of the narrow-field-of-view optical payload, and the spatial resolution of the narrow-field-of-view optical payload is higher than that of the wide-field-of-view optical payload.
[0062] The ground computing center establishes a satellite-to-ground communication link with the satellite cluster to inject data. Wide field-of-view (WFP) and narrow field-of-view (NFP) satellite nodes establish a cross-link network topology through inter-satellite communication terminals. Within the WFP satellite nodes, the onboard processing unit communicates with the WFP optical payload, the inter-satellite communication terminal, and the attitude actuators. Within the NFP satellite nodes, the onboard processing unit communicates with the NFP optical payload, the inter-satellite communication terminal, and the attitude actuators. The image processing module receives image sequences acquired by the WFP optical payload and performs calculations; the dynamics calculation module processes the received data frames to generate maneuver commands; and the attitude actuators receive control commands to adjust their spatial pointing.
[0063] See attached document Figure 2 A cluster-cooperative method for space target search and orbit determination includes the following steps:
[0064] S1, the ground computing center generates prior guidance data for the space target and injects it into the star cluster;
[0065] S2, the star cluster scheduling large field-of-view satellite nodes perform sky search based on prior guidance data, and extract the two-dimensional observation error covariance of space targets through dimensionality reduction and shift overlay processing;
[0066] S3, the large field-of-view satellite node will send the two-dimensional observation error covariance and instantaneous pose to the narrow field-of-view satellite node through inter-satellite data frames;
[0067] S4, the narrow field-of-view satellite node receives inter-satellite data frames, combines the prior distance error variance with the geocentric inertial coordinate system to perform reference alignment and state extrapolation, and generates an extrapolated three-dimensional error ellipsoid;
[0068] S5, narrow field-of-view satellite nodes generate line-of-sight maneuver trajectories based on extrapolated three-dimensional error ellipsoids and lock onto space targets. The star cluster performs state convergence based on the cross-line-of-sight network to complete the final cooperative orbit determination.
[0069] The following paragraphs will explain in detail the specific processing mechanisms and implementation principles of each of the above steps.
[0070] The specific processing sub-steps of step S1 are as follows:
[0071] S101, the ground computing center acquires historical observation data including radar ranging and optical angle measurement sequences. After timestamp synchronization and matching, it uses an orbital dynamics model (such as the Gauss-Jackson numerical integration algorithm) to perform orbital recursion, calculating and generating the nominal spatial state parameters and three-dimensional state error covariance matrix of the target at the predicted observation time. Together, they constitute the prior guidance data and are sent uplink to the star cluster.
[0072] S102, a large field-of-view satellite node receives prior guidance data and performs analysis on the three-dimensional state error covariance matrix. Eigenvalue decomposition is performed to transform it into an initial error ellipsoidal physical model, and its broadening geometric scales on the lateral observation plane and radial depth plane are calculated. If any broadening geometric scale is greater than the single-star field-of-view coverage limit parameter (which introduces a preset boundary coefficient ranging from 0.8 to 0.9), the cluster cooperative search mission planning is triggered.
[0073] S103, a local line-of-sight coordinate system is established for the large field-of-sight satellite node. After verification that the determinant of the orthogonal transformation matrix is non-zero, the three-dimensional state error covariance matrix is... Project the data onto the local view coordinate system; extract the diagonal elements of the projected covariance matrix corresponding to the target view direction, and define them as the prior distance error variance. And write it into the shared state library.
[0074] The specific sub-steps of step S2 are as follows:
[0075] S201: After receiving the trigger command, the large field-of-view satellite node extracts the position error probability density distribution function from the prior guidance data and performs spatial discretization grid segmentation on the uncertain sky region exceeding the single-star field-of-view coverage limit parameter. The physical boundary size of the grid is slightly smaller than the physical field of view of the large field-of-view optical payload, and the overlap rate of adjacent grids is set to 10% to 15%. After grid segmentation, the onboard processing unit allocates independent staring and step-scan task sequences to drive the large field-of-view satellite node to perform gridded parallel search.
[0076] S202 is a large field-of-view optical payload that continuously acquires optical image sequences of the target sky region. The image processing module constructs a nonlinear observation equation from the local three-dimensional space to the two-dimensional optical focal plane based on the principle of optical collinearity equations, and obtains the Jacobian matrix by taking its partial derivative.
[0077] S203, based on the pixel-level angular velocity error search boundary on the aforementioned two-dimensional plane, the image processing module employs a hierarchical multi-hypothesis shift and superposition algorithm to detect targets in continuously acquired image sequences. The core technical objective of this algorithm is to improve the signal-to-noise ratio (SNR) of weak targets through inter-frame energy accumulation. Within this two-dimensional analytical search boundary, the image processing module generates a first-level coarse-grained velocity hypothesis set and performs pixel-level shift and gray-level superposition operations on the image sequence according to each hypothetical velocity vector. For the composite image after shift and superposition, the image processing module obtains the SNR value of each local region by calculating the ratio of the mean gray-level of the target signal pixels to the standard deviation of the gray-level of the local background region. The system presets two judgment thresholds: a low detection threshold and a high confirmation threshold.
[0078] In this embodiment, the low detection threshold is set to be 3 to 5 times higher than the variance of the thermal noise distribution in the image background. This range is selected based on the lower confidence limit of statistical significance under Gaussian white noise background. The high confirmation threshold is dynamically weighted and generated by combining the stray light dispersion variance of the current spatial background with the cumulative gain over multiple frames. When the signal-to-noise ratio of a candidate region exceeds the low detection threshold, the image processing module triggers a secondary shift and superposition of the second-level fine-grained velocity hypothesis set for that local neighborhood. When the highest signal-to-noise ratio in that local neighborhood breaks through the dynamically generated high confirmation threshold, and the energy peak maintains morphological convergence over multiple consecutive frames of observation, the image processing module determines that the spatial target has been initially captured based on this multi-dimensional feature weighting logic.
[0079] S204, to quantify observation uncertainty, the image processing module reconstructs the observation error parameters using the distribution of the intermediate discrete hypothesis set that exceeds the low detection threshold. The image processing module extracts the set of candidate pixel position vectors whose corresponding signal-to-noise ratio is greater than the low detection threshold. The weighted scatter center formula is used to calculate the focal plane weighted scatter center, which is:
[0080] ;
[0081] in, Indicates the focal plane weighted scattering center; This represents the total number of valid hypothesis vectors in the set of candidate pixel location vectors; Indicates the vector index number; Indicates the first One effective pixel position vector; Indicates the relationship with the first Signal-to-noise ratio weighting coefficients corresponding to each effective pixel position vector; Indicates the vector index number From 1 to Perform a summation operation; This represents the sum of all signal-to-noise ratio weighting coefficients.
[0082] The image processing module has built-in division anti-crash logic here. If it determines... If the calculated value approaches zero, meaning there is no candidate target source with basic confidence in the current field of view, then the update calculation of the current pose coordinates is stopped and the process waits for the next scan cycle.
[0083] Based on the obtained focal plane weighted scatter center, the image processing module calculates the two-dimensional observation error covariance using the two-dimensional observation covariance reconstruction formula. The two-dimensional observation covariance reconstruction formula is as follows:
[0084] ;
[0085] in, It represents the two-dimensional observation error covariance, which mathematically characterizes the local observation confidence and energy dispersion characteristics of a single-star pure goniometric optical sensor on the current focusing plane; Indicates the first The deviation vector between the effective pixel position vector and the weighted scattering center of the focal plane; The transpose matrix of the deviation vector; This represents the self-multiplication outer product of the deviation vector and its transpose matrix. This self-multiplication outer product represents the local structural error of a single assumed vector. After weighted summation and normalization using all signal-to-noise ratio weighting coefficients, the final two-dimensional observation error covariance is obtained.
[0086] The specific processing sub-steps of step S3 are as follows:
[0087] S301, the large field-of-view satellite node obtains the reference timestamp of the target imaging exposure moment through the onboard atomic clock, and simultaneously latches the spatial orbital state parameters and three-dimensional attitude parameters of the large field-of-view satellite node at the moment of imaging exposure. All parameters are uniformly reduced to the J2000 geocentric inertial coordinate system to generate instantaneous pose.
[0088] S302, the large field-of-view satellite node uses a linear interpolation algorithm to perform timestamp matching on the data, and combines the focal plane weighted scattering center, two-dimensional observation error covariance, reference timestamp, and instantaneous pose reduced to the J2000 coordinate system in a structured way, adds a synchronization header, virtual channel identifier and cyclic redundancy check code, and encapsulates it to generate inter-satellite data frames.
[0089] S303: After data packet encapsulation, the large field-of-view satellite node activates its internal communication connection to establish an inter-satellite communication link with the inter-satellite communication terminal mounted on the narrow field-of-view satellite node. Before data frame transmission, the inter-satellite communication terminal performs a multi-dimensional link quality assessment based on the received signal strength indicator and the channel bit error rate. When this comprehensive assessment index is better than a preset safe communication threshold, data transmission is activated. Here, the safe communication threshold is dynamically calculated based on the current space electromagnetic interference background and inter-satellite distance, and its upper limit for the channel bit error rate is typically set to 10. -6 This avoids the risk of packet loss due to relying solely on a single signal strength for judgment. Based on the established network topology link, the large field-of-view satellite node directionally transmits the inter-satellite data frame to the narrow field-of-view satellite node. This transmission mechanism completes the cross-satellite flow of target information at the physical level, providing a measured data source with a unified spatiotemporal reference for subsequent benchmark alignment and state extrapolation performed by the narrow field-of-view satellite node.
[0090] The specific processing sub-steps of step S4 are as follows:
[0091] S401, in this embodiment, the narrow field-of-view satellite node receives inter-satellite data frames from the wide field-of-view satellite node via its inter-satellite communication terminal. The onboard processing unit inside the narrow field-of-view satellite node parses the inter-satellite data frames, extracting the pixel centroid coordinates of the space target on the two-dimensional focal plane, the two-dimensional observation error covariance, and the reference timestamp. Since single-satellite optical observations lack depth information, the onboard processing unit accesses the cluster's shared state library and retrieves the prior distance error variance extracted and written during the prior mission phase.
[0092] To mathematically complete the three-dimensional spatial uncertainty of the target, based on the general principle of orthogonal fusion of multi-source errors, the dynamics solution module configured within the onboard processing unit reconstructs the dimensions of the two-dimensional observation error covariance and the prior distance error variance in a local polar coordinate system. Choosing a local polar coordinate system for fusion effectively isolates the lateral angle measurement error and radial ranging error of the optical sensor in mathematical derivation, avoiding the introduction of nonlinear cross-coupling components from direct splicing in a Cartesian coordinate system. As a preferred method, the dynamics solution module uses the local polar coordinate system three-dimensional covariance construction formula to calculate the local polar coordinate system three-dimensional covariance matrix. The local polar coordinate system three-dimensional covariance construction formula is as follows:
[0093] ;
[0094] in, It represents the three-dimensional covariance matrix of the local polar coordinate system, and its physical meaning is the expression of the spatial uncertainty including the combined errors of angle measurement and distance measurement in the local observation space with the large field of view optical load as the origin; This represents the two-dimensional observation error covariance extracted from the data frame; Represents the variance of the prior distance error retrieved; matrix elements This represents the cross-correlation term of cross-dimensional errors. Since it is assumed that the pure angle measurement error and the prior distance measurement error are independent, they are treated as zero vectors or zero matrices to match the alignment requirements of the dimensions. This dimensionality upscaling operation effectively overcomes the depth blind zone of a single optical sensor and provides underlying data support for subsequent three-dimensional spatial geometric intersection.
[0095] S402, after completing the covariance dimensionality increase in the local polar coordinate system, the dynamics solution module performs spatial reference alignment by transforming to the common geocentric inertial coordinate system. Based on the technical requirement of multi-satellite collaborative unified spatial reference, the dynamics solution module constructs a nonlinear spatial mapping function from the local polar coordinate system to the J2000 geocentric inertial coordinate system. This nonlinear spatial mapping function takes the target's azimuth, pitch angle, and prior range values as input, and outputs the target's three-dimensional position coordinates in the J2000 coordinate system through the geometric transformation relationship from spherical coordinates to rectangular coordinates.
[0096] By obtaining the first-order partial derivative of the nonlinear spatial mapping function, the dynamics solution module obtains the corresponding coordinate transformation Jacobian matrix. During the calculation of this matrix, the dynamics solution module monitors its condition number in real time. When the condition number exceeds the warning threshold that triggers ill-conditioning of the matrix, the dynamics solution module employs regularization compensation logic. This warning threshold is typically set to 10. 4 Up to 10 5 The order of magnitude, and its specific value, is obtained by jointly calibrating the effective number of floating-point operations of the onboard computing unit and the machine precision.
[0097] If the limit is exceeded, the dynamics solution module introduces a small regularization perturbation constant term on the diagonal to avoid singularity collapse during covariance propagation. After the above robustness treatment, the dynamics solution module calculates the initial three-dimensional covariance matrix of the geocentric inertial coordinate system using the spatial reference alignment mapping formula, which is:
[0098] ;
[0099] in, Indicates the base timestamp The initial three-dimensional covariance matrix of the geocentric inertial coordinate system at time t is physically represented by the covariance distribution after transforming local observation errors into a global unified inertial space. This represents the coordinate system transformation Jacobian matrix obtained by solving the above problem and verifying its robustness. Represents the three-dimensional covariance matrix in the local polar coordinate system; This represents the transpose of the coordinate system transformation Jacobian matrix. This step achieves a unified transformation of the spatial error benchmark between nodes, eliminating observation parallax interference caused by differences in the positions and attitudes of multiple satellite platforms.
[0100] S403, after obtaining the initial three-dimensional covariance matrix of the geocentric inertial coordinate system, considering the objective time delay span from data generation and cross-link transmission to the receiving end's resolution, directly using the historical state without compensation would lead to the narrow field-of-view optical payload missing its target. To address this physical causal relationship, the dynamics solution module triggers dynamic extrapolation logic based on cross-satellite communication delay compensation. The dynamics solution module uses the internal onboard clock to obtain the current target timestamp for planned maneuver capture and performs a difference operation with the reference timestamp to extract the time delay span caused by communication and processing. Based on orbital perturbation theory, the dynamics solution module constructs dynamic equations including perturbation terms from Earth's non-spherical gravity and atmospheric drag, and linearizes them to obtain the state transition matrix.
[0101] The dynamics solution module uses the error ellipsoid dynamics extrapolation formula to calculate the extrapolated three-dimensional error covariance matrix at the current execution time. The error ellipsoid dynamics extrapolation formula is as follows:
[0102] ;
[0103] in, Indicates the current target timestamp The extrapolated three-dimensional error covariance matrix at time step; Indicates from the base timestamp up to the current target timestamp The state transition matrix represents the linear evolution of the target orbit dynamic state over time; This represents the initial three-dimensional covariance matrix of the geocentric inertial coordinate system; The transpose of the state transition matrix; This represents the process noise covariance matrix.
[0104] By solving the extrapolated three-dimensional error covariance matrix, the dynamic solution module equivalently maps its eigenvectors and eigenvalues to a three-dimensional confidence interval in geometric space, thus generating the final extrapolated three-dimensional error ellipsoid. This extrapolated three-dimensional error ellipsoid achieves dynamic synchronization with the narrow field-of-view payload's actions in the spatiotemporal dimensions, providing a direct input boundary for the narrow field-of-view satellite nodes to generate line-of-sight maneuver trajectories and lock onto space targets based on the extrapolated three-dimensional error ellipsoid in subsequent step S5.
[0105] The specific sub-steps of step S5 are as follows:
[0106] S501, in this embodiment, along with the spatiotemporal synchronization error boundary output by the preceding steps, the onboard processing unit inside the narrow field-of-view satellite node mobilizes the dynamics solution module to execute fault-tolerant acquisition planning. Because the physical field of view of the narrow field-of-view optical payload is limited, directly guiding the line of sight towards the target prediction center has a high probability of missing the target.
[0107] Based on the general technical principle of spatial uncertainty reduction projection, the dynamic solution module orthogonally projects the extrapolated three-dimensional error ellipsoid in three-dimensional space onto the two-dimensional physical focal plane of the narrow field-of-view optical payload along the current observation line of sight.
[0108] As a preferred method, the dynamics solution module uses the view plane covariance projection formula to calculate the two-dimensional error covariance matrix of the view plane. The view plane covariance projection formula is as follows:
[0109] ;
[0110] in, This represents the two-dimensional error covariance matrix of the view plane, and its physical meaning is the local two-dimensional mapping boundary of the three-dimensional spatial uncertainty on the sensor focal plane; The constructed view plane projection Jacobian matrix represents the partial derivative mapping relationship from the three-dimensional geocentric inertial coordinate system to the two-dimensional focal plane coordinate system. This represents the extrapolated three-dimensional error covariance matrix obtained from the preceding steps; This represents the transpose of the view plane projection Jacobian matrix.
[0111] After obtaining the two-dimensional error covariance matrix of the view plane, the dynamics solution module performs eigenvalue decomposition on it, extracting the major and minor semi-axis dimensions and the principal axis rotation angle, thereby reconstructing the two-dimensional search error envelope on the focal plane. Specifically, the square root of the matrix eigenvalue corresponds to the length of the principal and secondary axes of the error envelope, and the eigenvectors determine the spatial orientation of the error envelope on the focal plane.
[0112] Based on this, and considering the instantaneous effective field of view of the narrow field-of-view optical payload, the dynamics solution module adaptively generates an Archimedean spiral scan or comb traversal trajectory covering this two-dimensional envelope. The physical reason for choosing these scan trajectories is that they can effectively balance the coverage density of the high-probability region at the error center with the search time of the low-probability region on the periphery. The dynamics solution module converts the generated trajectory into low-level drive commands. After receiving these control commands, the attitude actuators on the narrow field-of-view satellite node drive the entire satellite to perform nonlinear line-of-sight maneuvers.
[0113] During the maneuver, the dynamics calculation module combines the signal-to-noise ratio of the target signal in consecutive frames with the centroid pixel jitter variance to make a multi-dimensional comprehensive judgment. When the signal-to-noise ratio is higher than the set threshold (which is usually set to 5 to 6 based on the statistical characteristics of background star noise to balance the false alarm rate and the detection probability) and the centroid jitter variance of consecutive frames is lower than the pixel-level convergence threshold (usually set to 0.1 to 0.5 pixels), it is determined that the physical lock of the space target has been achieved.
[0114] After the narrow field-of-view satellite node completes target locking, the S502 system triggers the construction of a multi-node heterogeneous line-of-sight network and nonlinear filtering for coordinated orbit determination. To eliminate the geometric unobservability in the depth direction of single-satellite line-of-sight observations, the cluster schedules multiple nodes (including wide-field-of-sight and narrow-field-of-sight satellite nodes) distributed across different orbital planes to synchronously track the target. Each observation node shares its instantaneous inertial position and the extracted target line-of-sight vector through the inter-satellite network, forming a multi-intersecting heterogeneous network topology in the space physical configuration.
[0115] Before constructing the multi-source observation model, the dynamics solution module performs time alignment of cross-satellite observation data, unifying the line-of-sight vectors asynchronously acquired by each node to the same calibration epoch using a polynomial interpolation algorithm. After completing spatiotemporal synchronization, the dynamics solution module collects multi-source observation elements within the network topology and constructs a nonlinear observation model for state updates.
[0116] The dynamics solution module uses the cross-line observation residual formula to calculate the line-of-sight direction residual vector for the current cycle. The cross-line observation residual formula is as follows:
[0117] ;
[0118] in, The line-of-sight direction residual vector is physically represented as the spatial angular deviation between the sensor's measured optical axis direction and the mathematically predicted direction. This represents the measured line-of-sight unit vector extracted from the image plane of the optical sensor and transformed into the global coordinate system; This represents the predicted spatial target position vector for the current recursive period; This represents the satellite observation node position vector provided by the spaceborne GNSS system; This represents the relative spatial distance norm, which is the physical scalar distance between the target and the observation node. The overall representation is the predicted line-of-sight unit vector after normalization.
[0119] When the relative spatial distance norm is less than the preset safety collision avoidance threshold (set to 100 to 150 meters), the dynamics solution module suspends the current residual calculation and triggers the avoidance mechanism. After obtaining multi-source residual feedback, the dynamics solution module uses the extended Kalman filter algorithm to perform closed-loop iterative correction of the target's three-dimensional position and velocity state, completing the cooperative orbit determination.
[0120] Specific application examples:
[0121] To aid in understanding the present invention, a specific application example is provided here: a search mission for a failed low-Earth orbit satellite at an altitude of 800 kilometers.
[0122] The ground computing center collected radar ranging and optical angle measurement sequences of the failed satellite for the 72 hours prior to the communication outage. After completing timestamp synchronization matching, the ground computing center used the Gauss-Jackson numerical integration algorithm to extrapolate to the current observation epoch, generating nominal spatial state parameters and a three-dimensional state error covariance matrix. It is then injected upwards into the star cluster.
[0123] The onboard processing unit inside the large field-of-view satellite node processes the three-dimensional state error covariance matrix. Eigenvalue decomposition revealed that the maximum broadening of the corresponding uncertainty envelope reached 30 kilometers. Since the physical detection boundary for a single frame corresponding to the narrow field-of-view optical payload is only 15 kilometers, the onboard processing unit determined to trigger the cluster cooperative search mission planning.
[0124] Large field-of-view satellite nodes decouple the three-dimensional state error covariance matrix along the expected observation line of sight The extracted values are prior distance error variance And write it into the shared state library.
[0125] The large field-of-view satellite nodes perform a gridded parallel search with a 10% overlap rate on uncertain sky regions. The image processing module reduces the dimensionality of the 3D velocity error envelope to a 2D focal plane and uses a hierarchical multi-hypothesis shift stacking algorithm to process the image sequence.
[0126] When the local signal-to-noise ratio of a candidate region exceeds a low detection threshold set to 5 times the background noise, the image processing module extracts the angular velocity vector set of candidate pixels and reconstructs the two-dimensional observation error covariance. In this embodiment, the covariance is specifically represented as a second-order diagonal matrix with each diagonal element being 25 microradians squared.
[0127] The large field-of-view satellite node packages this matrix and the instantaneous orbital attitude parameters at this moment, reduced to the J2000 geocentric inertial coordinate system, into an inter-satellite data frame for transmission. After receiving the inter-satellite data frame, the narrow field-of-view satellite node's dynamics solution module retrieves the prior range error variance from the shared state library. .
[0128] The dynamics solution module uses the formula for constructing the three-dimensional covariance of the local polar coordinate system to calculate the three-dimensional covariance matrix of the local polar coordinate system. Substituting the extracted values above, the calculated three-dimensional covariance matrix of the local polar coordinate system is as follows: .
[0129] Subsequently, the dynamics solution module combines the target azimuth parameters to obtain the coordinate system transformation Jacobian matrix, maps the local polar coordinate system three-dimensional covariance matrix to the J2000 coordinate system, and performs state transition matrix deduction based on the 1.5-second inter-satellite communication and processing delay span to generate an extrapolated three-dimensional error ellipsoid.
[0130] The dynamics solution module projects the ellipsoid onto the focal plane to guide the entire satellite to perform an Archimedes spiral scan. When the centroid jitter is less than 0.2 pixels in three consecutive frames, the narrow field-of-view satellite node determination achieves physical locking.
[0131] A cross-line-of-view network is constructed by large field-of-view satellite nodes and narrow field-of-view satellite nodes, and an observation model including safe distance truncation logic is established. Extended Kalman filter is used to output the convergent orbit state of the target.
[0132] A Monte Carlo simulation test environment was set up to verify the method. Under the same failed satellite target scenario, the cluster-based space target search and orbit determination method provided by this invention was compared with the traditional single-satellite optical method. The traditional single-satellite optical method relies on the optical payload of a single platform for independent searching, and lacks depth constraints for inter-satellite line-of-sight during the filtering process.
[0133] See attached document Figure 3 , Figure 3 The variation trend of 3D position estimation error with observation period during orbit determination filtering process is shown. Figure 3 The solid black line represents the star cluster coordination method based on this invention, while the dark gray dashed line represents the traditional single-star optical method. Because the traditional single-star optical method relies solely on angular measurement information and lacks effective geometric constraints in the radial depth direction, the three-dimensional position error oscillates between 200 and 300 meters, making it difficult to achieve physical convergence of the spatial state.
[0134] This invention employs a scheme that schedules large-field-of-view satellite nodes and narrow-field-of-view satellite nodes to construct a spatial heterogeneous topology, and integrates multi-source observation elements to establish a nonlinear observation model, ensuring that the rank of the state update matrix satisfies the fully observable condition. As shown by the trend of the black solid line, after introducing multi-node cross-line-of-view constraints, the three-dimensional position error steadily decreases within 50 observation periods and converges stably to a steady-state range within 10 meters. This cross-satellite network topology physically completes the inherent depth blind zone information of single-satellite optical observations, supporting accurate analysis of the orbital state of space targets.
[0135] See attached document Figure 4 , Figure 4 The search capture statistics were recorded under different prior location error conditions. Figure 4 The solid black line represents the star cluster cooperative method based on this invention, while the dark gray dashed line represents the traditional single-star optical method. When the initial prior position error is in the low uncertainty range of less than 10 kilometers, the acquisition success rate of both methods remains at 95%. As the spatial prediction uncertainty increases, the traditional single-star optical method is limited by the hardware's single physical field of view envelope, requiring a long search cycle. The energy of weak targets diffuses at the focal plane, leading to omissions. The dark gray dashed line shows a significant decrease when the error exceeds 20 kilometers.
[0136] In the large field-of-view satellite node sky search phase, the present invention performs speed-based dimensionality reduction mapping based on spatial projective geometry and employs a hierarchical multi-hypothesis shift and superposition algorithm to accumulate target signal energy, thus broadening the system's tolerance boundary for initial spatial uncertainty. As shown by the black solid line, even with a priori position error reaching 50 km, the cluster collaboration method based on this invention maintains a physical lock probability exceeding 90%. The pre-processing of two-dimensional observation error covariance extraction and cross-link data transfer provides reasonable local observation boundary inputs for generating extrapolated three-dimensional error ellipsoids and planning line-of-sight maneuver trajectories for narrow field-of-sight satellite nodes, ensuring the robustness of the entire target handover link between satellite nodes.
Claims
1. A method for space target search and orbit determination using cluster-based collaborative methods, characterized in that, include: The ground computing center generates prior guidance data for the space target and uploads it to the star cluster; The cluster scheduling large field-of-view satellite nodes perform a sky search based on the prior guidance data, and extract the two-dimensional observation error covariance of the space target through dimensionality reduction and shift overlay processing; The large field-of-view satellite node will send inter-satellite data frames containing the two-dimensional observation error covariance and instantaneous pose to the narrow field-of-view satellite node; The narrow field-of-view satellite node receives the inter-satellite data frames, combines the prior distance error variance with the geocentric inertial coordinate system to perform reference alignment and state extrapolation, and generates an extrapolated three-dimensional error ellipsoid. The narrow field-of-view satellite node generates a line-of-sight maneuver trajectory based on the extrapolated three-dimensional error ellipsoid to obtain a physical lock on the space target, and the star cluster performs state convergence based on the cross-line-of-sight network to complete the final cooperative orbit determination.
2. The method for space target search and orbit determination using cluster-based collaborative methods according to claim 1, characterized in that, The ground computing center generates prior guidance data for the space target and injects it into the star cluster. The specific processing steps include: Historical observation data of the space target is obtained. After time-stamp synchronization matching of the historical observation data, which includes radar ranging sequences and optical angle measurement sequences, orbit recursion is performed based on the orbit dynamics model to calculate and generate the nominal spatial state parameters and three-dimensional state error covariance matrix of the target at the predicted observation time. The nominal spatial state parameters and the three-dimensional state error covariance matrix are combined to form the prior guidance data, which is then injected into the star cluster.
3. The method for space target search and orbit determination using cluster-based coordination according to claim 2, characterized in that, Before the cluster scheduling large field-of-view satellite nodes perform a sky search based on the prior guidance data, the method further includes a step of extracting the prior distance error variance, specifically including: The prior guidance data is analyzed, and the extracted three-dimensional state error covariance matrix is decomposed into an initial error ellipsoid physical model. By comparing the expansion geometric scale of the initial error ellipsoid physical model on the lateral observation plane or radial depth plane with the single-star field-of-view coverage limit parameter, when it is determined that the expansion geometric scale is greater than the single-star field-of-view coverage limit parameter, the cluster cooperative search mission planning is triggered. In response to the star cluster cooperative search task planning, a local line-of-sight coordinate system is established and the three-dimensional state error covariance matrix is projected into the coordinate system. The error component corresponding to the target line-of-sight depth after projection is extracted, defined as the prior distance error variance, and written into the shared state library.
4. The method for space target search and orbit determination using cluster-based coordination according to claim 3, characterized in that, The specific steps for the cluster scheduling of large field-of-view satellite nodes to perform sky search based on the prior guidance data include: The specific steps for the cluster scheduling of large field-of-view satellite nodes to perform sky search based on the prior guidance data include: Extract the position error probability density distribution function from the prior guidance data, and perform spatial discretization grid segmentation on the uncertain sky region that exceeds the single-star field of view coverage limit parameter. After grid segmentation, allocate independent staring and step-scan task sequences to drive the large field of view satellite nodes to perform gridded parallel search. During the gridded parallel search process, optical image sequences are continuously acquired. Based on the principle of optical collinearity equations, a nonlinear observation equation is constructed from the local three-dimensional space to the two-dimensional optical focal plane. The Jacobian matrix is obtained by solving the partial derivatives of the nonlinear observation equation. By using the Jacobian matrix, the velocity error envelope in three-dimensional space is reduced in dimension and mapped to a two-dimensional physical focal plane, generating an analytical search boundary for pixel-level angular velocity error.
5. The method for space target search and orbit determination using cluster-based coordination according to claim 4, characterized in that, The specific steps for extracting the two-dimensional observation error covariance of the space target through dimensionality reduction and shift stacking processing include: Within the analytical search boundary, a hierarchical multi-hypothesis shift and superposition algorithm is used to generate a hypothetical velocity vector. Pixel-level shift and gray-level superposition operations are performed on the continuously acquired image sequence. The signal-to-noise ratio value is obtained by calculating the ratio of the mean gray level of the target signal pixel to the standard deviation of the gray level of the local background region. When the signal-to-noise ratio value is determined to be greater than the low detection threshold, the corresponding candidate pixel position vector set is extracted, and the weighted scattering center formula is used to calculate and generate the focal plane weighted scattering center. Using the weighted scattering center of the focal plane as the calculation benchmark, the two-dimensional observation covariance reconstruction formula is used to calculate, generate, and extract the two-dimensional observation error covariance. The low detection threshold is a feature value that is 3 to 5 times higher than the variance of the thermal noise distribution in the image background.
6. The method for space target search and orbit determination using cluster-based coordination according to claim 5, characterized in that, The large field-of-view satellite node transmits the inter-satellite data frame containing the two-dimensional observation error covariance and instantaneous pose to the narrow field-of-view satellite node. The specific steps include: The reference timestamp of the target imaging exposure moment is obtained by the satellite platform time, and the spatial orbit state parameters and three-dimensional attitude parameters of the large field of view satellite node at the moment of imaging exposure are simultaneously locked. The spatial orbit state parameters and the three-dimensional attitude parameters are uniformly reduced to the J2000 geocentric inertial coordinate system to generate the instantaneous pose. The previously generated focal plane weighted scattering center, the extracted two-dimensional observation error covariance, the reference timestamp, and the instantaneous pose are structurally combined and encapsulated to jointly generate the inter-satellite data frame; An inter-satellite communication link is established, and the inter-satellite data frames are directionally transmitted to the narrow field-of-view satellite node.
7. The method for space target search and orbit determination using cluster-based coordination according to claim 6, characterized in that, The narrow field-of-view satellite node receives the inter-satellite data frames and performs reference alignment and state extrapolation by combining the prior distance error variance with the geocentric inertial coordinate system. During the process of generating the extrapolated three-dimensional error ellipsoid, the specific steps of the reference alignment include: The inter-satellite data frames are analyzed to extract the pixel centroid coordinates of the target on the two-dimensional focal plane, the two-dimensional observation error covariance, and the reference timestamp. Access the shared state library and retrieve the saved prior distance error variance; In the local polar coordinate system, the three-dimensional covariance of the local polar coordinate system is constructed using the formula. The extracted two-dimensional observation error covariance and the retrieved prior distance error variance are reconstructed in dimension to generate the three-dimensional covariance matrix of the local polar coordinate system. A nonlinear spatial mapping function from the local polar coordinate system to the J2000 geocentric inertial coordinate system is constructed, and the first-order partial derivative is obtained to obtain the coordinate system transformation Jacobian matrix. The spatial reference alignment mapping formula is used to calculate the three-dimensional covariance matrix of the local polar coordinate system, and the initial three-dimensional covariance matrix of the geocentric inertial coordinate system is obtained and output.
8. The method for space target search and orbit determination using cluster-based coordination according to claim 7, characterized in that, The narrow field-of-view satellite node receives the inter-satellite data frames and performs reference alignment and state extrapolation in combination with the prior distance error variance and the geocentric inertial coordinate system to generate the extrapolated three-dimensional error ellipsoid. The specific steps for performing the state extrapolation and generating the extrapolated three-dimensional error ellipsoid include: The current target timestamp is obtained using the onboard clock, and the time delay span is extracted by differential operation with the extracted reference timestamp. A dynamic equation containing the perturbation terms of Earth's non-spherical gravity and atmospheric drag is constructed and linearized to obtain the state transition matrix. Using the error ellipsoid dynamic extrapolation formula and based on the state transition matrix, the initial three-dimensional covariance matrix of the geocentric inertial coordinate system is dynamically extrapolated and calculated to generate the extrapolated three-dimensional error covariance matrix at the current execution time. The eigenvectors and eigenvalues of the extrapolated three-dimensional error covariance matrix are mapped to three-dimensional confidence intervals in geometric space, thereby generating and outputting the extrapolated three-dimensional error ellipsoid.
9. The method for space target search and orbit determination using cluster-based collaborative methods according to claim 8, characterized in that, The specific steps for the narrow field-of-view satellite node to generate a line-of-sight maneuver trajectory based on the extrapolated three-dimensional error ellipsoid and obtain a physical lock on the space target include: The extrapolated three-dimensional error ellipsoid is orthogonally projected onto the two-dimensional physical focal plane along the current line of sight using the view plane covariance projection formula. The two-dimensional error covariance matrix of the view plane is calculated. The major and minor semi-axis dimensions and principal axis rotation angle are extracted by eigenvalue decomposition to reconstruct the two-dimensional search error envelope. The scanning traversal trajectory covering the two-dimensional search error envelope is adaptively generated by combining the instantaneous effective field of view size as the line-of-sight maneuver trajectory, driving the entire satellite to perform nonlinear line-of-sight maneuvers; During the scanning traversal trajectory maneuver, the signal-to-noise ratio and centroid pixel jitter variance are combined for determination. When the signal-to-noise ratio is higher than the signal-to-noise ratio set threshold and the centroid jitter variance of multiple consecutive frames is lower than the pixel-level convergence threshold, the physical lock on the spatial target is determined to be obtained. The signal-to-noise ratio threshold is set to a value of 5 to 6 based on the statistical characteristics of background star noise, and the pixel-level convergence threshold is set to a variance boundary value of 0.1 to 0.5 pixels.
10. A method for space target search and orbit determination using cluster-based coordination according to claim 9, characterized in that, The specific steps for the star cluster to achieve final cooperative orbit determination through state convergence based on the cross-line-of-sight network include: The system schedules multiple nodes distributed in different orbital planes within the star cluster to synchronously track and aim at the space target that is in the physical locking state. By unifying the spatiotemporal reference through a polynomial interpolation algorithm, a heterogeneous network topology with multiple points of intersection is formed in the space physical configuration as the cross-line-of-sight network. Collect multi-source observation elements within the cross-line-of-sight network, calculate the line-of-sight direction residual vector using the cross-line-of-sight observation residual formula, and suspend residual calculation to trigger an avoidance mechanism when the relative spatial distance norm is less than a preset safety collision avoidance threshold, thereby obtaining multi-source residual feedback. Based on the multi-source residual feedback, the extended Kalman filter algorithm is used to perform closed-loop iterative correction of the target's three-dimensional position and velocity state, thereby achieving state convergence and completing the final cooperative orbit determination. The safety collision avoidance threshold is a distance limit set between 100 meters and 150 meters.